TSTP Solution File: NUM801^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM801^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n123.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 13:11:47 EST 2018
% Result : Timeout 297.39s
% 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 : NUM801^1 : TPTP v7.0.0. Released v3.7.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n123.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 : Fri Jan 5 14:22:05 CST 2018
% 0.02/0.23 % CPUTime :
% 0.07/0.25 Python 2.7.13
% 0.08/0.51 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.08/0.51 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM006^0.ax, trying next directory
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f865248>, <kernel.DependentProduct object at 0x2b951f865320>) of role type named zero
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring zero:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f945128>, <kernel.DependentProduct object at 0x2b951f865b00>) of role type named one
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring one:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f8658c0>, <kernel.DependentProduct object at 0x2b951f865320>) of role type named two
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring two:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f865fc8>, <kernel.DependentProduct object at 0x2b951f865b00>) of role type named three
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring three:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f865908>, <kernel.DependentProduct object at 0x2b951f865320>) of role type named four
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring four:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f865200>, <kernel.DependentProduct object at 0x2b951f865b00>) of role type named five
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring five:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f865e60>, <kernel.DependentProduct object at 0x2b951f865320>) of role type named six
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring six:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f865248>, <kernel.DependentProduct object at 0x2b951f865b00>) of role type named seven
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring seven:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f865830>, <kernel.DependentProduct object at 0x2b951f865320>) of role type named eight
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring eight:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f8658c0>, <kernel.DependentProduct object at 0x2b951f865b00>) of role type named nine
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring nine:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f865fc8>, <kernel.DependentProduct object at 0x2b951f865320>) of role type named ten
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring ten:((fofType->fofType)->(fofType->fofType))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f865908>, <kernel.DependentProduct object at 0x2b951f865830>) of role type named succ
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring succ:(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951fcc2128>, <kernel.DependentProduct object at 0x2b951f859680>) of role type named plus
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring plus:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.08/0.51 FOF formula (<kernel.Constant object at 0x2b951f859248>, <kernel.DependentProduct object at 0x2b951f865320>) of role type named mult
% 0.08/0.51 Using role type
% 0.08/0.51 Declaring mult:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.08/0.51 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y)) of role definition named zero_ax
% 0.08/0.51 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y))
% 0.08/0.51 Defined: zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y)
% 0.08/0.51 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))) of role definition named one_ax
% 0.08/0.51 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)))
% 0.08/0.51 Defined: one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))
% 0.08/0.51 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))) of role definition named two_ax
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))))
% 0.08/0.53 Defined: two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))
% 0.08/0.53 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))) of role definition named three_ax
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))))
% 0.08/0.53 Defined: three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))
% 0.08/0.53 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
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))))
% 0.08/0.53 Defined: four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))
% 0.08/0.53 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
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))))
% 0.08/0.53 Defined: five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))
% 0.08/0.53 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
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))))
% 0.08/0.53 Defined: six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))
% 0.08/0.53 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
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))))
% 0.08/0.53 Defined: seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))
% 0.08/0.53 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
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))))
% 0.08/0.53 Defined: eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))
% 0.08/0.53 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
% 0.08/0.53 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)))))))))))
% 0.08/0.53 Defined: nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))
% 0.08/0.53 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
% 0.08/0.53 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))))))))))))
% 0.08/0.53 Defined: ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))
% 0.08/0.53 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
% 0.08/0.53 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))))
% 0.08/0.53 Defined: succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))
% 0.08/0.53 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
% 0.35/0.54 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))))
% 0.35/0.54 Defined: plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))
% 0.35/0.54 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
% 0.35/0.54 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)))
% 0.35/0.54 Defined: mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))
% 0.35/0.54 FOF formula ((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) of role conjecture named thm
% 0.35/0.54 Conjecture to prove = ((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))):Prop
% 0.35/0.54 Parameter fofType_DUMMY:fofType.
% 0.35/0.54 We need to prove ['((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))']
% 0.35/0.54 Parameter fofType:Type.
% 0.35/0.54 Definition zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 Definition ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.35/0.54 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))).
% 0.35/0.54 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)))).
% 2.16/2.39 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)))).
% 2.16/2.39 Trying to prove ((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 2.16/2.39 Found eq_ref00:=(eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 2.16/2.39 Found (eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) b)
% 2.16/2.39 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) b)
% 2.16/2.39 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) b)
% 2.16/2.39 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M)))))) b)
% 2.16/2.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 3.28/3.46 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))))
% 3.28/3.46 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))))
% 3.28/3.46 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))))
% 3.28/3.46 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))))
% 3.28/3.46 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)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M))))))
% 3.28/3.46 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 3.28/3.46 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))))
% 3.28/3.46 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))))
% 3.28/3.46 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))))
% 3.28/3.46 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))))
% 3.28/3.46 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)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M))))))
% 3.28/3.46 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 3.28/3.46 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.28/3.46 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.28/3.46 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.28/3.46 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 3.28/3.46 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.28/3.46 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.28/3.46 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.28/3.46 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 3.36/3.56 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 3.36/3.56 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 3.36/3.56 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 3.36/3.56 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.36/3.56 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 3.36/3.56 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 3.79/3.99 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 3.79/3.99 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 3.79/3.99 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 3.79/3.99 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 3.79/3.99 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.79/3.99 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.79/3.99 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.79/3.99 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.79/3.99 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.79/3.99 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 3.79/3.99 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.79/3.99 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.79/3.99 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 3.87/4.05 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 3.87/4.05 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 3.87/4.05 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.87/4.05 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 3.96/4.17 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 3.96/4.17 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 3.96/4.17 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 3.96/4.17 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 3.96/4.17 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 4.03/4.25 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 4.03/4.25 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 4.03/4.25 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 4.03/4.25 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 11.17/11.37 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 11.17/11.37 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 11.17/11.37 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 11.17/11.37 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 11.17/11.37 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 11.17/11.37 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 11.17/11.37 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 11.17/11.37 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 11.17/11.37 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 22.96/23.17 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 22.96/23.17 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 22.96/23.17 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 22.96/23.17 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 22.96/23.17 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 22.96/23.17 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 22.96/23.17 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 22.96/23.17 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 22.96/23.17 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 22.96/23.17 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 22.96/23.17 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 22.96/23.17 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 22.96/23.17 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 22.96/23.17 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) (fun (x:((fofType->fofType)->(fofType->fofType)))=> (a x)))
% 22.96/23.17 Found (eta_expansion_dep00 a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 22.96/23.17 Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 22.96/23.17 Found (((eta_expansion_dep ((fofType->fofType)->(fofType->fofType))) (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 22.96/23.17 Found (((eta_expansion_dep ((fofType->fofType)->(fofType->fofType))) (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 22.96/23.17 Found (((eta_expansion_dep ((fofType->fofType)->(fofType->fofType))) (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 22.96/23.17 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (x:((fofType->fofType)->(fofType->fofType)))=> (b x)))
% 22.96/23.17 Found (eta_expansion_dep00 b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 22.96/23.17 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)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 23.92/24.14 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)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 23.92/24.14 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)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 23.92/24.14 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)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 23.92/24.14 Found eq_ref00:=(eq_ref0 b):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) b)
% 23.92/24.14 Found (eq_ref0 b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 23.92/24.14 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 23.92/24.14 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 23.92/24.14 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) four)) ((plus five) M))))))
% 23.92/24.14 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 23.92/24.14 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.92/24.14 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.92/24.14 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.92/24.14 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.92/24.14 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 23.92/24.14 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 23.98/24.23 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 23.98/24.23 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 23.98/24.23 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 23.98/24.23 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 23.98/24.23 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 24.41/24.62 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 24.41/24.62 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 24.41/24.62 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 24.41/24.62 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 24.41/24.62 Found eta_expansion000:=(eta_expansion00 (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) (fun (x0:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0))))
% 24.41/24.62 Found (eta_expansion00 (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) b)
% 24.41/24.62 Found ((eta_expansion0 Prop) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) b)
% 24.59/24.80 Found (((eta_expansion ((fofType->fofType)->(fofType->fofType))) Prop) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) b)
% 24.59/24.80 Found (((eta_expansion ((fofType->fofType)->(fofType->fofType))) Prop) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) b)
% 24.59/24.80 Found (((eta_expansion ((fofType->fofType)->(fofType->fofType))) Prop) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) M)))) b)
% 24.59/24.80 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 24.59/24.80 Found (eta_expansion00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 24.59/24.80 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.80 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 24.59/24.80 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.85 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.59/24.85 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 24.67/24.85 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 24.67/24.85 Found (eq_ref0 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 24.67/24.85 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.67/24.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 24.76/24.98 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 24.76/24.98 Found (eq_ref0 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 24.76/24.98 Found (eta_expansion00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 24.76/24.98 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 24.76/24.98 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 25.48/25.71 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 25.48/25.71 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 25.48/25.71 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 25.48/25.71 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 25.48/25.71 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 25.48/25.71 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 25.48/25.71 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.48/25.71 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 25.61/25.79 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 25.61/25.79 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 25.61/25.79 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.61/25.79 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 25.77/25.96 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 25.77/25.96 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 25.77/25.96 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.77/25.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 25.86/26.06 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 25.86/26.06 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 25.86/26.06 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 25.86/26.06 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.86/26.06 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 25.96/26.14 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 25.96/26.14 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 25.96/26.14 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 25.96/26.14 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 25.96/26.14 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 25.96/26.14 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.08/26.28 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 26.08/26.28 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.08/26.28 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 26.08/26.28 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.08/26.28 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 26.08/26.28 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.08/26.28 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.21/26.41 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 26.21/26.41 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.21/26.41 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 26.21/26.41 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.21/26.41 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.21/26.41 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 26.21/26.41 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.26/26.44 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 26.26/26.44 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.26/26.44 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 26.26/26.44 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.44 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.26/26.51 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 26.26/26.51 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.26/26.51 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 26.26/26.51 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 26.26/26.51 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 26.26/26.51 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 26.26/26.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 29.17/29.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 29.17/29.45 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 29.17/29.45 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0)))
% 29.17/29.45 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0)))
% 29.17/29.45 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0)))
% 29.17/29.45 Found (fun (x0:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0)))
% 29.17/29.45 Found (fun (x0:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:((fofType->fofType)->(fofType->fofType))), (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0))))
% 29.17/29.45 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 29.17/29.45 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0)))
% 29.17/29.45 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0)))
% 29.17/29.45 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0)))
% 29.17/29.45 Found (fun (x0:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0)))
% 29.17/29.45 Found (fun (x0:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:((fofType->fofType)->(fofType->fofType))), (((eq Prop) (f x0)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) ((plus five) x0))))
% 29.17/29.45 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 29.17/29.45 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.17/29.45 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.17/29.45 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.17/29.45 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 29.17/29.45 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.17/29.45 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.17/29.45 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.17/29.45 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.17/29.45 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 29.17/29.45 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.17/29.45 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 29.47/29.66 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 29.47/29.66 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 29.47/29.66 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 29.47/29.66 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 29.47/29.66 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 30.75/30.98 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 30.75/30.98 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 30.75/30.98 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 30.75/30.98 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 30.75/30.98 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.75/30.98 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.75/30.98 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.75/30.98 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.75/30.98 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.75/30.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.75/30.98 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 30.75/30.98 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.75/30.98 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.75/30.98 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.75/30.98 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 30.91/31.13 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 30.91/31.13 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 30.91/31.13 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 30.91/31.13 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.91/31.13 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 30.98/31.21 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 30.98/31.21 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 30.98/31.21 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 30.98/31.21 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 31.15/31.36 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 31.15/31.36 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 31.15/31.36 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 31.15/31.36 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 33.48/33.68 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 33.48/33.68 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.48/33.68 Found x000:(P ((mult x) four))
% 33.48/33.68 Found (fun (x000:(P ((mult x) four)))=> x000) as proof of (P ((mult x) four))
% 33.48/33.68 Found (fun (x000:(P ((mult x) four)))=> x000) as proof of (P0 ((mult x) four))
% 33.48/33.68 Found x001:(P ((mult x) four))
% 33.48/33.68 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P ((mult x) four))
% 33.48/33.68 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P0 ((mult x) four))
% 33.48/33.68 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 33.48/33.68 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.48/33.68 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.48/33.68 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.48/33.68 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.48/33.68 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 33.76/33.94 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 33.76/33.94 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 33.76/33.94 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 33.76/33.94 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.76/33.94 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 33.76/33.94 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.76/33.94 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.76/33.94 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.76/33.94 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.76/33.94 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.76/33.94 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 33.82/34.02 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 33.82/34.02 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 33.82/34.02 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.82/34.02 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 33.82/34.02 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 33.87/34.08 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 33.87/34.08 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 33.87/34.08 Found x001:(P ((mult x) four))
% 33.87/34.08 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P ((mult x) four))
% 33.87/34.08 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P0 ((mult x) four))
% 33.87/34.08 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 33.87/34.08 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.87/34.08 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 33.87/34.08 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 34.15/34.34 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 34.15/34.34 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 34.15/34.34 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 34.15/34.34 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 34.15/34.34 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 34.15/34.34 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.15/34.34 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 34.22/34.42 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 34.22/34.42 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 34.22/34.42 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 34.22/34.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 35.59/35.80 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 35.59/35.80 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 35.59/35.80 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 35.59/35.80 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 35.59/35.80 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) x0))
% 57.07/57.30 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) x0))
% 57.07/57.30 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) x0))
% 57.07/57.30 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) x0))
% 57.07/57.30 Found eta_expansion_dep000:=(eta_expansion_dep00 ((mult x) four)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) (fun (x0:(fofType->fofType))=> (((mult x) four) x0)))
% 57.07/57.30 Found (eta_expansion_dep00 ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 57.07/57.30 Found ((eta_expansion_dep0 (fun (x2:(fofType->fofType))=> (fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 57.07/57.30 Found (((eta_expansion_dep (fofType->fofType)) (fun (x2:(fofType->fofType))=> (fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 57.07/57.30 Found (((eta_expansion_dep (fofType->fofType)) (fun (x2:(fofType->fofType))=> (fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 57.07/57.30 Found (((eta_expansion_dep (fofType->fofType)) (fun (x2:(fofType->fofType))=> (fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 57.07/57.30 Found x001:(P ((mult x) four))
% 57.07/57.30 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P ((mult x) four))
% 57.07/57.30 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P0 ((mult x) four))
% 57.07/57.30 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 57.07/57.30 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 57.07/57.30 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 57.07/57.30 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.07/57.30 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 57.32/57.51 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 57.32/57.51 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 57.32/57.51 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 57.32/57.51 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 57.32/57.51 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 57.32/57.51 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 64.21/64.44 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 64.21/64.44 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 64.21/64.44 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 64.21/64.44 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 64.21/64.44 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 64.21/64.44 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 64.21/64.44 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 64.21/64.44 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 64.21/64.44 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 64.21/64.44 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) four))
% 64.21/64.44 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) four))
% 64.21/64.44 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) four))
% 64.21/64.44 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) four))
% 64.21/64.44 Found eta_expansion000:=(eta_expansion00 ((plus five) x0)):(((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) x0)) (fun (x:(fofType->fofType))=> (((plus five) x0) x)))
% 64.21/64.44 Found (eta_expansion00 ((plus five) x0)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) x0)) b)
% 64.21/64.44 Found ((eta_expansion0 (fofType->fofType)) ((plus five) x0)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) x0)) b)
% 64.21/64.44 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((plus five) x0)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) x0)) b)
% 64.21/64.44 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((plus five) x0)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) x0)) b)
% 64.21/64.44 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((plus five) x0)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((plus five) x0)) b)
% 64.21/64.44 Found x11:(P ((plus five) x0))
% 64.21/64.44 Found (fun (x11:(P ((plus five) x0)))=> x11) as proof of (P ((plus five) x0))
% 64.21/64.44 Found (fun (x11:(P ((plus five) x0)))=> x11) as proof of (P0 ((plus five) x0))
% 64.21/64.44 Found x11:(P ((plus five) x0))
% 64.21/64.44 Found (fun (x11:(P ((plus five) x0)))=> x11) as proof of (P ((plus five) x0))
% 64.21/64.44 Found (fun (x11:(P ((plus five) x0)))=> x11) as proof of (P0 ((plus five) x0))
% 64.21/64.44 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 64.21/64.44 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.21/64.44 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.21/64.44 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.21/64.44 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.21/64.44 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.21/64.44 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.21/64.44 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 64.27/64.52 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 64.27/64.52 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 64.27/64.52 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 64.27/64.52 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.27/64.52 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 64.58/64.78 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 64.58/64.78 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 64.58/64.78 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.58/64.78 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 64.58/64.78 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 64.68/64.86 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 64.68/64.86 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 64.68/64.86 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 64.68/64.86 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 66.67/66.88 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 66.67/66.88 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (b x00)))
% 66.67/66.88 Found x010:(P (((mult x) four) x00))
% 66.67/66.88 Found (fun (x010:(P (((mult x) four) x00)))=> x010) as proof of (P (((mult x) four) x00))
% 66.67/66.88 Found (fun (x010:(P (((mult x) four) x00)))=> x010) as proof of (P0 (((mult x) four) x00))
% 66.67/66.88 Found x010:(P (((mult x) four) x00))
% 66.67/66.88 Found (fun (x010:(P (((mult x) four) x00)))=> x010) as proof of (P (((mult x) four) x00))
% 66.67/66.88 Found (fun (x010:(P (((mult x) four) x00)))=> x010) as proof of (P0 (((mult x) four) x00))
% 66.67/66.88 Found eq_ref00:=(eq_ref0 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (((mult x) four) x1))
% 66.67/66.88 Found (eq_ref0 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 66.67/66.88 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 66.67/66.88 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 66.67/66.88 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 66.67/66.88 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 66.67/66.88 Found ((eq_sym10 (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 66.67/66.88 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 66.67/66.88 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 66.67/66.88 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 66.87/67.06 Found eq_ref00:=(eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M))))))))))
% 66.87/67.06 Found (eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))) b)
% 66.87/67.06 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))) b)
% 66.87/67.06 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))) b)
% 66.87/67.06 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))) b)
% 68.18/68.39 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 68.18/68.39 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 68.18/68.39 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 68.18/68.39 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 68.18/68.39 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 68.18/68.39 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((plus five) x0) x1))->(P (((mult x) four) x1))))
% 68.18/68.39 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 68.18/68.39 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.18/68.39 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.18/68.39 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.18/68.39 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.18/68.39 Found eq_ref00:=(eq_ref0 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (((mult x) four) x1))
% 68.18/68.39 Found (eq_ref0 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.18/68.39 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found ((eq_sym10 (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found eq_ref00:=(eq_ref0 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (((mult x) four) x1))
% 68.42/68.61 Found (eq_ref0 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found ((eq_sym10 (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 68.42/68.61 Found (eta_expansion_dep00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 68.42/68.61 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 68.42/68.61 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 72.56/72.78 Found x11:(P ((plus five) x0))
% 72.56/72.78 Found (fun (x11:(P ((plus five) x0)))=> x11) as proof of (P ((plus five) x0))
% 72.56/72.78 Found (fun (x11:(P ((plus five) x0)))=> x11) as proof of (P0 ((plus five) x0))
% 72.56/72.78 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 72.56/72.78 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) b)
% 72.56/72.78 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) b)
% 72.56/72.78 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) b)
% 72.56/72.78 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) b)
% 72.56/72.78 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 72.56/72.78 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 72.56/72.78 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 72.56/72.78 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 72.56/72.78 Found (((eq_trans000 (fun (Y:fofType)=> ((x (four x00)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (four x00)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 72.56/72.78 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((plus five) x0) x00))) (fun (Y:fofType)=> ((x (four x00)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (four x00)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 72.56/72.78 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) four) x00)) b) (((plus five) x0) x00))) (fun (Y:fofType)=> ((x (four x00)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (four x00)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 72.56/72.78 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) four) x00)) b) (((plus five) x0) x00))) (fun (Y:fofType)=> ((x (four x00)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (four x00)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 72.56/72.78 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 72.56/72.78 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) b)
% 72.56/72.78 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) b)
% 72.56/72.78 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) b)
% 78.26/78.48 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) b)
% 78.26/78.48 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 78.26/78.48 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.48 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.48 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.48 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.48 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.48 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 78.26/78.48 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.49 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 78.26/78.49 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 78.26/78.49 Found (((eq_trans000 (fun (Y:fofType)=> ((x (four x00)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Y:fofType)=> ((x (four x00)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 78.26/78.49 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((plus five) x0) x00))) (fun (Y:fofType)=> ((x (four x00)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Y:fofType)=> ((x (four x00)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 78.26/78.49 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) four) x00)) b) (((plus five) x0) x00))) (fun (Y:fofType)=> ((x (four x00)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Y:fofType)=> ((x (four x00)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 78.26/78.49 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) four) x00)) b) (((plus five) x0) x00))) (fun (Y:fofType)=> ((x (four x00)) Y))) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Y:fofType)=> ((x (four x00)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 78.26/78.49 Found x011:(P (((mult x) four) x00))
% 78.26/78.49 Found (fun (x011:(P (((mult x) four) x00)))=> x011) as proof of (P (((mult x) four) x00))
% 78.26/78.49 Found (fun (x011:(P (((mult x) four) x00)))=> x011) as proof of (P0 (((mult x) four) x00))
% 78.26/78.49 Found x011:(P (((mult x) four) x00))
% 78.26/78.49 Found (fun (x011:(P (((mult x) four) x00)))=> x011) as proof of (P (((mult x) four) x00))
% 78.26/78.49 Found (fun (x011:(P (((mult x) four) x00)))=> x011) as proof of (P0 (((mult x) four) x00))
% 78.26/78.49 Found x011:(P (((mult x) four) x00))
% 78.26/78.49 Found (fun (x011:(P (((mult x) four) x00)))=> x011) as proof of (P (((mult x) four) x00))
% 78.26/78.49 Found (fun (x011:(P (((mult x) four) x00)))=> x011) as proof of (P0 (((mult x) four) x00))
% 78.26/78.49 Found x011:(P (((mult x) four) x00))
% 78.26/78.49 Found (fun (x011:(P (((mult x) four) x00)))=> x011) as proof of (P (((mult x) four) x00))
% 78.26/78.49 Found (fun (x011:(P (((mult x) four) x00)))=> x011) as proof of (P0 (((mult x) four) x00))
% 87.21/87.43 Found x010:(P ((((mult x) four) x00) y))
% 87.21/87.43 Found (fun (x010:(P ((((mult x) four) x00) y)))=> x010) as proof of (P ((((mult x) four) x00) y))
% 87.21/87.43 Found (fun (x010:(P ((((mult x) four) x00) y)))=> x010) as proof of (P0 ((((mult x) four) x00) y))
% 87.21/87.43 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 87.21/87.43 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))
% 87.21/87.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))
% 87.21/87.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))
% 87.21/87.43 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))
% 87.21/87.43 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)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M))))))))))
% 87.21/87.43 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 87.21/87.43 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))
% 87.21/87.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))
% 87.21/87.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))
% 87.21/87.43 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M)))))))))
% 87.21/87.43 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)) ((ex ((fofType->fofType)->(fofType->fofType))) (fun (M:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3)))))) (succ (succ (succ (succ (succ M))))))))))
% 87.21/87.43 Found eq_ref00:=(eq_ref0 ((((mult x) four) x00) y)):(((eq fofType) ((((mult x) four) x00) y)) ((((mult x) four) x00) y))
% 87.21/87.43 Found (eq_ref0 ((((mult x) four) x00) y)) as proof of (((eq fofType) ((((mult x) four) x00) y)) b)
% 87.21/87.43 Found ((eq_ref fofType) ((((mult x) four) x00) y)) as proof of (((eq fofType) ((((mult x) four) x00) y)) b)
% 101.92/102.11 Found ((eq_ref fofType) ((((mult x) four) x00) y)) as proof of (((eq fofType) ((((mult x) four) x00) y)) b)
% 101.92/102.11 Found ((eq_ref fofType) ((((mult x) four) x00) y)) as proof of (((eq fofType) ((((mult x) four) x00) y)) b)
% 101.92/102.11 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 101.92/102.11 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) x0) x00) y))
% 101.92/102.11 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) y))
% 101.92/102.11 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) y))
% 101.92/102.11 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) y))
% 101.92/102.11 Found eq_ref00:=(eq_ref0 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (((mult x) four) x1))
% 101.92/102.11 Found (eq_ref0 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 101.92/102.11 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 101.92/102.11 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 101.92/102.11 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 101.92/102.11 Found (eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 101.92/102.11 Found (eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 101.92/102.11 Found ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> ((eq_sym100 x00) P)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 101.92/102.11 Found ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((eq_sym10 (((plus five) x0) x1)) x00) P)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 101.92/102.11 Found ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> ((((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) x00) P)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 101.92/102.11 Found ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) x00) P)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 101.92/102.11 Found (fun (P:((fofType->fofType)->Prop))=> ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) x00) P)) ((eq_ref (fofType->fofType)) (((mult x) four) x1)))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 101.92/102.11 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 101.92/102.11 Found (eta_expansion_dep00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 101.92/102.11 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 101.92/102.11 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 101.92/102.11 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 101.92/102.11 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 101.92/102.11 Found (eq_sym1000 (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 102.39/102.60 Found (eq_sym1000 (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 102.39/102.60 Found ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> ((eq_sym100 x00) P)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 102.39/102.60 Found ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((eq_sym10 (((plus five) x0) x1)) x00) P)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 102.39/102.60 Found ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> ((((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) x00) P)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 102.39/102.60 Found ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) x00) P)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 102.39/102.60 Found (fun (P:((fofType->fofType)->Prop))=> ((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) x00) P)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) four) x1)))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 102.39/102.60 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 102.39/102.60 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.39/102.60 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.39/102.60 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.39/102.60 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.39/102.60 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.39/102.60 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.39/102.60 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.39/102.60 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.39/102.60 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.39/102.60 Found eq_ref00:=(eq_ref0 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (((mult x) four) x1))
% 102.39/102.60 Found (eq_ref0 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.39/102.60 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.39/102.60 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.39/102.60 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.39/102.60 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found ((eq_sym10 (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 102.98/103.23 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 102.98/103.23 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 102.98/103.23 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 102.98/103.23 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 103.28/103.49 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 103.28/103.49 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 103.28/103.49 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 103.28/103.49 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 103.28/103.49 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 103.28/103.49 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 103.28/103.49 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 103.28/103.49 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 103.28/103.49 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 103.28/103.49 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 103.28/103.49 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 103.28/103.49 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 128.75/128.95 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 128.75/128.95 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 128.75/128.95 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 128.75/128.95 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 128.75/128.95 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 128.75/128.95 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 128.75/128.95 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 128.75/128.95 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 128.75/128.95 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 128.75/128.95 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 128.75/128.95 Found ((eq_sym10 (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 128.75/128.95 Found (((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 128.75/128.95 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 128.75/128.95 Found eq_ref00:=(eq_ref0 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)):(((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))
% 128.75/128.95 Found (eq_ref0 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.75/128.95 Found ((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.75/128.95 Found ((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.75/128.95 Found eta_expansion000:=(eta_expansion00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)):(((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00) x0)))
% 128.75/128.95 Found (eta_expansion00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.75/128.95 Found ((eta_expansion0 fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x))))
% 128.88/129.14 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found eta_expansion000:=(eta_expansion00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)):(((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00) x0)))
% 128.88/129.14 Found (eta_expansion00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found ((eta_expansion0 fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x))))
% 128.88/129.14 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 128.88/129.14 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found eq_ref00:=(eq_ref0 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)):(((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))
% 129.00/129.22 Found (eq_ref0 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found ((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found ((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)):(((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00) x0)))
% 129.00/129.22 Found (eta_expansion_dep00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x))))
% 129.00/129.22 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 129.00/129.22 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)):(((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00) x0)))
% 130.33/130.56 Found (eta_expansion_dep00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x))))
% 130.33/130.56 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) ((succ (succ (succ (succ (succ x0))))) x00))
% 130.33/130.56 Found x20:(P (((plus five) x0) x1))
% 130.33/130.56 Found (fun (x20:(P (((plus five) x0) x1)))=> x20) as proof of (P (((plus five) x0) x1))
% 130.33/130.56 Found (fun (x20:(P (((plus five) x0) x1)))=> x20) as proof of (P0 (((plus five) x0) x1))
% 130.33/130.56 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 130.33/130.56 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.33/130.56 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.33/130.56 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.33/130.56 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.46/130.66 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.46/130.66 Found ((eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 130.46/130.66 Found ((eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 130.46/130.66 Found (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> ((eq_sym100 x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 130.46/130.66 Found (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((eq_sym10 (((plus five) x0) x1)) x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 130.46/130.66 Found (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> ((((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 130.46/130.66 Found (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 130.46/130.66 Found (fun (P:((fofType->fofType)->Prop))=> (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 130.46/130.66 Found x20:(P (((plus five) x0) x1))
% 130.46/130.66 Found (fun (x20:(P (((plus five) x0) x1)))=> x20) as proof of (P (((plus five) x0) x1))
% 130.46/130.66 Found (fun (x20:(P (((plus five) x0) x1)))=> x20) as proof of (P0 (((plus five) x0) x1))
% 130.46/130.66 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 130.46/130.66 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.46/130.66 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.46/130.66 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.46/130.66 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.46/130.66 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1))
% 130.46/130.66 Found ((eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 130.46/130.66 Found ((eq_sym1000 (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 130.46/130.66 Found (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> ((eq_sym100 x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 133.97/134.16 Found (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((eq_sym10 (((plus five) x0) x1)) x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 133.97/134.16 Found (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> ((((eq_sym1 (((mult x) four) x1)) (((plus five) x0) x1)) x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 133.97/134.16 Found (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20)) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 133.97/134.16 Found (fun (P:((fofType->fofType)->Prop))=> (((fun (x00:(((eq (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)))=> (((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (((plus five) x0) x1)) x00) (fun (x3:(fofType->fofType))=> ((P (((plus five) x0) x1))->(P x3))))) (((eta_expansion fofType) fofType) (((mult x) four) x1))) (fun (x20:(P (((plus five) x0) x1)))=> x20))) as proof of ((P (((plus five) x0) x1))->(P (((mult x) four) x1)))
% 133.97/134.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00) x0))))
% 133.97/134.16 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.16 Found ((eta_expansion_dep00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.16 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.16 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.16 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4))))->(P (fun (x:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x)))))
% 133.97/134.16 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.16 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))
% 133.97/134.24 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 133.97/134.24 Found eq_ref000:=(eq_ref00 P):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))
% 133.97/134.24 Found (eq_ref00 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found ((eq_ref0 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found (((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found (((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00) x0))))
% 134.16/134.34 Found (eta_expansion000 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found ((eta_expansion00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found (((eta_expansion0 fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found ((((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found ((((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4))))->(P (fun (x:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x)))))
% 134.16/134.34 Found (eta_expansion000 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.16/134.34 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))
% 134.27/134.53 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00) x0))))
% 134.27/134.53 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found ((eta_expansion_dep00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.27/134.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4))))->(P (fun (x:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x)))))
% 134.36/134.57 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))
% 134.36/134.57 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.36/134.57 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found eq_ref000:=(eq_ref00 P):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))
% 134.57/134.77 Found (eq_ref00 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found ((eq_ref0 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found (((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found (((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00) x0))))
% 134.57/134.77 Found (eta_expansion000 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found ((eta_expansion00 (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found (((eta_expansion0 fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found ((((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found ((((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 134.57/134.77 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4))))->(P (fun (x:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x)))))
% 134.57/134.77 Found (eta_expansion000 P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) P)) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))):((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))
% 135.18/135.37 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00)))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (((succ (succ (succ (succ x0)))) x00) x4)))) (fun (x1:(fofType->fofType))=> (P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))))) as proof of ((P (((mult x) (succ (succ (succ (fun (x3:(fofType->fofType))=> x3))))) x00))->(P ((succ (succ (succ (succ (succ x0))))) x00)))
% 135.18/135.37 Found eta_expansion_dep000:=(eta_expansion_dep00 (((plus five) x0) x1)):(((eq (fofType->fofType)) (((plus five) x0) x1)) (fun (x:fofType)=> ((((plus five) x0) x1) x)))
% 135.18/135.37 Found (eta_expansion_dep00 (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 135.18/135.37 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 136.79/137.02 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 136.79/137.02 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 136.79/137.02 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 136.79/137.02 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 136.79/137.02 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found eta_expansion000:=(eta_expansion00 (((plus five) x0) x1)):(((eq (fofType->fofType)) (((plus five) x0) x1)) (fun (x:fofType)=> ((((plus five) x0) x1) x)))
% 136.79/137.02 Found (eta_expansion00 (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 136.79/137.02 Found ((eta_expansion0 fofType) (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 136.79/137.02 Found (((eta_expansion fofType) fofType) (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 136.79/137.02 Found (((eta_expansion fofType) fofType) (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 136.79/137.02 Found (((eta_expansion fofType) fofType) (((plus five) x0) x1)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) b)
% 136.79/137.02 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 136.79/137.02 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 136.79/137.02 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 136.79/137.02 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 136.79/137.02 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 136.79/137.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 136.79/137.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 136.79/137.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 136.79/137.02 Found eta_expansion000:=(eta_expansion00 (((plus five) x0) x00)):(((eq (fofType->fofType)) (((plus five) x0) x00)) (fun (x:fofType)=> ((((plus five) x0) x00) x)))
% 136.79/137.02 Found (eta_expansion00 (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 136.79/137.02 Found ((eta_expansion0 fofType) (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 136.79/137.02 Found (((eta_expansion fofType) fofType) (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 136.79/137.02 Found (((eta_expansion fofType) fofType) (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 136.79/137.02 Found (((eta_expansion fofType) fofType) (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 136.79/137.02 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 153.29/153.51 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 153.29/153.51 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 153.29/153.51 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 153.29/153.51 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 153.29/153.51 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x00))
% 153.29/153.51 Found eta_expansion000:=(eta_expansion00 (((plus five) x0) x00)):(((eq (fofType->fofType)) (((plus five) x0) x00)) (fun (x:fofType)=> ((((plus five) x0) x00) x)))
% 153.29/153.51 Found (eta_expansion00 (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 153.29/153.51 Found ((eta_expansion0 fofType) (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 153.29/153.51 Found (((eta_expansion fofType) fofType) (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 153.29/153.51 Found (((eta_expansion fofType) fofType) (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 153.29/153.51 Found (((eta_expansion fofType) fofType) (((plus five) x0) x00)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 153.29/153.51 Found x21:(P (((plus five) x0) x1))
% 153.29/153.51 Found (fun (x21:(P (((plus five) x0) x1)))=> x21) as proof of (P (((plus five) x0) x1))
% 153.29/153.51 Found (fun (x21:(P (((plus five) x0) x1)))=> x21) as proof of (P0 (((plus five) x0) x1))
% 153.29/153.51 Found x11:(P (((plus five) x0) x00))
% 153.29/153.51 Found (fun (x11:(P (((plus five) x0) x00)))=> x11) as proof of (P (((plus five) x0) x00))
% 153.29/153.51 Found (fun (x11:(P (((plus five) x0) x00)))=> x11) as proof of (P0 (((plus five) x0) x00))
% 153.29/153.51 Found x11:(P (((plus five) x0) x00))
% 153.29/153.51 Found (fun (x11:(P (((plus five) x0) x00)))=> x11) as proof of (P (((plus five) x0) x00))
% 153.29/153.51 Found (fun (x11:(P (((plus five) x0) x00)))=> x11) as proof of (P0 (((plus five) x0) x00))
% 153.29/153.51 Found x21:(P (((plus five) x0) x1))
% 153.29/153.51 Found (fun (x21:(P (((plus five) x0) x1)))=> x21) as proof of (P (((plus five) x0) x1))
% 153.29/153.51 Found (fun (x21:(P (((plus five) x0) x1)))=> x21) as proof of (P0 (((plus five) x0) x1))
% 153.29/153.51 Found x11:(P (((plus five) x0) x00))
% 153.29/153.51 Found (fun (x11:(P (((plus five) x0) x00)))=> x11) as proof of (P (((plus five) x0) x00))
% 153.29/153.51 Found (fun (x11:(P (((plus five) x0) x00)))=> x11) as proof of (P0 (((plus five) x0) x00))
% 153.29/153.51 Found x21:(P (((plus five) x0) x1))
% 153.29/153.51 Found (fun (x21:(P (((plus five) x0) x1)))=> x21) as proof of (P (((plus five) x0) x1))
% 153.29/153.51 Found (fun (x21:(P (((plus five) x0) x1)))=> x21) as proof of (P0 (((plus five) x0) x1))
% 153.29/153.51 Found x21:(P (((plus five) x0) x1))
% 153.29/153.51 Found (fun (x21:(P (((plus five) x0) x1)))=> x21) as proof of (P (((plus five) x0) x1))
% 153.29/153.51 Found (fun (x21:(P (((plus five) x0) x1)))=> x21) as proof of (P0 (((plus five) x0) x1))
% 153.29/153.51 Found x11:(P (((plus five) x0) x00))
% 153.29/153.51 Found (fun (x11:(P (((plus five) x0) x00)))=> x11) as proof of (P (((plus five) x0) x00))
% 153.29/153.51 Found (fun (x11:(P (((plus five) x0) x00)))=> x11) as proof of (P0 (((plus five) x0) x00))
% 153.29/153.51 Found x020:(P ((((mult x) four) x00) x01))
% 153.29/153.51 Found (fun (x020:(P ((((mult x) four) x00) x01)))=> x020) as proof of (P ((((mult x) four) x00) x01))
% 153.29/153.51 Found (fun (x020:(P ((((mult x) four) x00) x01)))=> x020) as proof of (P0 ((((mult x) four) x00) x01))
% 153.29/153.51 Found x020:(P ((((mult x) four) x00) x01))
% 153.29/153.51 Found (fun (x020:(P ((((mult x) four) x00) x01)))=> x020) as proof of (P ((((mult x) four) x00) x01))
% 153.29/153.51 Found (fun (x020:(P ((((mult x) four) x00) x01)))=> x020) as proof of (P0 ((((mult x) four) x00) x01))
% 153.29/153.51 Found x020:(P ((((mult x) four) x00) x01))
% 153.29/153.51 Found (fun (x020:(P ((((mult x) four) x00) x01)))=> x020) as proof of (P ((((mult x) four) x00) x01))
% 153.29/153.51 Found (fun (x020:(P ((((mult x) four) x00) x01)))=> x020) as proof of (P0 ((((mult x) four) x00) x01))
% 153.29/153.51 Found x020:(P ((((mult x) four) x00) x01))
% 153.29/153.51 Found (fun (x020:(P ((((mult x) four) x00) x01)))=> x020) as proof of (P ((((mult x) four) x00) x01))
% 153.29/153.51 Found (fun (x020:(P ((((mult x) four) x00) x01)))=> x020) as proof of (P0 ((((mult x) four) x00) x01))
% 153.29/153.51 Found x20:(P ((((plus five) x0) x1) y))
% 155.45/155.65 Found (fun (x20:(P ((((plus five) x0) x1) y)))=> x20) as proof of (P ((((plus five) x0) x1) y))
% 155.45/155.65 Found (fun (x20:(P ((((plus five) x0) x1) y)))=> x20) as proof of (P0 ((((plus five) x0) x1) y))
% 155.45/155.65 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 155.45/155.65 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x00) y))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) y))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) y))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) y))
% 155.45/155.65 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x00) y)):(((eq fofType) ((((plus five) x0) x00) y)) ((((plus five) x0) x00) y))
% 155.45/155.65 Found (eq_ref0 ((((plus five) x0) x00) y)) as proof of (((eq fofType) ((((plus five) x0) x00) y)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((plus five) x0) x00) y)) as proof of (((eq fofType) ((((plus five) x0) x00) y)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((plus five) x0) x00) y)) as proof of (((eq fofType) ((((plus five) x0) x00) y)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((plus five) x0) x00) y)) as proof of (((eq fofType) ((((plus five) x0) x00) y)) b)
% 155.45/155.65 Found eq_ref00:=(eq_ref0 ((((mult x) four) x00) x01)):(((eq fofType) ((((mult x) four) x00) x01)) ((((mult x) four) x00) x01))
% 155.45/155.65 Found (eq_ref0 ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 155.45/155.65 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 155.45/155.65 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found eq_ref00:=(eq_ref0 ((((mult x) four) x00) x01)):(((eq fofType) ((((mult x) four) x00) x01)) ((((mult x) four) x00) x01))
% 155.45/155.65 Found (eq_ref0 ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found eq_ref00:=(eq_ref0 ((((mult x) four) x00) x01)):(((eq fofType) ((((mult x) four) x00) x01)) ((((mult x) four) x00) x01))
% 155.45/155.65 Found (eq_ref0 ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 155.45/155.65 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 155.45/155.65 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 155.45/155.65 Found eq_ref00:=(eq_ref0 ((((mult x) four) x00) x01)):(((eq fofType) ((((mult x) four) x00) x01)) ((((mult x) four) x00) x01))
% 179.75/179.94 Found (eq_ref0 ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 179.75/179.94 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 179.75/179.94 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 179.75/179.94 Found ((eq_ref fofType) ((((mult x) four) x00) x01)) as proof of (((eq fofType) ((((mult x) four) x00) x01)) b)
% 179.75/179.94 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 179.75/179.94 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 179.75/179.94 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 179.75/179.94 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 179.75/179.94 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x00) x01))
% 179.75/179.94 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x1) y)):(((eq fofType) ((((plus five) x0) x1) y)) ((((plus five) x0) x1) y))
% 179.75/179.94 Found (eq_ref0 ((((plus five) x0) x1) y)) as proof of (((eq fofType) ((((plus five) x0) x1) y)) b)
% 179.75/179.94 Found ((eq_ref fofType) ((((plus five) x0) x1) y)) as proof of (((eq fofType) ((((plus five) x0) x1) y)) b)
% 179.75/179.94 Found ((eq_ref fofType) ((((plus five) x0) x1) y)) as proof of (((eq fofType) ((((plus five) x0) x1) y)) b)
% 179.75/179.94 Found ((eq_ref fofType) ((((plus five) x0) x1) y)) as proof of (((eq fofType) ((((plus five) x0) x1) y)) b)
% 179.75/179.94 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 179.75/179.94 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x1) y))
% 179.75/179.94 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) y))
% 179.75/179.94 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) y))
% 179.75/179.94 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) y))
% 179.75/179.94 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 179.75/179.94 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.75/179.94 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.75/179.94 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.75/179.94 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.75/179.94 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.75/179.94 Found (eq_sym010 (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 179.75/179.94 Found ((eq_sym01 (((plus five) x0) x00)) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 179.75/179.94 Found (((eq_sym0 b) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 179.75/179.94 Found (((eq_sym0 b) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 179.75/179.94 Found ((eq_trans0000 (((eq_sym0 b) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) b))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 179.75/179.94 Found (((eq_trans000 (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 179.75/179.94 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 179.75/179.94 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 179.87/180.08 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 179.87/180.08 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 179.87/180.08 Found (eq_sym000 ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x00))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 179.87/180.08 Found ((eq_sym00 (((mult x) four) x00)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x00))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 179.87/180.08 Found (((eq_sym0 (((plus five) x0) x00)) (((mult x) four) x00)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x00))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 179.87/180.08 Found ((((eq_sym (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) ((((eq_sym (fofType->fofType)) (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (four x00))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 179.87/180.08 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 179.87/180.08 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.87/180.08 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.87/180.08 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.87/180.08 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.87/180.08 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((plus five) x0) x00))
% 179.87/180.08 Found (eq_sym010 (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 179.87/180.08 Found ((eq_sym01 (((plus five) x0) x00)) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 179.87/180.08 Found (((eq_sym0 b) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 179.87/180.08 Found (((eq_sym0 b) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) b)
% 179.87/180.08 Found ((eq_trans0000 (((eq_sym0 b) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) b))) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 180.86/181.05 Found (((eq_trans000 (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion fofType) fofType) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 180.86/181.05 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion fofType) fofType) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 180.86/181.05 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion fofType) fofType) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 180.86/181.05 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion fofType) fofType) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 180.86/181.05 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion fofType) fofType) (x (four x00)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00))
% 180.86/181.05 Found (eq_sym000 ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion fofType) fofType) (x (four x00))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 180.86/181.05 Found ((eq_sym00 (((mult x) four) x00)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion fofType) fofType) (x (four x00))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 180.86/181.05 Found (((eq_sym0 (((plus five) x0) x00)) (((mult x) four) x00)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) (((eq_sym0 (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion fofType) fofType) (x (four x00))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 180.86/181.05 Found ((((eq_sym (fofType->fofType)) (((plus five) x0) x00)) (((mult x) four) x00)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x00)) b) (((mult x) four) x00))) (x (four x00))) ((((eq_sym (fofType->fofType)) (x (four x00))) (((plus five) x0) x00)) (((eta_expansion fofType) fofType) (x (four x00))))) (((eta_expansion fofType) fofType) (x (four x00))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 180.86/181.05 Found eta_expansion000:=(eta_expansion00 (b x1)):(((eq (fofType->fofType)) (b x1)) (fun (x:fofType)=> ((b x1) x)))
% 180.86/181.05 Found (eta_expansion00 (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.86/181.05 Found ((eta_expansion0 fofType) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.86/181.05 Found (((eta_expansion fofType) fofType) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.86/181.05 Found (((eta_expansion fofType) fofType) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found eta_expansion000:=(eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x))))))))
% 180.95/181.16 Found (eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found ((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (b x1)):(((eq (fofType->fofType)) (b x1)) (fun (x:fofType)=> ((b x1) x)))
% 180.95/181.16 Found (eta_expansion_dep00 (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x))))))))
% 180.95/181.16 Found (eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found eq_ref00:=(eq_ref0 (b x1)):(((eq (fofType->fofType)) (b x1)) (b x1))
% 180.95/181.16 Found (eq_ref0 (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (b x1)):(((eq (fofType->fofType)) (b x1)) (fun (x:fofType)=> ((b x1) x)))
% 180.95/181.16 Found (eta_expansion_dep00 (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x))))))))
% 180.95/181.16 Found (eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 180.95/181.16 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found eta_expansion000:=(eta_expansion00 (b x1)):(((eq (fofType->fofType)) (b x1)) (fun (x:fofType)=> ((b x1) x)))
% 187.62/187.82 Found (eta_expansion00 (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found ((eta_expansion0 fofType) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found (((eta_expansion fofType) fofType) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found (((eta_expansion fofType) fofType) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found eta_expansion000:=(eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x))))))))
% 187.62/187.82 Found (eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found ((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found eq_ref00:=(eq_ref0 (b x1)):(((eq (fofType->fofType)) (b x1)) (b x1))
% 187.62/187.82 Found (eq_ref0 (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 187.62/187.82 Found eq_ref00:=(eq_ref0 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (((mult x) four) x1))
% 187.62/187.82 Found (eq_ref0 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) b)
% 187.62/187.82 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) b)
% 187.62/187.82 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) b)
% 187.62/187.82 Found ((eq_ref (fofType->fofType)) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) b)
% 187.62/187.82 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.62/187.82 Found ((eq_sym10 b) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.62/187.82 Found (((eq_sym1 (((mult x) four) x1)) b) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.62/187.82 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) b) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.62/187.82 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) b) ((eq_ref (fofType->fofType)) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.62/187.82 Found ((eq_trans0000 (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) b) ((eq_ref (fofType->fofType)) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 187.62/187.82 Found (((eq_trans000 (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) ((eq_ref (fofType->fofType)) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 187.91/188.10 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) four) x1))) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) ((eq_ref (fofType->fofType)) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 187.91/188.10 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((plus five) x0) x1)) b) (((mult x) four) x1))) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) ((eq_ref (fofType->fofType)) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 187.91/188.10 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x1)) b) (((mult x) four) x1))) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) ((eq_ref (fofType->fofType)) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 187.91/188.10 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x1)):(((eq (fofType->fofType)) (((mult x) four) x1)) (fun (x0:fofType)=> ((((mult x) four) x1) x0)))
% 187.91/188.10 Found (eta_expansion00 (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) b)
% 187.91/188.10 Found ((eta_expansion0 fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) b)
% 187.91/188.10 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) b)
% 187.91/188.10 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) b)
% 187.91/188.10 Found (((eta_expansion fofType) fofType) (((mult x) four) x1)) as proof of (((eq (fofType->fofType)) (((mult x) four) x1)) b)
% 187.91/188.10 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.91/188.10 Found ((eq_sym10 b) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.91/188.10 Found (((eq_sym1 (((mult x) four) x1)) b) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.91/188.10 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) b) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.91/188.10 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) b) (((eta_expansion fofType) fofType) (((mult x) four) x1))) as proof of (((eq (fofType->fofType)) b) (((mult x) four) x1))
% 187.91/188.10 Found ((eq_trans0000 (((eta_expansion fofType) fofType) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) b) (((eta_expansion fofType) fofType) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 187.91/188.10 Found (((eq_trans000 (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion fofType) fofType) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion fofType) fofType) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 187.91/188.10 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) four) x1))) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion fofType) fofType) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion fofType) fofType) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 188.44/188.64 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((plus five) x0) x1)) b) (((mult x) four) x1))) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion fofType) fofType) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion fofType) fofType) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 188.44/188.64 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((plus five) x0) x1)) b) (((mult x) four) x1))) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion fofType) fofType) (((plus five) x0) x1))) ((((eq_sym (fofType->fofType)) (((mult x) four) x1)) (fun (x4:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x4)))))))) (((eta_expansion fofType) fofType) (((mult x) four) x1)))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (((mult x) four) x1))
% 188.44/188.64 Found eta_expansion0000:=(eta_expansion000 P):((P (b x1))->(P (fun (x:fofType)=> ((b x1) x))))
% 188.44/188.64 Found (eta_expansion000 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found ((eta_expansion00 (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found (((eta_expansion0 fofType) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found ((((eta_expansion fofType) fofType) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found ((((eta_expansion fofType) fofType) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (b x1)) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5))))))))->(P (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x)))))))))
% 188.44/188.64 Found (eta_expansion000 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found eta_expansion0000:=(eta_expansion000 (fun (x2:(fofType->fofType))=> (P (b x1)))):((P (b x1))->(P (b x1)))
% 188.44/188.64 Found (eta_expansion000 (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.44/188.64 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.76/188.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1))))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.76/188.96 Found eq_ref00:=(eq_ref0 (b x1)):(((eq (fofType->fofType)) (b x1)) (b x1))
% 188.76/188.96 Found (eq_ref0 (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 188.76/188.96 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 188.76/188.96 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 188.76/188.96 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 188.76/188.96 Found (eq_sym100 ((eq_ref (fofType->fofType)) (b x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (b x1))
% 188.76/188.96 Found ((eq_sym10 (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (b x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (b x1))
% 188.76/188.96 Found (((eq_sym1 (b x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (b x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (b x1))
% 188.76/188.96 Found ((((eq_sym (fofType->fofType)) (b x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (b x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (b x1))
% 188.76/188.96 Found eq_ref000:=(eq_ref00 P):((P (b x1))->(P (b x1)))
% 188.76/188.96 Found (eq_ref00 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.76/188.96 Found ((eq_ref0 (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.76/188.96 Found (((eq_ref (fofType->fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.76/188.96 Found (((eq_ref (fofType->fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.76/188.96 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (b x1)) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.76/188.96 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 188.76/188.96 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 188.76/188.96 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 188.76/188.96 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 188.76/188.96 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 188.76/188.96 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) four) x00))) as proof of (((eq (fofType->fofType)) (b x00)) (((mult x) four) x00))
% 188.76/188.96 Found ((eq_sym10 (b x00)) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) as proof of (((eq (fofType->fofType)) (b x00)) (((mult x) four) x00))
% 188.76/188.96 Found (((eq_sym1 (((mult x) four) x00)) (b x00)) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) as proof of (((eq (fofType->fofType)) (b x00)) (((mult x) four) x00))
% 188.76/188.96 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x00)) (b x00)) ((eq_ref (fofType->fofType)) (((mult x) four) x00))) as proof of (((eq (fofType->fofType)) (b x00)) (((mult x) four) x00))
% 188.76/188.96 Found eq_ref00:=(eq_ref0 (b x1)):(((eq (fofType->fofType)) (b x1)) (b x1))
% 188.76/188.96 Found (eq_ref0 (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 188.76/188.96 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 188.76/188.96 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 188.76/188.96 Found ((eq_ref (fofType->fofType)) (b x1)) as proof of (((eq (fofType->fofType)) (b x1)) (((plus five) x0) x1))
% 188.76/188.96 Found (eq_sym100 ((eq_ref (fofType->fofType)) (b x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (b x1))
% 188.76/188.96 Found ((eq_sym10 (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (b x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (b x1))
% 188.76/188.96 Found (((eq_sym1 (b x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (b x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (b x1))
% 188.76/188.96 Found ((((eq_sym (fofType->fofType)) (b x1)) (((plus five) x0) x1)) ((eq_ref (fofType->fofType)) (b x1))) as proof of (((eq (fofType->fofType)) (((plus five) x0) x1)) (b x1))
% 188.97/189.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 188.97/189.16 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 188.97/189.16 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 188.97/189.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 188.97/189.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 188.97/189.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (b x00))
% 188.97/189.16 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00))) as proof of (((eq (fofType->fofType)) (b x00)) (((mult x) four) x00))
% 188.97/189.16 Found ((eq_sym10 (b x00)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00))) as proof of (((eq (fofType->fofType)) (b x00)) (((mult x) four) x00))
% 188.97/189.16 Found (((eq_sym1 (((mult x) four) x00)) (b x00)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00))) as proof of (((eq (fofType->fofType)) (b x00)) (((mult x) four) x00))
% 188.97/189.16 Found ((((eq_sym (fofType->fofType)) (((mult x) four) x00)) (b x00)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00))) as proof of (((eq (fofType->fofType)) (b x00)) (((mult x) four) x00))
% 188.97/189.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (b x1))->(P (fun (x:fofType)=> ((b x1) x))))
% 188.97/189.16 Found (eta_expansion_dep000 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found ((eta_expansion_dep00 (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5))))))))->(P (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x)))))))))
% 188.97/189.16 Found (eta_expansion_dep000 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 188.97/189.16 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P (b x1)))):((P (b x1))->(P (b x1)))
% 188.97/189.16 Found (eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1))))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found eq_ref000:=(eq_ref00 P):((P (b x1))->(P (b x1)))
% 189.06/189.26 Found (eq_ref00 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((eq_ref0 (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (((eq_ref (fofType->fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (((eq_ref (fofType->fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (b x1)) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found eta_expansion0000:=(eta_expansion000 P):((P (b x1))->(P (fun (x:fofType)=> ((b x1) x))))
% 189.06/189.26 Found (eta_expansion000 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((eta_expansion00 (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (((eta_expansion0 fofType) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((((eta_expansion fofType) fofType) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((((eta_expansion fofType) fofType) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (b x1)) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5))))))))->(P (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x)))))))))
% 189.06/189.26 Found (eta_expansion000 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found eta_expansion0000:=(eta_expansion000 (fun (x2:(fofType->fofType))=> (P (b x1)))):((P (b x1))->(P (b x1)))
% 189.06/189.26 Found (eta_expansion000 (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 189.06/189.26 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1))))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (b x1))->(P (fun (x:fofType)=> ((b x1) x))))
% 222.30/222.50 Found (eta_expansion_dep000 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((eta_expansion_dep00 (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (b x1)) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5))))))))->(P (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x)))))))))
% 222.30/222.50 Found (eta_expansion_dep000 P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) P)) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P (b x1)))):((P (b x1))->(P (b x1)))
% 222.30/222.50 Found (eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1)))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 ((x0 x1) x5)))))))) (fun (x2:(fofType->fofType))=> (P (b x1))))) as proof of ((P (b x1))->(P (((plus five) x0) x1)))
% 222.30/222.50 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 222.30/222.50 Found (eq_ref0 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 222.37/222.58 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 222.37/222.58 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 222.37/222.58 Found (eq_ref0 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.37/222.58 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 222.37/222.58 Found (eta_expansion00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 222.43/222.61 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 222.43/222.61 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 222.43/222.61 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 222.43/222.61 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 227.22/227.42 Found (eta_expansion00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 227.22/227.42 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 227.22/227.42 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.42 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.42 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.42 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.42 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.42 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.42 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 227.22/227.42 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.42 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.45 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 227.22/227.45 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.22/227.45 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 227.22/227.45 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.22/227.45 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.27/227.53 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 227.27/227.53 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found ((eta_expansion_dep00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.27/227.53 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 227.27/227.53 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.27/227.53 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 227.27/227.53 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.27/227.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.41/227.61 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 227.41/227.61 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.41/227.61 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 227.41/227.61 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.41/227.61 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 227.41/227.61 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.41/227.61 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.45/227.69 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) four) x00))->(P (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 227.45/227.69 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found ((eta_expansion00 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.45/227.69 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 227.45/227.69 Found (eta_expansion000 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 227.45/227.69 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 227.45/227.69 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 229.62/229.84 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00)))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 229.62/229.84 Found eq_ref000:=(eq_ref00 P):((P (((mult x) four) x00))->(P (((mult x) four) x00)))
% 229.62/229.84 Found (eq_ref00 P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found ((eq_ref0 (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of ((P (((mult x) four) x00))->(P (((plus five) x0) x00)))
% 229.62/229.84 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 229.62/229.84 Found x30:(P ((((plus five) x0) x1) x2))
% 229.62/229.84 Found (fun (x30:(P ((((plus five) x0) x1) x2)))=> x30) as proof of (P ((((plus five) x0) x1) x2))
% 229.62/229.84 Found (fun (x30:(P ((((plus five) x0) x1) x2)))=> x30) as proof of (P0 ((((plus five) x0) x1) x2))
% 229.62/229.84 Found x30:(P ((((plus five) x0) x1) x2))
% 229.62/229.84 Found (fun (x30:(P ((((plus five) x0) x1) x2)))=> x30) as proof of (P ((((plus five) x0) x1) x2))
% 229.62/229.84 Found (fun (x30:(P ((((plus five) x0) x1) x2)))=> x30) as proof of (P0 ((((plus five) x0) x1) x2))
% 229.62/229.84 Found x30:(P ((((plus five) x0) x1) x2))
% 229.62/229.84 Found (fun (x30:(P ((((plus five) x0) x1) x2)))=> x30) as proof of (P ((((plus five) x0) x1) x2))
% 229.62/229.84 Found (fun (x30:(P ((((plus five) x0) x1) x2)))=> x30) as proof of (P0 ((((plus five) x0) x1) x2))
% 229.62/229.84 Found x30:(P ((((plus five) x0) x1) x2))
% 229.62/229.84 Found (fun (x30:(P ((((plus five) x0) x1) x2)))=> x30) as proof of (P ((((plus five) x0) x1) x2))
% 229.62/229.84 Found (fun (x30:(P ((((plus five) x0) x1) x2)))=> x30) as proof of (P0 ((((plus five) x0) x1) x2))
% 229.62/229.84 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 229.62/229.84 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 229.62/229.84 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 229.62/229.84 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 229.62/229.84 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 229.62/229.84 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x00) x01)):(((eq fofType) ((((plus five) x0) x00) x01)) ((((plus five) x0) x00) x01))
% 229.62/229.84 Found (eq_ref0 ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 231.60/231.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x00) x01)):(((eq fofType) ((((plus five) x0) x00) x01)) ((((plus five) x0) x00) x01))
% 231.60/231.81 Found (eq_ref0 ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x00) x01)):(((eq fofType) ((((plus five) x0) x00) x01)) ((((plus five) x0) x00) x01))
% 231.60/231.81 Found (eq_ref0 ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 231.60/231.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x00) x01)):(((eq fofType) ((((plus five) x0) x00) x01)) ((((plus five) x0) x00) x01))
% 231.60/231.81 Found (eq_ref0 ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x00) x01)) as proof of (((eq fofType) ((((plus five) x0) x00) x01)) b)
% 231.60/231.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 231.60/231.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x00) x01))
% 231.60/231.81 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x1) x2)):(((eq fofType) ((((plus five) x0) x1) x2)) ((((plus five) x0) x1) x2))
% 231.60/231.81 Found (eq_ref0 ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 231.60/231.81 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 231.60/231.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 231.60/231.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 231.60/231.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x1) x2)):(((eq fofType) ((((plus five) x0) x1) x2)) ((((plus five) x0) x1) x2))
% 247.34/247.55 Found (eq_ref0 ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 247.34/247.55 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x1) x2)):(((eq fofType) ((((plus five) x0) x1) x2)) ((((plus five) x0) x1) x2))
% 247.34/247.55 Found (eq_ref0 ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 247.34/247.55 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found eq_ref00:=(eq_ref0 ((((plus five) x0) x1) x2)):(((eq fofType) ((((plus five) x0) x1) x2)) ((((plus five) x0) x1) x2))
% 247.34/247.55 Found (eq_ref0 ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((plus five) x0) x1) x2)) as proof of (((eq fofType) ((((plus five) x0) x1) x2)) b)
% 247.34/247.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 247.34/247.55 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) four) x1) x2))
% 247.34/247.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 247.34/247.55 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) x0) x1) y))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x1) y))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x1) y))
% 247.34/247.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x1) y))
% 247.34/247.55 Found eq_ref00:=(eq_ref0 ((((mult x) four) x1) y)):(((eq fofType) ((((mult x) four) x1) y)) ((((mult x) four) x1) y))
% 247.34/247.55 Found (eq_ref0 ((((mult x) four) x1) y)) as proof of (((eq fofType) ((((mult x) four) x1) y)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((mult x) four) x1) y)) as proof of (((eq fofType) ((((mult x) four) x1) y)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((mult x) four) x1) y)) as proof of (((eq fofType) ((((mult x) four) x1) y)) b)
% 247.34/247.55 Found ((eq_ref fofType) ((((mult x) four) x1) y)) as proof of (((eq fofType) ((((mult x) four) x1) y)) b)
% 247.34/247.55 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)):(((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1) x0)))
% 247.41/247.62 Found (eta_expansion_dep00 (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 247.41/247.62 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 247.41/247.62 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 247.41/247.62 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 247.41/247.62 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 247.41/247.62 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))) as proof of (((eq (fofType->fofType)) ((succ (succ (succ (succ (succ x0))))) x1)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))
% 247.41/247.62 Found ((eq_sym10 ((succ (succ (succ (succ (succ x0))))) x1)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))) as proof of (((eq (fofType->fofType)) ((succ (succ (succ (succ (succ x0))))) x1)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))
% 247.41/247.62 Found (((eq_sym1 (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))) as proof of (((eq (fofType->fofType)) ((succ (succ (succ (succ (succ x0))))) x1)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))
% 247.41/247.62 Found ((((eq_sym (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1)) (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))) as proof of (((eq (fofType->fofType)) ((succ (succ (succ (succ (succ x0))))) x1)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))
% 247.41/247.62 Found eta_expansion000:=(eta_expansion00 (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)):(((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) (fun (x0:fofType)=> ((((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1) x0)))
% 247.41/247.62 Found (eta_expansion00 (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 247.41/247.62 Found ((eta_expansion0 fofType) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 247.41/247.62 Found (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 248.75/248.99 Found (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 248.75/248.99 Found (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) as proof of (((eq (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1))
% 248.75/248.99 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))) as proof of (((eq (fofType->fofType)) ((succ (succ (succ (succ (succ x0))))) x1)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))
% 248.75/248.99 Found ((eq_sym10 ((succ (succ (succ (succ (succ x0))))) x1)) (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))) as proof of (((eq (fofType->fofType)) ((succ (succ (succ (succ (succ x0))))) x1)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))
% 248.75/248.99 Found (((eq_sym1 (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1)) (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))) as proof of (((eq (fofType->fofType)) ((succ (succ (succ (succ (succ x0))))) x1)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))
% 248.75/248.99 Found ((((eq_sym (fofType->fofType)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1)) ((succ (succ (succ (succ (succ x0))))) x1)) (((eta_expansion fofType) fofType) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))) as proof of (((eq (fofType->fofType)) ((succ (succ (succ (succ (succ x0))))) x1)) (((mult x) (succ (succ (succ (fun (x30:(fofType->fofType))=> x30))))) x1))
% 248.75/248.99 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 248.75/248.99 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.75/248.99 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.75/248.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.75/248.99 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.75/248.99 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 248.75/248.99 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.75/248.99 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.75/248.99 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.75/248.99 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.75/248.99 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 248.75/248.99 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.75/248.99 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 248.85/249.11 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 248.85/249.11 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 248.85/249.11 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 248.85/249.11 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 248.85/249.11 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 248.85/249.11 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 249.44/249.67 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 249.44/249.67 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 249.44/249.67 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 249.44/249.67 Found (eta_expansion00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.44/249.67 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.44/249.67 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.44/249.67 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.44/249.67 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.44/249.67 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 249.44/249.67 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.44/249.67 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.44/249.67 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 249.54/249.75 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 249.54/249.75 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 249.54/249.75 Found (eq_ref0 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 249.54/249.75 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.75 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 249.54/249.79 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 249.54/249.79 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 249.54/249.79 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.54/249.79 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 249.84/250.03 Found (eq_ref0 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 249.84/250.03 Found (eq_ref0 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 249.84/250.03 Found (eq_ref0 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 249.84/250.03 Found (eta_expansion00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 249.84/250.03 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 250.06/250.26 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 250.06/250.26 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 250.06/250.26 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 250.06/250.26 Found (eta_expansion00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.06/250.26 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 250.10/250.30 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 250.10/250.30 Found (eta_expansion00 (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 250.10/250.30 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 250.10/250.30 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 254.75/254.96 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 254.75/254.96 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 254.75/254.96 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 254.75/254.96 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 254.75/254.96 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.75/254.96 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 254.84/255.07 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 254.84/255.07 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 254.84/255.07 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.07 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 254.84/255.14 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 254.84/255.14 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 254.84/255.14 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 254.84/255.14 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 255.09/255.30 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 255.09/255.30 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.09/255.30 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.09/255.30 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.09/255.30 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found x000:(P ((mult x) four))
% 255.35/255.56 Found (fun (x000:(P ((mult x) four)))=> x000) as proof of (P ((mult x) four))
% 255.35/255.56 Found (fun (x000:(P ((mult x) four)))=> x000) as proof of (P0 ((mult x) four))
% 255.35/255.56 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 255.35/255.56 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.35/255.56 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 255.35/255.56 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.35/255.56 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.35/255.56 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.35/255.56 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.45/255.64 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 255.45/255.64 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.45/255.64 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 255.45/255.64 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.45/255.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.45/255.64 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.49/255.72 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.49/255.72 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 255.49/255.72 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.49/255.72 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 255.49/255.72 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.49/255.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.65/255.87 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.65/255.87 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.65/255.87 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.65/255.87 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.65/255.87 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.65/255.87 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.65/255.87 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.74/255.98 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 255.74/255.98 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.74/255.98 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 255.74/255.98 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.74/255.98 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.74/255.98 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.74/255.98 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.86/256.08 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.86/256.08 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.86/256.08 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 255.86/256.08 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.86/256.08 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 255.86/256.08 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.86/256.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.94/256.18 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 255.94/256.18 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.94/256.18 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 255.94/256.18 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 255.94/256.18 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 255.94/256.18 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 255.94/256.18 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 256.03/256.26 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 256.03/256.26 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 256.03/256.26 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 256.03/256.26 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 256.03/256.26 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 256.03/256.26 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.03/256.26 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 256.16/256.38 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 256.16/256.38 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 256.16/256.38 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 256.16/256.38 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.16/256.38 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 256.24/256.53 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 256.24/256.53 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 256.24/256.53 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 256.24/256.53 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 256.24/256.53 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 256.24/256.53 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 262.80/263.01 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.80/263.01 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.80/263.01 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.80/263.01 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.80/263.01 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.80/263.01 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) four) x00))->(P (((plus five) x0) x00))))
% 262.80/263.01 Found x001:(P ((mult x) four))
% 262.80/263.01 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P ((mult x) four))
% 262.80/263.01 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P0 ((mult x) four))
% 262.80/263.01 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 262.80/263.01 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 262.80/263.01 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 262.80/263.01 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 262.80/263.01 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.80/263.01 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.91/263.13 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 262.91/263.13 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.91/263.13 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.91/263.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.91/263.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 262.91/263.13 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 262.91/263.13 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 262.91/263.13 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 262.91/263.13 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.91/263.13 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 262.94/263.21 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 262.94/263.21 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 262.94/263.21 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 262.94/263.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.34/263.59 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.34/263.59 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.34/263.59 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 263.34/263.59 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.34/263.59 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.34/263.59 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.34/263.59 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.34/263.59 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.34/263.59 Found x001:(P ((mult x) four))
% 263.34/263.59 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P ((mult x) four))
% 263.34/263.59 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P0 ((mult x) four))
% 263.34/263.59 Found eta_expansion000:=(eta_expansion00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 263.34/263.59 Found (eta_expansion00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found ((eta_expansion0 fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found (((eta_expansion fofType) fofType) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 263.34/263.59 Found (eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found eq_ref00:=(eq_ref0 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (((mult x) four) x00))
% 263.34/263.59 Found (eq_ref0 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found ((eq_ref (fofType->fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.34/263.59 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) four) x00)):(((eq (fofType->fofType)) (((mult x) four) x00)) (fun (x0:fofType)=> ((((mult x) four) x00) x0)))
% 263.34/263.59 Found (eta_expansion_dep00 (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.46/263.73 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.46/263.73 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.46/263.73 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.46/263.73 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x))))))))
% 263.46/263.73 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.46/263.73 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.46/263.73 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.46/263.73 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) four) x00)) (((plus five) x0) x00))
% 263.46/263.73 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 263.46/263.73 Found (eq_ref00 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found ((eq_ref0 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 263.46/263.73 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found ((eta_expansion_dep00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 263.46/263.73 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.46/263.73 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 263.59/263.81 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) four) x00))->(P1 (fun (x0:fofType)=> ((((mult x) four) x00) x0))))
% 263.59/263.81 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((eta_expansion00 (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found (((eta_expansion0 fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) four) x00)) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4))))))))->(P1 (fun (x:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x)))))))))
% 263.59/263.81 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 263.59/263.81 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 297.39/297.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) P1)) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 297.39/297.64 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))):((P1 (((mult x) four) x00))->(P1 (((mult x) four) x00)))
% 297.39/297.64 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 297.39/297.64 Found ((eta_expansion00 (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 297.39/297.64 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 297.39/297.64 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 297.39/297.64 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00)))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 297.39/297.64 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x00 (x00 (x00 (x00 (x00 ((x0 x00) x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) four) x00))))) as proof of ((P1 (((mult x) four) x00))->(P1 (((plus five) x0) x00)))
% 297.39/297.64 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 297.39/297.64 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) x0))
% 297.39/297.64 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) x0))
% 297.39/297.64 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) x0))
% 297.39/297.64 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((plus five) x0))
% 297.39/297.64 Found eta_expansion_dep000:=(eta_expansion_dep00 ((mult x) four)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) (fun (x0:(fofType->fofType))=> (((mult x) four) x0)))
% 297.39/297.64 Found (eta_expansion_dep00 ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 297.39/297.64 Found ((eta_expansion_dep0 (fun (x2:(fofType->fofType))=> (fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 297.39/297.64 Found (((eta_expansion_dep (fofType->fofType)) (fun (x2:(fofType->fofType))=> (fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 297.39/297.64 Found (((eta_expansion_dep (fofType->fofType)) (fun (x2:(fofType->fofType))=> (fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 297.39/297.64 Found (((eta_expansion_dep (fofType->fofType)) (fun (x2:(fofType->fofType))=> (fofType->fofType))) ((mult x) four)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) four)) b)
% 297.39/297.64 Found x001:(P ((mult x) four))
% 297.39/297.64 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P ((mult x) four))
% 297.39/297.64 Found (fun (x001:(P ((mult x) four)))=> x001) as proof of (P0 ((mult x) four))
% 297.39/297.64 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 297.39/297.64 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((plus five) x0) x1) x2))
% 297.39/297.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x1) x2))
% 297.39/297.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x1) x2))
% 297.39/297.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((plus five) x0) x1) x2
%------------------------------------------------------------------------------