TSTP Solution File: SYO249^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO249^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:00 EDT 2022
% Result : Timeout 300.08s 300.58s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SYO249^5 : TPTP v7.5.0. Released v4.0.0.
% 0.06/0.10 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % RAMPerCPU : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % DateTime : Fri Mar 11 21:36:02 EST 2022
% 0.10/0.29 % CPUTime :
% 0.10/0.30 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.10/0.30 Python 2.7.5
% 0.39/0.55 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efd98c0>, <kernel.DependentProduct object at 0x2b3a3efd9368>) of role type named cBIGPHI
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cBIGPHI:(fofType->fofType)
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x15a2e60>, <kernel.DependentProduct object at 0x2b3a3efd9638>) of role type named cHOM_FROM_HH_1
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cHOM_FROM_HH_1:((fofType->fofType)->Prop)
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efd98c0>, <kernel.DependentProduct object at 0x2b3a3efd90e0>) of role type named cPHI_2
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cPHI_2:(fofType->fofType)
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efd9638>, <kernel.DependentProduct object at 0x2b3a3efd9e18>) of role type named cHOM_FROM_SS_PRIME
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cHOM_FROM_SS_PRIME:((fofType->fofType)->Prop)
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efd90e0>, <kernel.DependentProduct object at 0x2b3a3efd9b90>) of role type named cPHI_1
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cPHI_1:(fofType->fofType)
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efd9e18>, <kernel.DependentProduct object at 0x2b3a3efd9680>) of role type named cSS_PRIME
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cSS_PRIME:(fofType->Prop)
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efd9b90>, <kernel.DependentProduct object at 0x2b3a3efb77e8>) of role type named el1
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring el1:(fofType->((fofType->Prop)->Prop))
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efd9170>, <kernel.DependentProduct object at 0x2b3a3efb7908>) of role type named cHH_1
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cHH_1:(fofType->Prop)
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efd9638>, <kernel.DependentProduct object at 0x2b3a374dfef0>) of role type named cBIGHI
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cBIGHI:(fofType->fofType)
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efb7908>, <kernel.DependentProduct object at 0x2b3a374df1b8>) of role type named cHH_2
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cHH_2:(fofType->Prop)
% 0.39/0.55 FOF formula (<kernel.Constant object at 0x2b3a3efd9638>, <kernel.DependentProduct object at 0x2b3a374df4d0>) of role type named cTIMES
% 0.39/0.55 Using role type
% 0.39/0.55 Declaring cTIMES:(fofType->(fofType->fofType))
% 0.39/0.55 FOF formula (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx1:fofType) (Xx2:fofType) (Xy1:fofType) (Xy2:fofType), (((and ((and ((and ((and ((and ((el1 Xx1) cHH_2)) ((el1 Xx2) cHH_2))) ((el1 Xy1) cHH_2))) ((el1 Xy2) cHH_2))) (((eq fofType) Xx1) Xx2))) (((eq fofType) Xy1) Xy2))->(((eq fofType) ((cTIMES Xx1) Xy1)) ((cTIMES Xx2) Xy2))))) (forall (Xx1:fofType) (Xx2:fofType), (((and ((el1 Xx1) cSS_PRIME)) ((el1 Xx2) cSS_PRIME))->((el1 ((cTIMES Xx1) Xx2)) cSS_PRIME))))) (forall (Xx1:fofType) (Xx2:fofType) (Xy1:fofType) (Xy2:fofType), (((and ((and ((and ((and ((and ((el1 Xx1) cHH_1)) ((el1 Xx2) cHH_1))) ((el1 Xy1) cHH_1))) ((el1 Xy2) cHH_1))) (((eq fofType) Xx1) Xx2))) (((eq fofType) Xy1) Xy2))->(((eq fofType) ((cTIMES Xx1) Xy1)) ((cTIMES Xx2) Xy2)))))) (forall (Xphi:(fofType->fofType)), ((iff (cHOM_FROM_SS_PRIME Xphi)) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cSS_PRIME)) ((el1 Xy) cSS_PRIME))->(((eq fofType) (Xphi ((cTIMES Xx) Xy))) ((cTIMES (Xphi Xx)) (Xphi Xy))))))))) ((iff (cHOM_FROM_HH_1 cBIGPHI)) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))->(((eq fofType) (cBIGPHI ((cTIMES Xx) Xy))) ((cTIMES (cBIGPHI Xx)) (cBIGPHI Xy)))))))) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))->((el1 ((cTIMES Xx) Xy)) cHH_1))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->((el1 (cPHI_2 Xx)) cHH_2))))) (forall (Xx:fofType), (((el1 Xx) cHH_1)->((el1 (cBIGPHI Xx)) cHH_2))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->((el1 (cPHI_1 Xx)) cHH_1))))) (forall (Xx:fofType) (Xy:fofType), (((and ((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))) (((eq fofType) Xx) Xy))->(((eq fofType) (cBIGHI Xx)) (cBIGPHI Xy)))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->(((eq fofType) (cBIGPHI (cPHI_1 Xx))) (cPHI_2 Xx)))))) (forall (Xy:fofType), (((el1 Xy) cHH_1)->((ex fofType) (fun (Xx:fofType)=> ((and ((el1 Xx) cSS_PRIME)) (((eq fofType) (cPHI_1 Xx)) Xy)))))))) (cHOM_FROM_SS_PRIME cPHI_1))) (cHOM_FROM_SS_PRIME cPHI_2))->(cHOM_FROM_HH_1 cBIGPHI)) of role conjecture named cPROB757
% 0.39/0.55 Conjecture to prove = (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx1:fofType) (Xx2:fofType) (Xy1:fofType) (Xy2:fofType), (((and ((and ((and ((and ((and ((el1 Xx1) cHH_2)) ((el1 Xx2) cHH_2))) ((el1 Xy1) cHH_2))) ((el1 Xy2) cHH_2))) (((eq fofType) Xx1) Xx2))) (((eq fofType) Xy1) Xy2))->(((eq fofType) ((cTIMES Xx1) Xy1)) ((cTIMES Xx2) Xy2))))) (forall (Xx1:fofType) (Xx2:fofType), (((and ((el1 Xx1) cSS_PRIME)) ((el1 Xx2) cSS_PRIME))->((el1 ((cTIMES Xx1) Xx2)) cSS_PRIME))))) (forall (Xx1:fofType) (Xx2:fofType) (Xy1:fofType) (Xy2:fofType), (((and ((and ((and ((and ((and ((el1 Xx1) cHH_1)) ((el1 Xx2) cHH_1))) ((el1 Xy1) cHH_1))) ((el1 Xy2) cHH_1))) (((eq fofType) Xx1) Xx2))) (((eq fofType) Xy1) Xy2))->(((eq fofType) ((cTIMES Xx1) Xy1)) ((cTIMES Xx2) Xy2)))))) (forall (Xphi:(fofType->fofType)), ((iff (cHOM_FROM_SS_PRIME Xphi)) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cSS_PRIME)) ((el1 Xy) cSS_PRIME))->(((eq fofType) (Xphi ((cTIMES Xx) Xy))) ((cTIMES (Xphi Xx)) (Xphi Xy))))))))) ((iff (cHOM_FROM_HH_1 cBIGPHI)) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))->(((eq fofType) (cBIGPHI ((cTIMES Xx) Xy))) ((cTIMES (cBIGPHI Xx)) (cBIGPHI Xy)))))))) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))->((el1 ((cTIMES Xx) Xy)) cHH_1))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->((el1 (cPHI_2 Xx)) cHH_2))))) (forall (Xx:fofType), (((el1 Xx) cHH_1)->((el1 (cBIGPHI Xx)) cHH_2))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->((el1 (cPHI_1 Xx)) cHH_1))))) (forall (Xx:fofType) (Xy:fofType), (((and ((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))) (((eq fofType) Xx) Xy))->(((eq fofType) (cBIGHI Xx)) (cBIGPHI Xy)))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->(((eq fofType) (cBIGPHI (cPHI_1 Xx))) (cPHI_2 Xx)))))) (forall (Xy:fofType), (((el1 Xy) cHH_1)->((ex fofType) (fun (Xx:fofType)=> ((and ((el1 Xx) cSS_PRIME)) (((eq fofType) (cPHI_1 Xx)) Xy)))))))) (cHOM_FROM_SS_PRIME cPHI_1))) (cHOM_FROM_SS_PRIME cPHI_2))->(cHOM_FROM_HH_1 cBIGPHI)):Prop
% 0.39/0.55 Parameter fofType_DUMMY:fofType.
% 0.39/0.55 We need to prove ['(((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx1:fofType) (Xx2:fofType) (Xy1:fofType) (Xy2:fofType), (((and ((and ((and ((and ((and ((el1 Xx1) cHH_2)) ((el1 Xx2) cHH_2))) ((el1 Xy1) cHH_2))) ((el1 Xy2) cHH_2))) (((eq fofType) Xx1) Xx2))) (((eq fofType) Xy1) Xy2))->(((eq fofType) ((cTIMES Xx1) Xy1)) ((cTIMES Xx2) Xy2))))) (forall (Xx1:fofType) (Xx2:fofType), (((and ((el1 Xx1) cSS_PRIME)) ((el1 Xx2) cSS_PRIME))->((el1 ((cTIMES Xx1) Xx2)) cSS_PRIME))))) (forall (Xx1:fofType) (Xx2:fofType) (Xy1:fofType) (Xy2:fofType), (((and ((and ((and ((and ((and ((el1 Xx1) cHH_1)) ((el1 Xx2) cHH_1))) ((el1 Xy1) cHH_1))) ((el1 Xy2) cHH_1))) (((eq fofType) Xx1) Xx2))) (((eq fofType) Xy1) Xy2))->(((eq fofType) ((cTIMES Xx1) Xy1)) ((cTIMES Xx2) Xy2)))))) (forall (Xphi:(fofType->fofType)), ((iff (cHOM_FROM_SS_PRIME Xphi)) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cSS_PRIME)) ((el1 Xy) cSS_PRIME))->(((eq fofType) (Xphi ((cTIMES Xx) Xy))) ((cTIMES (Xphi Xx)) (Xphi Xy))))))))) ((iff (cHOM_FROM_HH_1 cBIGPHI)) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))->(((eq fofType) (cBIGPHI ((cTIMES Xx) Xy))) ((cTIMES (cBIGPHI Xx)) (cBIGPHI Xy)))))))) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))->((el1 ((cTIMES Xx) Xy)) cHH_1))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->((el1 (cPHI_2 Xx)) cHH_2))))) (forall (Xx:fofType), (((el1 Xx) cHH_1)->((el1 (cBIGPHI Xx)) cHH_2))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->((el1 (cPHI_1 Xx)) cHH_1))))) (forall (Xx:fofType) (Xy:fofType), (((and ((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))) (((eq fofType) Xx) Xy))->(((eq fofType) (cBIGHI Xx)) (cBIGPHI Xy)))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->(((eq fofType) (cBIGPHI (cPHI_1 Xx))) (cPHI_2 Xx)))))) (forall (Xy:fofType), (((el1 Xy) cHH_1)->((ex fofType) (fun (Xx:fofType)=> ((and ((el1 Xx) cSS_PRIME)) (((eq fofType) (cPHI_1 Xx)) Xy)))))))) (cHOM_FROM_SS_PRIME cPHI_1))) (cHOM_FROM_SS_PRIME cPHI_2))->(cHOM_FROM_HH_1 cBIGPHI))']
% 3.91/4.07 Parameter fofType:Type.
% 3.91/4.07 Parameter cBIGPHI:(fofType->fofType).
% 3.91/4.07 Parameter cHOM_FROM_HH_1:((fofType->fofType)->Prop).
% 3.91/4.07 Parameter cPHI_2:(fofType->fofType).
% 3.91/4.07 Parameter cHOM_FROM_SS_PRIME:((fofType->fofType)->Prop).
% 3.91/4.07 Parameter cPHI_1:(fofType->fofType).
% 3.91/4.07 Parameter cSS_PRIME:(fofType->Prop).
% 3.91/4.07 Parameter el1:(fofType->((fofType->Prop)->Prop)).
% 3.91/4.07 Parameter cHH_1:(fofType->Prop).
% 3.91/4.07 Parameter cBIGHI:(fofType->fofType).
% 3.91/4.07 Parameter cHH_2:(fofType->Prop).
% 3.91/4.07 Parameter cTIMES:(fofType->(fofType->fofType)).
% 3.91/4.07 Trying to prove (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx1:fofType) (Xx2:fofType) (Xy1:fofType) (Xy2:fofType), (((and ((and ((and ((and ((and ((el1 Xx1) cHH_2)) ((el1 Xx2) cHH_2))) ((el1 Xy1) cHH_2))) ((el1 Xy2) cHH_2))) (((eq fofType) Xx1) Xx2))) (((eq fofType) Xy1) Xy2))->(((eq fofType) ((cTIMES Xx1) Xy1)) ((cTIMES Xx2) Xy2))))) (forall (Xx1:fofType) (Xx2:fofType), (((and ((el1 Xx1) cSS_PRIME)) ((el1 Xx2) cSS_PRIME))->((el1 ((cTIMES Xx1) Xx2)) cSS_PRIME))))) (forall (Xx1:fofType) (Xx2:fofType) (Xy1:fofType) (Xy2:fofType), (((and ((and ((and ((and ((and ((el1 Xx1) cHH_1)) ((el1 Xx2) cHH_1))) ((el1 Xy1) cHH_1))) ((el1 Xy2) cHH_1))) (((eq fofType) Xx1) Xx2))) (((eq fofType) Xy1) Xy2))->(((eq fofType) ((cTIMES Xx1) Xy1)) ((cTIMES Xx2) Xy2)))))) (forall (Xphi:(fofType->fofType)), ((iff (cHOM_FROM_SS_PRIME Xphi)) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cSS_PRIME)) ((el1 Xy) cSS_PRIME))->(((eq fofType) (Xphi ((cTIMES Xx) Xy))) ((cTIMES (Xphi Xx)) (Xphi Xy))))))))) ((iff (cHOM_FROM_HH_1 cBIGPHI)) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))->(((eq fofType) (cBIGPHI ((cTIMES Xx) Xy))) ((cTIMES (cBIGPHI Xx)) (cBIGPHI Xy)))))))) (forall (Xx:fofType) (Xy:fofType), (((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))->((el1 ((cTIMES Xx) Xy)) cHH_1))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->((el1 (cPHI_2 Xx)) cHH_2))))) (forall (Xx:fofType), (((el1 Xx) cHH_1)->((el1 (cBIGPHI Xx)) cHH_2))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->((el1 (cPHI_1 Xx)) cHH_1))))) (forall (Xx:fofType) (Xy:fofType), (((and ((and ((el1 Xx) cHH_1)) ((el1 Xy) cHH_1))) (((eq fofType) Xx) Xy))->(((eq fofType) (cBIGHI Xx)) (cBIGPHI Xy)))))) (forall (Xx:fofType), (((el1 Xx) cSS_PRIME)->(((eq fofType) (cBIGPHI (cPHI_1 Xx))) (cPHI_2 Xx)))))) (forall (Xy:fofType), (((el1 Xy) cHH_1)->((ex fofType) (fun (Xx:fofType)=> ((and ((el1 Xx) cSS_PRIME)) (((eq fofType) (cPHI_1 Xx)) Xy)))))))) (cHOM_FROM_SS_PRIME cPHI_1))) (cHOM_FROM_SS_PRIME cPHI_2))->(cHOM_FROM_HH_1 cBIGPHI))
% 3.91/4.07 Found eta_expansion_dep000:=(eta_expansion_dep00 cBIGPHI):(((eq (fofType->fofType)) cBIGPHI) (fun (x:fofType)=> (cBIGPHI x)))
% 3.91/4.07 Found (eta_expansion_dep00 cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 3.91/4.07 Found ((eta_expansion_dep0 (fun (x1:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 3.91/4.07 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 3.91/4.07 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 3.91/4.07 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 3.91/4.07 Found eq_ref00:=(eq_ref0 cBIGPHI):(((eq (fofType->fofType)) cBIGPHI) cBIGPHI)
% 3.91/4.07 Found (eq_ref0 cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 3.91/4.07 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 3.91/4.07 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 3.91/4.07 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 3.91/4.07 Found eq_ref00:=(eq_ref0 (f x0)):(((eq fofType) (f x0)) (f x0))
% 3.91/4.07 Found (eq_ref0 (f x0)) as proof of (((eq fofType) (f x0)) (cBIGPHI x0))
% 16.64/16.84 Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (cBIGPHI x0))
% 16.64/16.84 Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (cBIGPHI x0))
% 16.64/16.84 Found (fun (x0:fofType)=> ((eq_ref fofType) (f x0))) as proof of (((eq fofType) (f x0)) (cBIGPHI x0))
% 16.64/16.84 Found (fun (x0:fofType)=> ((eq_ref fofType) (f x0))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 16.64/16.84 Found eq_ref00:=(eq_ref0 (f x0)):(((eq fofType) (f x0)) (f x0))
% 16.64/16.84 Found (eq_ref0 (f x0)) as proof of (((eq fofType) (f x0)) (cBIGPHI x0))
% 16.64/16.84 Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (cBIGPHI x0))
% 16.64/16.84 Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (cBIGPHI x0))
% 16.64/16.84 Found (fun (x0:fofType)=> ((eq_ref fofType) (f x0))) as proof of (((eq fofType) (f x0)) (cBIGPHI x0))
% 16.64/16.84 Found (fun (x0:fofType)=> ((eq_ref fofType) (f x0))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 16.64/16.84 Found eq_ref00:=(eq_ref0 (f x2)):(((eq fofType) (f x2)) (f x2))
% 16.64/16.84 Found (eq_ref0 (f x2)) as proof of (((eq fofType) (f x2)) (cBIGPHI x2))
% 16.64/16.84 Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (cBIGPHI x2))
% 16.64/16.84 Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (cBIGPHI x2))
% 16.64/16.84 Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (((eq fofType) (f x2)) (cBIGPHI x2))
% 16.64/16.84 Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 16.64/16.84 Found eq_ref00:=(eq_ref0 (f x2)):(((eq fofType) (f x2)) (f x2))
% 16.64/16.84 Found (eq_ref0 (f x2)) as proof of (((eq fofType) (f x2)) (cBIGPHI x2))
% 16.64/16.84 Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (cBIGPHI x2))
% 16.64/16.84 Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (cBIGPHI x2))
% 16.64/16.84 Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (((eq fofType) (f x2)) (cBIGPHI x2))
% 16.64/16.84 Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 16.64/16.84 Found eq_ref00:=(eq_ref0 cBIGPHI):(((eq (fofType->fofType)) cBIGPHI) cBIGPHI)
% 16.64/16.84 Found (eq_ref0 cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 16.64/16.84 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 16.64/16.84 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 16.64/16.84 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 16.64/16.84 Found eq_ref00:=(eq_ref0 (f x4)):(((eq fofType) (f x4)) (f x4))
% 16.64/16.84 Found (eq_ref0 (f x4)) as proof of (((eq fofType) (f x4)) (cBIGPHI x4))
% 16.64/16.84 Found ((eq_ref fofType) (f x4)) as proof of (((eq fofType) (f x4)) (cBIGPHI x4))
% 16.64/16.84 Found ((eq_ref fofType) (f x4)) as proof of (((eq fofType) (f x4)) (cBIGPHI x4))
% 16.64/16.84 Found (fun (x4:fofType)=> ((eq_ref fofType) (f x4))) as proof of (((eq fofType) (f x4)) (cBIGPHI x4))
% 16.64/16.84 Found (fun (x4:fofType)=> ((eq_ref fofType) (f x4))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 16.64/16.84 Found eq_ref00:=(eq_ref0 (f x4)):(((eq fofType) (f x4)) (f x4))
% 16.64/16.84 Found (eq_ref0 (f x4)) as proof of (((eq fofType) (f x4)) (cBIGPHI x4))
% 16.64/16.84 Found ((eq_ref fofType) (f x4)) as proof of (((eq fofType) (f x4)) (cBIGPHI x4))
% 16.64/16.84 Found ((eq_ref fofType) (f x4)) as proof of (((eq fofType) (f x4)) (cBIGPHI x4))
% 16.64/16.84 Found (fun (x4:fofType)=> ((eq_ref fofType) (f x4))) as proof of (((eq fofType) (f x4)) (cBIGPHI x4))
% 16.64/16.84 Found (fun (x4:fofType)=> ((eq_ref fofType) (f x4))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 16.64/16.84 Found eta_expansion_dep000:=(eta_expansion_dep00 cBIGPHI):(((eq (fofType->fofType)) cBIGPHI) (fun (x:fofType)=> (cBIGPHI x)))
% 16.64/16.84 Found (eta_expansion_dep00 cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 16.64/16.84 Found ((eta_expansion_dep0 (fun (x7:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 16.64/16.84 Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 16.64/16.84 Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 16.64/16.84 Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found eq_ref00:=(eq_ref0 (f x6)):(((eq fofType) (f x6)) (f x6))
% 59.61/59.79 Found (eq_ref0 (f x6)) as proof of (((eq fofType) (f x6)) (cBIGPHI x6))
% 59.61/59.79 Found ((eq_ref fofType) (f x6)) as proof of (((eq fofType) (f x6)) (cBIGPHI x6))
% 59.61/59.79 Found ((eq_ref fofType) (f x6)) as proof of (((eq fofType) (f x6)) (cBIGPHI x6))
% 59.61/59.79 Found (fun (x6:fofType)=> ((eq_ref fofType) (f x6))) as proof of (((eq fofType) (f x6)) (cBIGPHI x6))
% 59.61/59.79 Found (fun (x6:fofType)=> ((eq_ref fofType) (f x6))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 59.61/59.79 Found eq_ref00:=(eq_ref0 (f x6)):(((eq fofType) (f x6)) (f x6))
% 59.61/59.79 Found (eq_ref0 (f x6)) as proof of (((eq fofType) (f x6)) (cBIGPHI x6))
% 59.61/59.79 Found ((eq_ref fofType) (f x6)) as proof of (((eq fofType) (f x6)) (cBIGPHI x6))
% 59.61/59.79 Found ((eq_ref fofType) (f x6)) as proof of (((eq fofType) (f x6)) (cBIGPHI x6))
% 59.61/59.79 Found (fun (x6:fofType)=> ((eq_ref fofType) (f x6))) as proof of (((eq fofType) (f x6)) (cBIGPHI x6))
% 59.61/59.79 Found (fun (x6:fofType)=> ((eq_ref fofType) (f x6))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 59.61/59.79 Found eta_expansion_dep000:=(eta_expansion_dep00 cBIGPHI):(((eq (fofType->fofType)) cBIGPHI) (fun (x:fofType)=> (cBIGPHI x)))
% 59.61/59.79 Found (eta_expansion_dep00 cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found ((eta_expansion_dep0 (fun (x9:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found eq_ref00:=(eq_ref0 (f x8)):(((eq fofType) (f x8)) (f x8))
% 59.61/59.79 Found (eq_ref0 (f x8)) as proof of (((eq fofType) (f x8)) (cBIGPHI x8))
% 59.61/59.79 Found ((eq_ref fofType) (f x8)) as proof of (((eq fofType) (f x8)) (cBIGPHI x8))
% 59.61/59.79 Found ((eq_ref fofType) (f x8)) as proof of (((eq fofType) (f x8)) (cBIGPHI x8))
% 59.61/59.79 Found (fun (x8:fofType)=> ((eq_ref fofType) (f x8))) as proof of (((eq fofType) (f x8)) (cBIGPHI x8))
% 59.61/59.79 Found (fun (x8:fofType)=> ((eq_ref fofType) (f x8))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 59.61/59.79 Found eq_ref00:=(eq_ref0 (f x8)):(((eq fofType) (f x8)) (f x8))
% 59.61/59.79 Found (eq_ref0 (f x8)) as proof of (((eq fofType) (f x8)) (cBIGPHI x8))
% 59.61/59.79 Found ((eq_ref fofType) (f x8)) as proof of (((eq fofType) (f x8)) (cBIGPHI x8))
% 59.61/59.79 Found ((eq_ref fofType) (f x8)) as proof of (((eq fofType) (f x8)) (cBIGPHI x8))
% 59.61/59.79 Found (fun (x8:fofType)=> ((eq_ref fofType) (f x8))) as proof of (((eq fofType) (f x8)) (cBIGPHI x8))
% 59.61/59.79 Found (fun (x8:fofType)=> ((eq_ref fofType) (f x8))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 59.61/59.79 Found eta_expansion_dep000:=(eta_expansion_dep00 cBIGPHI):(((eq (fofType->fofType)) cBIGPHI) (fun (x:fofType)=> (cBIGPHI x)))
% 59.61/59.79 Found (eta_expansion_dep00 cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found ((eta_expansion_dep0 (fun (x11:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found (((eta_expansion_dep fofType) (fun (x11:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found (((eta_expansion_dep fofType) (fun (x11:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found (((eta_expansion_dep fofType) (fun (x11:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 59.61/59.79 Found eq_ref00:=(eq_ref0 (f x10)):(((eq fofType) (f x10)) (f x10))
% 59.61/59.79 Found (eq_ref0 (f x10)) as proof of (((eq fofType) (f x10)) (cBIGPHI x10))
% 59.61/59.79 Found ((eq_ref fofType) (f x10)) as proof of (((eq fofType) (f x10)) (cBIGPHI x10))
% 59.61/59.79 Found ((eq_ref fofType) (f x10)) as proof of (((eq fofType) (f x10)) (cBIGPHI x10))
% 59.61/59.79 Found (fun (x10:fofType)=> ((eq_ref fofType) (f x10))) as proof of (((eq fofType) (f x10)) (cBIGPHI x10))
% 59.61/59.79 Found (fun (x10:fofType)=> ((eq_ref fofType) (f x10))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 59.61/59.79 Found eq_ref00:=(eq_ref0 (f x10)):(((eq fofType) (f x10)) (f x10))
% 107.49/107.69 Found (eq_ref0 (f x10)) as proof of (((eq fofType) (f x10)) (cBIGPHI x10))
% 107.49/107.69 Found ((eq_ref fofType) (f x10)) as proof of (((eq fofType) (f x10)) (cBIGPHI x10))
% 107.49/107.69 Found ((eq_ref fofType) (f x10)) as proof of (((eq fofType) (f x10)) (cBIGPHI x10))
% 107.49/107.69 Found (fun (x10:fofType)=> ((eq_ref fofType) (f x10))) as proof of (((eq fofType) (f x10)) (cBIGPHI x10))
% 107.49/107.69 Found (fun (x10:fofType)=> ((eq_ref fofType) (f x10))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 107.49/107.69 Found eta_expansion_dep000:=(eta_expansion_dep00 cBIGPHI):(((eq (fofType->fofType)) cBIGPHI) (fun (x:fofType)=> (cBIGPHI x)))
% 107.49/107.69 Found (eta_expansion_dep00 cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 107.49/107.69 Found ((eta_expansion_dep0 (fun (x13:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 107.49/107.69 Found (((eta_expansion_dep fofType) (fun (x13:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 107.49/107.69 Found (((eta_expansion_dep fofType) (fun (x13:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 107.49/107.69 Found (((eta_expansion_dep fofType) (fun (x13:fofType)=> fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 107.49/107.69 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 107.49/107.69 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 107.49/107.69 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->fofType)) a) a)
% 107.49/107.69 Found (eq_ref0 a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 107.49/107.69 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 107.49/107.69 Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->fofType)) a) (fun (x:fofType)=> (a x)))
% 107.49/107.69 Found (eta_expansion00 a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found ((eta_expansion0 fofType) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found (((eta_expansion fofType) fofType) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found (((eta_expansion fofType) fofType) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found (((eta_expansion fofType) fofType) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->fofType)) a) a)
% 107.49/107.69 Found (eq_ref0 a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 107.49/107.69 Found eq_ref00:=(eq_ref0 (f x12)):(((eq fofType) (f x12)) (f x12))
% 107.49/107.69 Found (eq_ref0 (f x12)) as proof of (((eq fofType) (f x12)) (cBIGPHI x12))
% 107.49/107.69 Found ((eq_ref fofType) (f x12)) as proof of (((eq fofType) (f x12)) (cBIGPHI x12))
% 107.49/107.69 Found ((eq_ref fofType) (f x12)) as proof of (((eq fofType) (f x12)) (cBIGPHI x12))
% 107.49/107.69 Found (fun (x12:fofType)=> ((eq_ref fofType) (f x12))) as proof of (((eq fofType) (f x12)) (cBIGPHI x12))
% 107.49/107.69 Found (fun (x12:fofType)=> ((eq_ref fofType) (f x12))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 107.49/107.69 Found eq_ref00:=(eq_ref0 (f x12)):(((eq fofType) (f x12)) (f x12))
% 107.49/107.69 Found (eq_ref0 (f x12)) as proof of (((eq fofType) (f x12)) (cBIGPHI x12))
% 107.49/107.69 Found ((eq_ref fofType) (f x12)) as proof of (((eq fofType) (f x12)) (cBIGPHI x12))
% 107.49/107.69 Found ((eq_ref fofType) (f x12)) as proof of (((eq fofType) (f x12)) (cBIGPHI x12))
% 228.99/229.28 Found (fun (x12:fofType)=> ((eq_ref fofType) (f x12))) as proof of (((eq fofType) (f x12)) (cBIGPHI x12))
% 228.99/229.28 Found (fun (x12:fofType)=> ((eq_ref fofType) (f x12))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 228.99/229.28 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 228.99/229.28 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 228.99/229.28 Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->fofType)) a) (fun (x:fofType)=> (a x)))
% 228.99/229.28 Found (eta_expansion00 a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found ((eta_expansion0 fofType) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found (((eta_expansion fofType) fofType) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found (((eta_expansion fofType) fofType) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found (((eta_expansion fofType) fofType) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->fofType)) a) a)
% 228.99/229.28 Found (eq_ref0 a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found eq_ref00:=(eq_ref0 cBIGPHI):(((eq (fofType->fofType)) cBIGPHI) cBIGPHI)
% 228.99/229.28 Found (eq_ref0 cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 228.99/229.28 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 228.99/229.28 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) cBIGPHI)
% 228.99/229.28 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->fofType)) a) a)
% 228.99/229.28 Found (eq_ref0 a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) a) as proof of (((eq (fofType->fofType)) a) b)
% 228.99/229.28 Found eq_ref00:=(eq_ref0 (f x14)):(((eq fofType) (f x14)) (f x14))
% 228.99/229.28 Found (eq_ref0 (f x14)) as proof of (((eq fofType) (f x14)) (cBIGPHI x14))
% 228.99/229.28 Found ((eq_ref fofType) (f x14)) as proof of (((eq fofType) (f x14)) (cBIGPHI x14))
% 228.99/229.28 Found ((eq_ref fofType) (f x14)) as proof of (((eq fofType) (f x14)) (cBIGPHI x14))
% 228.99/229.28 Found (fun (x14:fofType)=> ((eq_ref fofType) (f x14))) as proof of (((eq fofType) (f x14)) (cBIGPHI x14))
% 228.99/229.28 Found (fun (x14:fofType)=> ((eq_ref fofType) (f x14))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 228.99/229.28 Found eq_ref00:=(eq_ref0 (f x14)):(((eq fofType) (f x14)) (f x14))
% 228.99/229.28 Found (eq_ref0 (f x14)) as proof of (((eq fofType) (f x14)) (cBIGPHI x14))
% 228.99/229.28 Found ((eq_ref fofType) (f x14)) as proof of (((eq fofType) (f x14)) (cBIGPHI x14))
% 228.99/229.28 Found ((eq_ref fofType) (f x14)) as proof of (((eq fofType) (f x14)) (cBIGPHI x14))
% 228.99/229.28 Found (fun (x14:fofType)=> ((eq_ref fofType) (f x14))) as proof of (((eq fofType) (f x14)) (cBIGPHI x14))
% 228.99/229.28 Found (fun (x14:fofType)=> ((eq_ref fofType) (f x14))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (cBIGPHI x)))
% 228.99/229.28 Found eq_ref00:=(eq_ref0 cBIGPHI):(((eq (fofType->fofType)) cBIGPHI) cBIGPHI)
% 228.99/229.28 Found (eq_ref0 cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) cBIGPHI) as proof of (((eq (fofType->fofType)) cBIGPHI) b)
% 228.99/229.28 Found ((eq_ref (fofType->fofType)) cBIGPHI) as pro
%------------------------------------------------------------------------------