TSTP Solution File: SYO500^1.004 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO500^1.004 : TPTP v7.5.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n021.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 00:51:57 EDT 2022
% Result : Timeout 300.03s 300.70s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO500^1.004 : TPTP v7.5.0. Released v4.1.0.
% 0.10/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % RAMPerCPU : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sun Mar 13 11:44:55 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.34 Python 2.7.5
% 4.88/5.05 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 4.88/5.05 FOF formula (<kernel.Constant object at 0x8c4878>, <kernel.Sort object at 0x2b8e78f25638>) of role type named x
% 4.88/5.05 Using role type
% 4.88/5.05 Declaring x:Prop
% 4.88/5.05 FOF formula (<kernel.Constant object at 0x8c40e0>, <kernel.DependentProduct object at 0x8c45a8>) of role type named f0
% 4.88/5.05 Using role type
% 4.88/5.05 Declaring f0:(Prop->Prop)
% 4.88/5.05 FOF formula (<kernel.Constant object at 0x8c4050>, <kernel.DependentProduct object at 0x8c4248>) of role type named f1
% 4.88/5.05 Using role type
% 4.88/5.05 Declaring f1:(Prop->Prop)
% 4.88/5.05 FOF formula (<kernel.Constant object at 0x8c45a8>, <kernel.DependentProduct object at 0x8a2e60>) of role type named f2
% 4.88/5.05 Using role type
% 4.88/5.05 Declaring f2:(Prop->Prop)
% 4.88/5.05 FOF formula (<kernel.Constant object at 0x8c4248>, <kernel.DependentProduct object at 0x8a2d40>) of role type named f3
% 4.88/5.05 Using role type
% 4.88/5.05 Declaring f3:(Prop->Prop)
% 4.88/5.05 FOF formula (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) of role conjecture named kaminski4
% 4.88/5.05 Conjecture to prove = (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):Prop
% 4.88/5.05 We need to prove ['(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))']
% 4.88/5.05 Parameter x:Prop.
% 4.88/5.05 Parameter f0:(Prop->Prop).
% 4.88/5.05 Parameter f1:(Prop->Prop).
% 4.88/5.05 Parameter f2:(Prop->Prop).
% 4.88/5.05 Parameter f3:(Prop->Prop).
% 4.88/5.05 Trying to prove (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 4.88/5.05 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 4.88/5.05 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 4.88/5.05 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 4.88/5.05 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 4.88/5.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 4.88/5.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 4.88/5.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 4.88/5.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 4.88/5.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 4.88/5.05 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))))
% 4.88/5.05 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 4.88/5.05 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 4.88/5.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 12.34/12.50 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 12.34/12.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 12.34/12.50 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 12.34/12.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 12.34/12.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 12.34/12.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 12.34/12.50 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 12.34/12.50 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 12.34/12.50 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 12.34/12.50 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 12.34/12.50 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 12.34/12.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 12.34/12.50 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 12.34/12.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 12.34/12.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 12.34/12.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 12.34/12.50 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 12.34/12.50 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 12.34/12.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 12.34/12.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 12.34/12.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 12.34/12.50 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))))
% 12.34/12.50 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 12.34/12.50 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 12.34/12.50 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 12.34/12.50 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 12.34/12.50 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 24.84/25.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 24.84/25.05 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 24.84/25.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 24.84/25.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 24.84/25.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.84/25.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 24.84/25.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 24.84/25.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 24.84/25.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 24.84/25.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 24.84/25.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 24.84/25.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.84/25.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 24.84/25.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 24.84/25.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 24.84/25.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 24.84/25.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 24.84/25.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 24.84/25.05 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 24.84/25.05 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 24.84/25.05 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 24.84/25.05 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 24.84/25.05 Instantiate: b:=(f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):Prop
% 24.84/25.05 Found x0 as proof of (P0 b)
% 24.84/25.05 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 24.84/25.05 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 24.84/25.05 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 24.84/25.05 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 24.84/25.05 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 27.84/28.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.84/28.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 27.84/28.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 27.84/28.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 27.84/28.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 27.84/28.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.84/28.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 27.84/28.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 27.84/28.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 27.84/28.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 27.84/28.08 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 27.84/28.08 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 27.84/28.08 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 27.84/28.08 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 27.84/28.08 Found x0:(P0 b)
% 27.84/28.08 Instantiate: b:=(f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):Prop
% 27.84/28.08 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 27.84/28.08 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 27.84/28.08 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 27.84/28.08 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 27.84/28.08 Instantiate: b:=(f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):Prop
% 27.84/28.08 Found x0 as proof of (P0 b)
% 27.84/28.08 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 27.84/28.08 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 27.84/28.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 27.84/28.08 Found x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 27.84/28.08 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x02) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 27.84/28.08 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x02) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 27.84/28.08 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 27.84/28.08 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 33.63/33.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.63/33.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 33.63/33.80 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b0)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b0)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b0)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b0)
% 33.63/33.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 33.63/33.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 33.63/33.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.63/33.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 33.63/33.80 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 33.63/33.80 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 33.63/33.80 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 33.63/33.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.63/33.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 33.63/33.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 40.01/40.26 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 40.01/40.26 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 40.01/40.26 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 40.01/40.26 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 40.01/40.26 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 40.01/40.26 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (P (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 40.01/40.26 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (P (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 40.01/40.26 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (P (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 40.01/40.26 Found x01:(P b)
% 40.01/40.26 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 40.01/40.26 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 40.01/40.26 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 40.01/40.26 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))):Prop
% 40.01/40.26 Found x0 as proof of (P0 b)
% 40.01/40.26 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 40.01/40.26 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 40.01/40.26 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 40.01/40.26 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 40.01/40.26 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 40.01/40.26 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))):Prop
% 40.01/40.26 Found x0 as proof of (P0 (f0 a))
% 40.01/40.26 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 40.01/40.26 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 40.01/40.26 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 40.01/40.26 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 40.01/40.26 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 40.01/40.26 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))):Prop
% 40.01/40.26 Found x0 as proof of (P0 (P (f0 a)))
% 40.01/40.26 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 40.01/40.26 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 40.01/40.26 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 40.01/40.26 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 40.01/40.26 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 40.01/40.26 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 40.01/40.26 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))):Prop
% 40.01/40.26 Found x0 as proof of (P0 a)
% 51.63/51.88 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 51.63/51.88 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 51.63/51.88 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x02) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 51.63/51.88 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x02) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 51.63/51.88 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 51.63/51.88 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 51.63/51.88 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 51.63/51.88 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 51.63/51.88 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 51.63/51.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 51.63/51.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 51.63/51.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 51.63/51.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 51.63/51.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 51.63/51.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 51.63/51.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 51.63/51.88 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 51.63/51.88 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 51.63/51.88 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 51.63/51.88 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 51.63/51.88 Found x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 51.63/51.88 Found (fun (x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x0) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 51.63/51.88 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x0) as proof of ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 51.63/51.88 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x0) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 51.63/51.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 51.63/51.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 51.63/51.88 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 51.63/51.88 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 51.63/51.88 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.72/52.93 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 52.72/52.93 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 52.72/52.93 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 52.72/52.93 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 52.72/52.93 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 52.72/52.93 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 52.72/52.93 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 52.72/52.93 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b0)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b0)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b0)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b0)
% 52.72/52.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.72/52.93 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 52.72/52.93 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.72/52.93 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 52.72/52.93 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 52.72/52.93 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 52.72/52.93 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.81/54.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 53.81/54.01 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.81/54.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 53.81/54.01 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.81/54.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 53.81/54.01 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.81/54.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 53.81/54.01 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 53.81/54.01 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 53.81/54.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 60.21/60.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 60.21/60.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 60.21/60.40 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 60.21/60.40 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 60.21/60.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 60.21/60.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 60.21/60.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 60.21/60.40 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 60.21/60.40 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 60.21/60.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 60.21/60.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 60.21/60.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 60.21/60.40 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 ((P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))->(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))))
% 60.21/60.40 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 ((P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))->(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))))
% 60.21/60.40 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b0)
% 60.21/60.40 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b0)
% 60.21/60.40 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b0)
% 60.21/60.40 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b0)
% 60.21/60.40 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 60.21/60.40 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 60.21/60.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 60.21/60.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 60.21/60.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 60.21/60.40 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 60.21/60.40 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 60.21/60.40 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 60.21/60.40 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 63.61/63.85 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 72.10/72.31 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 72.10/72.31 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (P (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (P (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (P (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 72.10/72.31 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 72.10/72.31 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 72.10/72.31 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 72.10/72.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.10/72.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 72.10/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 72.10/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 72.10/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 72.10/72.31 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 72.10/72.31 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 72.10/72.31 Found x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 72.10/72.31 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x02) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 72.10/72.31 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x02) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 72.10/72.31 Found x0:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 72.10/72.31 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))):Prop
% 72.10/72.31 Found x0 as proof of (P0 b)
% 72.10/72.31 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 72.10/72.31 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 72.10/72.31 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 72.10/72.31 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 72.10/72.31 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 72.10/72.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.10/72.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 72.10/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 81.01/81.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 81.01/81.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 81.01/81.28 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 81.01/81.28 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 81.01/81.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 81.01/81.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 81.01/81.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 81.01/81.28 Found x0:(P0 b)
% 81.01/81.28 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))):Prop
% 81.01/81.28 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 81.01/81.28 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 81.01/81.28 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 81.01/81.28 Found x0:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 81.01/81.28 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))):Prop
% 81.01/81.28 Found x0 as proof of (P0 b)
% 81.01/81.28 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 81.01/81.28 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 81.01/81.28 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 81.01/81.28 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 81.01/81.28 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 81.01/81.28 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 81.01/81.28 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 81.01/81.28 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 81.01/81.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 81.01/81.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 81.01/81.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 81.01/81.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 81.01/81.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 81.01/81.28 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 81.01/81.28 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 81.01/81.28 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 81.01/81.28 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 81.01/81.28 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 81.01/81.28 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 81.01/81.28 Instantiate: a:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))):Prop
% 81.01/81.28 Found x0 as proof of (P0 (f0 a))
% 81.01/81.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 81.01/81.28 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 81.01/81.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 81.01/81.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 81.01/81.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 81.01/81.28 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 81.01/81.28 Instantiate: a:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))):Prop
% 81.01/81.28 Found x0 as proof of (P0 a)
% 81.01/81.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 81.01/81.28 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 81.01/81.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 110.49/110.81 Instantiate: a:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))):Prop
% 110.49/110.81 Found x0 as proof of (P0 (P (f0 a)))
% 110.49/110.81 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 110.49/110.81 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 110.49/110.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 110.49/110.81 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 110.49/110.81 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 110.49/110.81 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 110.49/110.81 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 110.49/110.81 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 110.49/110.81 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 110.49/110.81 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 110.49/110.81 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 x)))))))
% 110.49/110.81 Found x0:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 110.49/110.81 Found (fun (x0:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x0) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 110.49/110.81 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x0) as proof of ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 110.49/110.81 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x0) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 110.49/110.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 110.49/110.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 110.49/110.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 113.28/113.56 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 113.28/113.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 113.28/113.56 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 113.28/113.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 113.28/113.56 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 113.28/113.56 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 113.28/113.56 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 113.28/113.56 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))))
% 113.28/113.56 Found x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 113.28/113.56 Found (fun (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 113.28/113.56 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 113.28/113.56 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))))
% 113.28/113.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 113.28/113.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 113.28/113.56 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 114.57/114.82 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 114.57/114.82 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 114.57/114.82 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 114.57/114.82 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 114.57/114.82 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 114.57/114.82 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 114.57/114.82 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.57/114.82 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 114.57/114.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 114.57/114.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 114.57/114.82 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 114.57/114.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.57/114.82 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 114.57/114.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 114.57/114.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 114.57/114.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 114.57/114.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.57/114.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 114.57/114.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 114.57/114.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 114.57/114.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 114.57/114.82 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 114.57/114.82 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.57/114.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 114.57/114.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 114.57/114.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 114.57/114.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 114.57/114.82 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 114.57/114.82 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 114.57/114.82 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 114.57/114.82 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 116.08/116.32 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 116.08/116.32 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 116.08/116.32 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 116.08/116.32 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))))
% 116.08/116.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.08/116.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 116.08/116.32 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.08/116.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 116.08/116.32 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.08/116.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 116.08/116.32 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 116.08/116.32 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 116.08/116.32 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 116.08/116.32 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 116.08/116.32 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 116.08/116.32 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 116.08/116.32 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 117.46/117.76 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 117.46/117.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.46/117.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 117.46/117.76 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.46/117.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 117.46/117.76 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.46/117.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 117.46/117.76 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.46/117.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 117.46/117.76 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 117.46/117.76 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 117.46/117.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.18/121.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 121.18/121.42 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.18/121.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 121.18/121.42 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 121.18/121.42 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 121.18/121.42 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 121.18/121.42 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 121.18/121.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.18/121.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 121.18/121.42 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 121.18/121.42 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 122.78/123.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 122.78/123.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 122.78/123.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 122.78/123.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 122.78/123.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 122.78/123.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 122.78/123.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 122.78/123.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 122.78/123.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 123.83/124.16 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 123.83/124.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 123.83/124.16 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 123.83/124.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 123.83/124.16 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 123.83/124.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 123.83/124.16 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 123.83/124.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 123.83/124.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 123.83/124.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 134.14/134.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 134.14/134.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 134.14/134.40 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.40 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 134.14/134.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 134.14/134.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 134.14/134.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 134.14/134.40 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.40 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 134.14/134.41 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 134.14/134.41 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 134.14/134.41 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 134.14/134.41 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 134.14/134.41 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 148.70/148.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 148.70/148.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 148.70/148.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 148.70/148.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 148.70/148.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 148.70/148.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 148.70/148.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 148.70/148.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 148.70/148.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 148.70/148.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 148.70/148.97 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 148.70/148.97 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))) b)
% 148.70/148.97 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 148.70/148.97 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 148.70/148.97 Found x0:(P0 b)
% 148.70/148.97 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))):Prop
% 148.70/148.97 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 148.70/148.97 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 148.70/148.97 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 148.70/148.97 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 148.70/148.97 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))):Prop
% 148.70/148.97 Found x0 as proof of (P0 b)
% 148.70/148.97 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 148.70/148.97 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 148.70/148.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 148.70/148.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 148.70/148.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 148.70/148.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 148.70/148.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 148.70/148.97 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 148.70/148.97 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 148.70/148.97 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 170.71/171.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 170.71/171.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 170.71/171.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 170.71/171.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 170.71/171.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 170.71/171.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 170.71/171.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 170.71/171.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 170.71/171.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 170.71/171.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 170.71/171.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 170.71/171.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 170.71/171.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 170.71/171.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 170.71/171.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 170.71/171.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 170.71/171.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 170.71/171.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 170.71/171.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 170.71/171.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 179.09/179.42 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 179.09/179.42 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 179.09/179.42 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 179.09/179.42 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 179.09/179.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 179.09/179.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 179.09/179.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.09/179.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.09/179.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.09/179.42 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 179.09/179.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 179.09/179.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 179.09/179.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 179.09/179.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.09/179.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 179.09/179.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 179.09/179.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 179.09/179.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 179.09/179.42 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 179.09/179.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 179.09/179.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 179.09/179.42 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 179.09/179.42 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.09/179.42 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 179.09/179.42 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 179.09/179.42 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 179.09/179.42 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 179.09/179.42 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 179.09/179.42 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 194.05/194.36 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 194.05/194.36 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 194.05/194.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 194.05/194.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 194.05/194.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 194.05/194.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 194.05/194.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 194.05/194.36 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 194.05/194.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 194.05/194.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 194.05/194.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b0)
% 194.05/194.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 194.05/194.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 194.05/194.36 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 194.05/194.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 194.05/194.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 194.05/194.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 194.05/194.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 194.05/194.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 194.05/194.36 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 194.05/194.36 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 194.05/194.36 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))))
% 194.05/194.36 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 194.05/194.36 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 194.05/194.36 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))))
% 194.05/194.36 Found x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 194.05/194.36 Found (fun (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 194.05/194.36 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 202.72/203.05 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))))
% 202.72/203.05 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 202.72/203.05 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 202.72/203.05 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 202.72/203.05 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 202.72/203.05 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 202.72/203.05 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 202.72/203.05 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 202.72/203.05 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 202.72/203.05 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 202.72/203.05 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 202.72/203.05 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 202.72/203.05 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))
% 206.85/207.20 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))))
% 206.85/207.20 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 206.85/207.20 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 206.85/207.20 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 206.85/207.20 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 x)))))))
% 206.85/207.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.85/207.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 206.85/207.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 206.85/207.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 206.85/207.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 206.85/207.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 206.85/207.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.85/207.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 206.85/207.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 206.85/207.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 206.85/207.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 206.85/207.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 206.85/207.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.85/207.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 206.85/207.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 206.85/207.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 206.85/207.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.82/213.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 212.82/213.14 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.82/213.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 212.82/213.14 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 212.82/213.14 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))
% 212.82/213.14 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 212.82/213.14 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))) b)
% 212.82/213.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.82/213.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 212.82/213.14 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 212.82/213.14 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 214.73/215.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 214.73/215.12 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 214.73/215.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 214.73/215.12 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 214.73/215.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 214.73/215.12 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 214.73/215.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 214.73/215.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 214.73/215.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 216.11/216.47 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.11/216.47 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 216.11/216.47 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.11/216.47 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 216.11/216.47 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.11/216.47 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 216.11/216.47 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 216.11/216.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.11/216.47 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 216.11/216.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 265.20/265.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x02) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))))=> x02) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 265.20/265.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b)
% 265.20/265.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 265.20/265.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 265.20/265.56 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 265.20/265.56 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 272.61/272.96 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 272.61/272.96 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 272.61/272.96 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 272.61/272.96 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 272.61/272.96 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 272.61/272.96 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 272.61/272.96 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 272.61/272.96 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 272.61/272.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 272.61/272.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 272.61/272.96 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 272.61/272.96 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 272.61/272.96 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 272.61/272.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 272.61/272.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 272.61/272.96 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 272.61/272.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 272.61/272.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 272.61/272.96 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 283.28/283.66 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 283.28/283.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 283.28/283.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 283.28/283.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 283.28/283.66 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 283.28/283.66 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 283.28/283.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 283.28/283.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 283.28/283.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 283.28/283.66 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))) b)
% 283.28/283.66 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 x)))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 283.28/283.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 x))))))))
% 283.28/283.66 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x))))))))
% 283.28/283.66 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 283.28/283.66 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 x)))))))) b0)
% 283.28/283.66 Found
%------------------------------------------------------------------------------