TSTP Solution File: SYO500^1.006 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO500^1.006 : TPTP v7.5.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n027.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 286.01s 286.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO500^1.006 : TPTP v7.5.0. Released v4.1.0.
% 0.06/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sun Mar 13 12:17:14 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 5.84/6.05 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 5.84/6.05 FOF formula (<kernel.Constant object at 0x21b69e0>, <kernel.Sort object at 0x2afaf2909638>) of role type named x
% 5.84/6.05 Using role type
% 5.84/6.05 Declaring x:Prop
% 5.84/6.05 FOF formula (<kernel.Constant object at 0x21b6f38>, <kernel.DependentProduct object at 0x1ef26c8>) of role type named f0
% 5.84/6.05 Using role type
% 5.84/6.05 Declaring f0:(Prop->Prop)
% 5.84/6.05 FOF formula (<kernel.Constant object at 0x21b6f80>, <kernel.DependentProduct object at 0x1ef2ea8>) of role type named f1
% 5.84/6.05 Using role type
% 5.84/6.05 Declaring f1:(Prop->Prop)
% 5.84/6.05 FOF formula (<kernel.Constant object at 0x21b6f80>, <kernel.DependentProduct object at 0x1ef2a70>) of role type named f2
% 5.84/6.05 Using role type
% 5.84/6.05 Declaring f2:(Prop->Prop)
% 5.84/6.05 FOF formula (<kernel.Constant object at 0x1ef2ea8>, <kernel.DependentProduct object at 0x1ef2cf8>) of role type named f3
% 5.84/6.05 Using role type
% 5.84/6.05 Declaring f3:(Prop->Prop)
% 5.84/6.05 FOF formula (<kernel.Constant object at 0x1ef2a70>, <kernel.DependentProduct object at 0x1ef2cb0>) of role type named f4
% 5.84/6.05 Using role type
% 5.84/6.05 Declaring f4:(Prop->Prop)
% 5.84/6.05 FOF formula (<kernel.Constant object at 0x1ef2cf8>, <kernel.DependentProduct object at 0x1ef2680>) of role type named f5
% 5.84/6.05 Using role type
% 5.84/6.05 Declaring f5:(Prop->Prop)
% 5.84/6.05 FOF formula (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) of role conjecture named kaminski6
% 5.84/6.05 Conjecture to prove = (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):Prop
% 5.84/6.05 We need to prove ['(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))']
% 5.84/6.05 Parameter x:Prop.
% 5.84/6.05 Parameter f0:(Prop->Prop).
% 5.84/6.05 Parameter f1:(Prop->Prop).
% 5.84/6.05 Parameter f2:(Prop->Prop).
% 5.84/6.05 Parameter f3:(Prop->Prop).
% 5.84/6.05 Parameter f4:(Prop->Prop).
% 5.84/6.05 Parameter f5:(Prop->Prop).
% 5.84/6.05 Trying to prove (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 5.84/6.05 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 5.84/6.05 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 5.84/6.05 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 5.84/6.05 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 5.84/6.05 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 5.84/6.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 5.84/6.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 5.84/6.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 5.84/6.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 5.84/6.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 5.84/6.05 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 5.84/6.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 5.84/6.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 5.84/6.05 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 5.84/6.05 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))))
% 15.63/15.83 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 15.63/15.83 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))
% 15.63/15.83 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))
% 15.63/15.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 15.63/15.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 15.63/15.83 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 15.63/15.83 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 15.63/15.83 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 15.63/15.83 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 15.63/15.83 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 15.63/15.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 15.63/15.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 15.63/15.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 15.63/15.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 15.63/15.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 15.63/15.83 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 15.63/15.83 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 25.47/25.72 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 25.47/25.72 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 25.47/25.72 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 25.47/25.72 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))))
% 25.47/25.72 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 25.47/25.72 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 25.47/25.72 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 25.47/25.72 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 25.47/25.72 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 25.47/25.72 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 25.47/25.72 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 25.47/25.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 25.47/25.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 25.47/25.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 25.47/25.72 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 25.47/25.72 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 25.47/25.72 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 31.66/31.88 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 31.66/31.88 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 31.66/31.88 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 31.66/31.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 31.66/31.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 31.66/31.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 31.66/31.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 31.66/31.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 31.66/31.88 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 31.66/31.88 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 31.66/31.88 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 31.66/31.88 Instantiate: b:=(f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):Prop
% 31.66/31.88 Found x0 as proof of (P0 b)
% 31.66/31.88 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 31.66/31.88 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 31.66/31.88 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 31.66/31.88 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 31.66/31.88 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 33.55/33.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.55/33.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 33.55/33.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 33.55/33.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 33.55/33.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 33.55/33.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.55/33.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 33.55/33.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 33.55/33.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 33.55/33.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 33.55/33.76 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 33.55/33.76 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 33.55/33.76 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 33.55/33.76 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 33.55/33.76 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 33.55/33.76 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 33.55/33.76 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 33.55/33.76 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 33.55/33.76 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 33.55/33.76 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 33.55/33.76 Found x0:(P0 b)
% 33.55/33.76 Instantiate: b:=(f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):Prop
% 33.55/33.76 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 33.55/33.76 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))
% 33.55/33.76 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 33.55/33.76 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 33.55/33.76 Instantiate: b:=(f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):Prop
% 33.55/33.76 Found x0 as proof of (P0 b)
% 33.55/33.76 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 33.55/33.76 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 33.55/33.76 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 33.55/33.76 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 40.00/40.19 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 40.00/40.19 Found x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 40.00/40.19 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x02) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 40.00/40.19 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x02) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 40.00/40.19 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 40.00/40.19 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 40.00/40.19 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 40.00/40.19 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 40.00/40.19 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 40.00/40.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 40.00/40.19 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 40.00/40.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 40.00/40.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 40.00/40.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 40.00/40.19 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 40.00/40.19 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b0)
% 40.00/40.19 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b0)
% 40.00/40.19 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b0)
% 40.00/40.19 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b0)
% 40.00/40.19 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 40.00/40.19 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 40.00/40.19 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 40.00/40.19 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 40.00/40.19 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 40.00/40.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 40.00/40.19 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 40.00/40.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 40.00/40.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 40.00/40.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 40.00/40.19 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 45.07/45.27 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 45.07/45.27 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 45.07/45.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 45.07/45.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 45.07/45.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 45.07/45.27 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 45.07/45.27 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 45.07/45.27 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 45.07/45.27 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 45.07/45.27 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 45.07/45.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 45.07/45.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 45.07/45.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 45.07/45.27 Found x01:(P b)
% 45.07/45.27 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 45.07/45.27 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 45.07/45.27 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 45.07/45.27 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))):Prop
% 45.07/45.27 Found x0 as proof of (P0 b)
% 45.07/45.27 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 45.07/45.27 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 61.16/61.39 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 61.16/61.39 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 61.16/61.39 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 61.16/61.39 Found x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 61.16/61.39 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x02) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 61.16/61.39 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x02) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 61.16/61.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.16/61.39 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 61.16/61.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 61.16/61.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 61.16/61.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 61.16/61.39 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 61.16/61.39 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 61.16/61.39 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 61.16/61.39 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 61.16/61.39 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 61.16/61.39 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 61.16/61.39 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 61.16/61.39 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 61.16/61.39 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 61.16/61.39 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 61.16/61.39 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 61.16/61.39 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b0)
% 61.16/61.39 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b0)
% 61.16/61.39 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b0)
% 61.16/61.39 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b0)
% 61.16/61.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.16/61.39 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 61.16/61.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 61.16/61.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 61.16/61.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 63.76/64.01 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 63.76/64.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 63.76/64.01 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 63.76/64.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 63.76/64.01 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 63.76/64.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 63.76/64.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 63.76/64.01 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 64.85/65.12 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.85/65.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 64.85/65.12 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.85/65.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 64.85/65.12 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 64.85/65.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.85/65.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 64.85/65.12 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 65.88/66.09 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 65.88/66.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 65.88/66.09 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 65.88/66.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 65.88/66.09 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 65.88/66.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 65.88/66.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 65.88/66.09 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 65.88/66.09 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 70.76/71.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 70.76/71.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 70.76/71.01 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 70.76/71.01 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b0)
% 70.76/71.01 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b0)
% 70.76/71.01 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b0)
% 70.76/71.01 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b0)
% 70.76/71.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 70.76/71.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 70.76/71.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 70.76/71.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 70.76/71.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 70.76/71.01 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 ((P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))->(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))))
% 70.76/71.01 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 ((P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))->(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))))
% 70.76/71.01 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 70.76/71.01 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 70.76/71.01 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 70.76/71.01 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 75.23/75.46 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 84.59/84.83 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 84.59/84.83 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 84.59/84.83 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 84.59/84.83 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 84.59/84.83 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 84.59/84.83 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 84.59/84.83 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 84.59/84.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 84.59/84.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 84.59/84.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 84.59/84.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 84.59/84.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 84.59/84.83 Found x0:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 84.59/84.83 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))):Prop
% 84.59/84.83 Found x0 as proof of (P0 b)
% 84.59/84.83 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 84.59/84.83 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 84.59/84.83 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 84.59/84.83 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 94.21/94.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 94.21/94.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 94.21/94.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 94.21/94.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 94.21/94.53 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 94.21/94.53 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 94.21/94.53 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x02) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 94.21/94.53 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x02) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 94.21/94.53 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 94.21/94.53 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 94.21/94.53 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 94.21/94.53 Found x0:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 94.21/94.53 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))):Prop
% 94.21/94.53 Found x0 as proof of (P0 b)
% 94.21/94.53 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 94.21/94.53 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 94.21/94.53 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 94.21/94.53 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 94.21/94.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 94.21/94.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 126.48/126.76 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 126.48/126.76 Found x0:(P0 b)
% 126.48/126.76 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))):Prop
% 126.48/126.76 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 126.48/126.76 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 126.48/126.76 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 126.48/126.76 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 126.48/126.76 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 126.48/126.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 126.48/126.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 126.48/126.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 126.48/126.76 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 126.48/126.76 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b0)
% 126.48/126.76 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b0)
% 126.48/126.76 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b0)
% 126.48/126.76 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b0)
% 126.48/126.76 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 126.48/126.76 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))):Prop
% 126.48/126.76 Found x0 as proof of (P0 a)
% 126.48/126.76 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 126.48/126.76 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 126.48/126.76 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))):Prop
% 126.48/126.76 Found x0 as proof of (P0 (P (f0 a)))
% 126.48/126.76 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 126.48/126.76 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 126.48/126.76 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))):Prop
% 126.48/126.76 Found x0 as proof of (P0 (f0 a))
% 126.48/126.76 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 126.48/126.76 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 126.48/126.76 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 126.48/126.76 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 126.48/126.76 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))))
% 128.87/129.13 Found x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 128.87/129.13 Found (fun (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 128.87/129.13 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))
% 128.87/129.13 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))))
% 128.87/129.13 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 128.87/129.13 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 128.87/129.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 128.87/129.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 128.87/129.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 128.87/129.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.87/129.13 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 128.87/129.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 128.87/129.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 128.87/129.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 128.87/129.13 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 128.87/129.13 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 128.87/129.13 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 128.87/129.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.87/129.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 128.87/129.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 128.87/129.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 128.87/129.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 128.87/129.13 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 128.87/129.13 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 128.87/129.13 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 128.87/129.13 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 128.87/129.13 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 128.87/129.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.87/129.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 128.87/129.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 128.87/129.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 128.87/129.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 128.87/129.13 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 128.87/129.13 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 131.59/131.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 131.59/131.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 131.59/131.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 131.59/131.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.59/131.86 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 131.59/131.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 131.59/131.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 131.59/131.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 131.59/131.86 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 131.59/131.86 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 131.59/131.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 131.59/131.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 131.59/131.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 131.59/131.86 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 131.59/131.86 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 131.59/131.86 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 131.59/131.86 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 131.59/131.86 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 131.59/131.86 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))
% 131.59/131.86 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 131.59/131.86 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 131.59/131.86 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))))
% 131.59/131.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.59/131.86 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 131.59/131.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 131.59/131.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 131.59/131.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 131.59/131.86 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 131.59/131.86 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 131.59/131.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 133.20/133.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 133.20/133.46 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 133.20/133.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 133.20/133.46 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 133.20/133.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 133.20/133.46 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 133.20/133.46 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 133.20/133.46 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 134.24/134.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 134.24/134.53 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 134.24/134.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 134.24/134.53 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 134.24/134.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 134.24/134.53 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 134.24/134.53 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 134.24/134.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 136.42/136.72 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 136.42/136.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 136.42/136.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 136.42/136.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 136.42/136.72 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 136.42/136.72 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 136.42/136.72 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 136.42/136.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 136.42/136.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 136.42/136.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 136.42/136.72 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 136.42/136.72 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 136.42/136.72 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 136.42/136.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 136.42/136.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 136.42/136.72 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 136.42/136.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 136.42/136.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 136.42/136.72 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 136.42/136.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 136.42/136.72 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 138.61/138.88 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 138.61/138.88 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 138.61/138.88 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 138.61/138.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 138.61/138.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 138.61/138.88 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 138.61/138.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 138.61/138.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 138.61/138.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 138.61/138.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 138.61/138.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 138.61/138.88 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 138.61/138.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 138.61/138.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 138.61/138.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 138.61/138.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 138.61/138.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 138.61/138.88 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 138.61/138.88 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 138.61/138.88 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 141.80/142.11 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 141.80/142.11 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 141.80/142.11 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 141.80/142.11 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 141.80/142.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 141.80/142.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 141.80/142.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 141.80/142.11 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 141.80/142.11 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 141.80/142.11 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 141.80/142.11 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 141.80/142.11 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 141.80/142.11 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 141.80/142.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 141.80/142.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 141.80/142.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 141.80/142.11 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 141.80/142.11 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 145.09/145.39 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 145.09/145.39 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 145.09/145.39 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 145.09/145.39 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 145.09/145.39 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 145.09/145.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 145.09/145.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 145.09/145.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 145.09/145.39 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 145.09/145.39 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 146.11/146.40 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 146.11/146.40 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 146.11/146.40 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 146.11/146.40 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 146.11/146.40 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 146.11/146.40 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 146.11/146.40 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 146.11/146.40 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 147.06/147.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 147.06/147.37 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 147.06/147.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 147.06/147.37 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 147.06/147.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 147.06/147.37 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 147.06/147.37 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 147.06/147.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 168.54/168.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 168.54/168.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 168.54/168.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.54/168.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 168.54/168.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 168.54/168.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 168.54/168.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 168.54/168.83 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 168.54/168.83 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 168.54/168.83 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 168.54/168.83 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 168.54/168.83 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 168.54/168.83 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 168.54/168.83 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 168.54/168.83 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 168.54/168.83 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 168.54/168.83 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))) b)
% 168.54/168.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.54/168.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 168.54/168.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 168.54/168.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 168.54/168.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 168.54/168.83 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 168.54/168.83 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 168.54/168.83 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 168.54/168.83 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 168.54/168.83 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 168.54/168.83 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 181.06/181.38 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 181.06/181.38 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 181.06/181.38 Found x0:(P0 b)
% 181.06/181.38 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))):Prop
% 181.06/181.38 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 181.06/181.38 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 181.06/181.38 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 181.06/181.38 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 181.06/181.38 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))):Prop
% 181.06/181.38 Found x0 as proof of (P0 b)
% 181.06/181.38 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 181.06/181.38 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 181.06/181.38 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 181.06/181.38 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 181.06/181.38 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 181.06/181.38 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.06/181.38 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 181.06/181.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 181.06/181.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 181.06/181.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 181.06/181.38 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 181.06/181.38 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 181.06/181.38 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 181.06/181.38 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 181.06/181.38 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 181.06/181.38 Found x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 181.06/181.38 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 181.06/181.38 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 181.06/181.38 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 181.06/181.38 Instantiate: a:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))):Prop
% 181.06/181.38 Found x0 as proof of (P0 (P (f0 a)))
% 181.06/181.38 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 181.06/181.38 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 181.06/181.38 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 181.06/181.38 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 193.82/194.20 Instantiate: a:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))):Prop
% 193.82/194.20 Found x0 as proof of (P0 (f0 a))
% 193.82/194.20 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 193.82/194.20 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 193.82/194.20 Instantiate: a:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))):Prop
% 193.82/194.20 Found x0 as proof of (P0 a)
% 193.82/194.20 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 193.82/194.20 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 193.82/194.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 193.82/194.20 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 193.82/194.20 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 193.82/194.20 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 193.82/194.20 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b)
% 193.82/194.20 Found x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 193.82/194.20 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 193.82/194.20 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 193.82/194.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 193.82/194.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 193.82/194.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 193.82/194.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 193.82/194.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 193.82/194.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 214.34/214.73 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 214.34/214.73 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 214.34/214.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 214.34/214.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 214.34/214.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.34/214.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.34/214.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.34/214.73 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 214.34/214.73 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 214.34/214.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 214.34/214.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.34/214.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.34/214.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.34/214.73 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 214.34/214.73 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 214.34/214.73 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 214.34/214.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 214.34/214.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 214.34/214.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 214.34/214.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 214.34/214.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 214.34/214.73 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 214.34/214.73 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 219.71/220.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 219.71/220.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 219.71/220.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 219.71/220.06 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 219.71/220.06 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 219.71/220.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 219.71/220.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 219.71/220.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 219.71/220.06 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 219.71/220.06 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 219.71/220.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 219.71/220.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 219.71/220.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))) b0)
% 219.71/220.06 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 219.71/220.06 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 219.71/220.06 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 219.71/220.06 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 219.71/220.06 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 219.71/220.06 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 219.71/220.06 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 219.71/220.06 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 219.71/220.06 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 219.71/220.06 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 219.71/220.06 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))))
% 219.71/220.06 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 219.71/220.06 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 219.71/220.06 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))))
% 219.71/220.06 Found x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 219.71/220.06 Found (fun (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 222.53/222.91 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 222.53/222.91 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))))
% 222.53/222.91 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 222.53/222.91 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 222.53/222.91 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 222.53/222.91 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))
% 222.53/222.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 222.53/222.91 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 222.53/222.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 222.53/222.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 222.53/222.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 222.53/222.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 222.53/222.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 222.53/222.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 222.53/222.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 222.53/222.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 222.53/222.91 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 222.53/222.91 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 222.53/222.91 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 222.53/222.91 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 222.53/222.91 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 222.53/222.91 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 222.53/222.91 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 222.53/222.91 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 222.53/222.91 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 222.53/222.91 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 222.53/222.91 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 233.61/233.98 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 233.61/233.98 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 233.61/233.98 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))))
% 233.61/233.98 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 233.61/233.98 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 233.61/233.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 233.61/233.98 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 233.61/233.98 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 233.61/233.98 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.02/235.41 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 235.02/235.41 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.02/235.41 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 235.02/235.41 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.02/235.41 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 235.02/235.41 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 235.02/235.41 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 235.02/235.41 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 237.08/237.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 237.08/237.46 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))))
% 237.08/237.46 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 237.08/237.46 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 237.08/237.46 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))) b)
% 237.08/237.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 237.08/237.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 237.08/237.46 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 237.08/237.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 237.08/237.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 237.08/237.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 240.14/240.49 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 240.14/240.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 240.14/240.49 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 240.14/240.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 240.14/240.49 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 240.14/240.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 240.14/240.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 240.14/240.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 241.66/242.00 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 241.66/242.00 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 241.66/242.00 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 241.66/242.00 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 241.66/242.00 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 241.66/242.00 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 241.66/242.00 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 241.66/242.00 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 286.01/286.40 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 286.01/286.40 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 286.01/286.40 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x)))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 286.01/286.40 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 x))))))))))))
% 286.01/286.40 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x))))))))))))
% 286.01/286.40 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 x)))))))))))) b)
% 286.01/286.40 F
%------------------------------------------------------------------------------