TSTP Solution File: SYO500^1.005 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO500^1.005 : TPTP v7.5.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 294.03s 294.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO500^1.005 : TPTP v7.5.0. Released v4.1.0.
% 0.06/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Mar 13 12:01:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 5.25/5.45 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 5.25/5.45 FOF formula (<kernel.Constant object at 0x1917a70>, <kernel.Sort object at 0x2b84d1691638>) of role type named x
% 5.25/5.45 Using role type
% 5.25/5.45 Declaring x:Prop
% 5.25/5.45 FOF formula (<kernel.Constant object at 0x1917a28>, <kernel.DependentProduct object at 0x1917f38>) of role type named f0
% 5.25/5.45 Using role type
% 5.25/5.45 Declaring f0:(Prop->Prop)
% 5.25/5.45 FOF formula (<kernel.Constant object at 0x1917998>, <kernel.DependentProduct object at 0x1917680>) of role type named f1
% 5.25/5.45 Using role type
% 5.25/5.45 Declaring f1:(Prop->Prop)
% 5.25/5.45 FOF formula (<kernel.Constant object at 0x1917f38>, <kernel.DependentProduct object at 0x193c8c0>) of role type named f2
% 5.25/5.45 Using role type
% 5.25/5.45 Declaring f2:(Prop->Prop)
% 5.25/5.45 FOF formula (<kernel.Constant object at 0x1917680>, <kernel.DependentProduct object at 0x193cf80>) of role type named f3
% 5.25/5.45 Using role type
% 5.25/5.45 Declaring f3:(Prop->Prop)
% 5.25/5.45 FOF formula (<kernel.Constant object at 0x1917d40>, <kernel.DependentProduct object at 0x193c6c8>) of role type named f4
% 5.25/5.45 Using role type
% 5.25/5.45 Declaring f4:(Prop->Prop)
% 5.25/5.45 FOF formula (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) of role conjecture named kaminski5
% 5.25/5.45 Conjecture to prove = (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):Prop
% 5.25/5.45 We need to prove ['(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))']
% 5.25/5.45 Parameter x:Prop.
% 5.25/5.45 Parameter f0:(Prop->Prop).
% 5.25/5.45 Parameter f1:(Prop->Prop).
% 5.25/5.45 Parameter f2:(Prop->Prop).
% 5.25/5.45 Parameter f3:(Prop->Prop).
% 5.25/5.45 Parameter f4:(Prop->Prop).
% 5.25/5.45 Trying to prove (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 5.25/5.45 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 5.25/5.45 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 5.25/5.45 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 5.25/5.45 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 5.25/5.45 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 5.25/5.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 5.25/5.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 5.25/5.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 5.25/5.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 5.25/5.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 5.25/5.45 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 5.25/5.45 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 5.25/5.45 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 5.25/5.45 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 5.25/5.45 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 5.25/5.45 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))))
% 5.25/5.45 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 5.25/5.45 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 5.25/5.45 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 14.15/14.34 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 14.15/14.34 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 14.15/14.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 14.15/14.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 14.15/14.34 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 14.15/14.34 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 14.15/14.34 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 14.15/14.34 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 14.15/14.34 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 14.15/14.34 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 14.15/14.34 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 14.15/14.34 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 14.15/14.34 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 14.15/14.34 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 14.15/14.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 14.15/14.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 14.15/14.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 14.15/14.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 14.15/14.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 14.15/14.34 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 14.15/14.34 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 14.15/14.34 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))))
% 14.15/14.34 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 14.15/14.34 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 22.56/22.79 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 22.56/22.79 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 22.56/22.79 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 22.56/22.79 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 22.56/22.79 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 22.56/22.79 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 22.56/22.79 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 22.56/22.79 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 22.56/22.79 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 22.56/22.79 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 22.56/22.79 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 22.56/22.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 22.56/22.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 22.56/22.79 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 22.56/22.79 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 22.56/22.79 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 22.56/22.79 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 22.56/22.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 22.56/22.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 22.56/22.79 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 22.56/22.79 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 22.56/22.79 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 22.56/22.79 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 22.56/22.79 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 31.72/31.91 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 31.72/31.91 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 31.72/31.91 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 31.72/31.91 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 31.72/31.91 Instantiate: b:=(f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):Prop
% 31.72/31.91 Found x0 as proof of (P0 b)
% 31.72/31.91 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 31.72/31.91 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 31.72/31.91 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 31.72/31.91 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 31.72/31.91 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 31.72/31.91 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 31.72/31.91 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 31.72/31.91 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 31.72/31.91 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 31.72/31.91 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 31.72/31.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 31.72/31.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 31.72/31.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 31.72/31.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 31.72/31.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 31.72/31.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 31.72/31.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 31.72/31.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 31.72/31.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 31.72/31.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 31.72/31.91 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 31.72/31.91 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 31.72/31.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 31.72/31.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 31.72/31.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 31.72/31.91 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 31.72/31.91 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 33.05/33.22 Found x0:(P0 b)
% 33.05/33.22 Instantiate: b:=(f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):Prop
% 33.05/33.22 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 33.05/33.22 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 33.05/33.22 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 33.05/33.22 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 33.05/33.22 Instantiate: b:=(f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):Prop
% 33.05/33.22 Found x0 as proof of (P0 b)
% 33.05/33.22 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 33.05/33.22 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 33.05/33.22 Found x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 33.05/33.22 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x02) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 33.05/33.22 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x02) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 33.05/33.22 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 33.05/33.22 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 33.05/33.22 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.05/33.22 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 33.05/33.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 33.05/33.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 33.05/33.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 33.05/33.22 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 33.05/33.22 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b0)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b0)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b0)
% 33.05/33.22 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b0)
% 36.84/37.08 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 36.84/37.08 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 36.84/37.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 36.84/37.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 36.84/37.08 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 36.84/37.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 36.84/37.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 36.84/37.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 36.84/37.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 36.84/37.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 36.84/37.08 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 36.84/37.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 36.84/37.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 36.84/37.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 36.84/37.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 36.84/37.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 36.84/37.08 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 36.84/37.08 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 36.84/37.08 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 53.90/54.13 Found x01:(P b)
% 53.90/54.13 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 53.90/54.13 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 53.90/54.13 Found x0:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 53.90/54.13 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))):Prop
% 53.90/54.13 Found x0 as proof of (P0 b)
% 53.90/54.13 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 53.90/54.13 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 53.90/54.13 Found x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 53.90/54.13 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x02) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 53.90/54.13 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x02) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 53.90/54.13 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 53.90/54.13 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 53.90/54.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.90/54.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 53.90/54.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 53.90/54.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 53.90/54.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 53.90/54.13 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 53.90/54.13 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 53.90/54.13 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 53.90/54.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.90/54.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 53.90/54.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 53.90/54.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 56.32/56.58 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b0)
% 56.32/56.58 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b0)
% 56.32/56.58 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b0)
% 56.32/56.58 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b0)
% 56.32/56.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 56.32/56.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 56.32/56.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 56.32/56.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 56.32/56.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 56.32/56.58 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 56.32/56.58 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 56.32/56.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 56.32/56.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 56.32/56.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 56.32/56.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 56.32/56.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 56.32/56.58 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 56.32/56.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 56.32/56.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 56.32/56.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 56.32/56.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 56.32/56.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 56.32/56.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 56.32/56.58 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 57.29/57.58 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 57.29/57.58 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 57.29/57.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 57.29/57.58 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 57.29/57.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 57.29/57.58 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 57.29/57.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 57.29/57.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 57.29/57.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 60.90/61.17 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 60.90/61.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 60.90/61.17 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 60.90/61.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 60.90/61.17 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 60.90/61.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 60.90/61.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 60.90/61.17 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 60.90/61.17 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b0)
% 60.90/61.17 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b0)
% 60.90/61.17 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b0)
% 63.90/64.12 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b0)
% 63.90/64.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 63.90/64.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 63.90/64.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 63.90/64.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 63.90/64.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 63.90/64.12 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 ((P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))->(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))))
% 63.90/64.12 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 ((P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))->(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))))
% 63.90/64.12 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 63.90/64.12 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 63.90/64.12 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 63.90/64.12 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 63.90/64.12 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 63.90/64.12 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 72.99/73.28 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P2 (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 72.99/73.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 72.99/73.28 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 72.99/73.28 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 72.99/73.28 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 72.99/73.28 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 72.99/73.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 75.87/76.14 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 75.87/76.14 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 75.87/76.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 75.87/76.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 75.87/76.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 75.87/76.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 75.87/76.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 75.87/76.14 Found x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 75.87/76.14 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 75.87/76.14 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 75.87/76.14 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 75.87/76.14 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 75.87/76.14 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 75.87/76.14 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 75.87/76.14 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 75.87/76.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 75.87/76.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 75.87/76.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 75.87/76.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 75.87/76.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 75.87/76.14 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 75.87/76.14 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))):Prop
% 75.87/76.14 Found x0 as proof of (P0 b)
% 75.87/76.14 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 75.87/76.14 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 75.87/76.14 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 75.87/76.14 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 75.87/76.14 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 75.87/76.14 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 75.87/76.14 Instantiate: a:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))):Prop
% 75.87/76.14 Found x0 as proof of (P0 (P (f0 a)))
% 75.87/76.14 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 75.87/76.14 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 75.87/76.14 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 75.87/76.14 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 75.87/76.14 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 75.87/76.14 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 75.87/76.14 Instantiate: a:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))):Prop
% 75.87/76.14 Found x0 as proof of (P0 (f0 a))
% 75.87/76.14 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 75.87/76.14 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 87.56/87.81 Instantiate: a:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))):Prop
% 87.56/87.81 Found x0 as proof of (P0 a)
% 87.56/87.81 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 87.56/87.81 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 87.56/87.81 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 87.56/87.81 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 87.56/87.81 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 87.56/87.81 Found x0:(P0 b)
% 87.56/87.81 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))):Prop
% 87.56/87.81 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 87.56/87.81 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 87.56/87.81 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 87.56/87.81 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 87.56/87.81 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))):Prop
% 87.56/87.81 Found x0 as proof of (P0 b)
% 87.56/87.81 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 87.56/87.81 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 87.56/87.81 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 87.56/87.81 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 87.56/87.81 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 87.56/87.81 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 87.56/87.81 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 87.56/87.81 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 87.56/87.81 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 87.56/87.81 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b0)
% 87.56/87.81 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b0)
% 87.56/87.81 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b0)
% 87.56/87.81 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b0)
% 87.56/87.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 87.56/87.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 116.38/116.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 116.38/116.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 116.38/116.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 116.38/116.67 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 116.38/116.67 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))):Prop
% 116.38/116.67 Found x0 as proof of (P0 a)
% 116.38/116.67 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 116.38/116.67 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 116.38/116.67 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))):Prop
% 116.38/116.67 Found x0 as proof of (P0 (P (f0 a)))
% 116.38/116.67 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 116.38/116.67 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 116.38/116.67 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))):Prop
% 116.38/116.67 Found x0 as proof of (P0 (f0 a))
% 116.38/116.67 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 116.38/116.67 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 116.38/116.67 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 116.38/116.67 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))))
% 116.38/116.67 Found x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 116.38/116.67 Found (fun (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 116.38/116.67 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 116.38/116.67 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))))
% 116.38/116.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.38/116.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 116.38/116.67 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 116.38/116.67 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 116.38/116.67 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 118.06/118.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 118.06/118.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 118.06/118.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 118.06/118.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 118.06/118.36 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 118.06/118.36 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 118.06/118.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 118.06/118.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 118.06/118.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 118.06/118.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 118.06/118.36 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 118.06/118.36 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 118.06/118.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 118.06/118.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 118.06/118.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 118.06/118.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 118.06/118.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 118.06/118.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 118.06/118.36 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 118.06/118.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 118.06/118.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 118.06/118.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 118.06/118.36 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 118.06/118.36 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 118.06/118.36 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 118.06/118.36 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 118.06/118.36 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 118.06/118.36 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 120.76/121.06 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 120.76/121.06 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 120.76/121.06 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 120.76/121.06 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 120.76/121.06 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 120.76/121.06 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 120.76/121.06 Found x01:(P b)
% 120.76/121.06 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 120.76/121.06 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 120.76/121.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 120.76/121.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 120.76/121.06 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 120.76/121.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 120.76/121.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 120.76/121.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 120.76/121.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 120.76/121.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 120.76/121.06 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 120.76/121.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 120.76/121.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 120.76/121.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 120.76/121.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 120.76/121.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 120.76/121.06 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 120.76/121.06 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.82/122.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 121.82/122.14 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.82/122.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 121.82/122.14 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.82/122.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 121.82/122.14 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 121.82/122.14 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 121.82/122.14 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 123.27/123.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 123.27/123.53 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 123.27/123.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 123.27/123.53 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 123.27/123.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 123.27/123.53 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 123.27/123.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 123.27/123.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 123.27/123.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 125.91/126.16 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 125.91/126.16 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.91/126.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 125.91/126.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 125.91/126.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 125.91/126.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 125.91/126.16 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 125.91/126.16 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.91/126.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 125.91/126.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 125.91/126.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 125.91/126.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 125.91/126.16 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 125.91/126.16 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 125.91/126.16 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 125.91/126.16 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 125.91/126.16 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 125.91/126.16 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 125.91/126.16 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 125.91/126.16 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 125.91/126.16 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 128.78/129.04 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 128.78/129.04 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 128.78/129.04 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 128.78/129.04 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 128.78/129.04 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 128.78/129.04 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 128.78/129.04 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 128.78/129.04 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 128.78/129.04 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 128.78/129.04 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 128.78/129.04 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 128.78/129.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.78/129.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 128.78/129.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 128.78/129.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 128.78/129.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 128.78/129.04 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 128.78/129.04 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 128.78/129.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 128.78/129.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 128.78/129.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 128.78/129.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.78/129.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 128.78/129.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 128.78/129.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 128.78/129.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 128.78/129.04 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 128.78/129.04 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 128.78/129.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 128.78/129.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 128.78/129.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 128.78/129.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.78/129.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 128.78/129.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 130.56/130.84 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 130.56/130.84 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 130.56/130.84 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 130.56/130.84 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 130.56/130.84 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 130.56/130.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 130.56/130.84 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 130.56/130.84 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 131.65/131.91 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.65/131.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 131.65/131.91 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.65/131.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 131.65/131.91 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.65/131.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 131.65/131.91 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 131.65/131.91 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 131.65/131.91 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 136.55/136.87 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 136.55/136.87 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 136.55/136.87 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 136.55/136.87 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (P (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 136.55/136.87 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (P (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 136.55/136.87 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (P (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 152.56/152.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 152.56/152.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 152.56/152.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 152.56/152.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 152.56/152.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 152.56/152.89 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 152.56/152.89 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 152.56/152.89 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 152.56/152.89 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 152.56/152.89 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 152.56/152.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 152.56/152.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 152.56/152.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 152.56/152.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 152.56/152.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 152.56/152.89 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 152.56/152.89 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 152.56/152.89 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 152.56/152.89 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 152.56/152.89 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) b)
% 152.56/152.89 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 152.56/152.89 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 152.56/152.89 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 152.56/152.89 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 152.56/152.89 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 152.56/152.89 Found x0:(P0 b)
% 152.56/152.89 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))):Prop
% 152.56/152.89 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 152.56/152.89 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 x))))))))))))
% 152.56/152.89 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 152.56/152.89 Found x0:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 152.56/152.89 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))):Prop
% 152.56/152.89 Found x0 as proof of (P0 b)
% 152.56/152.89 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 182.71/183.00 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 182.71/183.00 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 182.71/183.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 182.71/183.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 182.71/183.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 182.71/183.00 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 182.71/183.00 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 182.71/183.00 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x02) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 182.71/183.00 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x02) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 182.71/183.00 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 182.71/183.00 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 182.71/183.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 182.71/183.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 182.71/183.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 182.71/183.00 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 182.71/183.00 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 182.71/183.00 Found x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 182.71/183.00 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x02) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 182.71/183.00 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x02) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 182.71/183.00 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 182.71/183.00 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 182.71/183.00 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 182.71/183.00 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 193.04/193.36 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 193.04/193.36 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))
% 193.04/193.36 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 193.04/193.36 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 193.04/193.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 193.04/193.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 193.04/193.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 193.04/193.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 193.04/193.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 193.04/193.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 193.04/193.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 193.04/193.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 193.04/193.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 193.04/193.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 193.04/193.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 193.04/193.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 193.04/193.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 193.04/193.36 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 193.04/193.36 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 193.04/193.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 193.04/193.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 193.04/193.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 193.04/193.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 193.04/193.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 193.04/193.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 193.04/193.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 193.04/193.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 193.04/193.36 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 193.04/193.36 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 193.04/193.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 193.04/193.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 197.89/198.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 197.89/198.20 Found x0:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 197.89/198.20 Found (fun (x0:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x0) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 197.89/198.20 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x0) as proof of ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))
% 197.89/198.20 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))))=> x0) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 197.89/198.20 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 197.89/198.20 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 197.89/198.20 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 197.89/198.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 197.89/198.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 197.89/198.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 197.89/198.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 197.89/198.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 197.89/198.20 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 197.89/198.20 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 197.89/198.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 197.89/198.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 197.89/198.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 197.89/198.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 197.89/198.20 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 197.89/198.20 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 197.89/198.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 197.89/198.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 197.89/198.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 211.82/212.17 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 211.82/212.17 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 211.82/212.17 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 211.82/212.17 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 211.82/212.17 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 211.82/212.17 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 211.82/212.17 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 211.82/212.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 211.82/212.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 211.82/212.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 211.82/212.17 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 211.82/212.17 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 211.82/212.17 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 211.82/212.17 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 211.82/212.17 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b0)
% 211.82/212.17 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 211.82/212.17 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 211.82/212.17 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))))
% 211.82/212.17 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 211.82/212.17 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 211.82/212.17 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))))
% 211.82/212.17 Found x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 211.82/212.17 Found (fun (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 211.82/212.17 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 211.82/212.17 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))))
% 211.82/212.17 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 211.82/212.17 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 211.82/212.17 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 211.82/212.17 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 211.82/212.17 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 211.82/212.17 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 222.06/222.39 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 222.06/222.39 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 222.06/222.39 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 222.06/222.39 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 222.06/222.39 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 222.06/222.39 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 222.06/222.39 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (P (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 222.06/222.39 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (P (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 222.06/222.39 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) as proof of (P (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 222.06/222.39 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 222.06/222.39 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 222.06/222.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 222.06/222.39 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.59 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 223.28/223.59 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.59 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.59 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.59 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 223.28/223.59 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.59 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 223.28/223.59 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.59 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.59 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.59 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.60 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 223.28/223.60 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 223.28/223.60 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.60 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.60 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.60 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 223.28/223.60 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 223.28/223.60 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 223.28/223.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 233.29/233.64 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 233.29/233.64 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 233.29/233.64 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 233.29/233.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 233.29/233.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 233.29/233.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 233.29/233.64 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 233.29/233.64 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))
% 233.29/233.64 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))) b)
% 233.29/233.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 233.29/233.64 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 233.29/233.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 233.29/233.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 233.29/233.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 233.29/233.64 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 233.29/233.64 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 233.29/233.64 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 233.29/233.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.56/235.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.56/235.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 235.56/235.91 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.56/235.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 235.56/235.91 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.56/235.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 235.56/235.91 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 235.56/235.91 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 235.56/235.91 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.89/237.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 236.89/237.23 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.89/237.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 236.89/237.23 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.89/237.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 236.89/237.23 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 236.89/237.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.89/237.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 236.89/237.23 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 263.82/264.19 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 263.82/264.19 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 263.82/264.19 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 263.82/264.19 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 263.82/264.19 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 263.82/264.19 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 263.82/264.19 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 263.82/264.19 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 263.82/264.19 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 263.82/264.19 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 263.82/264.19 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 263.82/264.19 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 263.82/264.19 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 263.82/264.19 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))
% 263.82/264.19 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 263.82/264.19 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 263.82/264.19 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 263.82/264.19 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 263.82/264.19 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 263.82/264.19 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 294.03/294.45 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 294.03/294.45 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 294.03/294.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 294.03/294.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 294.03/294.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 294.03/294.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 294.03/294.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 294.03/294.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 294.03/294.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 294.03/294.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 294.03/294.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 294.03/294.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 294.03/294.45 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 294.03/294.45 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 294.03/294.45 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 294.03/294.45 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b)
% 294.03/294.45 Found x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 294.03/294.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 294.03/294.45 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 294.03/294.45 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 294.03/294.45 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 294.03/294.45 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 294.03/294.45 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 294.03/294.45 Found x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 294.03/294.45 Found (fun (x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x0) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))
% 294.03/294.45 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x0) as proof of ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))
% 297.26/297.64 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))))=> x0) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 297.26/297.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 297.26/297.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 297.26/297.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 297.26/297.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 297.26/297.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 297.26/297.64 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 297.26/297.64 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b0)
% 297.26/297.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b0)
% 297.26/297.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b0)
% 297.26/297.64 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x))))))))) b0)
% 297.26/297.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 297.26/297.64 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 297.26/297.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 297.26/297.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 297.26/297.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 297.26/297.64 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 297.26/297.64 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 297.26/297.64 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 297.26/297.64 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 297.26/297.64 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 297.26/297.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 297.26/297.64 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 297.26/297.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 297.26/297.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 297.26/297.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 x)))))))))
% 297.26/297.64 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 297.26/297.64 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 297.26/297.64 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 297.26/297.64 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 297.26/297.64 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))) b)
% 297.26/297.64 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 297.26/297.64 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 297.26/297.64 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 x)))))))))))
% 297.26/297.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop
%------------------------------------------------------------------------------