TSTP Solution File: SYO500^1.008 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO500^1.008 : TPTP v7.5.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 288.55s 288.93s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO500^1.008 : TPTP v7.5.0. Released v4.1.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n001.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sun Mar 13 12:34:15 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 3.10/3.27 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 3.10/3.27 FOF formula (<kernel.Constant object at 0x1f9d1b8>, <kernel.Sort object at 0x2b4ca40a6638>) of role type named x
% 3.10/3.27 Using role type
% 3.10/3.27 Declaring x:Prop
% 3.10/3.27 FOF formula (<kernel.Constant object at 0x1f9d7a0>, <kernel.DependentProduct object at 0x2b4ca40ad4d0>) of role type named f0
% 3.10/3.27 Using role type
% 3.10/3.27 Declaring f0:(Prop->Prop)
% 3.10/3.27 FOF formula (<kernel.Constant object at 0x1f9d7e8>, <kernel.DependentProduct object at 0x2b4ca40adcf8>) of role type named f1
% 3.10/3.27 Using role type
% 3.10/3.27 Declaring f1:(Prop->Prop)
% 3.10/3.27 FOF formula (<kernel.Constant object at 0x1f9d1b8>, <kernel.DependentProduct object at 0x2b4ca40ad290>) of role type named f2
% 3.10/3.27 Using role type
% 3.10/3.27 Declaring f2:(Prop->Prop)
% 3.10/3.27 FOF formula (<kernel.Constant object at 0x1f9d7e8>, <kernel.DependentProduct object at 0x2b4ca40ad710>) of role type named f3
% 3.10/3.27 Using role type
% 3.10/3.27 Declaring f3:(Prop->Prop)
% 3.10/3.27 FOF formula (<kernel.Constant object at 0x1f9d1b8>, <kernel.DependentProduct object at 0x2b4ca40ad998>) of role type named f4
% 3.10/3.27 Using role type
% 3.10/3.27 Declaring f4:(Prop->Prop)
% 3.10/3.27 FOF formula (<kernel.Constant object at 0x1f9d1b8>, <kernel.DependentProduct object at 0x2b4ca40ad1b8>) of role type named f5
% 3.10/3.27 Using role type
% 3.10/3.27 Declaring f5:(Prop->Prop)
% 3.10/3.27 FOF formula (<kernel.Constant object at 0x2b4ca40ad998>, <kernel.DependentProduct object at 0x2b4ca40adfc8>) of role type named f6
% 3.10/3.27 Using role type
% 3.10/3.27 Declaring f6:(Prop->Prop)
% 3.10/3.27 FOF formula (<kernel.Constant object at 0x2b4ca40ad1b8>, <kernel.DependentProduct object at 0x2b4ca40ad0e0>) of role type named f7
% 3.10/3.27 Using role type
% 3.10/3.27 Declaring f7:(Prop->Prop)
% 3.10/3.27 FOF formula (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) of role conjecture named kaminski8
% 3.10/3.27 Conjecture to prove = (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):Prop
% 3.10/3.27 We need to prove ['(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))']
% 3.10/3.27 Parameter x:Prop.
% 3.10/3.27 Parameter f0:(Prop->Prop).
% 3.10/3.27 Parameter f1:(Prop->Prop).
% 3.10/3.27 Parameter f2:(Prop->Prop).
% 3.10/3.27 Parameter f3:(Prop->Prop).
% 3.10/3.27 Parameter f4:(Prop->Prop).
% 3.10/3.27 Parameter f5:(Prop->Prop).
% 3.10/3.27 Parameter f6:(Prop->Prop).
% 3.10/3.27 Parameter f7:(Prop->Prop).
% 3.10/3.27 Trying to prove (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 3.10/3.27 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 3.10/3.27 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 3.10/3.27 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 3.10/3.27 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 3.10/3.27 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 3.10/3.27 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 3.10/3.27 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 3.10/3.27 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 10.06/10.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 10.06/10.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 10.06/10.25 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))))
% 10.06/10.25 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 10.06/10.25 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))
% 10.06/10.25 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))
% 10.06/10.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.06/10.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 10.06/10.25 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 24.03/24.19 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 24.03/24.19 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 24.03/24.19 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 24.03/24.19 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 24.03/24.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.03/24.19 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 24.03/24.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 24.03/24.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 24.03/24.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 24.03/24.19 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 24.03/24.19 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 24.03/24.19 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 24.03/24.19 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 24.03/24.19 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 24.03/24.19 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 24.03/24.19 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 24.03/24.19 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))))
% 24.03/24.19 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 24.03/24.19 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 24.03/24.19 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 24.03/24.19 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 24.03/24.19 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 37.11/37.28 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 37.11/37.28 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 37.11/37.28 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 37.11/37.28 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 37.11/37.28 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 37.11/37.28 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 37.11/37.28 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 37.11/37.28 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 37.11/37.28 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 37.11/37.28 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 37.11/37.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.11/37.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 37.11/37.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 37.11/37.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 37.11/37.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 37.11/37.28 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 37.11/37.28 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 37.11/37.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 37.11/37.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 37.11/37.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 37.11/37.28 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 37.11/37.28 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 37.11/37.28 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 37.11/37.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.11/37.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 37.11/37.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 41.19/41.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 41.19/41.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 41.19/41.41 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 41.19/41.41 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 41.19/41.41 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 41.19/41.41 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 41.19/41.41 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 41.19/41.41 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 41.19/41.41 Instantiate: b:=(f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):Prop
% 41.19/41.41 Found x0 as proof of (P0 b)
% 41.19/41.41 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 41.19/41.41 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 41.19/41.41 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 41.19/41.41 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 41.19/41.41 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 41.19/41.41 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 41.19/41.41 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 41.19/41.41 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 41.19/41.41 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 41.19/41.41 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 41.19/41.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 41.19/41.41 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 43.66/43.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 43.66/43.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 43.66/43.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 43.66/43.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 43.66/43.84 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 43.66/43.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 43.66/43.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 43.66/43.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 43.66/43.84 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 43.66/43.84 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 43.66/43.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 43.66/43.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 43.66/43.84 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 43.66/43.84 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 43.66/43.84 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 43.66/43.84 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 43.66/43.84 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 43.66/43.84 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 43.66/43.84 Found x0:(P0 b)
% 43.66/43.84 Instantiate: b:=(f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):Prop
% 43.66/43.84 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 43.66/43.84 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))
% 43.66/43.84 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 43.66/43.84 Found x0:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 43.66/43.84 Instantiate: b:=(f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):Prop
% 43.66/43.84 Found x0 as proof of (P0 b)
% 43.66/43.84 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 44.49/44.67 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 44.49/44.67 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 44.49/44.67 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 44.49/44.67 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 44.49/44.67 Found x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 44.49/44.67 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x02) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 44.49/44.67 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x02) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 44.49/44.67 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 44.49/44.67 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 44.49/44.67 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 44.49/44.67 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 44.49/44.67 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 44.49/44.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 44.49/44.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 44.49/44.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 44.49/44.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 44.49/44.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 44.49/44.67 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 44.49/44.67 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b0)
% 44.49/44.67 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b0)
% 44.49/44.67 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b0)
% 44.49/44.67 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b0)
% 48.69/48.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 48.69/48.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 48.69/48.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 48.69/48.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 48.69/48.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 48.69/48.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 48.69/48.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 48.69/48.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 48.69/48.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 48.69/48.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 48.69/48.92 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 48.69/48.92 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 48.69/48.92 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 48.69/48.92 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 48.69/48.92 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 48.69/48.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 48.69/48.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 48.69/48.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 48.69/48.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 48.69/48.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 48.69/48.92 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 48.69/48.92 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 48.69/48.92 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 48.69/48.92 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 48.69/48.92 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 66.58/66.81 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 66.58/66.81 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 66.58/66.81 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 66.58/66.81 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 66.58/66.81 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 66.58/66.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 66.58/66.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 66.58/66.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 66.58/66.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 66.58/66.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 66.58/66.81 Found x01:(P b)
% 66.58/66.81 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 66.58/66.81 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 66.58/66.81 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 66.58/66.81 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))):Prop
% 66.58/66.81 Found x0 as proof of (P0 b)
% 66.58/66.81 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 66.58/66.81 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 66.58/66.81 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 66.58/66.81 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 66.58/66.81 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 66.58/66.81 Found x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 66.58/66.81 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x02) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 66.58/66.81 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x02) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 66.58/66.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 66.58/66.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 66.58/66.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 66.58/66.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 78.08/78.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 78.08/78.28 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 78.08/78.28 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 78.08/78.28 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 78.08/78.28 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 78.08/78.28 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 78.08/78.28 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 78.08/78.28 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b0)
% 78.08/78.28 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b0)
% 78.08/78.28 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b0)
% 78.08/78.28 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b0)
% 78.08/78.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 78.08/78.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 78.08/78.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 78.08/78.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 78.08/78.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 78.08/78.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 78.08/78.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 78.08/78.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 78.08/78.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 78.08/78.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 78.08/78.28 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 78.08/78.28 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 78.08/78.28 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 78.08/78.28 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 79.78/79.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 79.78/79.98 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 79.78/79.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 79.78/79.98 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 79.78/79.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 79.78/79.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 79.78/79.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 80.96/81.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 80.96/81.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 80.96/81.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 80.96/81.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 80.96/81.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 80.96/81.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 80.96/81.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 80.96/81.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 80.96/81.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 80.96/81.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 80.96/81.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 80.96/81.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 80.96/81.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 80.96/81.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 80.96/81.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 81.99/82.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 81.99/82.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 81.99/82.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 81.99/82.20 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 81.99/82.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 81.99/82.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 81.99/82.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 83.17/83.40 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 83.17/83.40 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 83.17/83.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 83.17/83.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 83.17/83.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 83.17/83.40 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 83.17/83.40 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 83.17/83.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 83.17/83.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 83.17/83.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 83.17/83.40 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 83.17/83.40 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 83.17/83.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 83.17/83.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 83.17/83.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 83.17/83.40 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 83.17/83.40 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b0)
% 83.17/83.40 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b0)
% 83.17/83.40 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b0)
% 83.17/83.40 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b0)
% 83.17/83.40 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 83.17/83.40 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 83.17/83.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 83.17/83.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 88.09/88.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 88.09/88.31 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 ((P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))->(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))))
% 88.09/88.31 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 ((P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))->(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))))
% 88.09/88.31 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 88.09/88.31 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 88.09/88.31 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 88.09/88.31 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 88.09/88.31 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 96.13/96.34 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 96.13/96.34 Found x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P2 (P1 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 96.13/96.34 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 96.13/96.34 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 96.13/96.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 105.75/105.94 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 105.75/105.94 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 105.75/105.94 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 105.75/105.94 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 105.75/105.94 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 105.75/105.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 105.75/105.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 105.75/105.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 105.75/105.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 105.75/105.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 105.75/105.94 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 105.75/105.94 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 123.90/124.15 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 123.90/124.15 Found x0:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 123.90/124.15 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))):Prop
% 123.90/124.15 Found x0 as proof of (P0 b)
% 123.90/124.15 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 123.90/124.15 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 123.90/124.15 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 123.90/124.15 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 123.90/124.15 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 123.90/124.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 123.90/124.15 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 123.90/124.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 123.90/124.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 123.90/124.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 123.90/124.15 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 123.90/124.15 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 123.90/124.15 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 123.90/124.15 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 123.90/124.15 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 123.90/124.15 Found x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 123.90/124.15 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x02) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 123.90/124.15 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x02) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 123.90/124.15 Found x0:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 123.90/124.15 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))):Prop
% 123.90/124.15 Found x0 as proof of (P0 b)
% 123.90/124.15 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 162.79/163.04 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 162.79/163.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 162.79/163.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 162.79/163.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 162.79/163.04 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 162.79/163.04 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 162.79/163.04 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 162.79/163.04 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 162.79/163.04 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 162.79/163.04 Found x0:(P0 b)
% 162.79/163.04 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))):Prop
% 162.79/163.04 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 162.79/163.04 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 162.79/163.04 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 162.79/163.04 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 162.79/163.04 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 162.79/163.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 162.79/163.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 162.79/163.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 162.79/163.04 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 162.79/163.04 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b0)
% 162.79/163.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b0)
% 162.79/163.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b0)
% 162.79/163.04 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b0)
% 162.79/163.04 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 162.79/163.04 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))))
% 167.21/167.48 Found x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))
% 167.21/167.48 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))))
% 167.21/167.48 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 167.21/167.48 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 167.21/167.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 167.21/167.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 167.21/167.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 167.21/167.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 167.21/167.48 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 167.21/167.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 167.21/167.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 167.21/167.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 167.21/167.48 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 167.21/167.48 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))
% 167.21/167.48 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 167.21/167.48 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))))
% 170.66/170.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 170.66/170.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 170.66/170.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 170.66/170.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 170.66/170.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 170.66/170.92 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 170.66/170.92 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 170.66/170.92 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 170.66/170.92 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 170.66/170.92 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 170.66/170.92 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 170.66/170.92 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 170.66/170.92 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 170.66/170.92 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 170.66/170.92 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 170.66/170.92 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 170.66/170.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 170.66/170.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 170.66/170.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 170.66/170.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 170.66/170.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 170.66/170.92 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 170.66/170.92 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 170.66/170.92 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 170.66/170.92 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.70/171.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 171.70/171.94 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.70/171.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 171.70/171.94 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 171.70/171.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.70/171.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 171.70/171.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 172.83/173.10 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 172.83/173.10 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 172.83/173.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 172.83/173.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 172.83/173.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 172.83/173.10 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 172.83/173.10 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 172.83/173.10 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 172.83/173.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 172.83/173.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 172.83/173.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 172.83/173.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 172.83/173.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 172.83/173.10 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 172.83/173.10 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 172.83/173.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 172.83/173.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 172.83/173.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 172.83/173.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 172.83/173.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 172.83/173.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 172.83/173.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 172.83/173.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 172.83/173.10 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 174.27/174.53 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 174.27/174.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 174.27/174.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 174.27/174.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 174.27/174.53 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 174.27/174.53 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 174.27/174.53 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 174.27/174.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.27/174.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 174.27/174.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 174.27/174.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 174.27/174.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 174.27/174.53 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 174.27/174.53 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 174.27/174.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 174.27/174.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 174.27/174.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 174.27/174.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.27/174.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 174.27/174.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 174.27/174.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 174.27/174.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 174.27/174.53 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 174.27/174.53 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 174.27/174.53 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 175.41/175.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 175.41/175.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 175.41/175.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 175.41/175.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 175.41/175.71 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 175.41/175.71 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 175.41/175.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 175.41/175.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 175.41/175.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 175.41/175.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 175.41/175.71 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 175.41/175.71 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 175.41/175.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 175.41/175.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 175.41/175.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 179.03/179.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 179.03/179.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 179.03/179.32 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 179.03/179.32 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 179.03/179.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 179.03/179.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 179.03/179.32 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 179.03/179.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.03/179.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 179.03/179.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 179.03/179.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 179.03/179.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 179.03/179.32 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 179.03/179.32 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 179.03/179.32 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 179.03/179.32 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 179.03/179.32 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 179.03/179.32 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 179.03/179.32 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 179.03/179.32 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 179.03/179.32 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 179.03/179.32 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))) b)
% 185.72/185.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 185.72/185.99 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 185.72/185.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 185.72/185.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 185.72/185.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 185.72/185.99 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 185.72/185.99 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 185.72/185.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 185.72/185.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 185.72/185.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 185.72/185.99 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 185.72/185.99 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 187.99/188.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 187.99/188.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 187.99/188.28 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 187.99/188.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 187.99/188.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 187.99/188.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 187.99/188.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 187.99/188.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 187.99/188.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 189.01/189.31 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 189.01/189.31 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.01/189.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 189.01/189.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 189.01/189.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 189.01/189.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 189.01/189.31 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 189.01/189.31 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.01/189.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 189.01/189.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 189.01/189.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 189.01/189.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 189.01/189.31 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 189.01/189.31 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 189.01/189.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.80/191.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 190.80/191.10 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.80/191.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 190.80/191.10 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 190.80/191.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.80/191.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 190.80/191.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 191.79/192.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 191.79/192.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 191.79/192.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 191.79/192.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 191.79/192.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 191.79/192.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 191.79/192.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 191.79/192.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 191.79/192.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 191.79/192.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 191.79/192.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 191.79/192.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 191.79/192.05 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 191.79/192.05 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 191.79/192.05 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 192.88/193.15 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 192.88/193.15 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 192.88/193.15 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 192.88/193.15 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 192.88/193.15 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 192.88/193.15 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 192.88/193.15 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 231.77/232.06 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 231.77/232.06 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 231.77/232.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 231.77/232.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 231.77/232.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 231.77/232.06 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 231.77/232.06 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 231.77/232.06 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 231.77/232.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 231.77/232.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 231.77/232.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 231.77/232.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 231.77/232.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 231.77/232.06 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 231.77/232.06 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 231.77/232.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 231.77/232.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 231.77/232.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 231.77/232.06 Found x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 231.77/232.06 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 231.77/232.06 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 231.77/232.06 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 231.77/232.06 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))):Prop
% 231.77/232.06 Found x0 as proof of (P0 b)
% 231.77/232.06 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 247.08/247.40 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found x0:(P0 b)
% 247.08/247.40 Instantiate: b:=(f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))):Prop
% 247.08/247.40 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 247.08/247.40 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 247.08/247.40 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 247.08/247.40 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 247.08/247.40 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 247.08/247.40 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 247.08/247.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 247.08/247.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 247.08/247.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 247.08/247.40 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 247.08/247.40 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 247.08/247.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b)
% 262.61/262.94 Found x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 262.61/262.94 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 262.61/262.94 Found (fun (x02:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 262.61/262.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 262.61/262.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 262.61/262.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 262.61/262.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 262.61/262.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 262.61/262.94 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 262.61/262.94 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 262.61/262.94 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 262.61/262.94 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 262.61/262.94 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 262.61/262.94 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 262.61/262.94 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 262.61/262.94 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 262.61/262.94 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 262.61/262.94 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 262.61/262.94 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 262.61/262.94 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 262.61/262.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 262.61/262.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 262.61/262.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 262.61/262.94 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 262.61/262.94 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 262.61/262.94 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 267.23/267.54 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 267.23/267.54 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 267.23/267.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 267.23/267.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 267.23/267.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 267.23/267.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 267.23/267.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 267.23/267.54 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 267.23/267.54 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 267.23/267.54 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 267.23/267.54 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 267.23/267.54 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 267.23/267.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 267.23/267.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 267.23/267.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 267.23/267.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 267.23/267.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 267.23/267.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.23/267.54 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 267.23/267.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 267.23/267.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 267.23/267.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 267.23/267.54 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 267.23/267.54 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 267.23/267.54 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 267.23/267.54 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 271.11/271.40 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 271.11/271.40 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 271.11/271.40 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 271.11/271.40 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))))
% 271.11/271.40 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 271.11/271.40 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 271.11/271.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 271.11/271.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 271.11/271.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 271.11/271.40 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))):(((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 271.11/271.40 Found (eq_ref0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 271.11/271.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 271.11/271.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 271.11/271.40 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))) b0)
% 271.11/271.40 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 271.11/271.40 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 271.11/271.40 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))->(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))))
% 271.11/271.40 Found x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 271.11/271.40 Found (fun (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 271.11/271.40 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 271.11/271.40 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))->(P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))))
% 271.11/271.40 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 271.11/271.40 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 271.11/271.40 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 276.08/276.41 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 276.08/276.41 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 276.08/276.41 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 276.08/276.41 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 276.08/276.41 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 276.08/276.41 Found x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))
% 276.08/276.41 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))))
% 288.55/288.93 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 288.55/288.93 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))):Prop
% 288.55/288.93 Found x0 as proof of (P0 (f0 a))
% 288.55/288.93 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 288.55/288.93 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 288.55/288.93 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))):Prop
% 288.55/288.93 Found x0 as proof of (P0 (P (f0 a)))
% 288.55/288.93 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 288.55/288.93 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 288.55/288.93 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))):Prop
% 288.55/288.93 Found x0 as proof of (P0 a)
% 288.55/288.93 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 288.55/288.93 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 288.55/288.93 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 288.55/288.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.55/288.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.55/288.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.55/288.93 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 288.55/288.93 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 288.55/288.93 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 288.55/288.93 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 288.55/288.93 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 288.55/288.93 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 288.55/288.93 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 288.55/288.93 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found (fun (x01:(P (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x)))))))))))))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))))
% 296.46/296.83 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 296.46/296.83 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 296.46/296.83 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))) b)
% 296.46/296.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 296.46/296.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 296.46/296.83 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 296.46/296.83 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 296.46/296.83 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 296.46/296.83 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 296.46/296.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 296.46/296.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 296.46/296.83 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 297.37/297.75 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 297.37/297.75 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 297.37/297.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 297.37/297.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 297.37/297.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 297.37/297.75 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 297.37/297.75 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 297.37/297.75 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 297.37/297.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 297.37/297.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 297.37/297.75 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 (f3 (f3 (f3 (f4 (f5 (f5 (f5 (f6 (f7 (f7 (f7 x))))))))))))))))
% 297.37/297.75 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x))))))))))))))))
% 297.37/297.75 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) b)
% 297.37/297.75 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6 (f6 (f7 x)))))))))))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 (f3 (f4 (f4 (f4 (f5 (f6 (f6
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