TSTP Solution File: SYO225^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO225^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 00:50:57 EDT 2022
% Result : Timeout 299.77s 300.11s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO225^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % RAMPerCPU : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Fri Mar 11 19:55:54 EST 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.34 Python 2.7.5
% 0.38/0.60 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x1495248>, <kernel.Type object at 0x1495128>) of role type named g_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring g:Type
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x2b6ff5a92200>, <kernel.Type object at 0x1495878>) of role type named b_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring b:Type
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x14955a8>, <kernel.Type object at 0x14956c8>) of role type named a_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring a:Type
% 0.38/0.60 FOF formula ((g->b)->((b->a)->((g->Prop)->((g->(g->g))->((b->Prop)->((b->(b->b))->(forall (Xh10:(g->b)) (Xh20:(b->a)) (Xs10:(g->Prop)) (Xf10:(g->(g->g))) (Xs20:(b->Prop)) (Xf20:(b->(b->b))) (Xs3:(a->Prop)) (Xf3:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(Xs10 ((Xf10 Xx) Xy))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(((eq b) (Xh10 ((Xf10 Xx) Xy))) ((Xf20 (Xh10 Xx)) (Xh10 Xy))))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:b), ((Xs20 Xx)->(Xs3 (Xh20 Xx)))))) (forall (Xx:b) (Xy:b), (((and (Xs20 Xx)) (Xs20 Xy))->(((eq a) (Xh20 ((Xf20 Xx) Xy))) ((Xf3 (Xh20 Xx)) (Xh20 Xy))))))->((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(Xs10 ((Xf10 Xx) Xy))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))))))))))) of role conjecture named cTHM126_CORRECTED_pme
% 0.38/0.60 Conjecture to prove = ((g->b)->((b->a)->((g->Prop)->((g->(g->g))->((b->Prop)->((b->(b->b))->(forall (Xh10:(g->b)) (Xh20:(b->a)) (Xs10:(g->Prop)) (Xf10:(g->(g->g))) (Xs20:(b->Prop)) (Xf20:(b->(b->b))) (Xs3:(a->Prop)) (Xf3:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(Xs10 ((Xf10 Xx) Xy))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(((eq b) (Xh10 ((Xf10 Xx) Xy))) ((Xf20 (Xh10 Xx)) (Xh10 Xy))))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:b), ((Xs20 Xx)->(Xs3 (Xh20 Xx)))))) (forall (Xx:b) (Xy:b), (((and (Xs20 Xx)) (Xs20 Xy))->(((eq a) (Xh20 ((Xf20 Xx) Xy))) ((Xf3 (Xh20 Xx)) (Xh20 Xy))))))->((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(Xs10 ((Xf10 Xx) Xy))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))))))))))):Prop
% 0.38/0.60 Parameter g_DUMMY:g.
% 0.38/0.60 Parameter b_DUMMY:b.
% 0.38/0.60 Parameter a_DUMMY:a.
% 0.38/0.60 We need to prove ['((g->b)->((b->a)->((g->Prop)->((g->(g->g))->((b->Prop)->((b->(b->b))->(forall (Xh10:(g->b)) (Xh20:(b->a)) (Xs10:(g->Prop)) (Xf10:(g->(g->g))) (Xs20:(b->Prop)) (Xf20:(b->(b->b))) (Xs3:(a->Prop)) (Xf3:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(Xs10 ((Xf10 Xx) Xy))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(((eq b) (Xh10 ((Xf10 Xx) Xy))) ((Xf20 (Xh10 Xx)) (Xh10 Xy))))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:b), ((Xs20 Xx)->(Xs3 (Xh20 Xx)))))) (forall (Xx:b) (Xy:b), (((and (Xs20 Xx)) (Xs20 Xy))->(((eq a) (Xh20 ((Xf20 Xx) Xy))) ((Xf3 (Xh20 Xx)) (Xh20 Xy))))))->((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(Xs10 ((Xf10 Xx) Xy))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))))))))))']
% 6.76/6.94 Parameter g:Type.
% 6.76/6.94 Parameter b:Type.
% 6.76/6.94 Parameter a:Type.
% 6.76/6.94 Trying to prove ((g->b)->((b->a)->((g->Prop)->((g->(g->g))->((b->Prop)->((b->(b->b))->(forall (Xh10:(g->b)) (Xh20:(b->a)) (Xs10:(g->Prop)) (Xf10:(g->(g->g))) (Xs20:(b->Prop)) (Xf20:(b->(b->b))) (Xs3:(a->Prop)) (Xf3:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(Xs10 ((Xf10 Xx) Xy))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs20 (Xh10 Xx)))))) (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(((eq b) (Xh10 ((Xf10 Xx) Xy))) ((Xf20 (Xh10 Xx)) (Xh10 Xy))))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:b), ((Xs20 Xx)->(Xs3 (Xh20 Xx)))))) (forall (Xx:b) (Xy:b), (((and (Xs20 Xx)) (Xs20 Xy))->(((eq a) (Xh20 ((Xf20 Xx) Xy))) ((Xf3 (Xh20 Xx)) (Xh20 Xy))))))->((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs10 Xx)) (Xs10 Xy))->(Xs10 ((Xf10 Xx) Xy))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))))))))))
% 6.76/6.94 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))
% 6.76/6.94 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 6.76/6.94 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 6.76/6.94 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 6.76/6.94 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 6.76/6.94 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 6.76/6.94 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 6.76/6.94 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 14.37/14.55 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 14.37/14.55 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 14.37/14.55 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 14.37/14.55 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 14.37/14.55 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 14.37/14.55 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 14.37/14.55 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 14.37/14.55 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 14.37/14.55 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 14.37/14.55 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 14.37/14.55 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 14.37/14.55 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 14.37/14.55 Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% 14.37/14.55 Instantiate: b0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% 14.37/14.55 Found choice_operator as proof of b0
% 14.37/14.55 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))
% 14.37/14.55 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 14.37/14.55 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 14.37/14.55 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 14.37/14.55 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 14.37/14.55 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 14.37/14.55 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 14.37/14.55 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 14.37/14.55 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 23.03/23.21 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 23.03/23.21 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 23.03/23.21 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 23.03/23.21 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 23.03/23.21 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 23.03/23.21 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 23.03/23.21 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 23.03/23.21 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 23.03/23.21 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 23.03/23.21 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 23.03/23.21 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 23.03/23.21 Found relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% 23.03/23.21 Instantiate: b0:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y)))))))))):Prop
% 23.03/23.21 Found relational_choice as proof of b0
% 23.03/23.21 Found relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% 23.03/23.21 Instantiate: b0:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y)))))))))):Prop
% 23.03/23.21 Found relational_choice as proof of b0
% 23.03/23.21 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))
% 23.03/23.21 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 23.03/23.21 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 23.03/23.21 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 23.03/23.21 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 38.31/38.53 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 38.31/38.53 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))
% 38.31/38.53 Found (eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 38.31/38.53 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 38.31/38.53 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 38.31/38.53 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 38.31/38.53 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 38.31/38.53 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 38.31/38.53 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 38.31/38.53 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 38.31/38.53 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 38.31/38.53 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 38.31/38.53 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 38.31/38.53 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 38.31/38.53 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 38.31/38.53 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 38.31/38.53 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 38.31/38.53 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 38.31/38.53 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 38.31/38.53 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 38.31/38.53 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 38.31/38.53 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 38.31/38.53 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 38.31/38.53 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 55.52/55.75 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 55.52/55.75 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 55.52/55.75 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 55.52/55.75 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 55.52/55.75 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 55.52/55.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 55.52/55.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 55.52/55.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 55.52/55.75 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 55.52/55.75 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 55.52/55.75 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 55.52/55.75 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 55.52/55.75 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 55.52/55.75 Found or_second:=(fun (A:Prop) (B:Prop) (x:((or A) B))=> (((or_first B) A) (((or_comm_i A) B) x))):(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B)))
% 55.52/55.75 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B))):Prop
% 55.52/55.75 Found or_second as proof of b0
% 55.52/55.75 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 55.52/55.75 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 55.52/55.75 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 55.52/55.75 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 55.52/55.75 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 55.52/55.75 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 55.52/55.75 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 55.52/55.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 55.52/55.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 55.52/55.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 55.52/55.75 Found or_second:=(fun (A:Prop) (B:Prop) (x:((or A) B))=> (((or_first B) A) (((or_comm_i A) B) x))):(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B)))
% 55.52/55.75 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B))):Prop
% 55.52/55.75 Found or_second as proof of b0
% 55.52/55.75 Found or_second:=(fun (A:Prop) (B:Prop) (x:((or A) B))=> (((or_first B) A) (((or_comm_i A) B) x))):(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B)))
% 55.52/55.75 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B))):Prop
% 55.52/55.75 Found or_second as proof of b0
% 55.52/55.75 Found x1:(P (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 55.52/55.75 Instantiate: b0:=(Xh20 (Xh10 ((Xf10 Xx) Xy))):a
% 55.52/55.75 Found x1 as proof of (P0 b0)
% 55.52/55.75 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))
% 55.52/55.75 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 55.52/55.75 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 72.63/72.82 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 72.63/72.82 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 72.63/72.82 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))
% 72.63/72.82 Found (eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 72.63/72.82 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 72.63/72.82 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 72.63/72.82 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 72.63/72.82 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 72.63/72.82 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 72.63/72.82 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 72.63/72.82 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 72.63/72.82 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 72.63/72.82 Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 72.63/72.82 Instantiate: b0:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% 72.63/72.82 Found eq_sym as proof of b0
% 72.63/72.82 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 72.63/72.82 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 72.63/72.82 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 72.63/72.82 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 72.63/72.82 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 72.63/72.82 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 72.63/72.82 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 72.63/72.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 72.63/72.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 72.63/72.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 72.63/72.82 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 72.63/72.82 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 72.63/72.82 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 109.62/109.84 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 109.62/109.84 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 109.62/109.84 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 109.62/109.84 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 109.62/109.84 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 109.62/109.84 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 109.62/109.84 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 109.62/109.84 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 109.62/109.84 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 109.62/109.84 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 109.62/109.84 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 109.62/109.84 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 109.62/109.84 Instantiate: b0:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% 109.62/109.84 Found conj as proof of b0
% 109.62/109.84 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 109.62/109.84 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 109.62/109.84 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 109.62/109.84 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 109.62/109.84 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 109.62/109.84 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 109.62/109.84 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 115.20/115.42 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 115.20/115.42 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 115.20/115.42 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))
% 115.20/115.42 Found (eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 115.20/115.42 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 115.20/115.42 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 115.20/115.42 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 115.20/115.42 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 115.20/115.42 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 115.20/115.42 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 115.20/115.42 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 115.20/115.42 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 115.20/115.42 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 115.20/115.42 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 115.20/115.42 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 115.20/115.42 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 115.20/115.42 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 115.20/115.42 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 115.20/115.42 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 115.20/115.42 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 115.20/115.42 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 115.20/115.42 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 115.20/115.42 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 115.20/115.42 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 115.20/115.42 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 115.20/115.42 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 115.20/115.42 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 115.20/115.42 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 115.20/115.42 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 115.20/115.42 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 115.20/115.42 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 115.20/115.42 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 115.20/115.42 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 115.20/115.42 Found (eq_ref0 b0) as proof of (P b0)
% 115.20/115.42 Found ((eq_ref a) b0) as proof of (P b0)
% 115.20/115.42 Found ((eq_ref a) b0) as proof of (P b0)
% 115.20/115.42 Found ((eq_ref a) b0) as proof of (P b0)
% 115.20/115.42 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 115.20/115.42 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 115.20/115.42 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 115.20/115.42 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found x3:(P (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 128.26/128.55 Instantiate: b0:=(Xh20 (Xh10 ((Xf10 Xx) Xy))):a
% 128.26/128.55 Found x3 as proof of (P0 b0)
% 128.26/128.55 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 128.26/128.55 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 128.26/128.55 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 128.26/128.55 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 128.26/128.55 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 128.26/128.55 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 128.26/128.55 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 128.26/128.55 Found iff_sym as proof of b0
% 128.26/128.55 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 128.26/128.55 Instantiate: b0:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% 128.26/128.55 Found conj as proof of b0
% 128.26/128.55 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 128.26/128.55 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 128.26/128.55 Instantiate: b0:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% 128.26/128.55 Found conj as proof of b0
% 128.26/128.55 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 128.26/128.55 Instantiate: b0:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% 128.26/128.55 Found conj as proof of b0
% 128.26/128.55 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 128.26/128.55 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 128.26/128.55 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 128.26/128.55 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 128.26/128.55 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 128.26/128.55 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 128.26/128.55 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 128.26/128.55 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))
% 128.26/128.55 Found (eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 128.26/128.55 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 128.26/128.55 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 128.26/128.55 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 128.26/128.55 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 143.90/144.14 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 143.90/144.14 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 143.90/144.14 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 143.90/144.14 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 143.90/144.14 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 143.90/144.14 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 143.90/144.14 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 143.90/144.14 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 143.90/144.14 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 143.90/144.14 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 143.90/144.14 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b00)
% 143.90/144.14 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b00)
% 143.90/144.14 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b00)
% 143.90/144.14 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b00)
% 143.90/144.14 Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% 143.90/144.14 Found (eq_ref0 b00) as proof of (((eq a) b00) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 143.90/144.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 143.90/144.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 143.90/144.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 143.90/144.14 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))
% 143.90/144.14 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 143.90/144.14 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 143.90/144.14 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 143.90/144.14 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))))) b0)
% 143.90/144.14 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 143.90/144.14 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 165.00/165.28 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 165.00/165.28 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 165.00/165.28 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 165.00/165.28 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 165.00/165.28 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 165.00/165.28 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 165.00/165.28 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 165.00/165.28 Found x1:(P ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 165.00/165.28 Instantiate: b0:=((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))):a
% 165.00/165.28 Found x1 as proof of (P0 b0)
% 165.00/165.28 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 165.00/165.28 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 165.00/165.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 165.00/165.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 165.00/165.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 165.00/165.28 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 165.00/165.28 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 165.00/165.28 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 165.00/165.28 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 183.10/183.43 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 183.10/183.43 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 183.10/183.43 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 183.10/183.43 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 183.10/183.43 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 183.10/183.43 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 183.10/183.43 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 183.10/183.43 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 183.10/183.43 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 183.10/183.43 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 183.10/183.43 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 183.10/183.43 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 183.10/183.43 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 183.10/183.43 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 183.10/183.43 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 183.10/183.43 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 183.10/183.43 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 183.10/183.43 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 183.10/183.43 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 183.10/183.43 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 183.10/183.43 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 183.10/183.43 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 183.10/183.43 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 183.10/183.43 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 183.10/183.43 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 183.10/183.43 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 199.87/200.15 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 199.87/200.15 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 199.87/200.15 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 199.87/200.15 Found (eq_ref0 a0) as proof of (((eq a) a0) (Xh20 (Xh10 Xy)))
% 199.87/200.15 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh20 (Xh10 Xy)))
% 199.87/200.15 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh20 (Xh10 Xy)))
% 199.87/200.15 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh20 (Xh10 Xy)))
% 199.87/200.15 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 199.87/200.15 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 199.87/200.15 Found (eq_ref0 a0) as proof of (((eq a) a0) (Xh20 (Xh10 Xy)))
% 199.87/200.15 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh20 (Xh10 Xy)))
% 199.87/200.15 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh20 (Xh10 Xy)))
% 199.87/200.15 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh20 (Xh10 Xy)))
% 199.87/200.15 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 199.87/200.15 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 199.87/200.15 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 199.87/200.15 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 199.87/200.15 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 199.87/200.15 Found x3:(P (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Instantiate: b0:=(Xh20 (Xh10 ((Xf10 Xx) Xy))):a
% 199.87/200.15 Found x3 as proof of (P0 b0)
% 199.87/200.15 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 199.87/200.15 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 199.87/200.15 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 199.87/200.15 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 199.87/200.15 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 223.51/223.84 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 223.51/223.84 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found x1:(P (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 223.51/223.84 Instantiate: b0:=(Xh20 (Xh10 ((Xf10 Xx) Xy))):a
% 223.51/223.84 Found x1 as proof of (P0 b0)
% 223.51/223.84 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 223.51/223.84 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 223.51/223.84 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 223.51/223.84 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 223.51/223.84 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 223.51/223.84 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 223.51/223.84 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 223.51/223.84 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 223.51/223.84 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 223.51/223.84 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 223.51/223.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 223.51/223.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 223.51/223.84 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 223.51/223.84 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 223.51/223.84 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 223.51/223.84 Found eq_ref00:=(eq_ref0 (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))):(((eq Prop) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))
% 223.51/223.84 Found (eq_ref0 (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))) as proof of (((eq Prop) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))) b0)
% 223.51/223.84 Found ((eq_ref Prop) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))) as proof of (((eq Prop) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))) b0)
% 223.51/223.84 Found ((eq_ref Prop) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))) as proof of (((eq Prop) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))) b0)
% 223.51/223.84 Found ((eq_ref Prop) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))) as proof of (((eq Prop) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))) b0)
% 223.51/223.84 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 223.51/223.84 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 239.83/240.10 Found iff_sym as proof of b0
% 239.83/240.10 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 239.83/240.10 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found eq_ref000:=(eq_ref00 P):((P (Xh20 (Xh10 ((Xf10 Xx) Xy))))->(P (Xh20 (Xh10 ((Xf10 Xx) Xy)))))
% 239.83/240.10 Found (eq_ref00 P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found ((eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found (((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) P) as proof of (P0 (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 239.83/240.10 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 239.83/240.10 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 239.83/240.10 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 239.83/240.10 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 239.83/240.10 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 239.83/240.10 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 239.83/240.10 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 239.83/240.10 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 239.83/240.10 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))
% 239.83/240.10 Found (eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 239.83/240.10 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 239.83/240.10 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 239.83/240.10 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 239.83/240.10 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 239.83/240.10 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 239.83/240.10 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 239.83/240.10 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 239.83/240.10 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 239.83/240.10 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 239.83/240.10 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 239.83/240.10 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 239.83/240.10 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b0)
% 239.83/240.10 Found x3:(P (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 239.83/240.10 Instantiate: b0:=(Xh20 (Xh10 ((Xf10 Xx) Xy))):a
% 239.83/240.10 Found x3 as proof of (P0 b0)
% 239.83/240.10 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 239.83/240.10 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 239.83/240.10 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 239.83/240.10 Found (eq_ref0 b0) as proof of (P b0)
% 239.83/240.10 Found ((eq_ref a) b0) as proof of (P b0)
% 266.07/266.36 Found ((eq_ref a) b0) as proof of (P b0)
% 266.07/266.36 Found ((eq_ref a) b0) as proof of (P b0)
% 266.07/266.36 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 266.07/266.36 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% 266.07/266.36 Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% 266.07/266.36 Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% 266.07/266.36 Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% 266.07/266.36 Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% 266.07/266.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 266.07/266.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))
% 266.07/266.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))
% 266.07/266.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))
% 266.07/266.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs10 Xx)) (Xs10 Xy))) (Xs10 Xx))) (Xs10 Xy))->(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))))))
% 266.07/266.36 Found x1:(P (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 266.07/266.36 Instantiate: b0:=(Xh20 (Xh10 ((Xf10 Xx) Xy))):a
% 266.07/266.36 Found x1 as proof of (P0 b0)
% 266.07/266.36 Found x1:(forall (Xx:b) (Xy:b), (((and (Xs20 Xx)) (Xs20 Xy))->(((eq a) (Xh20 ((Xf20 Xx) Xy))) ((Xf3 (Xh20 Xx)) (Xh20 Xy)))))
% 266.07/266.36 Instantiate: b0:=(forall (Xx:b) (Xy:b), (((and (Xs20 Xx)) (Xs20 Xy))->(((eq a) (Xh20 ((Xf20 Xx) Xy))) ((Xf3 (Xh20 Xx)) (Xh20 Xy))))):Prop
% 266.07/266.36 Found x1 as proof of b0
% 266.07/266.36 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 266.07/266.36 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found x5:(P (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 266.07/266.36 Instantiate: b0:=(Xh20 (Xh10 ((Xf10 Xx) Xy))):a
% 266.07/266.36 Found x5 as proof of (P0 b0)
% 266.07/266.36 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 266.07/266.36 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 266.07/266.36 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 266.07/266.36 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 266.07/266.36 Found proj1 as proof of b0
% 266.07/266.36 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 266.07/266.36 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 299.77/300.11 Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% 299.77/300.11 Found (eq_ref00 P) as proof of (P0 b0)
% 299.77/300.11 Found ((eq_ref0 b0) P) as proof of (P0 b0)
% 299.77/300.11 Found (((eq_ref a) b0) P) as proof of (P0 b0)
% 299.77/300.11 Found (((eq_ref a) b0) P) as proof of (P0 b0)
% 299.77/300.11 Found eq_ref00:=(eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))):(((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 299.77/300.11 Found (eq_ref0 (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b00)
% 299.77/300.11 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b00)
% 299.77/300.11 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b00)
% 299.77/300.11 Found ((eq_ref a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) as proof of (((eq a) (Xh20 (Xh10 ((Xf10 Xx) Xy)))) b00)
% 299.77/300.11 Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% 299.77/300.11 Found (eq_ref0 b00) as proof of (((eq a) b00) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 299.77/300.11 Found ((eq_ref a) b00) as proof of (((eq a) b00) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 299.77/300.11 Found ((eq_ref a) b00) as proof of (((eq a) b00) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 299.77/300.11 Found ((eq_ref a) b00) as proof of (((eq a) b00) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 299.77/300.11 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 299.77/300.11 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 299.77/300.11 Found iff_sym as proof of b0
% 299.77/300.11 Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 299.77/300.11 Instantiate: a0:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% 299.77/300.11 Found eq_sym as proof of a0
% 299.77/300.11 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 299.77/300.11 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 299.77/300.11 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 299.77/300.11 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 299.77/300.11 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 299.77/300.11 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx))))))
% 299.77/300.11 Found (eq_ref0 (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 299.77/300.11 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 299.77/300.11 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 299.77/300.11 Found ((eq_ref Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs10 Xx)->(Xs3 (Xh20 (Xh10 Xx)))))) b0)
% 299.77/300.11 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 299.77/300.11 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 299.77/300.11 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 299.77/300.11 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 299.77/300.11 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh20 (Xh10 ((Xf10 Xx) Xy))))
% 299.77/300.11 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))):(((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy))))
% 299.77/300.11 Found (eq_ref0 ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) b0)
% 299.77/300.11 Found ((eq_ref a) ((Xf3 (Xh20 (Xh10 Xx))) (Xh20 (Xh10 Xy)))) as proof of (((eq a) ((Xf3 (Xh20 (Xh10 Xx)))
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