TSTP Solution File: SYO228^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO228^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n031.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 300.04s 300.62s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO228^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % RAMPerCPU : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Fri Mar 11 20:25:28 EST 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.34 Python 2.7.5
% 0.42/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x23ecd88>, <kernel.Type object at 0x23ecab8>) of role type named g_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring g:Type
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x23ec680>, <kernel.Type object at 0x24122d8>) of role type named b_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring b:Type
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x23ecb00>, <kernel.Type object at 0x23ecab8>) of role type named a_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring a:Type
% 0.42/0.61 FOF formula (forall (Xh1:(g->b)) (Xh2:(b->a)) (Xs1:(g->Prop)) (Xf1:(g->(g->g))) (Xs2:(b->Prop)) (Xf2:(b->(b->b))) (Xs3:(a->Prop)) (Xf3:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(Xs1 ((Xf1 Xx) Xy))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(Xs2 ((Xf2 Xx) Xy)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs2 (Xh1 Xx)))))) (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(Xs2 ((Xf2 Xx) Xy)))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx)))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))))->((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(Xs1 ((Xf1 Xx) Xy))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))))) of role conjecture named cTHM126_EXPANDED_pme
% 0.42/0.61 Conjecture to prove = (forall (Xh1:(g->b)) (Xh2:(b->a)) (Xs1:(g->Prop)) (Xf1:(g->(g->g))) (Xs2:(b->Prop)) (Xf2:(b->(b->b))) (Xs3:(a->Prop)) (Xf3:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(Xs1 ((Xf1 Xx) Xy))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(Xs2 ((Xf2 Xx) Xy)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs2 (Xh1 Xx)))))) (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(Xs2 ((Xf2 Xx) Xy)))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx)))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))))->((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(Xs1 ((Xf1 Xx) Xy))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))))):Prop
% 0.42/0.61 Parameter g_DUMMY:g.
% 0.42/0.61 Parameter b_DUMMY:b.
% 0.42/0.61 Parameter a_DUMMY:a.
% 0.42/0.61 We need to prove ['(forall (Xh1:(g->b)) (Xh2:(b->a)) (Xs1:(g->Prop)) (Xf1:(g->(g->g))) (Xs2:(b->Prop)) (Xf2:(b->(b->b))) (Xs3:(a->Prop)) (Xf3:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(Xs1 ((Xf1 Xx) Xy))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(Xs2 ((Xf2 Xx) Xy)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs2 (Xh1 Xx)))))) (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(Xs2 ((Xf2 Xx) Xy)))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx)))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))))->((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(Xs1 ((Xf1 Xx) Xy))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))))']
% 8.29/8.50 Parameter g:Type.
% 8.29/8.50 Parameter b:Type.
% 8.29/8.50 Parameter a:Type.
% 8.29/8.50 Trying to prove (forall (Xh1:(g->b)) (Xh2:(b->a)) (Xs1:(g->Prop)) (Xf1:(g->(g->g))) (Xs2:(b->Prop)) (Xf2:(b->(b->b))) (Xs3:(a->Prop)) (Xf3:(a->(a->a))), (((and ((and ((and ((and ((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(Xs1 ((Xf1 Xx) Xy))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(Xs2 ((Xf2 Xx) Xy)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs2 (Xh1 Xx)))))) (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(Xs2 ((Xf2 Xx) Xy)))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx)))))) (forall (Xx:b) (Xy:b), (((and (Xs2 Xx)) (Xs2 Xy))->(((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))))->((and ((and ((and (forall (Xx:g) (Xy:g), (((and (Xs1 Xx)) (Xs1 Xy))->(Xs1 ((Xf1 Xx) Xy))))) (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))))
% 8.29/8.50 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% 8.29/8.50 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 8.29/8.50 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 8.29/8.50 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 8.29/8.50 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 8.29/8.50 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 8.29/8.50 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 8.29/8.50 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 8.29/8.50 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 8.29/8.50 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 8.29/8.50 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 8.29/8.50 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 8.29/8.50 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 16.49/16.67 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 16.49/16.67 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 16.49/16.67 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 16.49/16.67 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 16.49/16.67 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 16.49/16.67 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 16.49/16.67 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 16.49/16.67 Found eq_sym0:=(eq_sym Prop):(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a)))
% 16.49/16.67 Instantiate: b0:=(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a))):Prop
% 16.49/16.67 Found eq_sym0 as proof of b0
% 16.49/16.67 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% 16.49/16.67 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 16.49/16.67 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 16.49/16.67 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 16.49/16.67 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 16.49/16.67 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 16.49/16.67 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 16.49/16.67 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 16.49/16.67 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 16.49/16.67 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 16.49/16.67 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 16.49/16.67 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 16.49/16.67 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 16.49/16.67 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 16.49/16.67 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 16.49/16.67 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 16.49/16.67 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 16.49/16.67 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 16.49/16.67 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 32.30/32.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 32.30/32.48 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 32.30/32.48 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 32.30/32.48 Found or_comm_i as proof of b0
% 32.30/32.48 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% 32.30/32.48 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 32.30/32.48 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 32.30/32.48 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 32.30/32.48 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 32.30/32.48 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 32.30/32.48 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 32.30/32.48 Found or_comm_i as proof of b0
% 32.30/32.48 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 32.30/32.48 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 32.30/32.48 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 32.30/32.48 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 32.30/32.48 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 32.30/32.48 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 32.30/32.48 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 32.30/32.48 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 32.30/32.48 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 32.30/32.48 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 32.30/32.48 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 32.30/32.48 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 32.30/32.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 32.30/32.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 32.30/32.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 32.30/32.48 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 32.30/32.48 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 40.43/40.58 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 40.43/40.58 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 40.43/40.58 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 40.43/40.58 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 40.43/40.58 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 40.43/40.58 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 40.43/40.58 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))
% 40.43/40.58 Found (eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 40.43/40.58 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 40.43/40.58 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 40.43/40.58 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 40.43/40.58 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 40.43/40.58 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 40.43/40.58 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 40.43/40.58 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 40.43/40.58 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 40.43/40.58 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 40.43/40.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 40.43/40.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 40.43/40.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 40.43/40.58 Found x3:(forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx))))
% 40.43/40.58 Instantiate: b0:=(forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx)))):Prop
% 40.43/40.58 Found x3 as proof of b0
% 40.43/40.58 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 40.43/40.58 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 40.43/40.58 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 40.43/40.58 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 40.43/40.58 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 40.43/40.58 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 63.73/63.92 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 63.73/63.92 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 63.73/63.92 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 63.73/63.92 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 63.73/63.92 Found x3:(forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx))))
% 63.73/63.92 Instantiate: b0:=(forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx)))):Prop
% 63.73/63.92 Found x3 as proof of b0
% 63.73/63.92 Found x3:(forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx))))
% 63.73/63.92 Instantiate: b0:=(forall (Xx:b), ((Xs2 Xx)->(Xs3 (Xh2 Xx)))):Prop
% 63.73/63.92 Found x3 as proof of b0
% 63.73/63.92 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% 63.73/63.92 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 63.73/63.92 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 63.73/63.92 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 63.73/63.92 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 63.73/63.92 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 63.73/63.92 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 63.73/63.92 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 63.73/63.92 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 63.73/63.92 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 63.73/63.92 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))
% 63.73/63.92 Found (eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 63.73/63.92 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 63.73/63.92 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 63.73/63.92 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 63.73/63.92 Found x1:(P (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 63.73/63.92 Instantiate: b0:=(Xh2 (Xh1 ((Xf1 Xx) Xy))):a
% 63.73/63.92 Found x1 as proof of (P0 b0)
% 63.73/63.92 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 87.98/88.17 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 87.98/88.17 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 87.98/88.17 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 87.98/88.17 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 87.98/88.17 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 87.98/88.17 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 87.98/88.17 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 87.98/88.17 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 87.98/88.17 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 87.98/88.17 Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% 87.98/88.17 Instantiate: b0:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% 87.98/88.17 Found eq_substitution as proof of b0
% 87.98/88.17 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 87.98/88.17 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 87.98/88.17 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 87.98/88.17 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 87.98/88.17 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 87.98/88.17 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 87.98/88.17 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 87.98/88.17 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 87.98/88.17 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 87.98/88.17 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 122.55/122.80 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 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)))
% 122.55/122.80 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 122.55/122.80 Found iff_sym as proof of b0
% 122.55/122.80 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 122.55/122.80 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 122.55/122.80 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 122.55/122.80 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 122.55/122.80 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 122.55/122.80 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 122.55/122.80 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 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)))
% 122.55/122.80 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 122.55/122.80 Found iff_sym as proof of b0
% 122.55/122.80 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 122.55/122.80 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 122.55/122.80 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 122.55/122.80 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 122.55/122.80 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 122.55/122.80 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 122.55/122.80 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)))
% 122.55/122.80 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 122.55/122.80 Found iff_sym as proof of b0
% 122.55/122.80 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)))
% 122.55/122.80 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 122.55/122.80 Found iff_sym as proof of b0
% 122.55/122.80 Found x3:(P (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 122.55/122.80 Instantiate: b0:=(Xh2 (Xh1 ((Xf1 Xx) Xy))):a
% 125.59/125.84 Found x3 as proof of (P0 b0)
% 125.59/125.84 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 125.59/125.84 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 125.59/125.84 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 125.59/125.84 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 125.59/125.84 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 125.59/125.84 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 125.59/125.84 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 125.59/125.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 125.59/125.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 125.59/125.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 125.59/125.84 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 125.59/125.84 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 125.59/125.84 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 125.59/125.84 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 125.59/125.84 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 125.59/125.84 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 125.59/125.84 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 125.59/125.84 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 125.59/125.84 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 125.59/125.84 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 125.59/125.84 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 125.59/125.84 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 125.59/125.84 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 125.59/125.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 125.59/125.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 125.59/125.84 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 125.59/125.84 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))
% 125.59/125.84 Found (eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 125.59/125.84 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 125.59/125.84 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 125.59/125.84 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 125.59/125.84 Found eq_ref00:=(eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))):(((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% 131.78/132.03 Found (eq_ref0 (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 131.78/132.03 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 131.78/132.03 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 131.78/132.03 Found ((eq_ref Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) as proof of (((eq Prop) (forall (Xx:g) (Xy:g), (((and ((and ((and (Xs1 Xx)) (Xs1 Xy))) (Xs1 Xx))) (Xs1 Xy))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) b0)
% 131.78/132.03 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 131.78/132.03 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 131.78/132.03 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 131.78/132.03 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 131.78/132.03 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 131.78/132.03 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))
% 131.78/132.03 Found (eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 131.78/132.03 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 131.78/132.03 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 131.78/132.03 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 131.78/132.03 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))))))))
% 131.78/132.03 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
% 131.78/132.03 Found choice_operator as proof of b0
% 131.78/132.03 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 131.78/132.03 Found (eq_ref0 b0) as proof of (P b0)
% 131.78/132.03 Found ((eq_ref a) b0) as proof of (P b0)
% 131.78/132.03 Found ((eq_ref a) b0) as proof of (P b0)
% 131.78/132.03 Found ((eq_ref a) b0) as proof of (P b0)
% 131.78/132.03 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 156.44/156.73 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 156.44/156.73 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 156.44/156.73 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 156.44/156.73 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 156.44/156.73 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 156.44/156.73 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 156.44/156.73 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 156.44/156.73 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 156.44/156.73 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 156.44/156.73 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 156.44/156.73 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 156.44/156.73 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 156.44/156.73 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 156.44/156.73 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 169.49/169.75 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b00)
% 169.49/169.75 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b00)
% 169.49/169.75 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b00)
% 169.49/169.75 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b00)
% 169.49/169.75 Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% 169.49/169.75 Found (eq_ref0 b00) as proof of (((eq a) b00) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found ((eq_ref a) b00) as proof of (((eq a) b00) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found ((eq_ref a) b00) as proof of (((eq a) b00) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found ((eq_ref a) b00) as proof of (((eq a) b00) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 169.49/169.75 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 169.49/169.75 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 169.49/169.75 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 169.49/169.75 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 169.49/169.75 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 169.49/169.75 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 169.49/169.75 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 169.49/169.75 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 169.49/169.75 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 169.49/169.75 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 169.49/169.75 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 169.49/169.75 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 169.49/169.75 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 169.49/169.75 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 207.60/207.93 Found x1:(P ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Instantiate: b0:=((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))):a
% 207.60/207.93 Found x1 as proof of (P0 b0)
% 207.60/207.93 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 207.60/207.93 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 207.60/207.93 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 207.60/207.93 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 207.60/207.93 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 207.60/207.93 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 207.60/207.93 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 207.60/207.93 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 207.60/207.93 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 207.60/207.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 230.01/230.34 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 230.01/230.34 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 230.01/230.34 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 230.01/230.34 Found x3:(P (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 230.01/230.34 Instantiate: b0:=(Xh2 (Xh1 ((Xf1 Xx) Xy))):a
% 230.01/230.34 Found x3 as proof of (P0 b0)
% 230.01/230.34 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 230.01/230.34 Found (eq_ref0 a0) as proof of (((eq a) a0) (Xh2 (Xh1 Xy)))
% 230.01/230.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh2 (Xh1 Xy)))
% 230.01/230.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh2 (Xh1 Xy)))
% 230.01/230.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh2 (Xh1 Xy)))
% 230.01/230.34 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 230.01/230.34 Found (eq_ref0 a0) as proof of (((eq a) a0) (Xh2 (Xh1 Xy)))
% 230.01/230.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh2 (Xh1 Xy)))
% 230.01/230.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh2 (Xh1 Xy)))
% 230.01/230.34 Found ((eq_ref a) a0) as proof of (((eq a) a0) (Xh2 (Xh1 Xy)))
% 230.01/230.34 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 230.01/230.34 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 230.01/230.34 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 230.01/230.34 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 230.01/230.34 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 230.01/230.34 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 230.01/230.34 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 230.01/230.34 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 230.01/230.34 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 230.01/230.34 Found proj1 as proof of b0
% 230.01/230.34 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 230.01/230.34 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 230.01/230.34 Found x1:(P (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 230.01/230.34 Instantiate: b0:=(Xh2 (Xh1 ((Xf1 Xx) Xy))):a
% 230.01/230.34 Found x1 as proof of (P0 b0)
% 230.01/230.34 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 230.01/230.34 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 230.01/230.34 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 230.01/230.34 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 230.01/230.34 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 230.01/230.34 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 230.01/230.34 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 230.01/230.34 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 230.01/230.34 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 230.01/230.34 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 252.62/252.95 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 252.62/252.95 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 252.62/252.95 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 252.62/252.95 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 252.62/252.95 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 252.62/252.95 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 252.62/252.95 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 252.62/252.95 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 252.62/252.95 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 252.62/252.95 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 252.62/252.95 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 252.62/252.95 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 252.62/252.95 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 252.62/252.95 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 252.62/252.95 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 252.62/252.95 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 252.62/252.95 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 252.62/252.95 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 252.62/252.95 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 252.62/252.95 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 252.62/252.95 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 252.62/252.95 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))
% 252.62/252.95 Found (eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 252.62/252.95 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 252.62/252.95 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 252.62/252.95 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 252.62/252.95 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))))))))
% 252.62/252.95 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
% 252.62/252.95 Found choice_operator as proof of b0
% 252.62/252.95 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 252.62/252.95 Found (eq_ref0 b0) as proof of (P b0)
% 252.62/252.95 Found ((eq_ref a) b0) as proof of (P b0)
% 252.62/252.95 Found ((eq_ref a) b0) as proof of (P b0)
% 252.62/252.95 Found ((eq_ref a) b0) as proof of (P b0)
% 252.62/252.95 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 252.62/252.95 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 252.62/252.95 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 252.62/252.95 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 252.62/252.95 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 252.62/252.95 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 270.11/270.48 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 270.11/270.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 270.11/270.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 270.11/270.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 270.11/270.48 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 270.11/270.48 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 270.11/270.48 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 270.11/270.48 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 270.11/270.48 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 270.11/270.48 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)))))
% 270.11/270.48 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)
% 270.11/270.48 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)
% 270.11/270.48 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)
% 270.11/270.48 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)
% 270.11/270.48 Found x5:(forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 270.11/270.48 Found x5 as proof of (forall (Xx:a) (Xy:a), (((and (Xs3 Xx)) (Xs3 Xy))->(Xs3 ((Xf3 Xx) Xy))))
% 270.11/270.48 Found x5:(P (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 270.11/270.48 Instantiate: b0:=(Xh2 (Xh1 ((Xf1 Xx) Xy))):a
% 270.11/270.48 Found x5 as proof of (P0 b0)
% 270.11/270.48 Found x3:(P (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 270.11/270.48 Instantiate: b0:=(Xh2 (Xh1 ((Xf1 Xx) Xy))):a
% 270.11/270.48 Found x3 as proof of (P0 b0)
% 270.11/270.48 Found eq_ref000:=(eq_ref00 P):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 (Xh1 ((Xf1 Xx) Xy)))))
% 270.11/270.48 Found (eq_ref00 P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 270.11/270.48 Found ((eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 270.11/270.48 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 270.11/270.48 Found (((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) P) as proof of (P0 (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 270.11/270.48 Found eq_ref00:=(eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))):(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 270.11/270.48 Found (eq_ref0 (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 270.11/270.48 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 270.11/270.48 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 270.11/270.48 Found ((eq_ref a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) b0)
% 270.11/270.48 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 270.11/270.48 Found (eq_ref0 b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 270.11/270.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 270.11/270.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 270.11/270.48 Found ((eq_ref a) b0) as proof of (((eq a) b0) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 270.11/270.48 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))))))))))
% 270.11/270.48 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
% 284.24/284.61 Found relational_choice as proof of b0
% 284.24/284.61 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 284.24/284.61 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.61 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.61 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.61 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.61 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 284.24/284.61 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 284.24/284.61 Found proj1 as proof of b0
% 284.24/284.61 Found x1:(P (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 284.24/284.61 Instantiate: b0:=(Xh2 (Xh1 ((Xf1 Xx) Xy))):a
% 284.24/284.61 Found x1 as proof of (P0 b0)
% 284.24/284.61 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 284.24/284.62 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.62 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.62 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.62 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.62 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 284.24/284.62 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 284.24/284.62 Found proj1 as proof of b0
% 284.24/284.62 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 284.24/284.62 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 284.24/284.62 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 284.24/284.62 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 284.24/284.62 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xh2 (Xh1 ((Xf1 Xx) Xy))))
% 284.24/284.62 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 284.24/284.62 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.62 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.62 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.62 Found ((eq_ref a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
% 284.24/284.62 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 284.24/284.62 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 284.24/284.62 Found proj1 as proof of b0
% 284.24/284.62 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 284.24/284.62 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 284.24/284.62 Found proj1 as proof of b0
% 284.24/284.62 Found eq_ref00:=(eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))):(((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx))))))
% 284.24/284.62 Found (eq_ref0 (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 284.24/284.62 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 284.24/284.62 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 284.24/284.62 Found ((eq_ref Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) as proof of (((eq Prop) (forall (Xx:g), ((Xs1 Xx)->(Xs3 (Xh2 (Xh1 Xx)))))) b0)
% 284.24/284.62 Found eq_ref00:=(eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))):(((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% 284.24/284.62 Found (eq_ref0 ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) as proof of (((eq a) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))) b0)
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