TSTP Solution File: PHI004^4 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : PHI004^4 : TPTP v6.4.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 16091.75MB
% OS : Linux 3.10.0-327.10.1.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Mar 28 10:08:33 EDT 2016
% Result : Timeout 296.19s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI004^4 : TPTP v6.4.0. Released v6.4.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n011.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 16091.75MB
% 0.02/0.23 % OS : Linux 3.10.0-327.10.1.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Mar 25 13:56:42 CDT 2016
% 0.02/0.23 % CPUTime :
% 0.02/0.24 Python 2.7.8
% 0.08/0.52 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2aefe2108878>, <kernel.Type object at 0x2aefe23cf290>) of role type named ty_n_t__QML____S5U__O__092__060mu__062
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring qML_mu:Type
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2aefe2108170>, <kernel.Type object at 0x2aefe23cf998>) of role type named ty_n_t__QML____S5U__Oi
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring qML_i:Type
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2aefe21081b8>, <kernel.DependentProduct object at 0x2aefe23cf368>) of role type named sy_c_Scott__S5U_OG
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring scott_G:(qML_mu->(qML_i->Prop))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2aefe21081b8>, <kernel.DependentProduct object at 0x2aefe23cf440>) of role type named sy_c_Scott__S5U_ONE_001t__QML____S5U__O__092__060mu__062
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring scott_NE_QML_mu:(qML_mu->(qML_i->Prop))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2aefe23cf290>, <kernel.DependentProduct object at 0x2aefe23cf680>) of role type named sy_c_Scott__S5U_OP
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring scott_P:((qML_mu->(qML_i->Prop))->(qML_i->Prop))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2aefe23cf440>, <kernel.DependentProduct object at 0x2aefe23cf680>) of role type named sy_c_Scott__S5U_Oess_001t__QML____S5U__O__092__060mu__062
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring scott_ess_QML_mu:((qML_mu->(qML_i->Prop))->(qML_mu->(qML_i->Prop)))
% 0.08/0.52 FOF formula (((eq (qML_mu->(qML_i->Prop))) scott_G) (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) of role axiom named fact_0_G__def
% 0.08/0.52 A new axiom: (((eq (qML_mu->(qML_i->Prop))) scott_G) (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W)))))
% 0.08/0.52 FOF formula (qML_i->(forall (V:qML_i), ((ex qML_mu) (fun (X2:qML_mu)=> ((scott_G X2) V))))) of role axiom named fact_1_T3
% 0.08/0.52 A new axiom: (qML_i->(forall (V:qML_i), ((ex qML_mu) (fun (X2:qML_mu)=> ((scott_G X2) V)))))
% 0.08/0.52 FOF formula (forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P X3) W2)->(forall (X_1:qML_i), ((scott_P X3) X_1)))) of role axiom named fact_2_A4
% 0.08/0.52 A new axiom: (forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P X3) W2)->(forall (X_1:qML_i), ((scott_P X3) X_1))))
% 0.08/0.52 FOF formula (forall (X_1:qML_i), ((scott_P scott_G) X_1)) of role axiom named fact_3_A3
% 0.08/0.52 A new axiom: (forall (X_1:qML_i), ((scott_P scott_G) X_1))
% 0.08/0.52 FOF formula (((eq ((qML_mu->(qML_i->Prop))->(qML_mu->(qML_i->Prop)))) scott_ess_QML_mu) (fun (Phi:(qML_mu->(qML_i->Prop))) (X:qML_mu) (W:qML_i)=> ((and ((Phi X) W)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X) W)->(forall (V2:qML_i) (Z:qML_mu), (((Phi Z) V2)->((Y Z) V2)))))))) of role axiom named fact_4_ess__def
% 0.08/0.52 A new axiom: (((eq ((qML_mu->(qML_i->Prop))->(qML_mu->(qML_i->Prop)))) scott_ess_QML_mu) (fun (Phi:(qML_mu->(qML_i->Prop))) (X:qML_mu) (W:qML_i)=> ((and ((Phi X) W)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X) W)->(forall (V2:qML_i) (Z:qML_mu), (((Phi Z) V2)->((Y Z) V2))))))))
% 0.08/0.52 FOF formula (forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), ((((scott_P X3) W2)->False)->((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2))) of role axiom named fact_5_A1b
% 0.08/0.52 A new axiom: (forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), ((((scott_P X3) W2)->False)->((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)))
% 0.08/0.52 FOF formula (forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))) (Xa:(qML_mu->(qML_i->Prop))), (((and ((scott_P X3) W2)) (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->((Xa Xb) V3))))->((scott_P Xa) W2))) of role axiom named fact_6_A2
% 0.08/0.52 A new axiom: (forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))) (Xa:(qML_mu->(qML_i->Prop))), (((and ((scott_P X3) W2)) (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->((Xa Xb) V3))))->((scott_P Xa) W2)))
% 0.08/0.52 FOF formula (forall (X_1:qML_i), ((scott_P scott_NE_QML_mu) X_1)) of role axiom named fact_7_A5
% 0.08/0.52 A new axiom: (forall (X_1:qML_i), ((scott_P scott_NE_QML_mu) X_1))
% 0.08/0.52 FOF formula (forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False))) of role axiom named fact_8_A1a
% 31.14/31.31 A new axiom: (forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False)))
% 31.14/31.31 FOF formula (((eq (qML_mu->(qML_i->Prop))) scott_NE_QML_mu) (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), ((((scott_ess_QML_mu Y) X) W)->(forall (V2:qML_i), ((ex qML_mu) (fun (Z:qML_mu)=> ((Y Z) V2)))))))) of role axiom named fact_9_NE__def
% 31.14/31.31 A new axiom: (((eq (qML_mu->(qML_i->Prop))) scott_NE_QML_mu) (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), ((((scott_ess_QML_mu Y) X) W)->(forall (V2:qML_i), ((ex qML_mu) (fun (Z:qML_mu)=> ((Y Z) V2))))))))
% 31.14/31.31 FOF formula (forall (W3:qML_i) (X2:qML_mu), ((or (((scott_G X2) W3)->False)) (((scott_ess_QML_mu scott_G) X2) W3))) of role conjecture named conj_0
% 31.14/31.31 Conjecture to prove = (forall (W3:qML_i) (X2:qML_mu), ((or (((scott_G X2) W3)->False)) (((scott_ess_QML_mu scott_G) X2) W3))):Prop
% 31.14/31.31 Parameter qML_mu_DUMMY:qML_mu.
% 31.14/31.31 Parameter qML_i_DUMMY:qML_i.
% 31.14/31.31 We need to prove ['(forall (W3:qML_i) (X2:qML_mu), ((or (((scott_G X2) W3)->False)) (((scott_ess_QML_mu scott_G) X2) W3)))']
% 31.14/31.31 Parameter qML_mu:Type.
% 31.14/31.31 Parameter qML_i:Type.
% 31.14/31.31 Parameter scott_G:(qML_mu->(qML_i->Prop)).
% 31.14/31.31 Parameter scott_NE_QML_mu:(qML_mu->(qML_i->Prop)).
% 31.14/31.31 Parameter scott_P:((qML_mu->(qML_i->Prop))->(qML_i->Prop)).
% 31.14/31.31 Parameter scott_ess_QML_mu:((qML_mu->(qML_i->Prop))->(qML_mu->(qML_i->Prop))).
% 31.14/31.31 Axiom fact_0_G__def:(((eq (qML_mu->(qML_i->Prop))) scott_G) (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))).
% 31.14/31.31 Axiom fact_1_T3:(qML_i->(forall (V:qML_i), ((ex qML_mu) (fun (X2:qML_mu)=> ((scott_G X2) V))))).
% 31.14/31.31 Axiom fact_2_A4:(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P X3) W2)->(forall (X_1:qML_i), ((scott_P X3) X_1)))).
% 31.14/31.31 Axiom fact_3_A3:(forall (X_1:qML_i), ((scott_P scott_G) X_1)).
% 31.14/31.31 Axiom fact_4_ess__def:(((eq ((qML_mu->(qML_i->Prop))->(qML_mu->(qML_i->Prop)))) scott_ess_QML_mu) (fun (Phi:(qML_mu->(qML_i->Prop))) (X:qML_mu) (W:qML_i)=> ((and ((Phi X) W)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X) W)->(forall (V2:qML_i) (Z:qML_mu), (((Phi Z) V2)->((Y Z) V2)))))))).
% 31.14/31.31 Axiom fact_5_A1b:(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), ((((scott_P X3) W2)->False)->((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2))).
% 31.14/31.31 Axiom fact_6_A2:(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))) (Xa:(qML_mu->(qML_i->Prop))), (((and ((scott_P X3) W2)) (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->((Xa Xb) V3))))->((scott_P Xa) W2))).
% 31.14/31.31 Axiom fact_7_A5:(forall (X_1:qML_i), ((scott_P scott_NE_QML_mu) X_1)).
% 31.14/31.31 Axiom fact_8_A1a:(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False))).
% 31.14/31.31 Axiom fact_9_NE__def:(((eq (qML_mu->(qML_i->Prop))) scott_NE_QML_mu) (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), ((((scott_ess_QML_mu Y) X) W)->(forall (V2:qML_i), ((ex qML_mu) (fun (Z:qML_mu)=> ((Y Z) V2)))))))).
% 31.14/31.31 Trying to prove (forall (W3:qML_i) (X2:qML_mu), ((or (((scott_G X2) W3)->False)) (((scott_ess_QML_mu scott_G) X2) W3)))
% 31.14/31.31 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 31.14/31.31 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 31.14/31.31 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 31.14/31.31 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 31.14/31.31 Found eq_ref00:=(eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)):(((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) (((scott_ess_QML_mu scott_G) X2) W3))
% 31.14/31.31 Found (eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 31.14/31.31 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 31.14/31.31 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 31.14/31.31 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 31.14/31.31 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 31.14/31.31 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 31.14/31.31 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 42.95/43.14 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 42.95/43.14 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 42.95/43.14 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 42.95/43.14 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 42.95/43.14 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 42.95/43.14 Found x1:((X3 Xb) V3)
% 42.95/43.14 Found x1 as proof of False
% 42.95/43.14 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 42.95/43.14 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 42.95/43.14 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 42.95/43.14 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 42.95/43.14 Found x1:((X3 Xb) V3)
% 42.95/43.14 Found x1 as proof of False
% 42.95/43.14 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 42.95/43.14 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 42.95/43.14 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 42.95/43.14 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 42.95/43.14 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 42.95/43.14 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 42.95/43.14 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 42.95/43.14 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 42.95/43.14 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 42.95/43.14 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 42.95/43.14 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 42.95/43.14 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 42.95/43.14 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 42.95/43.14 Found eq_ref00:=(eq_ref0 (((scott_G X2) W3)->False)):(((eq Prop) (((scott_G X2) W3)->False)) (((scott_G X2) W3)->False))
% 42.95/43.14 Found (eq_ref0 (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 42.95/43.14 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 42.95/43.14 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 42.95/43.14 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 42.95/43.14 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 42.95/43.14 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 42.95/43.14 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 42.95/43.14 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 42.95/43.14 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 42.95/43.14 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 42.95/43.14 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 42.95/43.14 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 42.95/43.14 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 42.95/43.14 Found eq_ref00:=(eq_ref0 (not ((scott_G X2) W3))):(((eq Prop) (not ((scott_G X2) W3))) (not ((scott_G X2) W3)))
% 42.95/43.14 Found (eq_ref0 (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 42.95/43.14 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 42.95/43.14 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 42.95/43.14 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 42.95/43.14 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 42.95/43.14 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 42.95/43.14 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 42.95/43.14 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 42.95/43.14 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 42.95/43.14 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 45.96/46.13 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 45.96/46.13 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 45.96/46.13 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 45.96/46.13 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 45.96/46.13 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 45.96/46.13 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 45.96/46.13 Found eq_ref00:=(eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))):(((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))))
% 45.96/46.13 Found (eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 45.96/46.13 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 45.96/46.13 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 45.96/46.13 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 45.96/46.13 Found eq_ref00:=(eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))):(((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))))
% 45.96/46.13 Found (eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 45.96/46.13 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 45.96/46.13 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 45.96/46.13 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 45.96/46.13 Found fact_3_A30:=(fact_3_A3 W3):((scott_P scott_G) W3)
% 45.96/46.13 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 45.96/46.13 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 52.34/52.53 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 52.34/52.53 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 52.34/52.53 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 52.34/52.53 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 52.34/52.53 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 52.34/52.53 Found eq_ref00:=(eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))):(((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))))
% 52.34/52.53 Found (eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 52.34/52.53 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 52.34/52.53 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 52.34/52.53 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 52.34/52.53 Found x1:((X3 Xb) V3)
% 52.34/52.53 Found x1 as proof of False
% 52.34/52.53 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 52.34/52.53 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 52.34/52.53 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 52.34/52.53 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 52.34/52.53 Found x1:((X3 Xb) V3)
% 52.34/52.53 Found x1 as proof of False
% 52.34/52.53 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 52.34/52.53 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 52.34/52.53 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 52.34/52.53 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 52.34/52.53 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 52.34/52.53 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 52.34/52.53 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 52.34/52.53 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 52.34/52.53 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 52.34/52.53 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 52.34/52.53 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 52.34/52.53 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 52.34/52.53 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 52.34/52.53 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 52.34/52.53 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 52.34/52.53 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 52.34/52.53 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 52.34/52.53 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 52.34/52.53 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 52.34/52.53 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 52.34/52.53 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 52.34/52.53 Found eq_ref00:=(eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))):(((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))))
% 53.07/53.25 Found (eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 53.07/53.25 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 53.07/53.25 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 53.07/53.25 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 53.07/53.25 Found eq_ref00:=(eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))):(((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))))
% 53.07/53.25 Found (eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 53.07/53.25 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 53.07/53.25 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 53.07/53.25 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 53.07/53.25 Found eq_ref00:=(eq_ref0 (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)):(((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3))
% 53.07/53.25 Found (eq_ref0 (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) b)
% 53.07/53.25 Found ((eq_ref Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) b)
% 62.47/62.66 Found ((eq_ref Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) b)
% 62.47/62.66 Found ((eq_ref Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) b)
% 62.47/62.66 Found eq_ref00:=(eq_ref0 (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)):(((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3))
% 62.47/62.66 Found (eq_ref0 (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) b)
% 62.47/62.66 Found ((eq_ref Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) b)
% 62.47/62.66 Found ((eq_ref Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) b)
% 62.47/62.66 Found ((eq_ref Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu (fun (X:qML_mu) (W:qML_i)=> (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W)->((Y X) W))))) X2) W3)) b)
% 62.47/62.66 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 62.47/62.66 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 62.47/62.66 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 62.47/62.66 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 62.47/62.66 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 62.47/62.66 Found fact_3_A30:=(fact_3_A3 W3):((scott_P scott_G) W3)
% 62.47/62.66 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 62.47/62.66 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 62.47/62.66 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 62.47/62.66 Found fact_3_A30:=(fact_3_A3 W3):((scott_P scott_G) W3)
% 62.47/62.66 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 62.47/62.66 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 62.47/62.66 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 62.47/62.66 Found fact_3_A30:=(fact_3_A3 W3):((scott_P scott_G) W3)
% 62.47/62.66 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 62.47/62.66 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 62.47/62.66 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 62.47/62.66 Found x1:((X3 Xb) V3)
% 62.47/62.66 Found x1 as proof of False
% 62.47/62.66 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 62.47/62.66 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found x1:((X3 Xb) V3)
% 65.56/65.77 Found x1 as proof of False
% 65.56/65.77 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 65.56/65.77 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found x1:((X3 Xb) V3)
% 65.56/65.77 Found x1 as proof of False
% 65.56/65.77 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 65.56/65.77 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 65.56/65.77 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 65.56/65.77 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 65.56/65.77 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 65.56/65.77 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 65.56/65.77 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 65.56/65.77 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 65.56/65.77 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 65.56/65.77 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 65.56/65.77 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 65.56/65.77 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 65.56/65.77 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 65.56/65.77 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 65.56/65.77 Found eq_ref00:=(eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)):(((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) (((scott_ess_QML_mu scott_G) X2) W3))
% 65.56/65.77 Found (eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 65.56/65.77 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 65.56/65.77 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 65.56/65.77 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 65.56/65.77 Found x1:((X3 Xb) V3)
% 65.56/65.77 Found x1 as proof of False
% 65.56/65.77 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 65.56/65.77 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found eq_ref00:=(eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)):(((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) (((scott_ess_QML_mu scott_G) X2) W3))
% 65.56/65.77 Found (eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 65.56/65.77 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 65.56/65.77 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 65.56/65.77 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 65.56/65.77 Found x1:((X3 Xb) V3)
% 65.56/65.77 Found x1 as proof of False
% 65.56/65.77 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 65.56/65.77 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 65.56/65.77 Found eq_ref00:=(eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)):(((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) (((scott_ess_QML_mu scott_G) X2) W3))
% 65.56/65.77 Found (eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 69.65/69.85 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 69.65/69.85 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 69.65/69.85 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 69.65/69.85 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 69.65/69.85 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 69.65/69.85 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 69.65/69.85 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 69.65/69.85 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 69.65/69.85 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 69.65/69.85 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 69.65/69.85 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 69.65/69.85 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 69.65/69.85 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 69.65/69.85 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 69.65/69.85 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 69.65/69.85 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 69.65/69.85 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 69.65/69.85 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 69.65/69.85 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 69.65/69.85 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 69.65/69.85 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 69.65/69.85 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 69.65/69.85 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 69.65/69.85 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 69.65/69.85 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 69.65/69.85 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 69.65/69.85 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 71.28/71.42 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 71.28/71.42 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 71.28/71.42 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 71.28/71.42 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 71.28/71.42 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 71.28/71.42 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 71.28/71.42 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 72.77/72.93 Found eq_ref00:=(eq_ref0 (((scott_G X2) W3)->False)):(((eq Prop) (((scott_G X2) W3)->False)) (((scott_G X2) W3)->False))
% 72.77/72.93 Found (eq_ref0 (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 72.77/72.93 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 72.77/72.93 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 72.77/72.93 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 72.77/72.93 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 72.77/72.93 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 72.77/72.93 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 72.77/72.93 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 72.77/72.93 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 72.77/72.93 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 72.77/72.93 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 72.77/72.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 72.77/72.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 72.77/72.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 72.77/72.93 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 72.77/72.93 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 72.77/72.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 72.77/72.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 72.77/72.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 72.77/72.93 Found eq_ref00:=(eq_ref0 (((scott_G X2) W3)->False)):(((eq Prop) (((scott_G X2) W3)->False)) (((scott_G X2) W3)->False))
% 72.77/72.93 Found (eq_ref0 (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 72.77/72.93 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 72.77/72.93 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 72.77/72.93 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 80.48/80.64 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 80.48/80.64 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 80.48/80.64 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 80.48/80.64 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 80.48/80.64 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 80.48/80.64 Found eq_ref00:=(eq_ref0 (((scott_G X2) W3)->False)):(((eq Prop) (((scott_G X2) W3)->False)) (((scott_G X2) W3)->False))
% 80.48/80.64 Found (eq_ref0 (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 80.48/80.64 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 80.48/80.64 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 80.48/80.64 Found ((eq_ref Prop) (((scott_G X2) W3)->False)) as proof of (((eq Prop) (((scott_G X2) W3)->False)) b)
% 80.48/80.64 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 80.48/80.64 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 80.48/80.64 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 80.48/80.64 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 80.48/80.64 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 80.48/80.64 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 80.48/80.64 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 82.76/82.98 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 82.76/82.98 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 82.76/82.98 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 82.76/82.98 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 82.76/82.98 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 82.76/82.98 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 84.89/85.02 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 84.89/85.02 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 84.89/85.02 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 84.89/85.02 Found eq_ref00:=(eq_ref0 (not ((scott_G X2) W3))):(((eq Prop) (not ((scott_G X2) W3))) (not ((scott_G X2) W3)))
% 84.90/85.02 Found (eq_ref0 (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 84.90/85.02 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 84.90/85.02 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 84.90/85.02 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 84.90/85.02 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 84.90/85.02 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 84.90/85.02 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 84.90/85.02 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 84.90/85.02 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 84.90/85.02 Found eq_ref00:=(eq_ref0 (not ((scott_G X2) W3))):(((eq Prop) (not ((scott_G X2) W3))) (not ((scott_G X2) W3)))
% 84.90/85.02 Found (eq_ref0 (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 84.90/85.02 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 84.90/85.02 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 84.90/85.02 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 84.90/85.02 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 84.90/85.02 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 84.90/85.02 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 84.90/85.02 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 84.90/85.02 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 84.90/85.02 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 84.90/85.02 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 84.90/85.02 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 84.90/85.02 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 84.90/85.02 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 84.90/85.02 Found eq_ref00:=(eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))):(((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))))
% 96.87/97.01 Found (eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 96.87/97.01 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 96.87/97.01 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 96.87/97.01 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 96.87/97.01 Found eq_ref00:=(eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))):(((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))))
% 96.87/97.01 Found (eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 96.87/97.01 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 96.87/97.01 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 96.87/97.01 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 96.87/97.01 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 96.87/97.01 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 96.87/97.01 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 96.87/97.01 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 96.87/97.01 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 96.87/97.01 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 96.87/97.01 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 96.87/97.01 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 96.87/97.01 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 96.87/97.01 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 96.87/97.01 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 96.87/97.01 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 96.87/97.01 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 96.87/97.01 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 96.87/97.01 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 96.87/97.01 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 105.07/105.28 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 105.07/105.28 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 105.07/105.28 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 105.07/105.28 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 105.07/105.28 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 105.07/105.28 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 105.07/105.28 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 105.07/105.28 Found fact_8_A1a:(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False)))
% 105.07/105.28 Instantiate: b:=(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False))):Prop
% 105.07/105.28 Found fact_8_A1a as proof of b
% 105.07/105.28 Found fact_8_A1a:(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False)))
% 105.07/105.28 Instantiate: b:=(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False))):Prop
% 105.07/105.28 Found fact_8_A1a as proof of b
% 105.07/105.28 Found fact_8_A1a:(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False)))
% 105.07/105.28 Instantiate: b:=(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False))):Prop
% 105.07/105.28 Found fact_8_A1a as proof of b
% 105.07/105.28 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 105.07/105.28 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found eq_ref00:=(eq_ref0 (not ((scott_G X2) W3))):(((eq Prop) (not ((scott_G X2) W3))) (not ((scott_G X2) W3)))
% 105.07/105.28 Found (eq_ref0 (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 105.07/105.28 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 105.07/105.28 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 105.07/105.28 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 105.07/105.28 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 105.07/105.28 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 105.07/105.28 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 105.07/105.28 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 105.07/105.28 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 105.07/105.28 Found eq_ref00:=(eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))):(((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))))
% 105.07/105.28 Found (eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 105.07/105.28 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 105.07/105.28 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 110.27/110.41 Found eq_ref00:=(eq_ref0 (not ((scott_G X2) W3))):(((eq Prop) (not ((scott_G X2) W3))) (not ((scott_G X2) W3)))
% 110.27/110.41 Found (eq_ref0 (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 110.27/110.41 Found eq_ref00:=(eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))):(((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))))
% 110.27/110.41 Found (eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 110.27/110.41 Found eq_ref00:=(eq_ref0 (not ((scott_G X2) W3))):(((eq Prop) (not ((scott_G X2) W3))) (not ((scott_G X2) W3)))
% 110.27/110.41 Found (eq_ref0 (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 110.27/110.41 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 110.27/110.41 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 110.27/110.41 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 110.27/110.41 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 110.27/110.41 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 110.27/110.41 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 110.27/110.41 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 110.27/110.41 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 110.27/110.41 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 110.27/110.41 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 110.27/110.41 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 110.27/110.41 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 110.27/110.41 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 110.27/110.41 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 110.27/110.41 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 110.27/110.41 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 110.27/110.41 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 110.27/110.41 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 110.27/110.41 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 113.58/113.76 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 113.58/113.76 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 113.58/113.76 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 113.58/113.76 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 113.58/113.76 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 113.58/113.76 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 113.58/113.76 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 113.58/113.76 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 113.58/113.76 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 113.58/113.76 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 113.58/113.76 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 113.58/113.76 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 113.58/113.76 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 113.58/113.76 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 113.58/113.76 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 113.58/113.76 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 113.58/113.76 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 113.58/113.76 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 113.58/113.76 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 113.58/113.76 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 113.58/113.76 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 113.58/113.76 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 113.58/113.76 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 113.58/113.76 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 113.58/113.76 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 113.58/113.76 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 113.58/113.76 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 113.58/113.76 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 113.58/113.76 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 113.58/113.76 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 113.58/113.76 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 113.58/113.76 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 113.58/113.76 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 113.58/113.76 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 113.58/113.76 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 114.78/114.93 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 114.78/114.93 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 114.78/114.93 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 114.78/114.93 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 114.78/114.93 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 114.78/114.93 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 114.78/114.93 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 114.78/114.93 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 114.78/114.93 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 114.78/114.93 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 114.78/114.93 Found eq_ref00:=(eq_ref0 ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))):(((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))))
% 114.78/114.93 Found (eq_ref0 ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.69/115.87 Found ((eq_ref Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.69/115.87 Found ((eq_ref Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.69/115.87 Found ((eq_ref Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.69/115.87 Found fact_8_A1a:(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False)))
% 115.69/115.87 Instantiate: b:=(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False))):Prop
% 115.69/115.87 Found fact_8_A1a as proof of b
% 115.69/115.87 Found x1:((X3 Xb) V3)
% 115.69/115.87 Found x1 as proof of False
% 115.69/115.87 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 115.69/115.87 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 115.69/115.87 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 115.69/115.87 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 115.69/115.87 Found eq_ref00:=(eq_ref0 ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))):(((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))))
% 115.69/115.87 Found (eq_ref0 ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.69/115.87 Found ((eq_ref Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.99/116.14 Found ((eq_ref Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.99/116.14 Found ((eq_ref Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.99/116.14 Found eq_ref00:=(eq_ref0 ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))):(((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))))
% 115.99/116.14 Found (eq_ref0 ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.99/116.14 Found ((eq_ref Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.99/116.14 Found ((eq_ref Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 115.99/116.14 Found ((eq_ref Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) as proof of (((eq Prop) ((and (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))) b)
% 120.06/120.18 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 120.06/120.18 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 120.06/120.18 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 120.06/120.18 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 120.06/120.18 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 120.06/120.18 Found fact_8_A1a:(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False)))
% 120.06/120.18 Instantiate: b:=(forall (W2:qML_i) (X3:(qML_mu->(qML_i->Prop))), (((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)->(((scott_P X3) W2)->False))):Prop
% 120.06/120.18 Found fact_8_A1a as proof of b
% 120.06/120.18 Found x1:((X3 Xb) V3)
% 120.06/120.18 Found x1 as proof of False
% 120.06/120.18 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 120.06/120.18 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 120.06/120.18 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 120.06/120.18 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 120.06/120.18 Found x1:((X3 Xb) V3)
% 120.06/120.18 Found x1 as proof of False
% 120.06/120.18 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 120.06/120.18 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 120.06/120.18 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 120.06/120.18 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 120.06/120.18 Found fact_3_A30:=(fact_3_A3 W3):((scott_P scott_G) W3)
% 120.06/120.18 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 120.06/120.18 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 120.06/120.18 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 120.06/120.18 Found fact_3_A30:=(fact_3_A3 W3):((scott_P scott_G) W3)
% 120.06/120.18 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 120.06/120.18 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 120.06/120.18 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 120.06/120.18 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 120.06/120.18 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 120.06/120.18 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 120.06/120.18 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 120.06/120.18 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 120.06/120.18 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 120.06/120.18 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 120.06/120.18 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 120.06/120.18 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 120.06/120.18 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 120.06/120.18 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 120.06/120.18 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 129.50/129.70 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 129.50/129.70 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 129.50/129.70 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 129.50/129.70 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 129.50/129.70 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 129.50/129.70 Found x1:((X3 Xb) V3)
% 129.50/129.70 Found x1 as proof of False
% 129.50/129.70 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 129.50/129.70 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 129.50/129.70 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 129.50/129.70 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 129.50/129.70 Found x1:((X3 Xb) V3)
% 129.50/129.70 Found x1 as proof of False
% 129.50/129.70 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 129.50/129.70 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 129.50/129.70 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 129.50/129.70 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 129.50/129.70 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 129.50/129.70 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 129.50/129.70 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 129.50/129.70 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 129.50/129.70 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 129.50/129.70 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 129.50/129.70 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 138.79/138.91 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 138.79/138.91 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 138.79/138.91 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 138.79/138.91 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 138.79/138.91 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 138.79/138.91 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 138.79/138.91 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 138.79/138.91 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 138.79/138.91 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 138.79/138.91 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 138.79/138.91 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 138.79/138.91 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 138.79/138.91 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 138.79/138.91 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 138.79/138.91 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 138.79/138.91 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 144.49/144.66 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 144.49/144.66 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 144.49/144.66 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 144.49/144.66 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 144.49/144.66 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 144.49/144.66 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 144.49/144.66 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 144.49/144.66 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 144.49/144.66 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 144.49/144.66 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 144.49/144.66 Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 144.49/144.66 Found classical_choice as proof of a
% 144.49/144.66 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 144.49/144.66 Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 144.49/144.66 Found classical_choice as proof of a
% 144.49/144.66 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 145.00/145.16 Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 145.00/145.16 Found classical_choice as proof of a
% 145.00/145.16 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 145.00/145.16 Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 145.00/145.16 Found classical_choice as proof of b
% 145.00/145.16 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 151.11/151.24 Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 151.11/151.24 Found classical_choice as proof of b
% 151.11/151.24 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 151.11/151.24 Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 151.11/151.24 Found classical_choice as proof of b
% 151.11/151.24 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 151.11/151.24 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 151.11/151.24 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 151.11/151.24 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 151.11/151.24 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 151.11/151.24 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 151.11/151.24 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 151.11/151.24 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 151.11/151.24 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 151.11/151.24 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 151.11/151.24 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 151.11/151.24 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 151.11/151.24 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 151.11/151.24 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 153.19/153.36 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 153.19/153.36 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 153.19/153.36 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 153.19/153.36 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 153.19/153.36 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 153.19/153.36 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 153.19/153.36 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 153.19/153.36 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 155.67/155.82 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 155.67/155.82 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 155.67/155.82 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 155.67/155.82 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 155.67/155.82 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 155.67/155.82 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 155.67/155.82 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 155.67/155.82 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 155.67/155.82 Found eq_ref00:=(eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)):(((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) (((scott_ess_QML_mu scott_G) X2) W3))
% 157.49/157.66 Found (eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 157.49/157.66 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 157.49/157.66 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 157.49/157.66 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 157.49/157.66 Found eq_ref00:=(eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)):(((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) (((scott_ess_QML_mu scott_G) X2) W3))
% 157.49/157.66 Found (eq_ref0 (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 157.49/157.66 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 157.49/157.66 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 157.49/157.66 Found ((eq_ref Prop) (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (((eq Prop) (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 157.49/157.66 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 157.49/157.66 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 157.49/157.66 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 157.49/157.66 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 157.49/157.66 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 157.49/157.66 Found eq_ref00:=(eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))):(((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))))
% 157.49/157.66 Found (eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 157.49/157.66 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 157.49/157.66 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 158.70/158.84 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 158.70/158.84 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 158.70/158.84 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 158.70/158.84 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 158.70/158.84 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 158.70/158.84 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 158.70/158.84 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 158.70/158.84 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 158.70/158.84 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 158.70/158.84 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 160.39/160.55 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 160.39/160.55 Found eq_ref00:=(eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))):(((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))))
% 160.39/160.55 Found (eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 160.39/160.55 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 160.39/160.55 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 160.39/160.55 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 160.39/160.55 Found eq_ref00:=(eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))):(((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3)))))
% 160.39/160.55 Found (eq_ref0 (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 160.39/160.55 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 160.39/160.55 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 160.39/160.55 Found ((eq_ref Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) as proof of (((eq Prop) (not (forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) W3)->((Y X2) W3))))) b)
% 160.39/160.55 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 160.39/160.55 Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 160.39/160.55 Found classical_choice as proof of a
% 162.20/162.34 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 162.20/162.94 Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 162.20/162.94 Found classical_choice as proof of a
% 162.20/162.94 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 162.20/162.94 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 162.20/162.94 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 162.20/162.94 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 162.20/162.94 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 162.20/162.94 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 162.20/162.94 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 162.20/162.94 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 162.20/162.94 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 162.20/162.94 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 162.20/162.94 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 162.20/162.94 Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 162.20/162.94 Found classical_choice as proof of b
% 162.20/162.94 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 187.04/187.19 Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 187.04/187.19 Found classical_choice as proof of b
% 187.04/187.19 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 187.04/187.19 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 187.04/187.19 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 187.04/187.19 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 187.04/187.19 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 187.04/187.19 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 187.04/187.19 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 187.04/187.19 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 187.04/187.19 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 187.04/187.19 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 187.04/187.19 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)))
% 187.04/187.19 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 187.04/187.19 Found iff_sym as proof of b
% 187.04/187.19 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 187.04/187.19 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 187.04/187.19 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 187.04/187.19 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 187.04/187.19 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 187.04/187.19 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 187.04/187.19 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 187.04/187.19 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 187.04/187.19 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 187.04/187.19 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)))
% 192.31/192.43 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 192.31/192.43 Found iff_sym as proof of b
% 192.31/192.43 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)))
% 192.31/192.43 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 192.31/192.43 Found iff_sym as proof of b
% 192.31/192.43 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 192.31/192.43 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 192.31/192.43 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 192.31/192.43 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 192.31/192.43 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 192.31/192.43 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 192.31/192.43 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 192.31/192.43 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 192.31/192.43 Found x0:=(x X3):(((scott_P X3) W3)->((X3 X2) W3))
% 192.31/192.43 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 200.87/200.99 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 200.87/200.99 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 200.87/200.99 Found (x X3) as proof of (((scott_P X3) W2)->False)
% 200.87/200.99 Found (fact_5_A1b00 (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 200.87/200.99 Found ((fact_5_A1b0 X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 200.87/200.99 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 200.87/200.99 Found (((fact_5_A1b W2) X3) (x X3)) as proof of ((scott_P (fun (Y:qML_mu) (Z:qML_i)=> (((X3 Y) Z)->False))) W2)
% 200.87/200.99 Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 200.87/200.99 Instantiate: a:=(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c)))):Prop
% 200.87/200.99 Found eq_trans as proof of a
% 200.87/200.99 Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 200.87/200.99 Instantiate: a:=(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c)))):Prop
% 200.87/200.99 Found eq_trans as proof of a
% 200.87/200.99 Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 200.87/200.99 Instantiate: a:=(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c)))):Prop
% 200.87/200.99 Found eq_trans as proof of a
% 200.87/200.99 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 200.87/200.99 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 200.87/200.99 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 200.87/200.99 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 200.87/200.99 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 200.87/200.99 Found eq_ref00:=(eq_ref0 a):(((eq qML_i) a) a)
% 200.87/200.99 Found (eq_ref0 a) as proof of (((eq qML_i) a) W3)
% 200.87/200.99 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 200.87/200.99 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 200.87/200.99 Found ((eq_ref qML_i) a) as proof of (((eq qML_i) a) W3)
% 200.87/200.99 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 200.87/200.99 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 200.87/200.99 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 200.87/200.99 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 200.87/200.99 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 200.87/200.99 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 200.87/200.99 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 200.87/200.99 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 200.87/200.99 Found x1:((X3 Xb) V3)
% 200.87/200.99 Found x1 as proof of False
% 200.87/200.99 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 200.87/200.99 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 200.87/200.99 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 200.87/200.99 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 200.87/200.99 Found x1:((X3 Xb) V3)
% 200.87/200.99 Found x1 as proof of False
% 200.87/200.99 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 200.87/200.99 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 200.87/200.99 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 200.87/200.99 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 200.87/200.99 Found eq_ref00:=(eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))):(((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))))
% 200.87/200.99 Found (eq_ref0 ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 202.29/202.40 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 202.29/202.40 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 202.29/202.40 Found ((eq_ref Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) as proof of (((eq Prop) ((and ((scott_G X2) W3)) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))) b)
% 202.29/202.40 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 202.29/202.40 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 202.29/202.40 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 202.29/202.40 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 202.29/202.40 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 202.29/202.40 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 202.29/202.40 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 203.78/203.90 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 203.78/203.90 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 203.78/203.90 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 203.78/203.90 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2))))))
% 203.78/203.90 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 203.78/203.90 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 203.78/203.90 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 203.78/203.90 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), ((forall (Y:(qML_mu->(qML_i->Prop))), (((scott_P Y) V2)->((Y Z) V2)))->((Y Z) V2)))))) b)
% 203.78/203.90 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 203.78/203.90 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 203.78/203.90 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 203.78/203.90 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 203.78/203.90 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 229.37/229.50 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 229.37/229.50 Instantiate: a:=(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c)))):Prop
% 229.37/229.50 Found eq_trans as proof of a
% 229.37/229.50 Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 229.37/229.50 Instantiate: a:=(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c)))):Prop
% 229.37/229.50 Found eq_trans as proof of a
% 229.37/229.50 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 229.37/229.50 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 229.37/229.50 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 229.37/229.50 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 229.37/229.50 Found classic0:=(classic (not ((scott_G X2) W3))):((or (not ((scott_G X2) W3))) (not (not ((scott_G X2) W3))))
% 229.37/229.50 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 229.37/229.50 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 229.37/229.50 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 229.37/229.50 Found (classic (not ((scott_G X2) W3))) as proof of (P b)
% 229.37/229.50 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)))
% 229.37/229.50 Instantiate: a:=(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B))):Prop
% 229.37/229.50 Found or_second as proof of a
% 229.37/229.50 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)))
% 229.37/229.50 Instantiate: a:=(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B))):Prop
% 229.37/229.50 Found or_second as proof of a
% 229.37/229.50 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)))
% 229.37/229.50 Instantiate: a:=(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B))):Prop
% 229.37/229.50 Found or_second as proof of a
% 229.37/229.50 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 229.37/229.50 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 229.37/229.50 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 229.37/229.50 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 229.37/229.50 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 229.37/229.50 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 229.37/229.50 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 229.37/229.50 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 238.16/238.28 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)))
% 238.16/238.28 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B))):Prop
% 238.16/238.28 Found or_second as proof of b
% 238.16/238.28 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)))
% 238.16/238.28 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B))):Prop
% 238.16/238.28 Found or_second as proof of b
% 238.16/238.28 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)))
% 238.16/238.28 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B))):Prop
% 238.16/238.28 Found or_second as proof of b
% 238.16/238.28 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 238.16/238.28 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 238.16/238.28 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 238.16/238.28 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 238.16/238.28 Found fact_3_A30:=(fact_3_A3 W3):((scott_P scott_G) W3)
% 238.16/238.28 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 238.16/238.28 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 238.16/238.28 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 238.16/238.28 Found x1:((X3 Xb) V3)
% 238.16/238.28 Found x1 as proof of False
% 238.16/238.28 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 238.16/238.28 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 238.16/238.28 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 238.16/238.28 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 238.16/238.28 Found x1:((X3 Xb) V3)
% 238.16/238.28 Found x1 as proof of False
% 238.16/238.28 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 238.16/238.28 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 238.16/238.28 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 238.16/238.28 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 238.16/238.28 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 238.16/238.28 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 238.16/238.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 238.16/238.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 238.16/238.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 238.16/238.28 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 238.16/238.28 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 238.16/238.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 238.16/238.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 238.16/238.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 238.16/238.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 238.16/238.28 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 238.16/238.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 238.16/238.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 238.16/238.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 238.16/238.28 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 238.16/238.28 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 238.16/238.28 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 238.16/238.28 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 238.16/238.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 238.16/238.28 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 238.16/238.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 238.16/238.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 238.16/238.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 244.72/244.84 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 244.72/244.84 Found (eq_ref0 a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 244.72/244.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 244.72/244.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 244.72/244.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 244.72/244.84 Found classic0:=(classic (((scott_ess_QML_mu scott_G) X2) W3)):((or (((scott_ess_QML_mu scott_G) X2) W3)) (not (((scott_ess_QML_mu scott_G) X2) W3)))
% 244.72/244.84 Found (classic (((scott_ess_QML_mu scott_G) X2) W3)) as proof of ((or (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 244.72/244.84 Found (classic (((scott_ess_QML_mu scott_G) X2) W3)) as proof of ((or (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 244.72/244.84 Found (classic (((scott_ess_QML_mu scott_G) X2) W3)) as proof of ((or (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 244.72/244.84 Found (classic (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (P b)
% 244.72/244.84 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 244.72/244.84 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 244.72/244.84 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 244.72/244.84 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 244.72/244.84 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 244.72/244.84 Found eq_ref00:=(eq_ref0 (not ((scott_G X2) W3))):(((eq Prop) (not ((scott_G X2) W3))) (not ((scott_G X2) W3)))
% 244.72/244.84 Found (eq_ref0 (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 244.72/244.84 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 244.72/244.84 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 244.72/244.84 Found ((eq_ref Prop) (not ((scott_G X2) W3))) as proof of (((eq Prop) (not ((scott_G X2) W3))) b)
% 244.72/244.84 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 244.72/244.84 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 244.72/244.84 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 244.72/244.84 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 244.72/244.84 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 244.72/244.84 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 244.72/244.84 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 244.72/244.84 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 244.72/244.84 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 244.72/244.84 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 244.72/244.84 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 244.72/244.84 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 244.72/244.84 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 267.84/267.93 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 267.84/267.93 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 267.84/267.93 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 267.84/267.93 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 267.84/267.93 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 267.84/267.93 Found x1:((X3 Xb) V3)
% 267.84/267.93 Found x1 as proof of False
% 267.84/267.93 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 267.84/267.93 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 267.84/267.93 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 267.84/267.93 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 267.84/267.93 Found x1:((X3 Xb) V3)
% 267.84/267.93 Found x1 as proof of False
% 267.84/267.93 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 267.84/267.93 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 267.84/267.93 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 267.84/267.93 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 267.84/267.93 Found eq_ref00:=(eq_ref0 V2):(((eq qML_i) V2) V2)
% 267.84/267.93 Found (eq_ref0 V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found eq_ref00:=(eq_ref0 V2):(((eq qML_i) V2) V2)
% 267.84/267.93 Found (eq_ref0 V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found eq_ref00:=(eq_ref0 V2):(((eq qML_i) V2) V2)
% 267.84/267.93 Found (eq_ref0 V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 267.84/267.93 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found classic0:=(classic (((scott_ess_QML_mu scott_G) X2) W3)):((or (((scott_ess_QML_mu scott_G) X2) W3)) (not (((scott_ess_QML_mu scott_G) X2) W3)))
% 267.84/267.93 Found (classic (((scott_ess_QML_mu scott_G) X2) W3)) as proof of ((or (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 267.84/267.93 Found (classic (((scott_ess_QML_mu scott_G) X2) W3)) as proof of ((or (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 267.84/267.93 Found (classic (((scott_ess_QML_mu scott_G) X2) W3)) as proof of ((or (((scott_ess_QML_mu scott_G) X2) W3)) b)
% 267.84/267.93 Found (classic (((scott_ess_QML_mu scott_G) X2) W3)) as proof of (P b)
% 267.84/267.93 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 267.84/267.93 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 267.84/267.93 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 267.84/267.93 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 267.84/267.93 Found eq_ref00:=(eq_ref0 V2):(((eq qML_i) V2) V2)
% 267.84/267.93 Found (eq_ref0 V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found eq_ref00:=(eq_ref0 V2):(((eq qML_i) V2) V2)
% 267.84/267.93 Found (eq_ref0 V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 267.84/267.93 Found x1:((X3 Xb) V3)
% 267.84/267.93 Found x1 as proof of False
% 267.84/267.93 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 267.84/267.93 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 270.86/271.00 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 270.86/271.00 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 270.86/271.00 Found x1:((X3 Xb) V3)
% 270.86/271.00 Found x1 as proof of False
% 270.86/271.00 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 270.86/271.00 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 270.86/271.00 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 270.86/271.00 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 270.86/271.00 Found x1:((X3 Xb) V3)
% 270.86/271.00 Found x1 as proof of False
% 270.86/271.00 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 270.86/271.00 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 270.86/271.00 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 270.86/271.00 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 270.86/271.00 Found classic0:=(classic (((scott_G X2) W3)->False)):((or (((scott_G X2) W3)->False)) (not (((scott_G X2) W3)->False)))
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of ((or (((scott_G X2) W3)->False)) b)
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of ((or (((scott_G X2) W3)->False)) b)
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of ((or (((scott_G X2) W3)->False)) b)
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of (P b)
% 270.86/271.00 Found classic0:=(classic (((scott_G X2) W3)->False)):((or (((scott_G X2) W3)->False)) (not (((scott_G X2) W3)->False)))
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of ((or (((scott_G X2) W3)->False)) b)
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of ((or (((scott_G X2) W3)->False)) b)
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of ((or (((scott_G X2) W3)->False)) b)
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of (P b)
% 270.86/271.00 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun
% (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 270.86/271.00 Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 270.86/271.00 Found classical_choice as proof of b
% 270.86/271.00 Found classic0:=(classic (((scott_G X2) W3)->False)):((or (((scott_G X2) W3)->False)) (not (((scott_G X2) W3)->False)))
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of ((or (((scott_G X2) W3)->False)) b)
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of ((or (((scott_G X2) W3)->False)) b)
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of ((or (((scott_G X2) W3)->False)) b)
% 270.86/271.00 Found (classic (((scott_G X2) W3)->False)) as proof of (P b)
% 270.86/271.00 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 283.25/283.35 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 283.25/283.35 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 283.25/283.35 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 283.25/283.35 Found fact_7_A50:=(fact_7_A5 W2):((scott_P scott_NE_QML_mu) W2)
% 283.25/283.35 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 283.25/283.35 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 283.25/283.35 Found (fact_7_A5 W2) as proof of ((scott_P X3) W2)
% 283.25/283.35 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 283.25/283.35 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 283.25/283.35 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 283.25/283.35 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 283.25/283.35 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 283.25/283.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 283.25/283.35 Found (eq_ref0 b) as proof of (((eq Prop) b) (((scott_ess_QML_mu scott_G) X2) W3))
% 283.25/283.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((scott_ess_QML_mu scott_G) X2) W3))
% 283.25/283.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((scott_ess_QML_mu scott_G) X2) W3))
% 283.25/283.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((scott_ess_QML_mu scott_G) X2) W3))
% 283.25/283.35 Found fact_3_A30:=(fact_3_A3 W2):((scott_P scott_G) W2)
% 283.25/283.35 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 283.25/283.35 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 283.25/283.35 Found (fact_3_A3 W2) as proof of ((scott_P X3) W2)
% 283.25/283.35 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 283.25/283.35 Instantiate: a:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 283.25/283.35 Found proj1 as proof of a
% 283.25/283.35 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 283.25/283.35 Instantiate: a:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 283.25/283.35 Found proj1 as proof of a
% 283.25/283.35 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 283.25/283.35 Instantiate: a:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 283.25/283.35 Found proj1 as proof of a
% 283.25/283.35 Found classic0:=(classic (not ((scott_G X2) W3))):((or (not ((scott_G X2) W3))) (not (not ((scott_G X2) W3))))
% 283.25/283.35 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 283.25/283.35 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 283.25/283.35 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 283.25/283.35 Found (classic (not ((scott_G X2) W3))) as proof of (P b)
% 283.25/283.35 Found classic0:=(classic (not ((scott_G X2) W3))):((or (not ((scott_G X2) W3))) (not (not ((scott_G X2) W3))))
% 283.25/283.35 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 283.25/283.35 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 283.25/283.35 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 283.25/283.35 Found (classic (not ((scott_G X2) W3))) as proof of (P b)
% 283.25/283.35 Found x1:((X3 Xb) V3)
% 283.25/283.35 Found x1 as proof of False
% 283.25/283.35 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 283.25/283.35 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 283.25/283.35 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 283.25/283.35 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 283.25/283.35 Found x1:((X3 Xb) V3)
% 283.25/283.35 Found x1 as proof of False
% 283.25/283.35 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 283.25/283.35 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 283.25/283.35 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 283.25/283.35 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 283.25/283.35 Found fact_7_A50:=(fact_7_A5 W3):((scott_P scott_NE_QML_mu) W3)
% 283.25/283.35 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 283.25/283.35 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 283.25/283.35 Found (fact_7_A5 W3) as proof of ((scott_P X3) W3)
% 283.25/283.35 Found fact_3_A30:=(fact_3_A3 W3):((scott_P scott_G) W3)
% 283.25/283.35 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 283.25/283.35 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 283.25/283.35 Found (fact_3_A3 W3) as proof of ((scott_P X3) W3)
% 283.25/283.35 Found fact_3_A30:=(fact_3_A3 V2):((scott_P scott_G) V2)
% 283.25/283.35 Found (fact_3_A3 V2) as proof of ((scott_P X3) V2)
% 283.25/283.35 Found (fact_3_A3 V2) as proof of ((scott_P X3) V2)
% 283.25/283.35 Found (fact_3_A3 V2) as proof of ((scott_P X3) V2)
% 283.25/283.35 Found fact_3_A30:=(fact_3_A3 V2):((scott_P scott_G) V2)
% 283.25/283.35 Found (fact_3_A3 V2) as proof of ((scott_P X3) V2)
% 296.19/296.28 Found (fact_3_A3 V2) as proof of ((scott_P X3) V2)
% 296.19/296.28 Found (fact_3_A3 V2) as proof of ((scott_P X3) V2)
% 296.19/296.28 Found fact_7_A50:=(fact_7_A5 V2):((scott_P scott_NE_QML_mu) V2)
% 296.19/296.28 Found (fact_7_A5 V2) as proof of ((scott_P X3) V2)
% 296.19/296.28 Found (fact_7_A5 V2) as proof of ((scott_P X3) V2)
% 296.19/296.28 Found (fact_7_A5 V2) as proof of ((scott_P X3) V2)
% 296.19/296.28 Found x1:((X3 Xb) V3)
% 296.19/296.28 Found x1 as proof of False
% 296.19/296.28 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 296.19/296.28 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 296.19/296.28 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 296.19/296.28 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 296.19/296.28 Found x1:((X3 Xb) V3)
% 296.19/296.28 Found x1 as proof of False
% 296.19/296.28 Found (fun (x1:((X3 Xb) V3))=> x1) as proof of False
% 296.19/296.28 Found (fun (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (((X3 Xb) V3)->False)
% 296.19/296.28 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->False))
% 296.19/296.28 Found (fun (V3:qML_i) (Xb:qML_mu) (x1:((X3 Xb) V3))=> x1) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->False))
% 296.19/296.28 Found eq_ref00:=(eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))):(((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2))))))
% 296.19/296.28 Found (eq_ref0 (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 296.19/296.28 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 296.19/296.28 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 296.19/296.28 Found ((eq_ref Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) as proof of (((eq Prop) (forall (Y:(qML_mu->(qML_i->Prop))), (((Y X2) W3)->(forall (V2:qML_i) (Z:qML_mu), (((scott_G Z) V2)->((Y Z) V2)))))) b)
% 296.19/296.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 296.19/296.28 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 296.19/296.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 296.19/296.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 296.19/296.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 296.19/296.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 296.19/296.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (((scott_G X2) W3)->False))
% 296.19/296.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((scott_G X2) W3)->False))
% 296.19/296.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((scott_G X2) W3)->False))
% 296.19/296.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((scott_G X2) W3)->False))
% 296.19/296.28 Found classic0:=(classic (not ((scott_G X2) W3))):((or (not ((scott_G X2) W3))) (not (not ((scott_G X2) W3))))
% 296.19/296.28 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 296.19/296.28 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 296.19/296.28 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 296.19/296.28 Found (classic (not ((scott_G X2) W3))) as proof of (P b)
% 296.19/296.28 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 296.19/296.28 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 296.19/296.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 296.19/296.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 296.19/296.28 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 296.19/296.28 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 296.19/296.28 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 298.14/298.24 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 298.14/298.24 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 298.14/298.24 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 298.14/298.24 Found eq_ref00:=(eq_ref0 W3):(((eq qML_i) W3) W3)
% 298.14/298.24 Found (eq_ref0 W3) as proof of (((eq qML_i) W3) b)
% 298.14/298.24 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 298.14/298.24 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 298.14/298.24 Found ((eq_ref qML_i) W3) as proof of (((eq qML_i) W3) b)
% 298.14/298.24 Found classic0:=(classic (not ((scott_G X2) W3))):((or (not ((scott_G X2) W3))) (not (not ((scott_G X2) W3))))
% 298.14/298.24 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 298.14/298.24 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 298.14/298.24 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 298.14/298.24 Found (classic (not ((scott_G X2) W3))) as proof of (P b)
% 298.14/298.24 Found classic0:=(classic (not ((scott_G X2) W3))):((or (not ((scott_G X2) W3))) (not (not ((scott_G X2) W3))))
% 298.14/298.24 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 298.14/298.24 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 298.14/298.24 Found (classic (not ((scott_G X2) W3))) as proof of ((or (not ((scott_G X2) W3))) b)
% 298.14/298.24 Found (classic (not ((scott_G X2) W3))) as proof of (P b)
% 298.14/298.24 Found fact_9_NE__def0:=(fact_9_NE__def (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3))):(((X3 Xb) V3)->((X3 Xb) V3))
% 298.14/298.24 Found (fact_9_NE__def (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3))) as proof of (((X3 Xb) V3)->((Y Xb) V3))
% 298.14/298.24 Found (fact_9_NE__def (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3))) as proof of (((X3 Xb) V3)->((Y Xb) V3))
% 298.14/298.24 Found (fun (Xb:qML_mu)=> (fact_9_NE__def (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3)))) as proof of (((X3 Xb) V3)->((Y Xb) V3))
% 298.14/298.24 Found (fun (V3:qML_i) (Xb:qML_mu)=> (fact_9_NE__def (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3)))) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->((Y Xb) V3)))
% 298.14/298.24 Found (fun (V3:qML_i) (Xb:qML_mu)=> (fact_9_NE__def (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3)))) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->((Y Xb) V3)))
% 298.14/298.24 Found fact_9_NE__def__eq_sym0:=(fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3))):(((X3 Xb) V3)->((X3 Xb) V3))
% 298.14/298.24 Found (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3))) as proof of (((X3 Xb) V3)->((Y Xb) V3))
% 298.14/298.24 Found (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3))) as proof of (((X3 Xb) V3)->((Y Xb) V3))
% 298.14/298.24 Found (fun (Xb:qML_mu)=> (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3)))) as proof of (((X3 Xb) V3)->((Y Xb) V3))
% 298.14/298.24 Found (fun (V3:qML_i) (Xb:qML_mu)=> (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3)))) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->((Y Xb) V3)))
% 298.14/298.24 Found (fun (V3:qML_i) (Xb:qML_mu)=> (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3)))) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->((Y Xb) V3)))
% 298.14/298.24 Found fact_9_NE__def__eq_sym0:=(fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3))):(((X3 Xb) V3)->((X3 Xb) V3))
% 298.14/298.24 Found (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3))) as proof of (((X3 Xb) V3)->((Y Xb) V3))
% 298.14/298.24 Found (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3))) as proof of (((X3 Xb) V3)->((Y Xb) V3))
% 298.14/298.24 Found (fun (Xb:qML_mu)=> (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3)))) as proof of (((X3 Xb) V3)->((Y Xb) V3))
% 298.14/298.24 Found (fun (V3:qML_i) (Xb:qML_mu)=> (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3)))) as proof of (forall (Xb:qML_mu), (((X3 Xb) V3)->((Y Xb) V3)))
% 298.14/298.24 Found (fun (V3:qML_i) (Xb:qML_mu)=> (fact_9_NE__def__eq_sym (fun (x:(qML_mu->(qML_i->Prop)))=> ((X3 Xb) V3)))) as proof of (forall (V3:qML_i) (Xb:qML_mu), (((X3 Xb) V3)->((Y Xb) V3)))
% 298.14/298.24 Found eq_ref00:=(eq_ref0 V2):(((eq qML_i) V2) V2)
% 298.14/298.24 Found (eq_ref0 V2) as proof of (((eq qML_i) V2) b)
% 298.14/298.24 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 298.14/298.24 Found ((eq_ref qML_i) V2) as proof of (((eq qML_i) V2) b)
% 298.14/298.24 Found (
%------------------------------------------------------------------------------