%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : PHI004^1 : TPTP v6.1.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n095.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:28:40 EDT 2014

% Result   : Timeout 300.11s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : PHI004^1 : TPTP v6.1.0. Released v6.1.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n095.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:24:26 CDT 2014
% % CPUTime  : 300.11 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL016^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x1520fc8>, <kernel.Type object at 0x1520c20>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0x1520bd8>, <kernel.DependentProduct object at 0x1713758>) of role type named meq_ind_type
% Using role type
% Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% FOF formula (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) of role definition named meq_ind
% A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% FOF formula (<kernel.Constant object at 0x15209e0>, <kernel.DependentProduct object at 0x1713ea8>) of role type named mtrue_type
% Using role type
% Declaring mtrue:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% Defined: mtrue:=(fun (W:fofType)=> True)
% FOF formula (<kernel.Constant object at 0x15209e0>, <kernel.DependentProduct object at 0x1713f38>) of role type named mfalse_type
% Using role type
% Declaring mfalse:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mfalse) (fun (W:fofType)=> False)) of role definition named mfalse
% A new definition: (((eq (fofType->Prop)) mfalse) (fun (W:fofType)=> False))
% Defined: mfalse:=(fun (W:fofType)=> False)
% FOF formula (<kernel.Constant object at 0x1713320>, <kernel.DependentProduct object at 0x1713f38>) of role type named mnot_type
% Using role type
% Declaring mnot:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% FOF formula (<kernel.Constant object at 0x1713248>, <kernel.DependentProduct object at 0x1713200>) of role type named mor_type
% Using role type
% Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))) of role definition named mor
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))))
% Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% FOF formula (<kernel.Constant object at 0x1713f38>, <kernel.DependentProduct object at 0x17150e0>) of role type named mand_type
% Using role type
% Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((and (Phi W)) (Psi W)))) of role definition named mand
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((and (Phi W)) (Psi W))))
% Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((and (Phi W)) (Psi W)))
% FOF formula (<kernel.Constant object at 0x1713f38>, <kernel.DependentProduct object at 0x1951ef0>) of role type named mimplies_type
% Using role type
% Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Phi W)->(Psi W)))) of role definition named mimplies
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Phi W)->(Psi W))))
% Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Phi W)->(Psi W)))
% FOF formula (<kernel.Constant object at 0x1713f38>, <kernel.DependentProduct object at 0x1714050>) of role type named mimplied_type
% Using role type
% Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Psi W)->(Phi W)))) of role definition named mimplied
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Psi W)->(Phi W))))
% Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Psi W)->(Phi W)))
% FOF formula (<kernel.Constant object at 0x1951ef0>, <kernel.DependentProduct object at 0x1714b48>) of role type named mequiv_type
% Using role type
% Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((iff (Phi W)) (Psi W)))) of role definition named mequiv
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((iff (Phi W)) (Psi W))))
% Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((iff (Phi W)) (Psi W)))
% FOF formula (<kernel.Constant object at 0x1951ef0>, <kernel.DependentProduct object at 0x17155a8>) of role type named mxor_type
% Using role type
% Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or ((and (Phi W)) ((Psi W)->False))) ((and ((Phi W)->False)) (Psi W))))) of role definition named mxor
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or ((and (Phi W)) ((Psi W)->False))) ((and ((Phi W)->False)) (Psi W)))))
% Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or ((and (Phi W)) ((Psi W)->False))) ((and ((Phi W)->False)) (Psi W))))
% FOF formula (<kernel.Constant object at 0x17140e0>, <kernel.DependentProduct object at 0x1715c68>) of role type named mforall_ind_type
% Using role type
% Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) of role definition named mforall_ind
% A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% FOF formula (<kernel.Constant object at 0x1714b48>, <kernel.DependentProduct object at 0x1715560>) of role type named mforall_indset_type
% Using role type
% Declaring mforall_indset:(((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))) mforall_indset) (fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> (forall (X:(mu->(fofType->Prop))), ((Phi X) W)))) of role definition named mforall_indset
% A new definition: (((eq (((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))) mforall_indset) (fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> (forall (X:(mu->(fofType->Prop))), ((Phi X) W))))
% Defined: mforall_indset:=(fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> (forall (X:(mu->(fofType->Prop))), ((Phi X) W)))
% FOF formula (<kernel.Constant object at 0x1715b90>, <kernel.DependentProduct object at 0x15055a8>) of role type named mforall_prop_type
% Using role type
% Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))) of role definition named mforall_prop
% A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))))
% Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% FOF formula (<kernel.Constant object at 0x17158c0>, <kernel.DependentProduct object at 0x15056c8>) of role type named mexists_ind_type
% Using role type
% Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> ((ex mu) (fun (X:mu)=> ((Phi X) W))))) of role definition named mexists_ind
% A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> ((ex mu) (fun (X:mu)=> ((Phi X) W)))))
% Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> ((ex mu) (fun (X:mu)=> ((Phi X) W))))
% FOF formula (<kernel.Constant object at 0x1715560>, <kernel.DependentProduct object at 0x15055a8>) of role type named mexists_indset_type
% Using role type
% Declaring mexists_indset:(((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))) mexists_indset) (fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> ((ex (mu->(fofType->Prop))) (fun (X:(mu->(fofType->Prop)))=> ((Phi X) W))))) of role definition named mexists_indset
% A new definition: (((eq (((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))) mexists_indset) (fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> ((ex (mu->(fofType->Prop))) (fun (X:(mu->(fofType->Prop)))=> ((Phi X) W)))))
% Defined: mexists_indset:=(fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> ((ex (mu->(fofType->Prop))) (fun (X:(mu->(fofType->Prop)))=> ((Phi X) W))))
% FOF formula (<kernel.Constant object at 0x15055a8>, <kernel.DependentProduct object at 0x1505710>) of role type named mexists_prop_type
% Using role type
% Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> ((ex (fofType->Prop)) (fun (P:(fofType->Prop))=> ((Phi P) W))))) of role definition named mexists_prop
% A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> ((ex (fofType->Prop)) (fun (P:(fofType->Prop))=> ((Phi P) W)))))
% Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> ((ex (fofType->Prop)) (fun (P:(fofType->Prop))=> ((Phi P) W))))
% FOF formula (<kernel.Constant object at 0x1505680>, <kernel.DependentProduct object at 0x1505878>) of role type named mbox_generic_type
% Using role type
% Declaring mbox_generic:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox_generic) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))) of role definition named mbox_generic
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox_generic) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))))
% Defined: mbox_generic:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% FOF formula (<kernel.Constant object at 0x15055a8>, <kernel.DependentProduct object at 0x1505a28>) of role type named mdia_generic_type
% Using role type
% Declaring mdia_generic:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia_generic) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> ((ex fofType) (fun (V:fofType)=> ((and ((R W) V)) (Phi V)))))) of role definition named mdia_generic
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia_generic) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> ((ex fofType) (fun (V:fofType)=> ((and ((R W) V)) (Phi V))))))
% Defined: mdia_generic:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> ((ex fofType) (fun (V:fofType)=> ((and ((R W) V)) (Phi V)))))
% FOF formula (<kernel.Constant object at 0x1505680>, <kernel.DependentProduct object at 0x1505830>) of role type named rel_type
% Using role type
% Declaring rel:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1505d88>, <kernel.DependentProduct object at 0x1505488>) of role type named mbox_type
% Using role type
% Declaring mbox:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox) (mbox_generic rel)) of role definition named mbox
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox) (mbox_generic rel))
% Defined: mbox:=(mbox_generic rel)
% FOF formula (<kernel.Constant object at 0x1505d88>, <kernel.DependentProduct object at 0x1505488>) of role type named mdia_type
% Using role type
% Declaring mdia:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia) (mdia_generic rel)) of role definition named mdia
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia) (mdia_generic rel))
% Defined: mdia:=(mdia_generic rel)
% FOF formula (<kernel.Constant object at 0x15059e0>, <kernel.DependentProduct object at 0x1505cf8>) of role type named mvalid_type
% Using role type
% Declaring mvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% FOF formula (<kernel.Constant object at 0x1505d88>, <kernel.DependentProduct object at 0x1505b90>) of role type named minvalid_type
% Using role type
% Declaring minvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/PHI001^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x15203f8>, <kernel.DependentProduct object at 0x15205a8>) of role type named positive_tp
% Using role type
% Declaring positive:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1520830>, <kernel.DependentProduct object at 0x1520440>) of role type named god_tp
% Using role type
% Declaring god:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x15204d0>, <kernel.DependentProduct object at 0x1520dd0>) of role type named essence_tp
% Using role type
% Declaring essence:((mu->(fofType->Prop))->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x15207e8>, <kernel.DependentProduct object at 0x15205a8>) of role type named necessary_existence_tp
% Using role type
% Declaring necessary_existence:(mu->(fofType->Prop))
% FOF formula (mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mequiv (positive (fun (X:mu)=> (mnot (Phi X))))) (mnot (positive Phi)))))) of role axiom named axA1
% A new axiom: (mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mequiv (positive (fun (X:mu)=> (mnot (Phi X))))) (mnot (positive Phi))))))
% FOF formula (mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies ((mand (positive Phi)) (mbox (mforall_ind (fun (X:mu)=> ((mimplies (Phi X)) (Psi X))))))) (positive Psi))))))) of role axiom named axA2
% A new axiom: (mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies ((mand (positive Phi)) (mbox (mforall_ind (fun (X:mu)=> ((mimplies (Phi X)) (Psi X))))))) (positive Psi)))))))
% FOF formula (((eq (mu->(fofType->Prop))) god) (fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (Phi X)))))) of role definition named defD1
% A new definition: (((eq (mu->(fofType->Prop))) god) (fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (Phi X))))))
% Defined: god:=(fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (Phi X)))))
% FOF formula (mvalid (positive god)) of role axiom named axA3
% A new axiom: (mvalid (positive god))
% FOF formula (mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (mbox (positive Phi)))))) of role axiom named axA4
% A new axiom: (mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (mbox (positive Phi))))))
% FOF formula (((eq ((mu->(fofType->Prop))->(mu->(fofType->Prop)))) essence) (fun (Phi:(mu->(fofType->Prop))) (X:mu)=> ((mand (Phi X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (Phi Y)) (Psi Y))))))))))) of role definition named defD2
% A new definition: (((eq ((mu->(fofType->Prop))->(mu->(fofType->Prop)))) essence) (fun (Phi:(mu->(fofType->Prop))) (X:mu)=> ((mand (Phi X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (Phi Y)) (Psi Y)))))))))))
% Defined: essence:=(fun (Phi:(mu->(fofType->Prop))) (X:mu)=> ((mand (Phi X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (Phi Y)) (Psi Y))))))))))
% FOF formula (((eq (mu->(fofType->Prop))) necessary_existence) (fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies ((essence Phi) X)) (mbox (mexists_ind (fun (Y:mu)=> (Phi Y))))))))) of role definition named defD3
% A new definition: (((eq (mu->(fofType->Prop))) necessary_existence) (fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies ((essence Phi) X)) (mbox (mexists_ind (fun (Y:mu)=> (Phi Y)))))))))
% Defined: necessary_existence:=(fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies ((essence Phi) X)) (mbox (mexists_ind (fun (Y:mu)=> (Phi Y))))))))
% FOF formula (mvalid (positive necessary_existence)) of role axiom named axA5
% A new axiom: (mvalid (positive necessary_existence))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mimplies (god X)) ((essence god) X))))) of role conjecture named thmT2
% Conjecture to prove = (mvalid (mforall_ind (fun (X:mu)=> ((mimplies (god X)) ((essence god) X))))):Prop
% Parameter mu_DUMMY:mu.
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(mvalid (mforall_ind (fun (X:mu)=> ((mimplies (god X)) ((essence god) X)))))']
% Parameter mu:Type.
% Parameter fofType:Type.
% Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% Definition mfalse:=(fun (W:fofType)=> False):(fofType->Prop).
% Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((and (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Phi W)->(Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Psi W)->(Phi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((iff (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or ((and (Phi W)) ((Psi W)->False))) ((and ((Phi W)->False)) (Psi W)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mforall_indset:=(fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> (forall (X:(mu->(fofType->Prop))), ((Phi X) W))):(((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop)).
% Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> ((ex mu) (fun (X:mu)=> ((Phi X) W)))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_indset:=(fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> ((ex (mu->(fofType->Prop))) (fun (X:(mu->(fofType->Prop)))=> ((Phi X) W)))):(((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> ((ex (fofType->Prop)) (fun (P:(fofType->Prop))=> ((Phi P) W)))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mbox_generic:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Definition mdia_generic:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> ((ex fofType) (fun (V:fofType)=> ((and ((R W) V)) (Phi V))))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Parameter rel:(fofType->(fofType->Prop)).
% Definition mbox:=(mbox_generic rel):((fofType->Prop)->(fofType->Prop)).
% Definition mdia:=(mdia_generic rel):((fofType->Prop)->(fofType->Prop)).
% Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% Parameter positive:((mu->(fofType->Prop))->(fofType->Prop)).
% Definition god:=(fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (Phi X))))):(mu->(fofType->Prop)).
% Definition essence:=(fun (Phi:(mu->(fofType->Prop))) (X:mu)=> ((mand (Phi X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (Phi Y)) (Psi Y)))))))))):((mu->(fofType->Prop))->(mu->(fofType->Prop))).
% Definition necessary_existence:=(fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies ((essence Phi) X)) (mbox (mexists_ind (fun (Y:mu)=> (Phi Y)))))))):(mu->(fofType->Prop)).
% Axiom axA1:(mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mequiv (positive (fun (X:mu)=> (mnot (Phi X))))) (mnot (positive Phi)))))).
% Axiom axA2:(mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies ((mand (positive Phi)) (mbox (mforall_ind (fun (X:mu)=> ((mimplies (Phi X)) (Psi X))))))) (positive Psi))))))).
% Axiom axA3:(mvalid (positive god)).
% Axiom axA4:(mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (mbox (positive Phi)))))).
% Axiom axA5:(mvalid (positive necessary_existence)).
% Trying to prove (mvalid (mforall_ind (fun (X:mu)=> ((mimplies (god X)) ((essence god) X)))))
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found (axA5 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x:((god X) W)
% Found x as proof of ((god X) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((fun (x10:fofType)=> ((and ((god X1) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10)))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (fun (x10:fofType)=> ((and ((god X) x10)) ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) x10))))))) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))))) W)
% Found x2:((X1 X2) V)
% Found x2 as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (x2:((X1 X2) V))=> x2) as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))) X2) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)
% Found (or_intror00 (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found x1:((X1 X2) V)
% Found x1 as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (x1:((X1 X2) V))=> x1) as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) X2) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)
% Found (or_intror00 (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))))) W)
% Found x2:((X1 X2) V)
% Found x2 as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (x2:((X1 X2) V))=> x2) as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))) X2) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)
% Found (or_intror00 (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) W)
% Found x2:((X1 X2) V)
% Found x2 as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (x2:((X1 X2) V))=> x2) as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))) X2) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)
% Found (or_intror00 (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X1 X2) V)
% Found x1 as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (x1:((X1 X2) V))=> x1) as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) X2) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)
% Found (or_intror00 (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found x1:((X1 X2) V)
% Found x1 as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (x1:((X1 X2) V))=> x1) as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) X2) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)
% Found (or_intror00 (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))))) W)
% Found x2:((X1 X2) V)
% Found x2 as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (x2:((X1 X2) V))=> x2) as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))) X2) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)
% Found (or_intror00 (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) W)
% Found x1:((X1 X2) V)
% Found x1 as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (x1:((X1 X2) V))=> x1) as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) X2) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)
% Found (or_intror00 (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))))) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X2) W)
% Found (axA5 W) as proof of ((positive X2) W)
% Found (axA5 W) as proof of ((positive X2) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))))) W)
% Found axA50:=(axA5 V):((positive necessary_existence) V)
% Found (axA5 V) as proof of ((positive X2) V)
% Found (axA5 V) as proof of ((positive X2) V)
% Found (axA5 V) as proof of ((positive X2) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (x1:((X0 X1) V))=> x1) as proof of ((mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X1)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))) X1) V)
% Found (fun (X1:mu) (x1:((X0 X1) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)
% Found (or_intror00 (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y))))))))))) V)) (fun (X1:mu) (x1:((X0 X1) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X0 X)) (mforall_indset (fun (Psi:(mu->(fofType->Prop)))=> ((mimplies (Psi X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (Psi Y)))))))))))) W)
% Found x2:((X1 X2) V)
% Found x2 as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (x2:((X1 X2) V))=> x2) as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))) X2) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)
% Found (or_intror00 (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) W)
% Found x2:((X1 X2) V)
% Found x2 as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (x2:((X1 X2) V))=> x2) as proof of ((mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))) X2) V)
% Found (fun (X2:mu) (x2:((X1 X2) V))=> x2) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)
% Found (or_intror00 (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) V)) (fun (X2:mu) (x2:((X1 X2) V))=> x2))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found x1:((X1 X2) V)
% Found x1 as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (x1:((X1 X2) V))=> x1) as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) X2) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)
% Found (or_intror00 (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))))) W)
% Found x1:((X1 X2) V)
% Found x1 as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (x1:((X1 X2) V))=> x1) as proof of (((mimplies (X0 X2)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of (((fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))) X2) V)
% Found (fun (X2:mu) (x1:((X1 X2) V))=> x1) as proof of ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)
% Found (or_intror00 (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found ((or_intror0 ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1)) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of (forall (V:fofType), ((or (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)))
% Found (fun (V:fofType)=> (((or_intror (((rel W) V)->False)) ((mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y))))))))) V)) (fun (X2:mu) (x1:((X1 X2) V))=> x1))) as proof of ((mbox (mforall_ind (fun (X:mu)=> ((mimplies (X1 X)) ((mimplies (X0 X)) (mbox (mforall_ind (fun (Y:mu)=> ((mimplies (god Y)) (X0 Y)))))))))) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found (axA3 W) as proof of ((positive X1) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found axA50:=(axA5 V):((positive necessary_existence) V)
% Found (axA5 V) as proof of ((positive X2) V)
% Found (axA5 V) as proof of ((positive X2) V)
% Found (axA5 V) as proof of ((positive X2) V)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found (axA5 W) as proof of ((positive X1) W)
% Found x1:((X0 X1) V)
% Found x1 as proof of ((god X1) V)
% Found axA50:=(axA5 W):((positive necessary_existence) W)
% Found (axA5 W) as proof of ((positive X2) W)
% Found (axA5 W) as proof of ((positive X2) W)
% Found (axA5 W) as proof of ((positive X2) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found (axA3 W) as proof of ((positive X2) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found (axA3 W) as proof of ((positive X0) W)
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive X0) W
% EOF
%------------------------------------------------------------------------------