TSTP Solution File: LCL602^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : LCL602^1 : TPTP v6.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n098.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 13:25:49 EDT 2014
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LCL602^1 : TPTP v6.1.0. Released v3.6.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n098.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 10:01:41 CDT 2014
% % CPUTime : 300.03
% 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/LCL008^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0xb20488>, <kernel.Constant object at 0xb203f8>) of role type named current_world
% Using role type
% Declaring current_world:fofType
% FOF formula (<kernel.Constant object at 0xb20488>, <kernel.DependentProduct object at 0xb20ea8>) of role type named prop_a
% Using role type
% Declaring prop_a:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0xb20d88>, <kernel.DependentProduct object at 0xb200e0>) of role type named prop_b
% Using role type
% Declaring prop_b:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0xb202d8>, <kernel.DependentProduct object at 0xb20e18>) of role type named prop_c
% Using role type
% Declaring prop_c:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0xb20d88>, <kernel.DependentProduct object at 0x93eef0>) of role type named mfalse_decl
% Using role type
% Declaring mfalse:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mfalse) (fun (X:fofType)=> False)) of role definition named mfalse
% A new definition: (((eq (fofType->Prop)) mfalse) (fun (X:fofType)=> False))
% Defined: mfalse:=(fun (X:fofType)=> False)
% FOF formula (<kernel.Constant object at 0xb20ea8>, <kernel.DependentProduct object at 0x93eef0>) of role type named mtrue_decl
% Using role type
% Declaring mtrue:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mtrue) (fun (X:fofType)=> True)) of role definition named mtrue
% A new definition: (((eq (fofType->Prop)) mtrue) (fun (X:fofType)=> True))
% Defined: mtrue:=(fun (X:fofType)=> True)
% FOF formula (<kernel.Constant object at 0xb20fc8>, <kernel.DependentProduct object at 0x93eb90>) of role type named mnot_decl
% Using role type
% Declaring mnot:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))) of role definition named mnot
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)))
% Defined: mnot:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))
% FOF formula (<kernel.Constant object at 0x93ee60>, <kernel.DependentProduct object at 0x93e9e0>) of role type named mor_decl
% Using role type
% Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))) of role definition named mor
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))))
% Defined: mor:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))
% FOF formula (<kernel.Constant object at 0x93eb90>, <kernel.DependentProduct object at 0x93ec20>) of role type named mand_decl
% Using role type
% Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))) of role definition named mand
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))))
% Defined: mand:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))
% FOF formula (<kernel.Constant object at 0x93ee60>, <kernel.DependentProduct object at 0x93e560>) of role type named mimpl_decl
% Using role type
% Declaring mimpl:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimpl) (fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V))) of role definition named mimpl
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimpl) (fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V)))
% Defined: mimpl:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V))
% FOF formula (<kernel.Constant object at 0x93ec20>, <kernel.DependentProduct object at 0x93ed40>) of role type named miff_decl
% Using role type
% Declaring miff:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) miff) (fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mand ((mimpl U) V)) ((mimpl V) U)))) of role definition named miff
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) miff) (fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mand ((mimpl U) V)) ((mimpl V) U))))
% Defined: miff:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mand ((mimpl U) V)) ((mimpl V) U)))
% FOF formula (<kernel.Constant object at 0x93ee60>, <kernel.DependentProduct object at 0x93eb90>) of role type named mbox_decl
% Using role type
% Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((R X) Y)->(P Y))))) of role definition named mbox
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((R X) Y)->(P Y)))))
% Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((R X) Y)->(P Y))))
% FOF formula (<kernel.Constant object at 0x93ec20>, <kernel.DependentProduct object at 0x93e680>) of role type named mdia_decl
% Using role type
% Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia) (fun (R:(fofType->(fofType->Prop))) (P:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R X) Y)) (P Y)))))) of role definition named mdia
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia) (fun (R:(fofType->(fofType->Prop))) (P:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R X) Y)) (P Y))))))
% Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (P:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R X) Y)) (P Y)))))
% FOF formula (<kernel.Constant object at 0x93ec20>, <kernel.Type object at 0x934950>) of role type named individuals_decl
% Using role type
% Declaring individuals:Type
% FOF formula (<kernel.Constant object at 0x93ec20>, <kernel.DependentProduct object at 0x934440>) of role type named mall_decl
% Using role type
% Declaring mall:((individuals->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((individuals->(fofType->Prop))->(fofType->Prop))) mall) (fun (P:(individuals->(fofType->Prop))) (W:fofType)=> (forall (X:individuals), ((P X) W)))) of role definition named mall
% A new definition: (((eq ((individuals->(fofType->Prop))->(fofType->Prop))) mall) (fun (P:(individuals->(fofType->Prop))) (W:fofType)=> (forall (X:individuals), ((P X) W))))
% Defined: mall:=(fun (P:(individuals->(fofType->Prop))) (W:fofType)=> (forall (X:individuals), ((P X) W)))
% FOF formula (<kernel.Constant object at 0x934440>, <kernel.DependentProduct object at 0x934488>) of role type named mexists_decl
% Using role type
% Declaring mexists:((individuals->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((individuals->(fofType->Prop))->(fofType->Prop))) mexists) (fun (P:(individuals->(fofType->Prop))) (W:fofType)=> ((ex individuals) (fun (X:individuals)=> ((P X) W))))) of role definition named mexists
% A new definition: (((eq ((individuals->(fofType->Prop))->(fofType->Prop))) mexists) (fun (P:(individuals->(fofType->Prop))) (W:fofType)=> ((ex individuals) (fun (X:individuals)=> ((P X) W)))))
% Defined: mexists:=(fun (P:(individuals->(fofType->Prop))) (W:fofType)=> ((ex individuals) (fun (X:individuals)=> ((P X) W))))
% FOF formula (<kernel.Constant object at 0x9348c0>, <kernel.DependentProduct object at 0x934710>) of role type named mvalid_decl
% Using role type
% Declaring mvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (P:(fofType->Prop))=> (forall (W:fofType), (P W)))) of role definition named mvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (P:(fofType->Prop))=> (forall (W:fofType), (P W))))
% Defined: mvalid:=(fun (P:(fofType->Prop))=> (forall (W:fofType), (P W)))
% FOF formula (<kernel.Constant object at 0x934440>, <kernel.DependentProduct object at 0x934200>) of role type named msatisfiable_decl
% Using role type
% Declaring msatisfiable:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (P W))))) of role definition named msatisfiable
% A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (P W)))))
% Defined: msatisfiable:=(fun (P:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (P W))))
% FOF formula (<kernel.Constant object at 0x9348c0>, <kernel.DependentProduct object at 0x934878>) of role type named mcountersatisfiable_decl
% Using role type
% Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((P W)->False))))) of role definition named mcountersatisfiable
% A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (P:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((P W)->False)))))
% Defined: mcountersatisfiable:=(fun (P:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((P W)->False))))
% FOF formula (<kernel.Constant object at 0x934440>, <kernel.DependentProduct object at 0x934a28>) of role type named minvalid_decl
% Using role type
% Declaring minvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (P:(fofType->Prop))=> (forall (W:fofType), ((P W)->False)))) of role definition named minvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (P:(fofType->Prop))=> (forall (W:fofType), ((P W)->False))))
% Defined: minvalid:=(fun (P:(fofType->Prop))=> (forall (W:fofType), ((P W)->False)))
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/SET008^2.ax, trying next directory
% FOF formula (<kernel.Constant object at 0xbd1200>, <kernel.DependentProduct object at 0xb20ef0>) of role type named cartesian_product_decl
% Using role type
% Declaring cartesian_product:((fofType->Prop)->((fofType->Prop)->(fofType->(fofType->Prop))))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->(fofType->Prop))))) cartesian_product) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType) (V:fofType)=> ((and (X U)) (Y V)))) of role definition named cartesian_product
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->(fofType->Prop))))) cartesian_product) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType) (V:fofType)=> ((and (X U)) (Y V))))
% Defined: cartesian_product:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType) (V:fofType)=> ((and (X U)) (Y V)))
% FOF formula (<kernel.Constant object at 0x80ce18>, <kernel.DependentProduct object at 0xb20f38>) of role type named pair_rel_decl
% Using role type
% Declaring pair_rel:(fofType->(fofType->(fofType->(fofType->Prop))))
% FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) pair_rel) (fun (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) V) Y)))) of role definition named pair_rel
% A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) pair_rel) (fun (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) V) Y))))
% Defined: pair_rel:=(fun (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) V) Y)))
% FOF formula (<kernel.Constant object at 0xb20f38>, <kernel.DependentProduct object at 0xb20e18>) of role type named id_rel_decl
% Using role type
% Declaring id_rel:((fofType->Prop)->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->(fofType->(fofType->Prop)))) id_rel) (fun (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) (((eq fofType) X) Y)))) of role definition named id_rel
% A new definition: (((eq ((fofType->Prop)->(fofType->(fofType->Prop)))) id_rel) (fun (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) (((eq fofType) X) Y))))
% Defined: id_rel:=(fun (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) (((eq fofType) X) Y)))
% FOF formula (<kernel.Constant object at 0xb20e18>, <kernel.DependentProduct object at 0xb20f38>) of role type named sub_rel_decl
% Using role type
% Declaring sub_rel:((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))) sub_rel) (fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R1 X) Y)->((R2 X) Y))))) of role definition named sub_rel
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))) sub_rel) (fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R1 X) Y)->((R2 X) Y)))))
% Defined: sub_rel:=(fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R1 X) Y)->((R2 X) Y))))
% FOF formula (<kernel.Constant object at 0xb20f38>, <kernel.DependentProduct object at 0xb202d8>) of role type named is_rel_on_decl
% Using role type
% Declaring is_rel_on:((fofType->(fofType->Prop))->((fofType->Prop)->((fofType->Prop)->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->((fofType->Prop)->Prop)))) is_rel_on) (fun (R:(fofType->(fofType->Prop))) (A:(fofType->Prop)) (B:(fofType->Prop))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((and (A X)) (B Y)))))) of role definition named is_rel_on
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->((fofType->Prop)->Prop)))) is_rel_on) (fun (R:(fofType->(fofType->Prop))) (A:(fofType->Prop)) (B:(fofType->Prop))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((and (A X)) (B Y))))))
% Defined: is_rel_on:=(fun (R:(fofType->(fofType->Prop))) (A:(fofType->Prop)) (B:(fofType->Prop))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((and (A X)) (B Y)))))
% FOF formula (<kernel.Constant object at 0xb202d8>, <kernel.DependentProduct object at 0xb203f8>) of role type named restrict_rel_domain_decl
% Using role type
% Declaring restrict_rel_domain:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))) restrict_rel_domain) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) ((R X) Y)))) of role definition named restrict_rel_domain
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))) restrict_rel_domain) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) ((R X) Y))))
% Defined: restrict_rel_domain:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) ((R X) Y)))
% FOF formula (<kernel.Constant object at 0xb203f8>, <kernel.DependentProduct object at 0xb204d0>) of role type named rel_diagonal_decl
% Using role type
% Declaring rel_diagonal:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) rel_diagonal) (fun (X:fofType) (Y:fofType)=> (((eq fofType) X) Y))) of role definition named rel_diagonal
% A new definition: (((eq (fofType->(fofType->Prop))) rel_diagonal) (fun (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)))
% Defined: rel_diagonal:=(fun (X:fofType) (Y:fofType)=> (((eq fofType) X) Y))
% FOF formula (<kernel.Constant object at 0xb202d8>, <kernel.DependentProduct object at 0x93e5a8>) of role type named rel_composition_decl
% Using role type
% Declaring rel_composition:((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) rel_composition) (fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop))) (X:fofType) (Z:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R1 X) Y)) ((R2 Y) Z)))))) of role definition named rel_composition
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) rel_composition) (fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop))) (X:fofType) (Z:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R1 X) Y)) ((R2 Y) Z))))))
% Defined: rel_composition:=(fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop))) (X:fofType) (Z:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R1 X) Y)) ((R2 Y) Z)))))
% FOF formula (<kernel.Constant object at 0xb203f8>, <kernel.DependentProduct object at 0x93eb00>) of role type named reflexive_decl
% Using role type
% Declaring reflexive:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) reflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X)))) of role definition named reflexive
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) reflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X))))
% Defined: reflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X)))
% FOF formula (<kernel.Constant object at 0xb203f8>, <kernel.DependentProduct object at 0x93e440>) of role type named irreflexive_decl
% Using role type
% Declaring irreflexive:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) irreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False)))) of role definition named irreflexive
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) irreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False))))
% Defined: irreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False)))
% FOF formula (<kernel.Constant object at 0xb203f8>, <kernel.DependentProduct object at 0x93eb00>) of role type named symmetric_decl
% Using role type
% Declaring symmetric:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) symmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X))))) of role definition named symmetric
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) symmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X)))))
% Defined: symmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X))))
% FOF formula (<kernel.Constant object at 0x93eb00>, <kernel.DependentProduct object at 0x93e4d0>) of role type named transitive_decl
% Using role type
% Declaring transitive:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) transitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z))))) of role definition named transitive
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) transitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))))
% Defined: transitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z))))
% FOF formula (<kernel.Constant object at 0x93e4d0>, <kernel.DependentProduct object at 0x93e5a8>) of role type named equiv_rel__decl
% Using role type
% Declaring equiv_rel:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) equiv_rel) (fun (R:(fofType->(fofType->Prop)))=> ((and ((and (reflexive R)) (symmetric R))) (transitive R)))) of role definition named equiv_rel
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) equiv_rel) (fun (R:(fofType->(fofType->Prop)))=> ((and ((and (reflexive R)) (symmetric R))) (transitive R))))
% Defined: equiv_rel:=(fun (R:(fofType->(fofType->Prop)))=> ((and ((and (reflexive R)) (symmetric R))) (transitive R)))
% FOF formula (<kernel.Constant object at 0x93e5a8>, <kernel.DependentProduct object at 0x93ed40>) of role type named rel_codomain_decl
% Using role type
% Declaring rel_codomain:((fofType->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_codomain) (fun (R:(fofType->(fofType->Prop))) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((R X) Y))))) of role definition named rel_codomain
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_codomain) (fun (R:(fofType->(fofType->Prop))) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((R X) Y)))))
% Defined: rel_codomain:=(fun (R:(fofType->(fofType->Prop))) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((R X) Y))))
% FOF formula (<kernel.Constant object at 0x93ed40>, <kernel.DependentProduct object at 0x93edd0>) of role type named rel_domain_decl
% Using role type
% Declaring rel_domain:((fofType->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_domain) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((R X) Y))))) of role definition named rel_domain
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_domain) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((R X) Y)))))
% Defined: rel_domain:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((R X) Y))))
% FOF formula (<kernel.Constant object at 0x93edd0>, <kernel.DependentProduct object at 0x93efc8>) of role type named rel_inverse_decl
% Using role type
% Declaring rel_inverse:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) rel_inverse) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X))) of role definition named rel_inverse
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) rel_inverse) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X)))
% Defined: rel_inverse:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X))
% FOF formula (<kernel.Constant object at 0x93e5f0>, <kernel.DependentProduct object at 0x93ed40>) of role type named equiv_classes_decl
% Using role type
% Declaring equiv_classes:((fofType->(fofType->Prop))->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->Prop))) equiv_classes) (fun (R:(fofType->(fofType->Prop))) (S1:(fofType->Prop))=> ((ex fofType) (fun (X:fofType)=> ((and (S1 X)) (forall (Y:fofType), ((iff (S1 Y)) ((R X) Y)))))))) of role definition named equiv_classes
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->Prop))) equiv_classes) (fun (R:(fofType->(fofType->Prop))) (S1:(fofType->Prop))=> ((ex fofType) (fun (X:fofType)=> ((and (S1 X)) (forall (Y:fofType), ((iff (S1 Y)) ((R X) Y))))))))
% Defined: equiv_classes:=(fun (R:(fofType->(fofType->Prop))) (S1:(fofType->Prop))=> ((ex fofType) (fun (X:fofType)=> ((and (S1 X)) (forall (Y:fofType), ((iff (S1 Y)) ((R X) Y)))))))
% FOF formula (<kernel.Constant object at 0x93ed40>, <kernel.DependentProduct object at 0x93e680>) of role type named restrict_rel_codomain_decl
% Using role type
% Declaring restrict_rel_codomain:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))) restrict_rel_codomain) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S Y)) ((R X) Y)))) of role definition named restrict_rel_codomain
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))) restrict_rel_codomain) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S Y)) ((R X) Y))))
% Defined: restrict_rel_codomain:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S Y)) ((R X) Y)))
% FOF formula (<kernel.Constant object at 0x93e4d0>, <kernel.DependentProduct object at 0x93ecb0>) of role type named rel_field_decl
% Using role type
% Declaring rel_field:((fofType->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_field) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((or ((rel_domain R) X)) ((rel_codomain R) X)))) of role definition named rel_field
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_field) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((or ((rel_domain R) X)) ((rel_codomain R) X))))
% Defined: rel_field:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((or ((rel_domain R) X)) ((rel_codomain R) X)))
% FOF formula (<kernel.Constant object at 0x93e5f0>, <kernel.DependentProduct object at 0x934488>) of role type named well_founded_decl
% Using role type
% Declaring well_founded:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) well_founded) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) W)->((X W)->False)))))))))) of role definition named well_founded
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) well_founded) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) W)->((X W)->False))))))))))
% Defined: well_founded:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) W)->((X W)->False)))))))))
% FOF formula (<kernel.Constant object at 0x93e440>, <kernel.DependentProduct object at 0x934638>) of role type named upwards_well_founded_decl
% Using role type
% Declaring upwards_well_founded:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) upwards_well_founded) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) Y)->((X W)->False)))))))))) of role definition named upwards_well_founded
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) upwards_well_founded) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) Y)->((X W)->False))))))))))
% Defined: upwards_well_founded:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) Y)->((X W)->False)))))))))
% FOF formula (forall (R:(fofType->(fofType->Prop))), ((iff (forall (A:(fofType->Prop)), ((and (mvalid ((mimpl ((mbox R) A)) ((mbox R) ((mbox R) A))))) (mvalid ((mimpl ((mbox R) A)) A))))) ((and (reflexive R)) (transitive R)))) of role conjecture named thm
% Conjecture to prove = (forall (R:(fofType->(fofType->Prop))), ((iff (forall (A:(fofType->Prop)), ((and (mvalid ((mimpl ((mbox R) A)) ((mbox R) ((mbox R) A))))) (mvalid ((mimpl ((mbox R) A)) A))))) ((and (reflexive R)) (transitive R)))):Prop
% Parameter individuals_DUMMY:individuals.
% We need to prove ['(forall (R:(fofType->(fofType->Prop))), ((iff (forall (A:(fofType->Prop)), ((and (mvalid ((mimpl ((mbox R) A)) ((mbox R) ((mbox R) A))))) (mvalid ((mimpl ((mbox R) A)) A))))) ((and (reflexive R)) (transitive R))))']
% Parameter fofType:Type.
% Parameter current_world:fofType.
% Parameter prop_a:(fofType->Prop).
% Parameter prop_b:(fofType->Prop).
% Parameter prop_c:(fofType->Prop).
% Definition mfalse:=(fun (X:fofType)=> False):(fofType->Prop).
% Definition mtrue:=(fun (X:fofType)=> True):(fofType->Prop).
% Definition mnot:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition mor:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mand:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimpl:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition miff:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mand ((mimpl U) V)) ((mimpl V) U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mbox:=(fun (R:(fofType->(fofType->Prop))) (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((R X) Y)->(P Y)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (P:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R X) Y)) (P Y))))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Parameter individuals:Type.
% Definition mall:=(fun (P:(individuals->(fofType->Prop))) (W:fofType)=> (forall (X:individuals), ((P X) W))):((individuals->(fofType->Prop))->(fofType->Prop)).
% Definition mexists:=(fun (P:(individuals->(fofType->Prop))) (W:fofType)=> ((ex individuals) (fun (X:individuals)=> ((P X) W)))):((individuals->(fofType->Prop))->(fofType->Prop)).
% Definition mvalid:=(fun (P:(fofType->Prop))=> (forall (W:fofType), (P W))):((fofType->Prop)->Prop).
% Definition msatisfiable:=(fun (P:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (P W)))):((fofType->Prop)->Prop).
% Definition mcountersatisfiable:=(fun (P:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((P W)->False)))):((fofType->Prop)->Prop).
% Definition minvalid:=(fun (P:(fofType->Prop))=> (forall (W:fofType), ((P W)->False))):((fofType->Prop)->Prop).
% Definition cartesian_product:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType) (V:fofType)=> ((and (X U)) (Y V))):((fofType->Prop)->((fofType->Prop)->(fofType->(fofType->Prop)))).
% Definition pair_rel:=(fun (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) V) Y))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% Definition id_rel:=(fun (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) (((eq fofType) X) Y))):((fofType->Prop)->(fofType->(fofType->Prop))).
% Definition sub_rel:=(fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R1 X) Y)->((R2 X) Y)))):((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop)).
% Definition is_rel_on:=(fun (R:(fofType->(fofType->Prop))) (A:(fofType->Prop)) (B:(fofType->Prop))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((and (A X)) (B Y))))):((fofType->(fofType->Prop))->((fofType->Prop)->((fofType->Prop)->Prop))).
% Definition restrict_rel_domain:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) ((R X) Y))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop)))).
% Definition rel_diagonal:=(fun (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)):(fofType->(fofType->Prop)).
% Definition rel_composition:=(fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop))) (X:fofType) (Z:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R1 X) Y)) ((R2 Y) Z))))):((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% Definition reflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X))):((fofType->(fofType->Prop))->Prop).
% Definition irreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False))):((fofType->(fofType->Prop))->Prop).
% Definition symmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X)))):((fofType->(fofType->Prop))->Prop).
% Definition transitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))):((fofType->(fofType->Prop))->Prop).
% Definition equiv_rel:=(fun (R:(fofType->(fofType->Prop)))=> ((and ((and (reflexive R)) (symmetric R))) (transitive R))):((fofType->(fofType->Prop))->Prop).
% Definition rel_codomain:=(fun (R:(fofType->(fofType->Prop))) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((R X) Y)))):((fofType->(fofType->Prop))->(fofType->Prop)).
% Definition rel_domain:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((R X) Y)))):((fofType->(fofType->Prop))->(fofType->Prop)).
% Definition rel_inverse:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X)):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% Definition equiv_classes:=(fun (R:(fofType->(fofType->Prop))) (S1:(fofType->Prop))=> ((ex fofType) (fun (X:fofType)=> ((and (S1 X)) (forall (Y:fofType), ((iff (S1 Y)) ((R X) Y))))))):((fofType->(fofType->Prop))->((fofType->Prop)->Prop)).
% Definition restrict_rel_codomain:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S Y)) ((R X) Y))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop)))).
% Definition rel_field:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((or ((rel_domain R) X)) ((rel_codomain R) X))):((fofType->(fofType->Prop))->(fofType->Prop)).
% Definition well_founded:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) W)->((X W)->False))))))))):((fofType->(fofType->Prop))->Prop).
% Definition upwards_well_founded:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) Y)->((X W)->False))))))))):((fofType->(fofType->Prop))->Prop).
% Trying to prove (forall (R:(fofType->(fofType->Prop))), ((iff (forall (A:(fofType->Prop)), ((and (mvalid ((mimpl ((mbox R) A)) ((mbox R) ((mbox R) A))))) (mvalid ((mimpl ((mbox R) A)) A))))) ((and (reflexive R)) (transitive R))))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) Z))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) Z))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) Z))
% Found x3:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=X:fofType
% Found (fun (x3:(A0 X0))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A0 X0))=> x3) as proof of ((A0 X0)->((R X) X))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=X:fofType
% Found (fun (x3:(A0 X0))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A0 X0))=> x3) as proof of ((A0 X0)->((R X) X))
% Found x3:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=X:fofType
% Found (fun (x3:(A0 X0))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A0 X0))=> x3) as proof of ((A0 X0)->((R X) X))
% Found x3:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=X:fofType
% Found (fun (x3:(A0 X0))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A0 X0))=> x3) as proof of ((A0 X0)->((R X) X))
% Found x4:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=Z:fofType
% Found (fun (x4:(A0 X0))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A0 X0))=> x4) as proof of ((A0 X0)->((R X) Z))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x5:((R X) Y)
% Instantiate: W:=X:fofType
% Found x5 as proof of ((R W) Y)
% Found (x300 x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> ((x30 x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R X) Y)->(((R Y) Z)->((R X) Z)))
% Found (and_rect10 (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found ((and_rect1 ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of ((R X) Z)
% Found (fun (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (((and ((R X) Y)) ((R Y) Z))->((R X) Z))
% Found (fun (Y:fofType) (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (forall (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x3:(A W))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A W))=> x3) as proof of ((A W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x3:(A0 X)
% Instantiate: A0:=(R X0):(fofType->Prop);X:=Z:fofType
% Found x3 as proof of ((R X0) Z)
% Found (fun (x4:((and ((R X0) Y)) ((R Y) Z)))=> x3) as proof of ((R X0) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x5:((R X) Y)
% Instantiate: W:=X:fofType
% Found x5 as proof of ((R W) Y)
% Found (x400 x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> ((x40 x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)) as proof of (((R X) Y)->(((R Y) Z)->((R X) Z)))
% Found (and_rect10 (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found ((and_rect1 ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x3)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (fun (x4:(((mbox R) ((mbox R) A)) W))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x3)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)))) as proof of ((R X) Z)
% Found (fun (x4:(((mbox R) ((mbox R) A)) W))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x3)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)))) as proof of ((((mbox R) ((mbox R) A)) W)->((R X) Z))
% Found x5:((R X) Y)
% Instantiate: W:=X:fofType
% Found x5 as proof of ((R W) Y)
% Found (x300 x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> ((x30 x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R X) Y)->(((R Y) Z)->((R X) Z)))
% Found (and_rect10 (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found ((and_rect1 ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of ((R X) Z)
% Found (fun (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (((and ((R X) Y)) ((R Y) Z))->((R X) Z))
% Found (fun (Y:fofType) (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (forall (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x6:(A0 W)
% Instantiate: A0:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A0 W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A0 W))=> x6) as proof of ((A0 W)->((R X) X))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) X))
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x3:(A0 X)
% Instantiate: A0:=(R X0):(fofType->Prop);X:=Z:fofType
% Found x3 as proof of ((R X0) Z)
% Found (fun (x4:((and ((R X0) Y)) ((R Y) Z)))=> x3) as proof of ((R X0) Z)
% Found x3:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=X:fofType
% Found (fun (x3:(A0 X0))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A0 X0))=> x3) as proof of ((A0 X0)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x3:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=X:fofType
% Found (fun (x3:(A0 X0))=> x3) as proof of ((R X) X)
% Found (fun (x3:(A0 X0))=> x3) as proof of ((A0 X0)->((R X) X))
% Found x4:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=Z:fofType
% Found (fun (x4:(A0 X0))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A0 X0))=> x4) as proof of ((A0 X0)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x4:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=Z:fofType
% Found (fun (x4:(A0 X0))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A0 X0))=> x4) as proof of ((A0 X0)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x4:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=Z:fofType
% Found (fun (x4:(A0 X0))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A0 X0))=> x4) as proof of ((A0 X0)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x4:(A W0)
% Instantiate: W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x4:((R X) Y)
% Instantiate: W:=X:fofType
% Found x4 as proof of ((R W) Y)
% Found x5:((R Y) Z)
% Found x5 as proof of ((R Y) Z)
% Found ((x600 x4) x5) as proof of ((R X) Z)
% Found (((x60 Y) x4) x5) as proof of ((R X) Z)
% Found ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5) as proof of ((R X) Z)
% Found ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5) as proof of ((R X) Z)
% Found (fun (x6:(((mbox R) ((mbox R) A)) W))=> ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5)) as proof of ((R X) Z)
% Found (fun (x6:(((mbox R) ((mbox R) A)) W))=> ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5)) as proof of ((((mbox R) ((mbox R) A)) W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x5:((R X) Y)
% Instantiate: W:=X:fofType
% Found x5 as proof of ((R W) Y)
% Found (x300 x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> ((x30 x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R X) Y)->(((R Y) Z)->((R X) Z)))
% Found (and_rect10 (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found ((and_rect1 ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of ((R X) Z)
% Found (fun (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (((and ((R X) Y)) ((R Y) Z))->((R X) Z))
% Found (fun (Y:fofType) (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (forall (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))
% Found x5:((R X) Y)
% Instantiate: W:=X:fofType
% Found x5 as proof of ((R W) Y)
% Found (x400 x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> ((x40 x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)) as proof of (((R X) Y)->(((R Y) Z)->((R X) Z)))
% Found (and_rect10 (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found ((and_rect1 ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x3)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (fun (x4:(((mbox R) ((mbox R) A)) W))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x3)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)))) as proof of ((R X) Z)
% Found (fun (x4:(((mbox R) ((mbox R) A)) W))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x3)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)))) as proof of ((((mbox R) ((mbox R) A)) W)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x3:(A0 X)
% Instantiate: A0:=(R X0):(fofType->Prop);X:=Z:fofType
% Found x3 as proof of ((R X0) Z)
% Found (fun (x4:((and ((R X0) Y)) ((R Y) Z)))=> x3) as proof of ((R X0) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x5:((R X) Y)
% Instantiate: W:=X:fofType
% Found x5 as proof of ((R W) Y)
% Found (x300 x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> ((x30 x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R X) Y)->(((R Y) Z)->((R X) Z)))
% Found (and_rect10 (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found ((and_rect1 ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of ((R X) Z)
% Found (fun (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (((and ((R X) Y)) ((R Y) Z))->((R X) Z))
% Found (fun (Y:fofType) (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (forall (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))
% Found x6:(A0 W)
% Instantiate: A0:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A0 W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A0 W))=> x6) as proof of ((A0 W)->((R X) X))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x6:(A0 W)
% Instantiate: A0:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A0 W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A0 W))=> x6) as proof of ((A0 W)->((R X) X))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) X))
% Found x3:(A0 X)
% Instantiate: A0:=(R X0):(fofType->Prop);X:=Z:fofType
% Found x3 as proof of ((R X0) Z)
% Found (fun (x4:((and ((R X0) Y)) ((R Y) Z)))=> x3) as proof of ((R X0) Z)
% Found x4:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x4:(A W))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A W))=> x4) as proof of ((A W)->((R X) Z))
% Found x5:((R X) Y)
% Instantiate: W:=X:fofType
% Found x5 as proof of ((R W) Y)
% Found (x400 x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> ((x40 x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)) as proof of (((R X) Y)->(((R Y) Z)->((R X) Z)))
% Found (and_rect10 (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found ((and_rect1 ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x3)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (fun (x4:(((mbox R) ((mbox R) A)) W))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x3)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)))) as proof of ((R X) Z)
% Found (fun (x4:(((mbox R) ((mbox R) A)) W))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x3)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)))) as proof of ((((mbox R) ((mbox R) A)) W)->((R X) Z))
% Found x7:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x7:(A W))=> x7) as proof of ((R X) Z)
% Found (fun (x7:(A W))=> x7) as proof of ((A W)->((R X) Z))
% Found x7:(A0 W)
% Instantiate: A0:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x7:(A0 W))=> x7) as proof of ((R X) Z)
% Found (fun (x7:(A0 W))=> x7) as proof of ((A0 W)->((R X) Z))
% Found x5:((R X) Y)
% Instantiate: W:=X:fofType
% Found x5 as proof of ((R W) Y)
% Found (x300 x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> ((x30 x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)) as proof of (((R X) Y)->(((R Y) Z)->((R X) Z)))
% Found (and_rect10 (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found ((and_rect1 ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of ((R X) Z)
% Found (fun (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (((and ((R X) Y)) ((R Y) Z))->((R X) Z))
% Found (fun (Y:fofType) (Z:fofType) (x4:((and ((R X) Y)) ((R Y) Z)))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x4)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x3 Y) x6) Z)) x5)))) as proof of (forall (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))
% Found x5:((R X) Y)
% Instantiate: W:=X:fofType
% Found x5 as proof of ((R W) Y)
% Found (x400 x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> ((x40 x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)) as proof of (((R Y) Z)->((R X) Z))
% Found (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)) as proof of (((R X) Y)->(((R Y) Z)->((R X) Z)))
% Found (and_rect10 (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found ((and_rect1 ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x0)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5))) as proof of ((R X) Z)
% Found (fun (x4:(((mbox R) ((mbox R) A)) W))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x0)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)))) as proof of ((R X) Z)
% Found (fun (x4:(((mbox R) ((mbox R) A)) W))=> (((fun (P:Type) (x5:(((R X) Y)->(((R Y) Z)->P)))=> (((((and_rect ((R X) Y)) ((R Y) Z)) P) x5) x0)) ((R X) Z)) (fun (x5:((R X) Y))=> ((fun (x6:((R W) Y))=> (((x4 Y) x6) Z)) x5)))) as proof of ((((mbox R) ((mbox R) A)) W)->((R X) Z))
% Found x3:(A0 X)
% Instantiate: A0:=(R X0):(fofType->Prop);X:=Z:fofType
% Found x3 as proof of ((R X0) Z)
% Found (fun (x4:((and ((R X0) Y)) ((R Y) Z)))=> x3) as proof of ((R X0) Z)
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) X))
% Found x6:(A0 W)
% Instantiate: A0:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A0 W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A0 W))=> x6) as proof of ((A0 W)->((R X) X))
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) Z))
% Found x4:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=Z:fofType
% Found (fun (x4:(A0 X0))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A0 X0))=> x4) as proof of ((A0 X0)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x4:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=Z:fofType
% Found (fun (x4:(A0 X0))=> x4) as proof of ((R X) Z)
% Found (fun (x4:(A0 X0))=> x4) as proof of ((A0 X0)->((R X) Z))
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x3:(A W)
% Instantiate: W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x4:(A W0)
% Instantiate: W0:=X:fofType
% Found x4 as proof of ((R X) X)
% Found x4:(A W0)
% Instantiate: W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x5:((R Y) Z)
% Found x5 as proof of ((R Y) Z)
% Found x4:((R X) Y)
% Instantiate: W:=X:fofType
% Found x4 as proof of ((R W) Y)
% Found ((x600 x4) x5) as proof of ((R X) Z)
% Found (((x60 Y) x4) x5) as proof of ((R X) Z)
% Found ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5) as proof of ((R X) Z)
% Found ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5) as proof of ((R X) Z)
% Found (fun (x6:(((mbox R) ((mbox R) A)) W))=> ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5)) as proof of ((R X) Z)
% Found (fun (x6:(((mbox R) ((mbox R) A)) W))=> ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5)) as proof of ((((mbox R) ((mbox R) A)) W)->((R X) Z))
% Found x4:(A W0)
% Instantiate: W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x6:(A0 W)
% Instantiate: A0:=(R X):(fofType->Prop);W:=Z:fofType
% Found x6 as proof of ((R X) Z)
% Found (fun (x7:((and ((R X) Y)) ((R Y) Z)))=> x6) as proof of ((R X) Z)
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x6 as proof of ((R X) Z)
% Found (fun (x7:((and ((R X) Y)) ((R Y) Z)))=> x6) as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found x3 as proof of ((R X) X)
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x6:(A0 X0)
% Instantiate: A0:=(R X):(fofType->Prop);X0:=Z:fofType
% Found (fun (x6:(A0 X0))=> x6) as proof of ((R X) Z)
% Found (fun (x6:(A0 X0))=> x6) as proof of ((A0 X0)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x5:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=Z:fofType
% Found (fun (x5:(A W0))=> x5) as proof of ((R X) Z)
% Found (fun (x5:(A W0))=> x5) as proof of ((A W0)->((R X) Z))
% Found x4:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=X:fofType
% Found (fun (x4:(A W0))=> x4) as proof of ((R X) X)
% Found (fun (x4:(A W0))=> x4) as proof of ((A W0)->((R X) X))
% Found x5:(A W0)
% Instantiate: A:=(R X):(fofType->Prop);W0:=Z:fofType
% Found (fun (x5:(A W0))=> x5) as proof of ((R X) Z)
% Found (fun (x5:(A W0))=> x5) as proof of ((A W0)->((R X) Z))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found (fun (x4:((and ((R X) Y)) ((R Y) Z)))=> x3) as proof of ((R X) Z)
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) X))
% Found x6:(A0 W)
% Instantiate: A0:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A0 W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A0 W))=> x6) as proof of ((A0 W)->((R X) X))
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x3:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=Z:fofType
% Found x3 as proof of ((R X) Z)
% Found x6:(A W)
% Instantiate: A:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A W))=> x6) as proof of ((A W)->((R X) X))
% Found x6:(A0 W)
% Instantiate: A0:=(R X):(fofType->Prop);W:=X:fofType
% Found (fun (x6:(A0 W))=> x6) as proof of ((R X) X)
% Found (fun (x6:(A0 W))=> x6) as proof of ((A0 W)->((R X) X))
% Found x4:((R X) Y)
% Instantiate: W:=X:fofType
% Found x4 as proof of ((R W) Y)
% Found x5:((R Y) Z)
% Found x5 as proof of ((R Y) Z)
% Found ((x600 x4) x5) as proof of ((R X) Z)
% Found (((x60 Y) x4) x5) as proof of ((R X) Z)
% Found ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5) as proof of ((R X) Z)
% Found ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5) as proof of ((R X) Z)
% Found (fun (x6:(((mbox R) ((mbox R) A)) W))=> ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y) x4) x5)) as proof of ((R X) Z)
% Found (fun (x6:(((mbox R) ((mbox R) A)) W))=> ((((fun (Y0:fofType) (x7:((R W) Y0))=> (((x6 Y0) x7) Z)) Y)
% EOF
%------------------------------------------------------------------------------