TSTP Solution File: LCL692^1 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : LCL692^1 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n100.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 13:26:07 EDT 2014
% Result : Unknown 40.04s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LCL692^1 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n100.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 10:36:11 CDT 2014
% % CPUTime : 40.04
% 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 0x22760e0>, <kernel.Constant object at 0x2276a70>) of role type named current_world
% Using role type
% Declaring current_world:fofType
% FOF formula (<kernel.Constant object at 0x22760e0>, <kernel.DependentProduct object at 0x2276ef0>) of role type named prop_a
% Using role type
% Declaring prop_a:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x22769e0>, <kernel.DependentProduct object at 0x2276ea8>) of role type named prop_b
% Using role type
% Declaring prop_b:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x2276a28>, <kernel.DependentProduct object at 0x2276dd0>) of role type named prop_c
% Using role type
% Declaring prop_c:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x22769e0>, <kernel.DependentProduct object at 0x22765f0>) 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 0x2276ef0>, <kernel.DependentProduct object at 0x22765a8>) 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 0x22769e0>, <kernel.DependentProduct object at 0x2276560>) 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 0x2276ef0>, <kernel.DependentProduct object at 0x2276560>) 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 0x22764d0>, <kernel.DependentProduct object at 0x2276830>) 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 0x2276830>, <kernel.DependentProduct object at 0x22d5518>) 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 0x22d52d8>, <kernel.DependentProduct object at 0x22d53b0>) 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 0x22d5518>, <kernel.DependentProduct object at 0x22d5710>) 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 0x22d52d8>, <kernel.DependentProduct object at 0x22774d0>) 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 0x22772d8>, <kernel.Type object at 0x2277560>) of role type named individuals_decl
% Using role type
% Declaring individuals:Type
% FOF formula (<kernel.Constant object at 0x2277758>, <kernel.DependentProduct object at 0x2277710>) 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 0x2277368>, <kernel.DependentProduct object at 0x2277248>) 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 0x2277758>, <kernel.DependentProduct object at 0x1e807a0>) 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 0x2277368>, <kernel.DependentProduct object at 0x1e807a0>) 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 0x1e807e8>, <kernel.DependentProduct object at 0x1e805a8>) 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 0x1e807a0>, <kernel.DependentProduct object at 0x1e80a70>) 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/LCL009^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x2276ab8>, <kernel.DependentProduct object at 0x2276a28>) of role type named reli
% Using role type
% Declaring reli:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2276dd0>, <kernel.DependentProduct object at 0x2276a70>) of role type named relr
% Using role type
% Declaring relr:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2276dd0>, <kernel.DependentProduct object at 0x2276a28>) of role type named cs4_atom_decl
% Using role type
% Declaring cs4_atom:((fofType->Prop)->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2276f80>, <kernel.DependentProduct object at 0x2276b00>) of role type named cs4_and_decl
% Using role type
% Declaring cs4_and:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x22765a8>, <kernel.DependentProduct object at 0x22767e8>) of role type named cs4_or_decl
% Using role type
% Declaring cs4_or:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x2276f38>, <kernel.DependentProduct object at 0x22762d8>) of role type named cs4_impl_decl
% Using role type
% Declaring cs4_impl:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x2276ab8>, <kernel.DependentProduct object at 0x2276a28>) of role type named cs4_true_decl
% Using role type
% Declaring cs4_true:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x2276dd0>, <kernel.DependentProduct object at 0x22767e8>) of role type named cs4_false_decl
% Using role type
% Declaring cs4_false:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x2276b00>, <kernel.DependentProduct object at 0x2276ef0>) of role type named cs4_all_decl
% Using role type
% Declaring cs4_all:((individuals->(fofType->Prop))->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x22762d8>, <kernel.DependentProduct object at 0x2276dd0>) of role type named cs4_box_decl
% Using role type
% Declaring cs4_box:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) cs4_atom) (fun (P:(fofType->Prop))=> ((mbox reli) P))) of role definition named cs4_atom
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) cs4_atom) (fun (P:(fofType->Prop))=> ((mbox reli) P)))
% Defined: cs4_atom:=(fun (P:(fofType->Prop))=> ((mbox reli) P))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) cs4_and) (fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mand A) B))) of role definition named cs4_and
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) cs4_and) (fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mand A) B)))
% Defined: cs4_and:=(fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mand A) B))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) cs4_or) (fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mor A) B))) of role definition named cs4_or
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) cs4_or) (fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mor A) B)))
% Defined: cs4_or:=(fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mor A) B))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) cs4_impl) (fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mbox reli) ((mimpl A) B)))) of role definition named cs4_impl
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) cs4_impl) (fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mbox reli) ((mimpl A) B))))
% Defined: cs4_impl:=(fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mbox reli) ((mimpl A) B)))
% FOF formula (((eq (fofType->Prop)) cs4_true) mtrue) of role definition named cs4_true
% A new definition: (((eq (fofType->Prop)) cs4_true) mtrue)
% Defined: cs4_true:=mtrue
% FOF formula (((eq (fofType->Prop)) cs4_false) mfalse) of role definition named cs4_false
% A new definition: (((eq (fofType->Prop)) cs4_false) mfalse)
% Defined: cs4_false:=mfalse
% FOF formula (((eq ((individuals->(fofType->Prop))->(fofType->Prop))) cs4_all) (fun (A:(individuals->(fofType->Prop)))=> ((mbox reli) (mall A)))) of role definition named cs4_all
% A new definition: (((eq ((individuals->(fofType->Prop))->(fofType->Prop))) cs4_all) (fun (A:(individuals->(fofType->Prop)))=> ((mbox reli) (mall A))))
% Defined: cs4_all:=(fun (A:(individuals->(fofType->Prop)))=> ((mbox reli) (mall A)))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) cs4_box) (fun (A:(fofType->Prop))=> ((mbox reli) ((mbox relr) A)))) of role definition named cs4_box
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) cs4_box) (fun (A:(fofType->Prop))=> ((mbox reli) ((mbox relr) A))))
% Defined: cs4_box:=(fun (A:(fofType->Prop))=> ((mbox reli) ((mbox relr) A)))
% FOF formula (<kernel.Constant object at 0x2276248>, <kernel.DependentProduct object at 0x22d53b0>) of role type named cs4_valid_decl
% Using role type
% Declaring cs4_valid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) cs4_valid) (fun (A:(fofType->Prop))=> (mvalid A))) of role definition named cs4_valid_def
% A new definition: (((eq ((fofType->Prop)->Prop)) cs4_valid) (fun (A:(fofType->Prop))=> (mvalid A)))
% Defined: cs4_valid:=(fun (A:(fofType->Prop))=> (mvalid A))
% FOF formula (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox reli) A)) A))) of role axiom named refl_axiom_i
% A new axiom: (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox reli) A)) A)))
% FOF formula (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox relr) A)) A))) of role axiom named refl_axiom_r
% A new axiom: (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox relr) A)) A)))
% FOF formula (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox reli) A)) ((mbox reli) ((mbox reli) A))))) of role axiom named trans_axiom_i
% A new axiom: (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox reli) A)) ((mbox reli) ((mbox reli) A)))))
% FOF formula (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox relr) A)) ((mbox relr) ((mbox relr) A))))) of role axiom named trans_axiom_r
% A new axiom: (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox relr) A)) ((mbox relr) ((mbox relr) A)))))
% FOF formula (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox reli) ((mbox relr) A))) ((mbox relr) ((mbox reli) A))))) of role axiom named ax_i_r_commute
% A new axiom: (forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox reli) ((mbox relr) A))) ((mbox relr) ((mbox reli) A)))))
% FOF formula (forall (A:(fofType->Prop)), (cs4_valid ((cs4_impl (cs4_box (cs4_atom A))) (cs4_box (cs4_box (cs4_atom A)))))) of role conjecture named cs4_trans
% Conjecture to prove = (forall (A:(fofType->Prop)), (cs4_valid ((cs4_impl (cs4_box (cs4_atom A))) (cs4_box (cs4_box (cs4_atom A)))))):Prop
% Parameter individuals_DUMMY:individuals.
% We need to prove ['(forall (A:(fofType->Prop)), (cs4_valid ((cs4_impl (cs4_box (cs4_atom A))) (cs4_box (cs4_box (cs4_atom A))))))']
% 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).
% Parameter reli:(fofType->(fofType->Prop)).
% Parameter relr:(fofType->(fofType->Prop)).
% Definition cs4_atom:=(fun (P:(fofType->Prop))=> ((mbox reli) P)):((fofType->Prop)->(fofType->Prop)).
% Definition cs4_and:=(fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mand A) B)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition cs4_or:=(fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mor A) B)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition cs4_impl:=(fun (A:(fofType->Prop)) (B:(fofType->Prop))=> ((mbox reli) ((mimpl A) B))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition cs4_true:=mtrue:(fofType->Prop).
% Definition cs4_false:=mfalse:(fofType->Prop).
% Definition cs4_all:=(fun (A:(individuals->(fofType->Prop)))=> ((mbox reli) (mall A))):((individuals->(fofType->Prop))->(fofType->Prop)).
% Definition cs4_box:=(fun (A:(fofType->Prop))=> ((mbox reli) ((mbox relr) A))):((fofType->Prop)->(fofType->Prop)).
% Definition cs4_valid:=(fun (A:(fofType->Prop))=> (mvalid A)):((fofType->Prop)->Prop).
% Axiom refl_axiom_i:(forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox reli) A)) A))).
% Axiom refl_axiom_r:(forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox relr) A)) A))).
% Axiom trans_axiom_i:(forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox reli) A)) ((mbox reli) ((mbox reli) A))))).
% Axiom trans_axiom_r:(forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox relr) A)) ((mbox relr) ((mbox relr) A))))).
% Axiom ax_i_r_commute:(forall (A:(fofType->Prop)), (mvalid ((mimpl ((mbox reli) ((mbox relr) A))) ((mbox relr) ((mbox reli) A))))).
% Trying to prove (forall (A:(fofType->Prop)), (cs4_valid ((cs4_impl (cs4_box (cs4_atom A))) (cs4_box (cs4_box (cs4_atom A))))))
% % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------