TSTP Solution File: GEG016^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : GEG016^1 : TPTP v6.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n097.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 13:21:31 EDT 2014
% Result : Unknown 14.78s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GEG016^1 : TPTP v6.1.0. Released v4.1.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n097.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:29:41 CDT 2014
% % CPUTime : 14.78
% 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/LCL013^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x2783290>, <kernel.Type object at 0x23a7f80>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0x2783320>, <kernel.DependentProduct object at 0x23a79e0>) of role type named meq_ind_type
% Using role type
% Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% FOF formula (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) of role definition named meq_ind
% A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% FOF formula (<kernel.Constant object at 0x2783320>, <kernel.DependentProduct object at 0x23a79e0>) of role type named meq_prop_type
% Using role type
% Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))) of role definition named meq_prop
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))))
% Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% FOF formula (<kernel.Constant object at 0x23a7b48>, <kernel.DependentProduct object at 0x23a7a70>) of role type named mnot_type
% Using role type
% Declaring mnot:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% FOF formula (<kernel.Constant object at 0x23a7a70>, <kernel.DependentProduct object at 0x23a74d0>) of role type named mor_type
% Using role type
% Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))) of role definition named mor
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))))
% Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% FOF formula (<kernel.Constant object at 0x23a74d0>, <kernel.DependentProduct object at 0x23a7c20>) of role type named mand_type
% Using role type
% Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))) of role definition named mand
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% FOF formula (<kernel.Constant object at 0x23a7c20>, <kernel.DependentProduct object at 0x23a7440>) of role type named mimplies_type
% Using role type
% Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))) of role definition named mimplies
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% FOF formula (<kernel.Constant object at 0x23a7440>, <kernel.DependentProduct object at 0x23a78c0>) of role type named mimplied_type
% Using role type
% Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))) of role definition named mimplied
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% FOF formula (<kernel.Constant object at 0x23a78c0>, <kernel.DependentProduct object at 0x23a7368>) of role type named mequiv_type
% Using role type
% Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))) of role definition named mequiv
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))))
% Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% FOF formula (<kernel.Constant object at 0x23a7368>, <kernel.DependentProduct object at 0x23a7f38>) of role type named mxor_type
% Using role type
% Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))) of role definition named mxor
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% FOF formula (<kernel.Constant object at 0x23a75f0>, <kernel.DependentProduct object at 0x27846c8>) of role type named mforall_ind_type
% Using role type
% Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) of role definition named mforall_ind
% A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% FOF formula (<kernel.Constant object at 0x23a74d0>, <kernel.DependentProduct object at 0x2784248>) of role type named mforall_prop_type
% Using role type
% Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))) of role definition named mforall_prop
% A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))))
% Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% FOF formula (<kernel.Constant object at 0x23a74d0>, <kernel.DependentProduct object at 0x27846c8>) of role type named mexists_ind_type
% Using role type
% Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))) of role definition named mexists_ind
% A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))))
% Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% FOF formula (<kernel.Constant object at 0x23a74d0>, <kernel.DependentProduct object at 0x2784560>) of role type named mexists_prop_type
% Using role type
% Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))) of role definition named mexists_prop
% A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))))
% Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% FOF formula (<kernel.Constant object at 0x27841b8>, <kernel.DependentProduct object at 0x2784440>) of role type named mtrue_type
% Using role type
% Declaring mtrue:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% Defined: mtrue:=(fun (W:fofType)=> True)
% FOF formula (<kernel.Constant object at 0x27842d8>, <kernel.DependentProduct object at 0x2784710>) of role type named mfalse_type
% Using role type
% Declaring mfalse:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% Defined: mfalse:=(mnot mtrue)
% FOF formula (<kernel.Constant object at 0x27840e0>, <kernel.DependentProduct object at 0x27842d8>) of role type named mbox_type
% 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))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))) of role definition named mbox
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))))
% Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% FOF formula (<kernel.Constant object at 0x27841b8>, <kernel.DependentProduct object at 0x239d908>) of role type named mdia_type
% 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))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))) of role definition named mdia
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))))
% Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% FOF formula (<kernel.Constant object at 0x2784710>, <kernel.DependentProduct object at 0x239d878>) of role type named mreflexive_type
% Using role type
% Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% FOF formula (<kernel.Constant object at 0x27840e0>, <kernel.DependentProduct object at 0x239d6c8>) of role type named msymmetric_type
% Using role type
% Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) msymmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))) of role definition named msymmetric
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) msymmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))))
% Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% FOF formula (<kernel.Constant object at 0x239d6c8>, <kernel.DependentProduct object at 0x239d518>) of role type named mserial_type
% Using role type
% Declaring mserial:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mserial) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))) of role definition named mserial
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mserial) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))))
% Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% FOF formula (<kernel.Constant object at 0x239d518>, <kernel.DependentProduct object at 0x239d638>) of role type named mtransitive_type
% Using role type
% Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mtransitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))) of role definition named mtransitive
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mtransitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))))
% Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% FOF formula (<kernel.Constant object at 0x239d638>, <kernel.DependentProduct object at 0x239d680>) of role type named meuclidean_type
% Using role type
% Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) meuclidean) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))) of role definition named meuclidean
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) meuclidean) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))))
% Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% FOF formula (<kernel.Constant object at 0x239d680>, <kernel.DependentProduct object at 0x239d830>) of role type named mpartially_functional_type
% Using role type
% Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mpartially_functional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U))))) of role definition named mpartially_functional
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mpartially_functional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))))
% Defined: mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U))))
% FOF formula (<kernel.Constant object at 0x239d830>, <kernel.DependentProduct object at 0x239da70>) of role type named mfunctional_type
% Using role type
% Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))) of role definition named mfunctional
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))))
% Defined: mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))
% FOF formula (<kernel.Constant object at 0x239da70>, <kernel.DependentProduct object at 0x239db00>) of role type named mweakly_dense_type
% Using role type
% Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))) of role definition named mweakly_dense
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))))
% Defined: mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))
% FOF formula (<kernel.Constant object at 0x239db00>, <kernel.DependentProduct object at 0x239d680>) of role type named mweakly_connected_type
% Using role type
% Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))) of role definition named mweakly_connected
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))))
% Defined: mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))
% FOF formula (<kernel.Constant object at 0x239d680>, <kernel.DependentProduct object at 0x239def0>) of role type named mweakly_directed_type
% Using role type
% Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))) of role definition named mweakly_directed
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))))
% Defined: mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))
% FOF formula (<kernel.Constant object at 0x239d5f0>, <kernel.DependentProduct object at 0x239dd88>) of role type named mvalid_type
% Using role type
% Declaring mvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% FOF formula (<kernel.Constant object at 0x239d680>, <kernel.DependentProduct object at 0x239d248>) of role type named minvalid_type
% Using role type
% Declaring minvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% FOF formula (<kernel.Constant object at 0x239dd88>, <kernel.DependentProduct object at 0x239dc68>) of role type named msatisfiable_type
% Using role type
% Declaring msatisfiable:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% FOF formula (<kernel.Constant object at 0x239d248>, <kernel.DependentProduct object at 0x239da70>) of role type named mcountersatisfiable_type
% Using role type
% Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL014^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x2783bd8>, <kernel.Type object at 0x23a73b0>) of role type named reg_type
% Using role type
% Declaring reg:Type
% FOF formula (<kernel.Constant object at 0x2783290>, <kernel.DependentProduct object at 0x23a7b48>) of role type named c_type
% Using role type
% Declaring c:(reg->(reg->Prop))
% FOF formula (<kernel.Constant object at 0x2783bd8>, <kernel.DependentProduct object at 0x23a7cb0>) of role type named dc_type
% Using role type
% Declaring dc:(reg->(reg->Prop))
% FOF formula (<kernel.Constant object at 0x2783320>, <kernel.DependentProduct object at 0x23a7dd0>) of role type named p_type
% Using role type
% Declaring p:(reg->(reg->Prop))
% FOF formula (<kernel.Constant object at 0x2783320>, <kernel.DependentProduct object at 0x23a7710>) of role type named eq_type
% Using role type
% Declaring _TPTP_eq:(reg->(reg->Prop))
% FOF formula (<kernel.Constant object at 0x23a7cb0>, <kernel.DependentProduct object at 0x23a75a8>) of role type named o_type
% Using role type
% Declaring o:(reg->(reg->Prop))
% FOF formula (<kernel.Constant object at 0x23a7dd0>, <kernel.DependentProduct object at 0x23a79e0>) of role type named po_type
% Using role type
% Declaring po:(reg->(reg->Prop))
% FOF formula (<kernel.Constant object at 0x23a7710>, <kernel.DependentProduct object at 0x23a7b48>) of role type named ec_type
% Using role type
% Declaring ec:(reg->(reg->Prop))
% FOF formula (<kernel.Constant object at 0x23a75a8>, <kernel.DependentProduct object at 0x23a7560>) of role type named pp_type
% Using role type
% Declaring pp:(reg->(reg->Prop))
% FOF formula (<kernel.Constant object at 0x23a79e0>, <kernel.DependentProduct object at 0x23a7cb0>) of role type named tpp_type
% Using role type
% Declaring tpp:(reg->(reg->Prop))
% FOF formula (<kernel.Constant object at 0x23a7b48>, <kernel.DependentProduct object at 0x23a7dd0>) of role type named ntpp_type
% Using role type
% Declaring ntpp:(reg->(reg->Prop))
% FOF formula (forall (X:reg), ((c X) X)) of role axiom named c_reflexive
% A new axiom: (forall (X:reg), ((c X) X))
% FOF formula (forall (X:reg) (Y:reg), (((c X) Y)->((c Y) X))) of role axiom named c_symmetric
% A new axiom: (forall (X:reg) (Y:reg), (((c X) Y)->((c Y) X)))
% FOF formula (((eq (reg->(reg->Prop))) dc) (fun (X:reg) (Y:reg)=> (((c X) Y)->False))) of role definition named dc
% A new definition: (((eq (reg->(reg->Prop))) dc) (fun (X:reg) (Y:reg)=> (((c X) Y)->False)))
% Defined: dc:=(fun (X:reg) (Y:reg)=> (((c X) Y)->False))
% FOF formula (((eq (reg->(reg->Prop))) p) (fun (X:reg) (Y:reg)=> (forall (Z:reg), (((c Z) X)->((c Z) Y))))) of role definition named p
% A new definition: (((eq (reg->(reg->Prop))) p) (fun (X:reg) (Y:reg)=> (forall (Z:reg), (((c Z) X)->((c Z) Y)))))
% Defined: p:=(fun (X:reg) (Y:reg)=> (forall (Z:reg), (((c Z) X)->((c Z) Y))))
% FOF formula (((eq (reg->(reg->Prop))) _TPTP_eq) (fun (X:reg) (Y:reg)=> ((and ((p X) Y)) ((p Y) X)))) of role definition named eq
% A new definition: (((eq (reg->(reg->Prop))) _TPTP_eq) (fun (X:reg) (Y:reg)=> ((and ((p X) Y)) ((p Y) X))))
% Defined: _TPTP_eq:=(fun (X:reg) (Y:reg)=> ((and ((p X) Y)) ((p Y) X)))
% FOF formula (((eq (reg->(reg->Prop))) o) (fun (X:reg) (Y:reg)=> ((ex reg) (fun (Z:reg)=> ((and ((p Z) X)) ((p Z) Y)))))) of role definition named o
% A new definition: (((eq (reg->(reg->Prop))) o) (fun (X:reg) (Y:reg)=> ((ex reg) (fun (Z:reg)=> ((and ((p Z) X)) ((p Z) Y))))))
% Defined: o:=(fun (X:reg) (Y:reg)=> ((ex reg) (fun (Z:reg)=> ((and ((p Z) X)) ((p Z) Y)))))
% FOF formula (((eq (reg->(reg->Prop))) po) (fun (X:reg) (Y:reg)=> ((and ((and ((o X) Y)) (((p X) Y)->False))) (((p Y) X)->False)))) of role definition named po
% A new definition: (((eq (reg->(reg->Prop))) po) (fun (X:reg) (Y:reg)=> ((and ((and ((o X) Y)) (((p X) Y)->False))) (((p Y) X)->False))))
% Defined: po:=(fun (X:reg) (Y:reg)=> ((and ((and ((o X) Y)) (((p X) Y)->False))) (((p Y) X)->False)))
% FOF formula (((eq (reg->(reg->Prop))) ec) (fun (X:reg) (Y:reg)=> ((and ((c X) Y)) (((o X) Y)->False)))) of role definition named ec
% A new definition: (((eq (reg->(reg->Prop))) ec) (fun (X:reg) (Y:reg)=> ((and ((c X) Y)) (((o X) Y)->False))))
% Defined: ec:=(fun (X:reg) (Y:reg)=> ((and ((c X) Y)) (((o X) Y)->False)))
% FOF formula (((eq (reg->(reg->Prop))) pp) (fun (X:reg) (Y:reg)=> ((and ((p X) Y)) (((p Y) X)->False)))) of role definition named pp
% A new definition: (((eq (reg->(reg->Prop))) pp) (fun (X:reg) (Y:reg)=> ((and ((p X) Y)) (((p Y) X)->False))))
% Defined: pp:=(fun (X:reg) (Y:reg)=> ((and ((p X) Y)) (((p Y) X)->False)))
% FOF formula (((eq (reg->(reg->Prop))) tpp) (fun (X:reg) (Y:reg)=> ((and ((pp X) Y)) ((ex reg) (fun (Z:reg)=> ((and ((ec Z) X)) ((ec Z) Y))))))) of role definition named tpp
% A new definition: (((eq (reg->(reg->Prop))) tpp) (fun (X:reg) (Y:reg)=> ((and ((pp X) Y)) ((ex reg) (fun (Z:reg)=> ((and ((ec Z) X)) ((ec Z) Y)))))))
% Defined: tpp:=(fun (X:reg) (Y:reg)=> ((and ((pp X) Y)) ((ex reg) (fun (Z:reg)=> ((and ((ec Z) X)) ((ec Z) Y))))))
% FOF formula (((eq (reg->(reg->Prop))) ntpp) (fun (X:reg) (Y:reg)=> ((and ((pp X) Y)) (((ex reg) (fun (Z:reg)=> ((and ((ec Z) X)) ((ec Z) Y))))->False)))) of role definition named ntpp
% A new definition: (((eq (reg->(reg->Prop))) ntpp) (fun (X:reg) (Y:reg)=> ((and ((pp X) Y)) (((ex reg) (fun (Z:reg)=> ((and ((ec Z) X)) ((ec Z) Y))))->False))))
% Defined: ntpp:=(fun (X:reg) (Y:reg)=> ((and ((pp X) Y)) (((ex reg) (fun (Z:reg)=> ((and ((ec Z) X)) ((ec Z) Y))))->False)))
% FOF formula (<kernel.Constant object at 0x2275320>, <kernel.Constant object at 0x238c488>) of role type named catalunya
% Using role type
% Declaring catalunya:reg
% FOF formula (<kernel.Constant object at 0x2275320>, <kernel.Constant object at 0x238c488>) of role type named france
% Using role type
% Declaring france:reg
% FOF formula (<kernel.Constant object at 0x238cb90>, <kernel.Constant object at 0x238c488>) of role type named spain
% Using role type
% Declaring spain:reg
% FOF formula (<kernel.Constant object at 0x238c4d0>, <kernel.Constant object at 0x238c488>) of role type named paris
% Using role type
% Declaring paris:reg
% FOF formula (<kernel.Constant object at 0x238c710>, <kernel.DependentProduct object at 0x238cb90>) of role type named a
% Using role type
% Declaring a:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x238c440>, <kernel.DependentProduct object at 0x238c4d0>) of role type named fool
% Using role type
% Declaring fool:(fofType->(fofType->Prop))
% FOF formula (mvalid (mforall_prop (fun (A:(fofType->Prop))=> ((mimplies ((mbox fool) A)) A)))) of role axiom named t_axiom_for_fool
% A new axiom: (mvalid (mforall_prop (fun (A:(fofType->Prop))=> ((mimplies ((mbox fool) A)) A))))
% FOF formula (mvalid (mforall_prop (fun (A:(fofType->Prop))=> ((mimplies ((mbox fool) A)) ((mbox fool) ((mbox fool) A)))))) of role axiom named k_axiom_for_fool
% A new axiom: (mvalid (mforall_prop (fun (A:(fofType->Prop))=> ((mimplies ((mbox fool) A)) ((mbox fool) ((mbox fool) A))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox fool) Phi)) ((mbox a) Phi))))) of role axiom named i_axiom_for_fool_a
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox fool) Phi)) ((mbox a) Phi)))))
% FOF formula (mvalid ((mbox a) (fun (X:fofType)=> ((tpp catalunya) spain)))) of role axiom named ax1
% A new axiom: (mvalid ((mbox a) (fun (X:fofType)=> ((tpp catalunya) spain))))
% FOF formula (mvalid ((mbox fool) (fun (X:fofType)=> ((ec spain) france)))) of role axiom named ax2
% A new axiom: (mvalid ((mbox fool) (fun (X:fofType)=> ((ec spain) france))))
% FOF formula (mvalid ((mbox a) (fun (X:fofType)=> ((ntpp paris) france)))) of role axiom named ax3
% A new axiom: (mvalid ((mbox a) (fun (X:fofType)=> ((ntpp paris) france))))
% FOF formula (mvalid ((mbox fool) (fun (X:fofType)=> (forall (Z:reg) (Y:reg), (((and ((p Z) spain)) ((p Y) france))->(((o Z) Y)->False)))))) of role conjecture named con
% Conjecture to prove = (mvalid ((mbox fool) (fun (X:fofType)=> (forall (Z:reg) (Y:reg), (((and ((p Z) spain)) ((p Y) france))->(((o Z) Y)->False)))))):Prop
% Parameter mu_DUMMY:mu.
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(mvalid ((mbox fool) (fun (X:fofType)=> (forall (Z:reg) (Y:reg), (((and ((p Z) spain)) ((p Y) france))->(((o Z) Y)->False))))))']
% Parameter mu:Type.
% Parameter fofType:Type.
% Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% Definition mfalse:=(mnot mtrue):(fofType->Prop).
% Definition mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% Definition mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))):((fofType->(fofType->Prop))->Prop).
% Definition meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))):((fofType->(fofType->Prop))->Prop).
% Definition mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))):((fofType->(fofType->Prop))->Prop).
% Definition mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))):((fofType->(fofType->Prop))->Prop).
% Definition mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))):((fofType->(fofType->Prop))->Prop).
% Definition mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))):((fofType->(fofType->Prop))->Prop).
% Definition mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))):((fofType->(fofType->Prop))->Prop).
% Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% Parameter reg:Type.
% Parameter c:(reg->(reg->Prop)).
% Definition dc:=(fun (X:reg) (Y:reg)=> (((c X) Y)->False)):(reg->(reg->Prop)).
% Definition p:=(fun (X:reg) (Y:reg)=> (forall (Z:reg), (((c Z) X)->((c Z) Y)))):(reg->(reg->Prop)).
% Definition _TPTP_eq:=(fun (X:reg) (Y:reg)=> ((and ((p X) Y)) ((p Y) X))):(reg->(reg->Prop)).
% Definition o:=(fun (X:reg) (Y:reg)=> ((ex reg) (fun (Z:reg)=> ((and ((p Z) X)) ((p Z) Y))))):(reg->(reg->Prop)).
% Definition po:=(fun (X:reg) (Y:reg)=> ((and ((and ((o X) Y)) (((p X) Y)->False))) (((p Y) X)->False))):(reg->(reg->Prop)).
% Definition ec:=(fun (X:reg) (Y:reg)=> ((and ((c X) Y)) (((o X) Y)->False))):(reg->(reg->Prop)).
% Definition pp:=(fun (X:reg) (Y:reg)=> ((and ((p X) Y)) (((p Y) X)->False))):(reg->(reg->Prop)).
% Definition tpp:=(fun (X:reg) (Y:reg)=> ((and ((pp X) Y)) ((ex reg) (fun (Z:reg)=> ((and ((ec Z) X)) ((ec Z) Y)))))):(reg->(reg->Prop)).
% Definition ntpp:=(fun (X:reg) (Y:reg)=> ((and ((pp X) Y)) (((ex reg) (fun (Z:reg)=> ((and ((ec Z) X)) ((ec Z) Y))))->False))):(reg->(reg->Prop)).
% Axiom c_reflexive:(forall (X:reg), ((c X) X)).
% Axiom c_symmetric:(forall (X:reg) (Y:reg), (((c X) Y)->((c Y) X))).
% Parameter catalunya:reg.
% Parameter france:reg.
% Parameter spain:reg.
% Parameter paris:reg.
% Parameter a:(fofType->(fofType->Prop)).
% Parameter fool:(fofType->(fofType->Prop)).
% Axiom t_axiom_for_fool:(mvalid (mforall_prop (fun (A:(fofType->Prop))=> ((mimplies ((mbox fool) A)) A)))).
% Axiom k_axiom_for_fool:(mvalid (mforall_prop (fun (A:(fofType->Prop))=> ((mimplies ((mbox fool) A)) ((mbox fool) ((mbox fool) A)))))).
% Axiom i_axiom_for_fool_a:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox fool) Phi)) ((mbox a) Phi))))).
% Axiom ax1:(mvalid ((mbox a) (fun (X:fofType)=> ((tpp catalunya) spain)))).
% Axiom ax2:(mvalid ((mbox fool) (fun (X:fofType)=> ((ec spain) france)))).
% Axiom ax3:(mvalid ((mbox a) (fun (X:fofType)=> ((ntpp paris) france)))).
% Trying to prove (mvalid ((mbox fool) (fun (X:fofType)=> (forall (Z:reg) (Y:reg), (((and ((p Z) spain)) ((p Y) france))->(((o Z) Y)->False))))))
% % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------