TSTP Solution File: NLP004^7 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NLP004^7 : TPTP v6.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n105.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 13:26:43 EDT 2014
% Result : Timeout 300.04s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : NLP004^7 : TPTP v6.1.0. Released v5.5.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n105.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 07:26:16 CDT 2014
% % CPUTime : 300.04
% 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/LCL015^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x216ef38>, <kernel.Type object at 0x216ecb0>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0x216ee60>, <kernel.DependentProduct object at 0x216ef38>) of role type named qmltpeq_type
% Using role type
% Declaring qmltpeq:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1f8cdd0>, <kernel.DependentProduct object at 0x1f8c5f0>) 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 0x1f8cb00>, <kernel.DependentProduct object at 0x1f8ccb0>) 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 0x1f8ccb0>, <kernel.DependentProduct object at 0x1f8cbd8>) 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 0x1f8cbd8>, <kernel.DependentProduct object at 0x1f8c7e8>) 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 0x1f8c7e8>, <kernel.DependentProduct object at 0x1f8c950>) 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 0x1f8c7e8>, <kernel.DependentProduct object at 0x1f8ce60>) 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 0x1f8c3b0>, <kernel.DependentProduct object at 0x1f8ca28>) 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 0x1f8c440>, <kernel.DependentProduct object at 0x1f8c7e8>) 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 0x1f8c7e8>, <kernel.DependentProduct object at 0x1f8ca28>) 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 0x1f8cbd8>, <kernel.DependentProduct object at 0x1f82830>) 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 0x1f8cbd8>, <kernel.DependentProduct object at 0x1f825a8>) 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 0x1f8cbd8>, <kernel.DependentProduct object at 0x1f82638>) 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 0x1f82638>, <kernel.DependentProduct object at 0x1f825a8>) 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 0x1f82638>, <kernel.DependentProduct object at 0x1f82908>) of role type named exists_in_world_type
% Using role type
% Declaring exists_in_world:(mu->(fofType->Prop))
% FOF formula (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))) of role axiom named nonempty_ax
% A new axiom: (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V))))
% FOF formula (<kernel.Constant object at 0x1f82248>, <kernel.DependentProduct object at 0x1f82290>) 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), (((exists_in_world X) W)->((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), (((exists_in_world X) W)->((Phi X) W)))))
% Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W))))
% FOF formula (<kernel.Constant object at 0x1f82680>, <kernel.DependentProduct object at 0x1f82128>) 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 0x1f82128>, <kernel.DependentProduct object at 0x1f82488>) 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 0x1f82290>, <kernel.DependentProduct object at 0x1f82c20>) 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 0x1f82c20>, <kernel.DependentProduct object at 0x1f82b90>) 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 0x1f82b90>, <kernel.DependentProduct object at 0x1f82c68>) 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 0x1f82c68>, <kernel.DependentProduct object at 0x1f82758>) 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 0x1f82758>, <kernel.DependentProduct object at 0x1f82f80>) 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 0x1f82f80>, <kernel.DependentProduct object at 0x1f82e18>) 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 0x1f82e18>, <kernel.DependentProduct object at 0x1f82b90>) 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 0x1f82b90>, <kernel.DependentProduct object at 0x1f82b00>) 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 0x1f82b00>, <kernel.DependentProduct object at 0x1f82dd0>) 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 0x1f82dd0>, <kernel.DependentProduct object at 0x1f82c20>) 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 0x1f82128>, <kernel.DependentProduct object at 0x1f82fc8>) 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 0x1f82dd0>, <kernel.DependentProduct object at 0x1f82b48>) 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 0x1f82fc8>, <kernel.DependentProduct object at 0x215c560>) 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))))
% FOF formula (<kernel.Constant object at 0x1f82128>, <kernel.DependentProduct object at 0x215c248>) of role type named minvalid_type
% Using role type
% Declaring minvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^5.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x216e098>, <kernel.DependentProduct object at 0x216e908>) of role type named rel_s4_type
% Using role type
% Declaring rel_s4:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x216ef80>, <kernel.DependentProduct object at 0x216e050>) of role type named mbox_s4_type
% Using role type
% Declaring mbox_s4:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))) of role definition named mbox_s4
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))))
% Defined: mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))
% FOF formula (<kernel.Constant object at 0x216e050>, <kernel.DependentProduct object at 0x216ed40>) of role type named mdia_s4_type
% Using role type
% Declaring mdia_s4:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))) of role definition named mdia_s4
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))))
% Defined: mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))
% FOF formula (mreflexive rel_s4) of role axiom named a1
% A new axiom: (mreflexive rel_s4)
% FOF formula (mtransitive rel_s4) of role axiom named a2
% A new axiom: (mtransitive rel_s4)
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL015^1.ax, trying next directory
% FOF formula (forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W))) of role axiom named cumulative_ax
% A new axiom: (forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W)))
% FOF formula (<kernel.Constant object at 0x1f71bd8>, <kernel.DependentProduct object at 0x1f71a70>) of role type named young_type
% Using role type
% Declaring young:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f715a8>, <kernel.DependentProduct object at 0x1f71cb0>) of role type named man_type
% Using role type
% Declaring man:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f716c8>, <kernel.DependentProduct object at 0x1f71bd8>) of role type named fellow_type
% Using role type
% Declaring fellow:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f71a70>, <kernel.DependentProduct object at 0x1f715f0>) of role type named in_type
% Using role type
% Declaring in:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1f71cb0>, <kernel.DependentProduct object at 0x1f714d0>) of role type named down_type
% Using role type
% Declaring down:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1f71bd8>, <kernel.DependentProduct object at 0x1f71440>) of role type named barrel_type
% Using role type
% Declaring barrel:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1f715f0>, <kernel.DependentProduct object at 0x1f71cb0>) of role type named old_type
% Using role type
% Declaring old:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f714d0>, <kernel.DependentProduct object at 0x1f71bd8>) of role type named dirty_type
% Using role type
% Declaring dirty:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f71440>, <kernel.DependentProduct object at 0x1f715f0>) of role type named white_type
% Using role type
% Declaring white:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f71cb0>, <kernel.DependentProduct object at 0x1f714d0>) of role type named car_type
% Using role type
% Declaring car:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e57290>, <kernel.DependentProduct object at 0x1f71440>) of role type named chevy_type
% Using role type
% Declaring chevy:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f71bd8>, <kernel.DependentProduct object at 0x1f71cb0>) of role type named lonely_type
% Using role type
% Declaring lonely:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f714d0>, <kernel.DependentProduct object at 0x23c8200>) of role type named way_type
% Using role type
% Declaring way:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f71440>, <kernel.DependentProduct object at 0x23c82d8>) of role type named street_type
% Using role type
% Declaring street:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f71368>, <kernel.DependentProduct object at 0x23c8200>) of role type named event_type
% Using role type
% Declaring event:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x216fb90>, <kernel.DependentProduct object at 0x23c82d8>) of role type named city_type
% Using role type
% Declaring city:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x214f518>, <kernel.DependentProduct object at 0x1f714d0>) of role type named hollywood_type
% Using role type
% Declaring hollywood:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x23c82d8>, <kernel.DependentProduct object at 0x23bdb48>) of role type named front_type
% Using role type
% Declaring front:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x23c8248>, <kernel.DependentProduct object at 0x23bd6c8>) of role type named furniture_type
% Using role type
% Declaring furniture:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x23c8248>, <kernel.DependentProduct object at 0x1f71368>) of role type named seat_type
% Using role type
% Declaring seat:(mu->(fofType->Prop))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((qmltpeq X) X)))) of role axiom named reflexivity
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((qmltpeq X) X))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> ((mimplies ((qmltpeq X) Y)) ((qmltpeq Y) X))))))) of role axiom named symmetry
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> ((mimplies ((qmltpeq X) Y)) ((qmltpeq Y) X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> (mforall_ind (fun (Z:mu)=> ((mimplies ((mand ((qmltpeq X) Y)) ((qmltpeq Y) Z))) ((qmltpeq X) Z))))))))) of role axiom named transitivity
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> (mforall_ind (fun (Z:mu)=> ((mimplies ((mand ((qmltpeq X) Y)) ((qmltpeq Y) Z))) ((qmltpeq X) Z)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((barrel A) C))) ((barrel B) C))))))))) of role axiom named barrel_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((barrel A) C))) ((barrel B) C)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((barrel C) A))) ((barrel C) B))))))))) of role axiom named barrel_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((barrel C) A))) ((barrel C) B)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (car A))) (car B))))))) of role axiom named car_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (car A))) (car B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (chevy A))) (chevy B))))))) of role axiom named chevy_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (chevy A))) (chevy B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (city A))) (city B))))))) of role axiom named city_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (city A))) (city B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (dirty A))) (dirty B))))))) of role axiom named dirty_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (dirty A))) (dirty B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((down A) C))) ((down B) C))))))))) of role axiom named down_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((down A) C))) ((down B) C)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((down C) A))) ((down C) B))))))))) of role axiom named down_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((down C) A))) ((down C) B)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (event A))) (event B))))))) of role axiom named event_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (event A))) (event B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (fellow A))) (fellow B))))))) of role axiom named fellow_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (fellow A))) (fellow B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (front A))) (front B))))))) of role axiom named front_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (front A))) (front B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (furniture A))) (furniture B))))))) of role axiom named furniture_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (furniture A))) (furniture B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (hollywood A))) (hollywood B))))))) of role axiom named hollywood_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (hollywood A))) (hollywood B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((in A) C))) ((in B) C))))))))) of role axiom named in_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((in A) C))) ((in B) C)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((in C) A))) ((in C) B))))))))) of role axiom named in_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((in C) A))) ((in C) B)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (lonely A))) (lonely B))))))) of role axiom named lonely_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (lonely A))) (lonely B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (man A))) (man B))))))) of role axiom named man_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (man A))) (man B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (old A))) (old B))))))) of role axiom named old_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (old A))) (old B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (seat A))) (seat B))))))) of role axiom named seat_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (seat A))) (seat B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (street A))) (street B))))))) of role axiom named street_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (street A))) (street B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (way A))) (way B))))))) of role axiom named way_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (way A))) (way B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (white A))) (white B))))))) of role axiom named white_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (white A))) (white B)))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (young A))) (young B))))))) of role axiom named young_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (young A))) (young B)))))))
% FOF formula (mvalid ((mand ((mimplies (mexists_ind (fun (U:mu)=> (mexists_ind (fun (V:mu)=> (mexists_ind (fun (W:mu)=> (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> (mexists_ind (fun (Z:mu)=> (mexists_ind (fun (X1:mu)=> (mexists_ind (fun (X2:mu)=> (mexists_ind (fun (X4:mu)=> (mexists_ind (fun (X5:mu)=> ((mand (seat U)) ((mand (furniture U)) ((mand (front U)) ((mand (seat V)) ((mand (furniture V)) ((mand (front V)) ((mand (hollywood W)) ((mand (city W)) ((mand (event X)) ((mand (street Y)) ((mand (way Y)) ((mand (lonely Y)) ((mand (chevy Z)) ((mand (car Z)) ((mand (white Z)) ((mand (dirty Z)) ((mand (old Z)) ((mand ((barrel X) Z)) ((mand ((down X) Y)) ((mand ((in X) W)) ((mand (mnot ((qmltpeq X1) X2))) ((mand (fellow X1)) ((mand (man X1)) ((mand (young X1)) ((mand (fellow X2)) ((mand (man X2)) ((mand (young X2)) ((mand ((qmltpeq X1) X4)) ((mand ((in X4) U)) ((mand ((qmltpeq X2) X5)) ((in X5) V)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X6:mu)=> (mexists_ind (fun (X7:mu)=> (mexists_ind (fun (X8:mu)=> (mexists_ind (fun (X9:mu)=> (mexists_ind (fun (X10:mu)=> (mexists_ind (fun (X11:mu)=> (mexists_ind (fun (X12:mu)=> (mexists_ind (fun (X13:mu)=> (mexists_ind (fun (X15:mu)=> (mexists_ind (fun (X16:mu)=> ((mand (seat X6)) ((mand (furniture X6)) ((mand (front X6)) ((mand (seat X7)) ((mand (furniture X7)) ((mand (front X7)) ((mand (hollywood X8)) ((mand (city X8)) ((mand (event X9)) ((mand (chevy X10)) ((mand (car X10)) ((mand (white X10)) ((mand (dirty X10)) ((mand (old X10)) ((mand (street X11)) ((mand (way X11)) ((mand (lonely X11)) ((mand ((barrel X9) X10)) ((mand ((down X9) X11)) ((mand ((in X9) X8)) ((mand (mnot ((qmltpeq X12) X13))) ((mand (fellow X12)) ((mand (man X12)) ((mand (young X12)) ((mand (fellow X13)) ((mand (man X13)) ((mand (young X13)) ((mand ((qmltpeq X12) X15)) ((mand ((in X15) X6)) ((mand ((qmltpeq X13) X16)) ((in X16) X7))))))))))))))))))))))))))))))))))))))))))))))))))))) ((mimplies (mexists_ind (fun (X17:mu)=> (mexists_ind (fun (X18:mu)=> (mexists_ind (fun (X19:mu)=> (mexists_ind (fun (X20:mu)=> (mexists_ind (fun (X21:mu)=> (mexists_ind (fun (X22:mu)=> (mexists_ind (fun (X23:mu)=> (mexists_ind (fun (X24:mu)=> (mexists_ind (fun (X26:mu)=> (mexists_ind (fun (X27:mu)=> ((mand (seat X17)) ((mand (furniture X17)) ((mand (front X17)) ((mand (seat X18)) ((mand (furniture X18)) ((mand (front X18)) ((mand (hollywood X19)) ((mand (city X19)) ((mand (event X20)) ((mand (chevy X21)) ((mand (car X21)) ((mand (white X21)) ((mand (dirty X21)) ((mand (old X21)) ((mand (street X22)) ((mand (way X22)) ((mand (lonely X22)) ((mand ((barrel X20) X21)) ((mand ((down X20) X22)) ((mand ((in X20) X19)) ((mand (mnot ((qmltpeq X23) X24))) ((mand (fellow X23)) ((mand (man X23)) ((mand (young X23)) ((mand (fellow X24)) ((mand (man X24)) ((mand (young X24)) ((mand ((qmltpeq X23) X26)) ((mand ((in X26) X17)) ((mand ((qmltpeq X24) X27)) ((in X27) X18)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X28:mu)=> (mexists_ind (fun (X29:mu)=> (mexists_ind (fun (X30:mu)=> (mexists_ind (fun (X31:mu)=> (mexists_ind (fun (X32:mu)=> (mexists_ind (fun (X33:mu)=> (mexists_ind (fun (X34:mu)=> (mexists_ind (fun (X35:mu)=> (mexists_ind (fun (X37:mu)=> (mexists_ind (fun (X38:mu)=> ((mand (seat X28)) ((mand (furniture X28)) ((mand (front X28)) ((mand (seat X29)) ((mand (furniture X29)) ((mand (front X29)) ((mand (hollywood X30)) ((mand (city X30)) ((mand (event X31)) ((mand (street X32)) ((mand (way X32)) ((mand (lonely X32)) ((mand (chevy X33)) ((mand (car X33)) ((mand (white X33)) ((mand (dirty X33)) ((mand (old X33)) ((mand ((barrel X31) X33)) ((mand ((down X31) X32)) ((mand ((in X31) X30)) ((mand (mnot ((qmltpeq X34) X35))) ((mand (fellow X34)) ((mand (man X34)) ((mand (young X34)) ((mand (fellow X35)) ((mand (man X35)) ((mand (young X35)) ((mand ((qmltpeq X34) X37)) ((mand ((in X37) X28)) ((mand ((qmltpeq X35) X38)) ((in X38) X29)))))))))))))))))))))))))))))))))))))))))))))))))))))) of role conjecture named co1
% Conjecture to prove = (mvalid ((mand ((mimplies (mexists_ind (fun (U:mu)=> (mexists_ind (fun (V:mu)=> (mexists_ind (fun (W:mu)=> (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> (mexists_ind (fun (Z:mu)=> (mexists_ind (fun (X1:mu)=> (mexists_ind (fun (X2:mu)=> (mexists_ind (fun (X4:mu)=> (mexists_ind (fun (X5:mu)=> ((mand (seat U)) ((mand (furniture U)) ((mand (front U)) ((mand (seat V)) ((mand (furniture V)) ((mand (front V)) ((mand (hollywood W)) ((mand (city W)) ((mand (event X)) ((mand (street Y)) ((mand (way Y)) ((mand (lonely Y)) ((mand (chevy Z)) ((mand (car Z)) ((mand (white Z)) ((mand (dirty Z)) ((mand (old Z)) ((mand ((barrel X) Z)) ((mand ((down X) Y)) ((mand ((in X) W)) ((mand (mnot ((qmltpeq X1) X2))) ((mand (fellow X1)) ((mand (man X1)) ((mand (young X1)) ((mand (fellow X2)) ((mand (man X2)) ((mand (young X2)) ((mand ((qmltpeq X1) X4)) ((mand ((in X4) U)) ((mand ((qmltpeq X2) X5)) ((in X5) V)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X6:mu)=> (mexists_ind (fun (X7:mu)=> (mexists_ind (fun (X8:mu)=> (mexists_ind (fun (X9:mu)=> (mexists_ind (fun (X10:mu)=> (mexists_ind (fun (X11:mu)=> (mexists_ind (fun (X12:mu)=> (mexists_ind (fun (X13:mu)=> (mexists_ind (fun (X15:mu)=> (mexists_ind (fun (X16:mu)=> ((mand (seat X6)) ((mand (furniture X6)) ((mand (front X6)) ((mand (seat X7)) ((mand (furniture X7)) ((mand (front X7)) ((mand (hollywood X8)) ((mand (city X8)) ((mand (event X9)) ((mand (chevy X10)) ((mand (car X10)) ((mand (white X10)) ((mand (dirty X10)) ((mand (old X10)) ((mand (street X11)) ((mand (way X11)) ((mand (lonely X11)) ((mand ((barrel X9) X10)) ((mand ((down X9) X11)) ((mand ((in X9) X8)) ((mand (mnot ((qmltpeq X12) X13))) ((mand (fellow X12)) ((mand (man X12)) ((mand (young X12)) ((mand (fellow X13)) ((mand (man X13)) ((mand (young X13)) ((mand ((qmltpeq X12) X15)) ((mand ((in X15) X6)) ((mand ((qmltpeq X13) X16)) ((in X16) X7))))))))))))))))))))))))))))))))))))))))))))))))))))) ((mimplies (mexists_ind (fun (X17:mu)=> (mexists_ind (fun (X18:mu)=> (mexists_ind (fun (X19:mu)=> (mexists_ind (fun (X20:mu)=> (mexists_ind (fun (X21:mu)=> (mexists_ind (fun (X22:mu)=> (mexists_ind (fun (X23:mu)=> (mexists_ind (fun (X24:mu)=> (mexists_ind (fun (X26:mu)=> (mexists_ind (fun (X27:mu)=> ((mand (seat X17)) ((mand (furniture X17)) ((mand (front X17)) ((mand (seat X18)) ((mand (furniture X18)) ((mand (front X18)) ((mand (hollywood X19)) ((mand (city X19)) ((mand (event X20)) ((mand (chevy X21)) ((mand (car X21)) ((mand (white X21)) ((mand (dirty X21)) ((mand (old X21)) ((mand (street X22)) ((mand (way X22)) ((mand (lonely X22)) ((mand ((barrel X20) X21)) ((mand ((down X20) X22)) ((mand ((in X20) X19)) ((mand (mnot ((qmltpeq X23) X24))) ((mand (fellow X23)) ((mand (man X23)) ((mand (young X23)) ((mand (fellow X24)) ((mand (man X24)) ((mand (young X24)) ((mand ((qmltpeq X23) X26)) ((mand ((in X26) X17)) ((mand ((qmltpeq X24) X27)) ((in X27) X18)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X28:mu)=> (mexists_ind (fun (X29:mu)=> (mexists_ind (fun (X30:mu)=> (mexists_ind (fun (X31:mu)=> (mexists_ind (fun (X32:mu)=> (mexists_ind (fun (X33:mu)=> (mexists_ind (fun (X34:mu)=> (mexists_ind (fun (X35:mu)=> (mexists_ind (fun (X37:mu)=> (mexists_ind (fun (X38:mu)=> ((mand (seat X28)) ((mand (furniture X28)) ((mand (front X28)) ((mand (seat X29)) ((mand (furniture X29)) ((mand (front X29)) ((mand (hollywood X30)) ((mand (city X30)) ((mand (event X31)) ((mand (street X32)) ((mand (way X32)) ((mand (lonely X32)) ((mand (chevy X33)) ((mand (car X33)) ((mand (white X33)) ((mand (dirty X33)) ((mand (old X33)) ((mand ((barrel X31) X33)) ((mand ((down X31) X32)) ((mand ((in X31) X30)) ((mand (mnot ((qmltpeq X34) X35))) ((mand (fellow X34)) ((mand (man X34)) ((mand (young X34)) ((mand (fellow X35)) ((mand (man X35)) ((mand (young X35)) ((mand ((qmltpeq X34) X37)) ((mand ((in X37) X28)) ((mand ((qmltpeq X35) X38)) ((in X38) X29)))))))))))))))))))))))))))))))))))))))))))))))))))))):Prop
% Parameter mu_DUMMY:mu.
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(mvalid ((mand ((mimplies (mexists_ind (fun (U:mu)=> (mexists_ind (fun (V:mu)=> (mexists_ind (fun (W:mu)=> (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> (mexists_ind (fun (Z:mu)=> (mexists_ind (fun (X1:mu)=> (mexists_ind (fun (X2:mu)=> (mexists_ind (fun (X4:mu)=> (mexists_ind (fun (X5:mu)=> ((mand (seat U)) ((mand (furniture U)) ((mand (front U)) ((mand (seat V)) ((mand (furniture V)) ((mand (front V)) ((mand (hollywood W)) ((mand (city W)) ((mand (event X)) ((mand (street Y)) ((mand (way Y)) ((mand (lonely Y)) ((mand (chevy Z)) ((mand (car Z)) ((mand (white Z)) ((mand (dirty Z)) ((mand (old Z)) ((mand ((barrel X) Z)) ((mand ((down X) Y)) ((mand ((in X) W)) ((mand (mnot ((qmltpeq X1) X2))) ((mand (fellow X1)) ((mand (man X1)) ((mand (young X1)) ((mand (fellow X2)) ((mand (man X2)) ((mand (young X2)) ((mand ((qmltpeq X1) X4)) ((mand ((in X4) U)) ((mand ((qmltpeq X2) X5)) ((in X5) V)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X6:mu)=> (mexists_ind (fun (X7:mu)=> (mexists_ind (fun (X8:mu)=> (mexists_ind (fun (X9:mu)=> (mexists_ind (fun (X10:mu)=> (mexists_ind (fun (X11:mu)=> (mexists_ind (fun (X12:mu)=> (mexists_ind (fun (X13:mu)=> (mexists_ind (fun (X15:mu)=> (mexists_ind (fun (X16:mu)=> ((mand (seat X6)) ((mand (furniture X6)) ((mand (front X6)) ((mand (seat X7)) ((mand (furniture X7)) ((mand (front X7)) ((mand (hollywood X8)) ((mand (city X8)) ((mand (event X9)) ((mand (chevy X10)) ((mand (car X10)) ((mand (white X10)) ((mand (dirty X10)) ((mand (old X10)) ((mand (street X11)) ((mand (way X11)) ((mand (lonely X11)) ((mand ((barrel X9) X10)) ((mand ((down X9) X11)) ((mand ((in X9) X8)) ((mand (mnot ((qmltpeq X12) X13))) ((mand (fellow X12)) ((mand (man X12)) ((mand (young X12)) ((mand (fellow X13)) ((mand (man X13)) ((mand (young X13)) ((mand ((qmltpeq X12) X15)) ((mand ((in X15) X6)) ((mand ((qmltpeq X13) X16)) ((in X16) X7))))))))))))))))))))))))))))))))))))))))))))))))))))) ((mimplies (mexists_ind (fun (X17:mu)=> (mexists_ind (fun (X18:mu)=> (mexists_ind (fun (X19:mu)=> (mexists_ind (fun (X20:mu)=> (mexists_ind (fun (X21:mu)=> (mexists_ind (fun (X22:mu)=> (mexists_ind (fun (X23:mu)=> (mexists_ind (fun (X24:mu)=> (mexists_ind (fun (X26:mu)=> (mexists_ind (fun (X27:mu)=> ((mand (seat X17)) ((mand (furniture X17)) ((mand (front X17)) ((mand (seat X18)) ((mand (furniture X18)) ((mand (front X18)) ((mand (hollywood X19)) ((mand (city X19)) ((mand (event X20)) ((mand (chevy X21)) ((mand (car X21)) ((mand (white X21)) ((mand (dirty X21)) ((mand (old X21)) ((mand (street X22)) ((mand (way X22)) ((mand (lonely X22)) ((mand ((barrel X20) X21)) ((mand ((down X20) X22)) ((mand ((in X20) X19)) ((mand (mnot ((qmltpeq X23) X24))) ((mand (fellow X23)) ((mand (man X23)) ((mand (young X23)) ((mand (fellow X24)) ((mand (man X24)) ((mand (young X24)) ((mand ((qmltpeq X23) X26)) ((mand ((in X26) X17)) ((mand ((qmltpeq X24) X27)) ((in X27) X18)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X28:mu)=> (mexists_ind (fun (X29:mu)=> (mexists_ind (fun (X30:mu)=> (mexists_ind (fun (X31:mu)=> (mexists_ind (fun (X32:mu)=> (mexists_ind (fun (X33:mu)=> (mexists_ind (fun (X34:mu)=> (mexists_ind (fun (X35:mu)=> (mexists_ind (fun (X37:mu)=> (mexists_ind (fun (X38:mu)=> ((mand (seat X28)) ((mand (furniture X28)) ((mand (front X28)) ((mand (seat X29)) ((mand (furniture X29)) ((mand (front X29)) ((mand (hollywood X30)) ((mand (city X30)) ((mand (event X31)) ((mand (street X32)) ((mand (way X32)) ((mand (lonely X32)) ((mand (chevy X33)) ((mand (car X33)) ((mand (white X33)) ((mand (dirty X33)) ((mand (old X33)) ((mand ((barrel X31) X33)) ((mand ((down X31) X32)) ((mand ((in X31) X30)) ((mand (mnot ((qmltpeq X34) X35))) ((mand (fellow X34)) ((mand (man X34)) ((mand (young X34)) ((mand (fellow X35)) ((mand (man X35)) ((mand (young X35)) ((mand ((qmltpeq X34) X37)) ((mand ((in X37) X28)) ((mand ((qmltpeq X35) X38)) ((in X38) X29))))))))))))))))))))))))))))))))))))))))))))))))))))))']
% Parameter mu:Type.
% Parameter fofType:Type.
% Parameter qmltpeq:(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 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 mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% Definition mfalse:=(mnot mtrue):(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 mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Parameter exists_in_world:(mu->(fofType->Prop)).
% Axiom nonempty_ax:(forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))).
% Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W)))):((mu->(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 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 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).
% Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% Parameter rel_s4:(fofType->(fofType->Prop)).
% Definition mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% Definition mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% Axiom a1:(mreflexive rel_s4).
% Axiom a2:(mtransitive rel_s4).
% Axiom cumulative_ax:(forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W))).
% Parameter young:(mu->(fofType->Prop)).
% Parameter man:(mu->(fofType->Prop)).
% Parameter fellow:(mu->(fofType->Prop)).
% Parameter in:(mu->(mu->(fofType->Prop))).
% Parameter down:(mu->(mu->(fofType->Prop))).
% Parameter barrel:(mu->(mu->(fofType->Prop))).
% Parameter old:(mu->(fofType->Prop)).
% Parameter dirty:(mu->(fofType->Prop)).
% Parameter white:(mu->(fofType->Prop)).
% Parameter car:(mu->(fofType->Prop)).
% Parameter chevy:(mu->(fofType->Prop)).
% Parameter lonely:(mu->(fofType->Prop)).
% Parameter way:(mu->(fofType->Prop)).
% Parameter street:(mu->(fofType->Prop)).
% Parameter event:(mu->(fofType->Prop)).
% Parameter city:(mu->(fofType->Prop)).
% Parameter hollywood:(mu->(fofType->Prop)).
% Parameter front:(mu->(fofType->Prop)).
% Parameter furniture:(mu->(fofType->Prop)).
% Parameter seat:(mu->(fofType->Prop)).
% Axiom reflexivity:(mvalid (mforall_ind (fun (X:mu)=> ((qmltpeq X) X)))).
% Axiom symmetry:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> ((mimplies ((qmltpeq X) Y)) ((qmltpeq Y) X))))))).
% Axiom transitivity:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> (mforall_ind (fun (Z:mu)=> ((mimplies ((mand ((qmltpeq X) Y)) ((qmltpeq Y) Z))) ((qmltpeq X) Z))))))))).
% Axiom barrel_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((barrel A) C))) ((barrel B) C))))))))).
% Axiom barrel_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((barrel C) A))) ((barrel C) B))))))))).
% Axiom car_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (car A))) (car B))))))).
% Axiom chevy_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (chevy A))) (chevy B))))))).
% Axiom city_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (city A))) (city B))))))).
% Axiom dirty_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (dirty A))) (dirty B))))))).
% Axiom down_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((down A) C))) ((down B) C))))))))).
% Axiom down_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((down C) A))) ((down C) B))))))))).
% Axiom event_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (event A))) (event B))))))).
% Axiom fellow_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (fellow A))) (fellow B))))))).
% Axiom front_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (front A))) (front B))))))).
% Axiom furniture_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (furniture A))) (furniture B))))))).
% Axiom hollywood_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (hollywood A))) (hollywood B))))))).
% Axiom in_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((in A) C))) ((in B) C))))))))).
% Axiom in_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((in C) A))) ((in C) B))))))))).
% Axiom lonely_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (lonely A))) (lonely B))))))).
% Axiom man_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (man A))) (man B))))))).
% Axiom old_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (old A))) (old B))))))).
% Axiom seat_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (seat A))) (seat B))))))).
% Axiom street_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (street A))) (street B))))))).
% Axiom way_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (way A))) (way B))))))).
% Axiom white_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (white A))) (white B))))))).
% Axiom young_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((mand ((qmltpeq A) B)) (young A))) (young B))))))).
% Trying to prove (mvalid ((mand ((mimplies (mexists_ind (fun (U:mu)=> (mexists_ind (fun (V:mu)=> (mexists_ind (fun (W:mu)=> (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> (mexists_ind (fun (Z:mu)=> (mexists_ind (fun (X1:mu)=> (mexists_ind (fun (X2:mu)=> (mexists_ind (fun (X4:mu)=> (mexists_ind (fun (X5:mu)=> ((mand (seat U)) ((mand (furniture U)) ((mand (front U)) ((mand (seat V)) ((mand (furniture V)) ((mand (front V)) ((mand (hollywood W)) ((mand (city W)) ((mand (event X)) ((mand (street Y)) ((mand (way Y)) ((mand (lonely Y)) ((mand (chevy Z)) ((mand (car Z)) ((mand (white Z)) ((mand (dirty Z)) ((mand (old Z)) ((mand ((barrel X) Z)) ((mand ((down X) Y)) ((mand ((in X) W)) ((mand (mnot ((qmltpeq X1) X2))) ((mand (fellow X1)) ((mand (man X1)) ((mand (young X1)) ((mand (fellow X2)) ((mand (man X2)) ((mand (young X2)) ((mand ((qmltpeq X1) X4)) ((mand ((in X4) U)) ((mand ((qmltpeq X2) X5)) ((in X5) V)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X6:mu)=> (mexists_ind (fun (X7:mu)=> (mexists_ind (fun (X8:mu)=> (mexists_ind (fun (X9:mu)=> (mexists_ind (fun (X10:mu)=> (mexists_ind (fun (X11:mu)=> (mexists_ind (fun (X12:mu)=> (mexists_ind (fun (X13:mu)=> (mexists_ind (fun (X15:mu)=> (mexists_ind (fun (X16:mu)=> ((mand (seat X6)) ((mand (furniture X6)) ((mand (front X6)) ((mand (seat X7)) ((mand (furniture X7)) ((mand (front X7)) ((mand (hollywood X8)) ((mand (city X8)) ((mand (event X9)) ((mand (chevy X10)) ((mand (car X10)) ((mand (white X10)) ((mand (dirty X10)) ((mand (old X10)) ((mand (street X11)) ((mand (way X11)) ((mand (lonely X11)) ((mand ((barrel X9) X10)) ((mand ((down X9) X11)) ((mand ((in X9) X8)) ((mand (mnot ((qmltpeq X12) X13))) ((mand (fellow X12)) ((mand (man X12)) ((mand (young X12)) ((mand (fellow X13)) ((mand (man X13)) ((mand (young X13)) ((mand ((qmltpeq X12) X15)) ((mand ((in X15) X6)) ((mand ((qmltpeq X13) X16)) ((in X16) X7))))))))))))))))))))))))))))))))))))))))))))))))))))) ((mimplies (mexists_ind (fun (X17:mu)=> (mexists_ind (fun (X18:mu)=> (mexists_ind (fun (X19:mu)=> (mexists_ind (fun (X20:mu)=> (mexists_ind (fun (X21:mu)=> (mexists_ind (fun (X22:mu)=> (mexists_ind (fun (X23:mu)=> (mexists_ind (fun (X24:mu)=> (mexists_ind (fun (X26:mu)=> (mexists_ind (fun (X27:mu)=> ((mand (seat X17)) ((mand (furniture X17)) ((mand (front X17)) ((mand (sea
% EOF
%------------------------------------------------------------------------------