TSTP Solution File: NLP005^7 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NLP005^7 : TPTP v6.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n115.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 13:26:44 EDT 2014
% Result : Timeout 300.08s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : NLP005^7 : TPTP v6.1.0. Released v5.5.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n115.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 07:29:26 CDT 2014
% % CPUTime : 300.08
% 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 0xf54a28>, <kernel.Type object at 0xf54290>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0xf54560>, <kernel.DependentProduct object at 0xf54a28>) of role type named qmltpeq_type
% Using role type
% Declaring qmltpeq:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0xf543b0>, <kernel.DependentProduct object at 0xf54170>) 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 0xf543b0>, <kernel.DependentProduct object at 0xf545a8>) 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 0xa45cf8>, <kernel.DependentProduct object at 0xf545f0>) 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 0xf545f0>, <kernel.DependentProduct object at 0xf547a0>) 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 0xf54b00>, <kernel.DependentProduct object at 0xfaf050>) 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 0xf54170>, <kernel.DependentProduct object at 0xfaf170>) 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 0xf54170>, <kernel.DependentProduct object at 0xfaf170>) 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 0xf545a8>, <kernel.DependentProduct object at 0xfaf368>) 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 0xfaf368>, <kernel.DependentProduct object at 0xfaf7a0>) 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 0xfaf7a0>, <kernel.DependentProduct object at 0xfaf248>) 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 0xfaf248>, <kernel.DependentProduct object at 0xfaf128>) 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 0xfafc68>, <kernel.DependentProduct object at 0xf34170>) 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 0xfafc68>, <kernel.DependentProduct object at 0xf34248>) 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 0xf34248>, <kernel.DependentProduct object at 0xb5c710>) 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 0xf34248>, <kernel.DependentProduct object at 0xb5c5a8>) 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 0xb5c878>, <kernel.DependentProduct object at 0xb5c560>) 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 0xb5c560>, <kernel.DependentProduct object at 0xb5c830>) 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 0xb5c908>, <kernel.DependentProduct object at 0xb5cc20>) 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 0xb5cc20>, <kernel.DependentProduct object at 0xb5cb90>) 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 0xb5cb90>, <kernel.DependentProduct object at 0xb5cc68>) 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 0xb5cc68>, <kernel.DependentProduct object at 0xb5c7e8>) 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 0xb5c7e8>, <kernel.DependentProduct object at 0xb5cf80>) 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 0xb5cf80>, <kernel.DependentProduct object at 0xb5ce18>) 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 0xb5ce18>, <kernel.DependentProduct object at 0xb5cb90>) 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 0xb5cb90>, <kernel.DependentProduct object at 0xb5cb00>) 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 0xb5cb00>, <kernel.DependentProduct object at 0xb5cdd0>) 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 0xb5cdd0>, <kernel.DependentProduct object at 0xb5cc20>) 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 0xb5c560>, <kernel.DependentProduct object at 0xb5cfc8>) 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 0xb5cdd0>, <kernel.DependentProduct object at 0xb5cb48>) 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 0xb5cfc8>, <kernel.DependentProduct object at 0xf41560>) 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 0xb5c560>, <kernel.DependentProduct object at 0xf41248>) 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 0xcf24d0>, <kernel.DependentProduct object at 0xf54128>) of role type named rel_s4_type
% Using role type
% Declaring rel_s4:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xfb0170>, <kernel.DependentProduct object at 0xf54128>) 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 0xfb0200>, <kernel.DependentProduct object at 0xf54488>) 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 0xf52128>, <kernel.DependentProduct object at 0xf52710>) of role type named young_type
% Using role type
% Declaring young:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf52908>, <kernel.DependentProduct object at 0xf53ea8>) of role type named man_type
% Using role type
% Declaring man:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf521b8>, <kernel.DependentProduct object at 0xf53050>) of role type named fellow_type
% Using role type
% Declaring fellow:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf52200>, <kernel.DependentProduct object at 0xf52b00>) of role type named in_type
% Using role type
% Declaring in:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0xf52908>, <kernel.DependentProduct object at 0xf53ea8>) of role type named down_type
% Using role type
% Declaring down:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0xf521b8>, <kernel.DependentProduct object at 0xf53ef0>) of role type named barrel_type
% Using role type
% Declaring barrel:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0xf52908>, <kernel.DependentProduct object at 0xf53ef0>) of role type named lonely_type
% Using role type
% Declaring lonely:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf52b00>, <kernel.DependentProduct object at 0xf53050>) of role type named way_type
% Using role type
% Declaring way:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf52908>, <kernel.DependentProduct object at 0xf53c20>) of role type named street_type
% Using role type
% Declaring street:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf52908>, <kernel.DependentProduct object at 0xf53cb0>) of role type named old_type
% Using role type
% Declaring old:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf53050>, <kernel.DependentProduct object at 0xf53830>) of role type named dirty_type
% Using role type
% Declaring dirty:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf53c20>, <kernel.DependentProduct object at 0xf53488>) of role type named white_type
% Using role type
% Declaring white:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf53cb0>, <kernel.DependentProduct object at 0xf53050>) of role type named car_type
% Using role type
% Declaring car:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf53830>, <kernel.DependentProduct object at 0xf53c20>) of role type named chevy_type
% Using role type
% Declaring chevy:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf53488>, <kernel.DependentProduct object at 0xf53cb0>) of role type named event_type
% Using role type
% Declaring event:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf53050>, <kernel.DependentProduct object at 0xf53830>) of role type named city_type
% Using role type
% Declaring city:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf53c20>, <kernel.DependentProduct object at 0xf53488>) of role type named hollywood_type
% Using role type
% Declaring hollywood:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf53cb0>, <kernel.DependentProduct object at 0xf53050>) of role type named front_type
% Using role type
% Declaring front:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xcf24d0>, <kernel.DependentProduct object at 0xf53c20>) of role type named furniture_type
% Using role type
% Declaring furniture:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf31cf8>, <kernel.DependentProduct object at 0xf53cb0>) 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 (X3:mu)=> (mexists_ind (fun (X4:mu)=> ((mand (seat U)) ((mand (furniture U)) ((mand (front U)) ((mand (hollywood V)) ((mand (city V)) ((mand (event W)) ((mand (chevy X)) ((mand (car X)) ((mand (white X)) ((mand (dirty X)) ((mand (old X)) ((mand (street Y)) ((mand (way Y)) ((mand (lonely Y)) ((mand ((barrel W) X)) ((mand ((down W) Y)) ((mand ((in W) V)) ((mand (mnot ((qmltpeq Z) X1))) ((mand (fellow Z)) ((mand (man Z)) ((mand (young Z)) ((mand (fellow X1)) ((mand (man X1)) ((mand (young X1)) ((mand ((qmltpeq Z) X3)) ((mand ((in X3) U)) ((mand ((qmltpeq X1) X4)) ((in X4) U))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X5:mu)=> (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 (X14:mu)=> (mexists_ind (fun (X15:mu)=> ((mand (seat X5)) ((mand (furniture X5)) ((mand (front X5)) ((mand (seat X6)) ((mand (furniture X6)) ((mand (front X6)) ((mand (hollywood X7)) ((mand (city X7)) ((mand (event X8)) ((mand (street X9)) ((mand (way X9)) ((mand (lonely X9)) ((mand (chevy X10)) ((mand (car X10)) ((mand (white X10)) ((mand (dirty X10)) ((mand (old X10)) ((mand ((barrel X8) X10)) ((mand ((down X8) X9)) ((mand ((in X8) X7)) ((mand (mnot ((qmltpeq X11) X12))) ((mand (fellow X11)) ((mand (man X11)) ((mand (young X11)) ((mand (fellow X12)) ((mand (man X12)) ((mand (young X12)) ((mand ((qmltpeq X11) X14)) ((mand ((in X14) X5)) ((mand ((qmltpeq X12) X15)) ((in X15) X6))))))))))))))))))))))))))))))))))))))))))))))))))))) ((mimplies (mexists_ind (fun (X16:mu)=> (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 (X25:mu)=> (mexists_ind (fun (X26:mu)=> ((mand (seat X16)) ((mand (furniture X16)) ((mand (front X16)) ((mand (seat X17)) ((mand (furniture X17)) ((mand (front X17)) ((mand (hollywood X18)) ((mand (city X18)) ((mand (event X19)) ((mand (street X20)) ((mand (way X20)) ((mand (lonely X20)) ((mand (chevy X21)) ((mand (car X21)) ((mand (white X21)) ((mand (dirty X21)) ((mand (old X21)) ((mand ((barrel X19) X21)) ((mand ((down X19) X20)) ((mand ((in X19) X18)) ((mand (mnot ((qmltpeq X22) X23))) ((mand (fellow X22)) ((mand (man X22)) ((mand (young X22)) ((mand (fellow X23)) ((mand (man X23)) ((mand (young X23)) ((mand ((qmltpeq X22) X25)) ((mand ((in X25) X16)) ((mand ((qmltpeq X23) X26)) ((in X26) X17)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X27:mu)=> (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 (X35:mu)=> (mexists_ind (fun (X36:mu)=> ((mand (seat X27)) ((mand (furniture X27)) ((mand (front X27)) ((mand (hollywood X28)) ((mand (city X28)) ((mand (event X29)) ((mand (chevy X30)) ((mand (car X30)) ((mand (white X30)) ((mand (dirty X30)) ((mand (old X30)) ((mand (street X31)) ((mand (way X31)) ((mand (lonely X31)) ((mand ((barrel X29) X30)) ((mand ((down X29) X31)) ((mand ((in X29) X28)) ((mand (mnot ((qmltpeq X32) X33))) ((mand (fellow X32)) ((mand (man X32)) ((mand (young X32)) ((mand (fellow X33)) ((mand (man X33)) ((mand (young X33)) ((mand ((qmltpeq X32) X35)) ((mand ((in X35) X27)) ((mand ((qmltpeq X33) X36)) ((in X36) X27))))))))))))))))))))))))))))))))))))))))))))))))) 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 (X3:mu)=> (mexists_ind (fun (X4:mu)=> ((mand (seat U)) ((mand (furniture U)) ((mand (front U)) ((mand (hollywood V)) ((mand (city V)) ((mand (event W)) ((mand (chevy X)) ((mand (car X)) ((mand (white X)) ((mand (dirty X)) ((mand (old X)) ((mand (street Y)) ((mand (way Y)) ((mand (lonely Y)) ((mand ((barrel W) X)) ((mand ((down W) Y)) ((mand ((in W) V)) ((mand (mnot ((qmltpeq Z) X1))) ((mand (fellow Z)) ((mand (man Z)) ((mand (young Z)) ((mand (fellow X1)) ((mand (man X1)) ((mand (young X1)) ((mand ((qmltpeq Z) X3)) ((mand ((in X3) U)) ((mand ((qmltpeq X1) X4)) ((in X4) U))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X5:mu)=> (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 (X14:mu)=> (mexists_ind (fun (X15:mu)=> ((mand (seat X5)) ((mand (furniture X5)) ((mand (front X5)) ((mand (seat X6)) ((mand (furniture X6)) ((mand (front X6)) ((mand (hollywood X7)) ((mand (city X7)) ((mand (event X8)) ((mand (street X9)) ((mand (way X9)) ((mand (lonely X9)) ((mand (chevy X10)) ((mand (car X10)) ((mand (white X10)) ((mand (dirty X10)) ((mand (old X10)) ((mand ((barrel X8) X10)) ((mand ((down X8) X9)) ((mand ((in X8) X7)) ((mand (mnot ((qmltpeq X11) X12))) ((mand (fellow X11)) ((mand (man X11)) ((mand (young X11)) ((mand (fellow X12)) ((mand (man X12)) ((mand (young X12)) ((mand ((qmltpeq X11) X14)) ((mand ((in X14) X5)) ((mand ((qmltpeq X12) X15)) ((in X15) X6))))))))))))))))))))))))))))))))))))))))))))))))))))) ((mimplies (mexists_ind (fun (X16:mu)=> (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 (X25:mu)=> (mexists_ind (fun (X26:mu)=> ((mand (seat X16)) ((mand (furniture X16)) ((mand (front X16)) ((mand (seat X17)) ((mand (furniture X17)) ((mand (front X17)) ((mand (hollywood X18)) ((mand (city X18)) ((mand (event X19)) ((mand (street X20)) ((mand (way X20)) ((mand (lonely X20)) ((mand (chevy X21)) ((mand (car X21)) ((mand (white X21)) ((mand (dirty X21)) ((mand (old X21)) ((mand ((barrel X19) X21)) ((mand ((down X19) X20)) ((mand ((in X19) X18)) ((mand (mnot ((qmltpeq X22) X23))) ((mand (fellow X22)) ((mand (man X22)) ((mand (young X22)) ((mand (fellow X23)) ((mand (man X23)) ((mand (young X23)) ((mand ((qmltpeq X22) X25)) ((mand ((in X25) X16)) ((mand ((qmltpeq X23) X26)) ((in X26) X17)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X27:mu)=> (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 (X35:mu)=> (mexists_ind (fun (X36:mu)=> ((mand (seat X27)) ((mand (furniture X27)) ((mand (front X27)) ((mand (hollywood X28)) ((mand (city X28)) ((mand (event X29)) ((mand (chevy X30)) ((mand (car X30)) ((mand (white X30)) ((mand (dirty X30)) ((mand (old X30)) ((mand (street X31)) ((mand (way X31)) ((mand (lonely X31)) ((mand ((barrel X29) X30)) ((mand ((down X29) X31)) ((mand ((in X29) X28)) ((mand (mnot ((qmltpeq X32) X33))) ((mand (fellow X32)) ((mand (man X32)) ((mand (young X32)) ((mand (fellow X33)) ((mand (man X33)) ((mand (young X33)) ((mand ((qmltpeq X32) X35)) ((mand ((in X35) X27)) ((mand ((qmltpeq X33) X36)) ((in X36) X27))))))))))))))))))))))))))))))))))))))))))))))))):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 (X3:mu)=> (mexists_ind (fun (X4:mu)=> ((mand (seat U)) ((mand (furniture U)) ((mand (front U)) ((mand (hollywood V)) ((mand (city V)) ((mand (event W)) ((mand (chevy X)) ((mand (car X)) ((mand (white X)) ((mand (dirty X)) ((mand (old X)) ((mand (street Y)) ((mand (way Y)) ((mand (lonely Y)) ((mand ((barrel W) X)) ((mand ((down W) Y)) ((mand ((in W) V)) ((mand (mnot ((qmltpeq Z) X1))) ((mand (fellow Z)) ((mand (man Z)) ((mand (young Z)) ((mand (fellow X1)) ((mand (man X1)) ((mand (young X1)) ((mand ((qmltpeq Z) X3)) ((mand ((in X3) U)) ((mand ((qmltpeq X1) X4)) ((in X4) U))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X5:mu)=> (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 (X14:mu)=> (mexists_ind (fun (X15:mu)=> ((mand (seat X5)) ((mand (furniture X5)) ((mand (front X5)) ((mand (seat X6)) ((mand (furniture X6)) ((mand (front X6)) ((mand (hollywood X7)) ((mand (city X7)) ((mand (event X8)) ((mand (street X9)) ((mand (way X9)) ((mand (lonely X9)) ((mand (chevy X10)) ((mand (car X10)) ((mand (white X10)) ((mand (dirty X10)) ((mand (old X10)) ((mand ((barrel X8) X10)) ((mand ((down X8) X9)) ((mand ((in X8) X7)) ((mand (mnot ((qmltpeq X11) X12))) ((mand (fellow X11)) ((mand (man X11)) ((mand (young X11)) ((mand (fellow X12)) ((mand (man X12)) ((mand (young X12)) ((mand ((qmltpeq X11) X14)) ((mand ((in X14) X5)) ((mand ((qmltpeq X12) X15)) ((in X15) X6))))))))))))))))))))))))))))))))))))))))))))))))))))) ((mimplies (mexists_ind (fun (X16:mu)=> (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 (X25:mu)=> (mexists_ind (fun (X26:mu)=> ((mand (seat X16)) ((mand (furniture X16)) ((mand (front X16)) ((mand (seat X17)) ((mand (furniture X17)) ((mand (front X17)) ((mand (hollywood X18)) ((mand (city X18)) ((mand (event X19)) ((mand (street X20)) ((mand (way X20)) ((mand (lonely X20)) ((mand (chevy X21)) ((mand (car X21)) ((mand (white X21)) ((mand (dirty X21)) ((mand (old X21)) ((mand ((barrel X19) X21)) ((mand ((down X19) X20)) ((mand ((in X19) X18)) ((mand (mnot ((qmltpeq X22) X23))) ((mand (fellow X22)) ((mand (man X22)) ((mand (young X22)) ((mand (fellow X23)) ((mand (man X23)) ((mand (young X23)) ((mand ((qmltpeq X22) X25)) ((mand ((in X25) X16)) ((mand ((qmltpeq X23) X26)) ((in X26) X17)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X27:mu)=> (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 (X35:mu)=> (mexists_ind (fun (X36:mu)=> ((mand (seat X27)) ((mand (furniture X27)) ((mand (front X27)) ((mand (hollywood X28)) ((mand (city X28)) ((mand (event X29)) ((mand (chevy X30)) ((mand (car X30)) ((mand (white X30)) ((mand (dirty X30)) ((mand (old X30)) ((mand (street X31)) ((mand (way X31)) ((mand (lonely X31)) ((mand ((barrel X29) X30)) ((mand ((down X29) X31)) ((mand ((in X29) X28)) ((mand (mnot ((qmltpeq X32) X33))) ((mand (fellow X32)) ((mand (man X32)) ((mand (young X32)) ((mand (fellow X33)) ((mand (man X33)) ((mand (young X33)) ((mand ((qmltpeq X32) X35)) ((mand ((in X35) X27)) ((mand ((qmltpeq X33) X36)) ((in X36) X27)))))))))))))))))))))))))))))))))))))))))))))))))']
% 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 lonely:(mu->(fofType->Prop)).
% Parameter way:(mu->(fofType->Prop)).
% Parameter street:(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 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 (X3:mu)=> (mexists_ind (fun (X4:mu)=> ((mand (seat U)) ((mand (furniture U)) ((mand (front U)) ((mand (hollywood V)) ((mand (city V)) ((mand (event W)) ((mand (chevy X)) ((mand (car X)) ((mand (white X)) ((mand (dirty X)) ((mand (old X)) ((mand (street Y)) ((mand (way Y)) ((mand (lonely Y)) ((mand ((barrel W) X)) ((mand ((down W) Y)) ((mand ((in W) V)) ((mand (mnot ((qmltpeq Z) X1))) ((mand (fellow Z)) ((mand (man Z)) ((mand (young Z)) ((mand (fellow X1)) ((mand (man X1)) ((mand (young X1)) ((mand ((qmltpeq Z) X3)) ((mand ((in X3) U)) ((mand ((qmltpeq X1) X4)) ((in X4) U))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X5:mu)=> (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 (X14:mu)=> (mexists_ind (fun (X15:mu)=> ((mand (seat X5)) ((mand (furniture X5)) ((mand (front X5)) ((mand (seat X6)) ((mand (furniture X6)) ((mand (front X6)) ((mand (hollywood X7)) ((mand (city X7)) ((mand (event X8)) ((mand (street X9)) ((mand (way X9)) ((mand (lonely X9)) ((mand (chevy X10)) ((mand (car X10)) ((mand (white X10)) ((mand (dirty X10)) ((mand (old X10)) ((mand ((barrel X8) X10)) ((mand ((down X8) X9)) ((mand ((in X8) X7)) ((mand (mnot ((qmltpeq X11) X12))) ((mand (fellow X11)) ((mand (man X11)) ((mand (young X11)) ((mand (fellow X12)) ((mand (man X12)) ((mand (young X12)) ((mand ((qmltpeq X11) X14)) ((mand ((in X14) X5)) ((mand ((qmltpeq X12) X15)) ((in X15) X6))))))))))))))))))))))))))))))))))))))))))))))))))))) ((mimplies (mexists_ind (fun (X16:mu)=> (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 (X25:mu)=> (mexists_ind (fun (X26:mu)=> ((mand (seat X16)) ((mand (furniture X16)) ((mand (front X16)) ((mand (seat X17)) ((mand (furniture X17)) ((mand (front X17)) ((mand (hollywood X18)) ((mand (city X18)) ((mand (event X19)) ((mand (street X20)) ((mand (way X20)) ((mand (lonely X20)) ((mand (chevy X21)) ((mand (car X21)) ((mand (white X21)) ((mand (dirty X21)) ((mand (old X21)) ((mand ((barrel X19) X21)) ((mand ((down X19) X20)) ((mand ((in X19) X18)) ((mand (mnot ((qmltpeq X22) X23))) ((mand (fellow X22)) ((mand (man X22)) ((mand (young X22)) ((mand (fellow X23)) ((mand (man X23)) ((mand (young X23)) ((mand ((qmltpeq X22) X25)) ((mand ((in X25) X16)) ((mand ((qmltpeq X23) X26)) ((in X26) X17)))))))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X27:mu)=> (mexists_ind (fun (X28:mu)=> (mexists_ind (fun (X29:mu)=> (mexists_ind (fun (X30:mu)=> (mexists_ind (fun (X31:mu)=> (mexists_ind (
% EOF
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