%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : NLP009^7 : TPTP v6.1.0. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n091.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 300.05s % Output : None % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----NO SOLUTION OUTPUT BY SYSTEM %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : NLP009^7 : TPTP v6.1.0. Released v5.5.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n091.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 07:35:31 CDT 2014 % % CPUTime : 300.05 % 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 0x1a71248>, <kernel.Type object at 0x1a8ff80>) of role type named mu_type % Using role type % Declaring mu:Type % FOF formula (<kernel.Constant object at 0x1a71290>, <kernel.DependentProduct object at 0x1a8f050>) of role type named qmltpeq_type % Using role type % Declaring qmltpeq:(mu->(mu->(fofType->Prop))) % FOF formula (<kernel.Constant object at 0x1a8f560>, <kernel.DependentProduct object at 0x1a8fa28>) 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 0x1a8f320>, <kernel.DependentProduct object at 0x1a8f950>) 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 0x1a8f950>, <kernel.DependentProduct object at 0x1a8fc20>) 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 0x1a8fc20>, <kernel.DependentProduct object at 0x1a8f368>) 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 0x1a8f368>, <kernel.DependentProduct object at 0x1a8f320>) 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 0x1a8f560>, <kernel.DependentProduct object at 0x1a8f950>) 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 0x1a8ff38>, <kernel.DependentProduct object at 0x1a8f440>) 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 0x1a8f3b0>, <kernel.DependentProduct object at 0x1a8fc20>) 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 0x1a8f560>, <kernel.DependentProduct object at 0x1a8fc20>) 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 0x1a8f6c8>, <kernel.DependentProduct object at 0x1a90a70>) 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 0x1a8f6c8>, <kernel.DependentProduct object at 0x1a90ea8>) 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 0x1a8f3b0>, <kernel.DependentProduct object at 0x1a90f38>) 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 0x1a90f38>, <kernel.DependentProduct object at 0x1a90ea8>) 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 0x1a90f38>, <kernel.DependentProduct object at 0x1699710>) 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 0x1a90a70>, <kernel.DependentProduct object at 0x16995f0>) 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 0x1699950>, <kernel.DependentProduct object at 0x1699488>) 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 0x1699488>, <kernel.DependentProduct object at 0x16996c8>) 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 0x16995f0>, <kernel.DependentProduct object at 0x1699c68>) 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 0x1699c68>, <kernel.DependentProduct object at 0x1699bd8>) 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 0x1699bd8>, <kernel.DependentProduct object at 0x1699cb0>) 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 0x1699cb0>, <kernel.DependentProduct object at 0x1699878>) 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 0x1699878>, <kernel.DependentProduct object at 0x16994d0>) 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 0x16994d0>, <kernel.DependentProduct object at 0x1699e60>) 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 0x1699e60>, <kernel.DependentProduct object at 0x16997a0>) 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 0x16997a0>, <kernel.DependentProduct object at 0x16995a8>) 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 0x16995a8>, <kernel.DependentProduct object at 0x1699c68>) 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 0x1699c68>, <kernel.DependentProduct object at 0x1699950>) 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 0x1699488>, <kernel.DependentProduct object at 0x1699b90>) 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 0x1699c68>, <kernel.DependentProduct object at 0x1a7e050>) 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 0x16994d0>, <kernel.DependentProduct object at 0x1a7e128>) 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 0x1699b90>, <kernel.DependentProduct object at 0x1a7e2d8>) 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 0x1a718c0>, <kernel.DependentProduct object at 0x1a71170>) of role type named rel_s4_type % Using role type % Declaring rel_s4:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1a71128>, <kernel.DependentProduct object at 0x1a8fdd0>) 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 0x1a71170>, <kernel.DependentProduct object at 0x1a8fe60>) 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 0x1aee8c0>, <kernel.DependentProduct object at 0x1aecd40>) of role type named young_type % Using role type % Declaring young:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aee8c0>, <kernel.DependentProduct object at 0x1aecdd0>) of role type named man_type % Using role type % Declaring man:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aecd88>, <kernel.DependentProduct object at 0x1aece60>) of role type named fellow_type % Using role type % Declaring fellow:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aecd40>, <kernel.DependentProduct object at 0x1aece18>) of role type named front_type % Using role type % Declaring front:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aecdd0>, <kernel.DependentProduct object at 0x1aecd88>) of role type named furniture_type % Using role type % Declaring furniture:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aece60>, <kernel.DependentProduct object at 0x1aecd40>) of role type named seat_type % Using role type % Declaring seat:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aece18>, <kernel.DependentProduct object at 0x1aeca28>) of role type named in_type % Using role type % Declaring in:(mu->(mu->(fofType->Prop))) % FOF formula (<kernel.Constant object at 0x1947050>, <kernel.DependentProduct object at 0x1aeccb0>) of role type named down_type % Using role type % Declaring down:(mu->(mu->(fofType->Prop))) % FOF formula (<kernel.Constant object at 0x19475f0>, <kernel.DependentProduct object at 0x1aecd88>) of role type named barrel_type % Using role type % Declaring barrel:(mu->(mu->(fofType->Prop))) % FOF formula (<kernel.Constant object at 0x1947050>, <kernel.DependentProduct object at 0x1aece60>) of role type named old_type % Using role type % Declaring old:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1947050>, <kernel.DependentProduct object at 0x1aecea8>) of role type named dirty_type % Using role type % Declaring dirty:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aecd88>, <kernel.DependentProduct object at 0x1a71560>) of role type named white_type % Using role type % Declaring white:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aece60>, <kernel.DependentProduct object at 0x1a71368>) of role type named car_type % Using role type % Declaring car:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aeccb0>, <kernel.DependentProduct object at 0x1a710e0>) of role type named chevy_type % Using role type % Declaring chevy:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aecd88>, <kernel.DependentProduct object at 0x1a710e0>) of role type named lonely_type % Using role type % Declaring lonely:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aece60>, <kernel.DependentProduct object at 0x1a710e0>) of role type named way_type % Using role type % Declaring way:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aecd88>, <kernel.DependentProduct object at 0x1a710e0>) of role type named street_type % Using role type % Declaring street:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aeccb0>, <kernel.DependentProduct object at 0x1a71488>) of role type named event_type % Using role type % Declaring event:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aecd88>, <kernel.DependentProduct object at 0x1a713f8>) of role type named city_type % Using role type % Declaring city:(mu->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1aecd88>, <kernel.DependentProduct object at 0x1a71560>) of role type named hollywood_type % Using role type % Declaring hollywood:(mu->(fofType->Prop)) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq X) X)))))) of role axiom named reflexivity % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq X) X)))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) X))))))))))) of role axiom named symmetry % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) X))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 (mforall_ind (fun (Z:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) Z)))) (mbox_s4 ((qmltpeq X) Z)))))))))))))) of role axiom named transitivity % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 (mforall_ind (fun (Z:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) Z)))) (mbox_s4 ((qmltpeq X) Z)))))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((barrel A) C)))) (mbox_s4 ((barrel B) C)))))))))))))) of role axiom named barrel_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((barrel A) C)))) (mbox_s4 ((barrel B) C)))))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((barrel C) A)))) (mbox_s4 ((barrel C) B)))))))))))))) of role axiom named barrel_substitution_2 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((barrel C) A)))) (mbox_s4 ((barrel C) B)))))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (car A)))) (mbox_s4 (car B))))))))))) of role axiom named car_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (car A)))) (mbox_s4 (car B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (chevy A)))) (mbox_s4 (chevy B))))))))))) of role axiom named chevy_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (chevy A)))) (mbox_s4 (chevy B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (city A)))) (mbox_s4 (city B))))))))))) of role axiom named city_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (city A)))) (mbox_s4 (city B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (dirty A)))) (mbox_s4 (dirty B))))))))))) of role axiom named dirty_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (dirty A)))) (mbox_s4 (dirty B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((down A) C)))) (mbox_s4 ((down B) C)))))))))))))) of role axiom named down_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((down A) C)))) (mbox_s4 ((down B) C)))))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((down C) A)))) (mbox_s4 ((down C) B)))))))))))))) of role axiom named down_substitution_2 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((down C) A)))) (mbox_s4 ((down C) B)))))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (event A)))) (mbox_s4 (event B))))))))))) of role axiom named event_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (event A)))) (mbox_s4 (event B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (fellow A)))) (mbox_s4 (fellow B))))))))))) of role axiom named fellow_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (fellow A)))) (mbox_s4 (fellow B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (front A)))) (mbox_s4 (front B))))))))))) of role axiom named front_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (front A)))) (mbox_s4 (front B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (furniture A)))) (mbox_s4 (furniture B))))))))))) of role axiom named furniture_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (furniture A)))) (mbox_s4 (furniture B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (hollywood A)))) (mbox_s4 (hollywood B))))))))))) of role axiom named hollywood_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (hollywood A)))) (mbox_s4 (hollywood B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((in A) C)))) (mbox_s4 ((in B) C)))))))))))))) of role axiom named in_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((in A) C)))) (mbox_s4 ((in B) C)))))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((in C) A)))) (mbox_s4 ((in C) B)))))))))))))) of role axiom named in_substitution_2 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((in C) A)))) (mbox_s4 ((in C) B)))))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (lonely A)))) (mbox_s4 (lonely B))))))))))) of role axiom named lonely_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (lonely A)))) (mbox_s4 (lonely B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (man A)))) (mbox_s4 (man B))))))))))) of role axiom named man_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (man A)))) (mbox_s4 (man B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (old A)))) (mbox_s4 (old B))))))))))) of role axiom named old_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (old A)))) (mbox_s4 (old B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (seat A)))) (mbox_s4 (seat B))))))))))) of role axiom named seat_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (seat A)))) (mbox_s4 (seat B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (street A)))) (mbox_s4 (street B))))))))))) of role axiom named street_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (street A)))) (mbox_s4 (street B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (way A)))) (mbox_s4 (way B))))))))))) of role axiom named way_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (way A)))) (mbox_s4 (way B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (white A)))) (mbox_s4 (white B))))))))))) of role axiom named white_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (white A)))) (mbox_s4 (white B))))))))))) % FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (young A)))) (mbox_s4 (young B))))))))))) of role axiom named young_substitution_1 % A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (young A)))) (mbox_s4 (young B))))))))))) % FOF formula (mvalid ((mand (mbox_s4 ((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 (X3:mu)=> ((mand (mbox_s4 (hollywood U))) ((mand (mbox_s4 (city U))) ((mand (mbox_s4 (event V))) ((mand (mbox_s4 (street W))) ((mand (mbox_s4 (way W))) ((mand (mbox_s4 (lonely W))) ((mand (mbox_s4 (chevy X))) ((mand (mbox_s4 (car X))) ((mand (mbox_s4 (white X))) ((mand (mbox_s4 (dirty X))) ((mand (mbox_s4 (old X))) ((mand (mbox_s4 ((barrel V) X))) ((mand (mbox_s4 ((down V) W))) ((mand (mbox_s4 ((in V) U))) ((mand (mbox_s4 (seat X1))) ((mand (mbox_s4 (furniture X1))) ((mand (mbox_s4 (front X1))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq Y) Z))))) ((mand (mbox_s4 (fellow Y))) ((mand (mbox_s4 (man Y))) ((mand (mbox_s4 (young Y))) ((mand (mbox_s4 (fellow Z))) ((mand (mbox_s4 (man Z))) ((mand (mbox_s4 (young Z))) ((mand (mbox_s4 ((qmltpeq Y) X2))) ((mand (mbox_s4 ((in X2) X1))) ((mand (mbox_s4 ((qmltpeq Z) X3))) (mbox_s4 ((in X3) X1)))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X4:mu)=> (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)=> ((mand (mbox_s4 (hollywood X4))) ((mand (mbox_s4 (city X4))) ((mand (mbox_s4 (event X5))) ((mand (mbox_s4 (chevy X6))) ((mand (mbox_s4 (car X6))) ((mand (mbox_s4 (white X6))) ((mand (mbox_s4 (dirty X6))) ((mand (mbox_s4 (old X6))) ((mand (mbox_s4 (street X7))) ((mand (mbox_s4 (way X7))) ((mand (mbox_s4 (lonely X7))) ((mand (mbox_s4 ((barrel X5) X6))) ((mand (mbox_s4 ((down X5) X7))) ((mand (mbox_s4 ((in X5) X4))) ((mand (mbox_s4 (seat X10))) ((mand (mbox_s4 (furniture X10))) ((mand (mbox_s4 (front X10))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq X8) X9))))) ((mand (mbox_s4 (fellow X8))) ((mand (mbox_s4 (man X8))) ((mand (mbox_s4 (young X8))) ((mand (mbox_s4 (fellow X9))) ((mand (mbox_s4 (man X9))) ((mand (mbox_s4 (young X9))) ((mand (mbox_s4 ((qmltpeq X8) X11))) ((mand (mbox_s4 ((in X11) X10))) ((mand (mbox_s4 ((qmltpeq X9) X12))) (mbox_s4 ((in X12) X10)))))))))))))))))))))))))))))))))))))))))))))))))) (mbox_s4 ((mimplies (mexists_ind (fun (X13:mu)=> (mexists_ind (fun (X14:mu)=> (mexists_ind (fun (X15:mu)=> (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)=> ((mand (mbox_s4 (hollywood X13))) ((mand (mbox_s4 (city X13))) ((mand (mbox_s4 (event X14))) ((mand (mbox_s4 (chevy X15))) ((mand (mbox_s4 (car X15))) ((mand (mbox_s4 (white X15))) ((mand (mbox_s4 (dirty X15))) ((mand (mbox_s4 (old X15))) ((mand (mbox_s4 (street X16))) ((mand (mbox_s4 (way X16))) ((mand (mbox_s4 (lonely X16))) ((mand (mbox_s4 ((barrel X14) X15))) ((mand (mbox_s4 ((down X14) X16))) ((mand (mbox_s4 ((in X14) X13))) ((mand (mbox_s4 (seat X19))) ((mand (mbox_s4 (furniture X19))) ((mand (mbox_s4 (front X19))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq X17) X18))))) ((mand (mbox_s4 (fellow X17))) ((mand (mbox_s4 (man X17))) ((mand (mbox_s4 (young X17))) ((mand (mbox_s4 (fellow X18))) ((mand (mbox_s4 (man X18))) ((mand (mbox_s4 (young X18))) ((mand (mbox_s4 ((qmltpeq X17) X20))) ((mand (mbox_s4 ((in X20) X19))) ((mand (mbox_s4 ((qmltpeq X18) X21))) (mbox_s4 ((in X21) X19)))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X22:mu)=> (mexists_ind (fun (X23:mu)=> (mexists_ind (fun (X24:mu)=> (mexists_ind (fun (X25:mu)=> (mexists_ind (fun (X26:mu)=> (mexists_ind (fun (X27:mu)=> (mexists_ind (fun (X28:mu)=> (mexists_ind (fun (X29:mu)=> (mexists_ind (fun (X30:mu)=> ((mand (mbox_s4 (hollywood X22))) ((mand (mbox_s4 (city X22))) ((mand (mbox_s4 (event X23))) ((mand (mbox_s4 (street X24))) ((mand (mbox_s4 (way X24))) ((mand (mbox_s4 (lonely X24))) ((mand (mbox_s4 (chevy X25))) ((mand (mbox_s4 (car X25))) ((mand (mbox_s4 (white X25))) ((mand (mbox_s4 (dirty X25))) ((mand (mbox_s4 (old X25))) ((mand (mbox_s4 ((barrel X23) X25))) ((mand (mbox_s4 ((down X23) X24))) ((mand (mbox_s4 ((in X23) X22))) ((mand (mbox_s4 (seat X28))) ((mand (mbox_s4 (furniture X28))) ((mand (mbox_s4 (front X28))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq X26) X27))))) ((mand (mbox_s4 (fellow X26))) ((mand (mbox_s4 (man X26))) ((mand (mbox_s4 (young X26))) ((mand (mbox_s4 (fellow X27))) ((mand (mbox_s4 (man X27))) ((mand (mbox_s4 (young X27))) ((mand (mbox_s4 ((qmltpeq X26) X29))) ((mand (mbox_s4 ((in X29) X28))) ((mand (mbox_s4 ((qmltpeq X27) X30))) (mbox_s4 ((in X30) X28))))))))))))))))))))))))))))))))))))))))))))))))))) of role conjecture named co1 % Conjecture to prove = (mvalid ((mand (mbox_s4 ((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 (X3:mu)=> ((mand (mbox_s4 (hollywood U))) ((mand (mbox_s4 (city U))) ((mand (mbox_s4 (event V))) ((mand (mbox_s4 (street W))) ((mand (mbox_s4 (way W))) ((mand (mbox_s4 (lonely W))) ((mand (mbox_s4 (chevy X))) ((mand (mbox_s4 (car X))) ((mand (mbox_s4 (white X))) ((mand (mbox_s4 (dirty X))) ((mand (mbox_s4 (old X))) ((mand (mbox_s4 ((barrel V) X))) ((mand (mbox_s4 ((down V) W))) ((mand (mbox_s4 ((in V) U))) ((mand (mbox_s4 (seat X1))) ((mand (mbox_s4 (furniture X1))) ((mand (mbox_s4 (front X1))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq Y) Z))))) ((mand (mbox_s4 (fellow Y))) ((mand (mbox_s4 (man Y))) ((mand (mbox_s4 (young Y))) ((mand (mbox_s4 (fellow Z))) ((mand (mbox_s4 (man Z))) ((mand (mbox_s4 (young Z))) ((mand (mbox_s4 ((qmltpeq Y) X2))) ((mand (mbox_s4 ((in X2) X1))) ((mand (mbox_s4 ((qmltpeq Z) X3))) (mbox_s4 ((in X3) X1)))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X4:mu)=> (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)=> ((mand (mbox_s4 (hollywood X4))) ((mand (mbox_s4 (city X4))) ((mand (mbox_s4 (event X5))) ((mand (mbox_s4 (chevy X6))) ((mand (mbox_s4 (car X6))) ((mand (mbox_s4 (white X6))) ((mand (mbox_s4 (dirty X6))) ((mand (mbox_s4 (old X6))) ((mand (mbox_s4 (street X7))) ((mand (mbox_s4 (way X7))) ((mand (mbox_s4 (lonely X7))) ((mand (mbox_s4 ((barrel X5) X6))) ((mand (mbox_s4 ((down X5) X7))) ((mand (mbox_s4 ((in X5) X4))) ((mand (mbox_s4 (seat X10))) ((mand (mbox_s4 (furniture X10))) ((mand (mbox_s4 (front X10))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq X8) X9))))) ((mand (mbox_s4 (fellow X8))) ((mand (mbox_s4 (man X8))) ((mand (mbox_s4 (young X8))) ((mand (mbox_s4 (fellow X9))) ((mand (mbox_s4 (man X9))) ((mand (mbox_s4 (young X9))) ((mand (mbox_s4 ((qmltpeq X8) X11))) ((mand (mbox_s4 ((in X11) X10))) ((mand (mbox_s4 ((qmltpeq X9) X12))) (mbox_s4 ((in X12) X10)))))))))))))))))))))))))))))))))))))))))))))))))) (mbox_s4 ((mimplies (mexists_ind (fun (X13:mu)=> (mexists_ind (fun (X14:mu)=> (mexists_ind (fun (X15:mu)=> (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)=> ((mand (mbox_s4 (hollywood X13))) ((mand (mbox_s4 (city X13))) ((mand (mbox_s4 (event X14))) ((mand (mbox_s4 (chevy X15))) ((mand (mbox_s4 (car X15))) ((mand (mbox_s4 (white X15))) ((mand (mbox_s4 (dirty X15))) ((mand (mbox_s4 (old X15))) ((mand (mbox_s4 (street X16))) ((mand (mbox_s4 (way X16))) ((mand (mbox_s4 (lonely X16))) ((mand (mbox_s4 ((barrel X14) X15))) ((mand (mbox_s4 ((down X14) X16))) ((mand (mbox_s4 ((in X14) X13))) ((mand (mbox_s4 (seat X19))) ((mand (mbox_s4 (furniture X19))) ((mand (mbox_s4 (front X19))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq X17) X18))))) ((mand (mbox_s4 (fellow X17))) ((mand (mbox_s4 (man X17))) ((mand (mbox_s4 (young X17))) ((mand (mbox_s4 (fellow X18))) ((mand (mbox_s4 (man X18))) ((mand (mbox_s4 (young X18))) ((mand (mbox_s4 ((qmltpeq X17) X20))) ((mand (mbox_s4 ((in X20) X19))) ((mand (mbox_s4 ((qmltpeq X18) X21))) (mbox_s4 ((in X21) X19)))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X22:mu)=> (mexists_ind (fun (X23:mu)=> (mexists_ind (fun (X24:mu)=> (mexists_ind (fun (X25:mu)=> (mexists_ind (fun (X26:mu)=> (mexists_ind (fun (X27:mu)=> (mexists_ind (fun (X28:mu)=> (mexists_ind (fun (X29:mu)=> (mexists_ind (fun (X30:mu)=> ((mand (mbox_s4 (hollywood X22))) ((mand (mbox_s4 (city X22))) ((mand (mbox_s4 (event X23))) ((mand (mbox_s4 (street X24))) ((mand (mbox_s4 (way X24))) ((mand (mbox_s4 (lonely X24))) ((mand (mbox_s4 (chevy X25))) ((mand (mbox_s4 (car X25))) ((mand (mbox_s4 (white X25))) ((mand (mbox_s4 (dirty X25))) ((mand (mbox_s4 (old X25))) ((mand (mbox_s4 ((barrel X23) X25))) ((mand (mbox_s4 ((down X23) X24))) ((mand (mbox_s4 ((in X23) X22))) ((mand (mbox_s4 (seat X28))) ((mand (mbox_s4 (furniture X28))) ((mand (mbox_s4 (front X28))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq X26) X27))))) ((mand (mbox_s4 (fellow X26))) ((mand (mbox_s4 (man X26))) ((mand (mbox_s4 (young X26))) ((mand (mbox_s4 (fellow X27))) ((mand (mbox_s4 (man X27))) ((mand (mbox_s4 (young X27))) ((mand (mbox_s4 ((qmltpeq X26) X29))) ((mand (mbox_s4 ((in X29) X28))) ((mand (mbox_s4 ((qmltpeq X27) X30))) (mbox_s4 ((in X30) X28))))))))))))))))))))))))))))))))))))))))))))))))))):Prop % Parameter mu_DUMMY:mu. % Parameter fofType_DUMMY:fofType. % We need to prove ['(mvalid ((mand (mbox_s4 ((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 (X3:mu)=> ((mand (mbox_s4 (hollywood U))) ((mand (mbox_s4 (city U))) ((mand (mbox_s4 (event V))) ((mand (mbox_s4 (street W))) ((mand (mbox_s4 (way W))) ((mand (mbox_s4 (lonely W))) ((mand (mbox_s4 (chevy X))) ((mand (mbox_s4 (car X))) ((mand (mbox_s4 (white X))) ((mand (mbox_s4 (dirty X))) ((mand (mbox_s4 (old X))) ((mand (mbox_s4 ((barrel V) X))) ((mand (mbox_s4 ((down V) W))) ((mand (mbox_s4 ((in V) U))) ((mand (mbox_s4 (seat X1))) ((mand (mbox_s4 (furniture X1))) ((mand (mbox_s4 (front X1))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq Y) Z))))) ((mand (mbox_s4 (fellow Y))) ((mand (mbox_s4 (man Y))) ((mand (mbox_s4 (young Y))) ((mand (mbox_s4 (fellow Z))) ((mand (mbox_s4 (man Z))) ((mand (mbox_s4 (young Z))) ((mand (mbox_s4 ((qmltpeq Y) X2))) ((mand (mbox_s4 ((in X2) X1))) ((mand (mbox_s4 ((qmltpeq Z) X3))) (mbox_s4 ((in X3) X1)))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X4:mu)=> (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)=> ((mand (mbox_s4 (hollywood X4))) ((mand (mbox_s4 (city X4))) ((mand (mbox_s4 (event X5))) ((mand (mbox_s4 (chevy X6))) ((mand (mbox_s4 (car X6))) ((mand (mbox_s4 (white X6))) ((mand (mbox_s4 (dirty X6))) ((mand (mbox_s4 (old X6))) ((mand (mbox_s4 (street X7))) ((mand (mbox_s4 (way X7))) ((mand (mbox_s4 (lonely X7))) ((mand (mbox_s4 ((barrel X5) X6))) ((mand (mbox_s4 ((down X5) X7))) ((mand (mbox_s4 ((in X5) X4))) ((mand (mbox_s4 (seat X10))) ((mand (mbox_s4 (furniture X10))) ((mand (mbox_s4 (front X10))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq X8) X9))))) ((mand (mbox_s4 (fellow X8))) ((mand (mbox_s4 (man X8))) ((mand (mbox_s4 (young X8))) ((mand (mbox_s4 (fellow X9))) ((mand (mbox_s4 (man X9))) ((mand (mbox_s4 (young X9))) ((mand (mbox_s4 ((qmltpeq X8) X11))) ((mand (mbox_s4 ((in X11) X10))) ((mand (mbox_s4 ((qmltpeq X9) X12))) (mbox_s4 ((in X12) X10)))))))))))))))))))))))))))))))))))))))))))))))))) (mbox_s4 ((mimplies (mexists_ind (fun (X13:mu)=> (mexists_ind (fun (X14:mu)=> (mexists_ind (fun (X15:mu)=> (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)=> ((mand (mbox_s4 (hollywood X13))) ((mand (mbox_s4 (city X13))) ((mand (mbox_s4 (event X14))) ((mand (mbox_s4 (chevy X15))) ((mand (mbox_s4 (car X15))) ((mand (mbox_s4 (white X15))) ((mand (mbox_s4 (dirty X15))) ((mand (mbox_s4 (old X15))) ((mand (mbox_s4 (street X16))) ((mand (mbox_s4 (way X16))) ((mand (mbox_s4 (lonely X16))) ((mand (mbox_s4 ((barrel X14) X15))) ((mand (mbox_s4 ((down X14) X16))) ((mand (mbox_s4 ((in X14) X13))) ((mand (mbox_s4 (seat X19))) ((mand (mbox_s4 (furniture X19))) ((mand (mbox_s4 (front X19))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq X17) X18))))) ((mand (mbox_s4 (fellow X17))) ((mand (mbox_s4 (man X17))) ((mand (mbox_s4 (young X17))) ((mand (mbox_s4 (fellow X18))) ((mand (mbox_s4 (man X18))) ((mand (mbox_s4 (young X18))) ((mand (mbox_s4 ((qmltpeq X17) X20))) ((mand (mbox_s4 ((in X20) X19))) ((mand (mbox_s4 ((qmltpeq X18) X21))) (mbox_s4 ((in X21) X19)))))))))))))))))))))))))))))))))))))))))))))))) (mexists_ind (fun (X22:mu)=> (mexists_ind (fun (X23:mu)=> (mexists_ind (fun (X24:mu)=> (mexists_ind (fun (X25:mu)=> (mexists_ind (fun (X26:mu)=> (mexists_ind (fun (X27:mu)=> (mexists_ind (fun (X28:mu)=> (mexists_ind (fun (X29:mu)=> (mexists_ind (fun (X30:mu)=> ((mand (mbox_s4 (hollywood X22))) ((mand (mbox_s4 (city X22))) ((mand (mbox_s4 (event X23))) ((mand (mbox_s4 (street X24))) ((mand (mbox_s4 (way X24))) ((mand (mbox_s4 (lonely X24))) ((mand (mbox_s4 (chevy X25))) ((mand (mbox_s4 (car X25))) ((mand (mbox_s4 (white X25))) ((mand (mbox_s4 (dirty X25))) ((mand (mbox_s4 (old X25))) ((mand (mbox_s4 ((barrel X23) X25))) ((mand (mbox_s4 ((down X23) X24))) ((mand (mbox_s4 ((in X23) X22))) ((mand (mbox_s4 (seat X28))) ((mand (mbox_s4 (furniture X28))) ((mand (mbox_s4 (front X28))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq X26) X27))))) ((mand (mbox_s4 (fellow X26))) ((mand (mbox_s4 (man X26))) ((mand (mbox_s4 (young X26))) ((mand (mbox_s4 (fellow X27))) ((mand (mbox_s4 (man X27))) ((mand (mbox_s4 (young X27))) ((mand (mbox_s4 ((qmltpeq X26) X29))) ((mand (mbox_s4 ((in X29) X28))) ((mand (mbox_s4 ((qmltpeq X27) X30))) (mbox_s4 ((in X30) X28)))))))))))))))))))))))))))))))))))))))))))))))))))'] % 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 front:(mu->(fofType->Prop)). % Parameter furniture:(mu->(fofType->Prop)). % Parameter seat:(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)). % Axiom reflexivity:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq X) X)))))). % Axiom symmetry:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) X))))))))))). % Axiom transitivity:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 (mforall_ind (fun (Z:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) Z)))) (mbox_s4 ((qmltpeq X) Z)))))))))))))). % Axiom barrel_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((barrel A) C)))) (mbox_s4 ((barrel B) C)))))))))))))). % Axiom barrel_substitution_2:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((barrel C) A)))) (mbox_s4 ((barrel C) B)))))))))))))). % Axiom car_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (car A)))) (mbox_s4 (car B))))))))))). % Axiom chevy_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (chevy A)))) (mbox_s4 (chevy B))))))))))). % Axiom city_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (city A)))) (mbox_s4 (city B))))))))))). % Axiom dirty_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (dirty A)))) (mbox_s4 (dirty B))))))))))). % Axiom down_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((down A) C)))) (mbox_s4 ((down B) C)))))))))))))). % Axiom down_substitution_2:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((down C) A)))) (mbox_s4 ((down C) B)))))))))))))). % Axiom event_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (event A)))) (mbox_s4 (event B))))))))))). % Axiom fellow_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (fellow A)))) (mbox_s4 (fellow B))))))))))). % Axiom front_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (front A)))) (mbox_s4 (front B))))))))))). % Axiom furniture_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (furniture A)))) (mbox_s4 (furniture B))))))))))). % Axiom hollywood_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (hollywood A)))) (mbox_s4 (hollywood B))))))))))). % Axiom in_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((in A) C)))) (mbox_s4 ((in B) C)))))))))))))). % Axiom in_substitution_2:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((in C) A)))) (mbox_s4 ((in C) B)))))))))))))). % Axiom lonely_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (lonely A)))) (mbox_s4 (lonely B))))))))))). % Axiom man_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (man A)))) (mbox_s4 (man B))))))))))). % Axiom old_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (old A)))) (mbox_s4 (old B))))))))))). % Axiom seat_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (seat A)))) (mbox_s4 (seat B))))))))))). % Axiom street_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (street A)))) (mbox_s4 (street B))))))))))). % Axiom way_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (way A)))) (mbox_s4 (way B))))))))))). % Axiom white_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (white A)))) (mbox_s4 (white B))))))))))). % Axiom young_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 (young A)))) (mbox_s4 (young B))))))))))). % Trying to prove (mvalid ((mand (mbox_s4 ((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 (X3:mu)=> ((mand (mbox_s4 (hollywood U))) ((mand (mbox_s4 (city U))) ((mand (mbox_s4 (event V))) ((mand (mbox_s4 (street W))) ((mand (mbox_s4 (way W))) ((mand (mbox_s4 (lonely W))) ((mand (mbox_s4 (chevy X))) ((mand (mbox_s4 (car X))) ((mand (mbox_s4 (white X))) ((mand (mbox_s4 (dirty X))) ((mand (mbox_s4 (old X))) ((mand (mbox_s4 ((barrel V) X))) ((mand (mbox_s4 ((down V) W))) ((mand (mbox_s4 ((in V) U))) ((mand (mbox_s4 (seat X1))) ((mand (mbox_s4 (furniture X1))) ((mand (mbox_s4 (front X1))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq Y) Z))))) ((mand (mbox_s4 (fellow Y))) ((mand (mbox_s4 (man Y))) ((mand (mbox_s4 (young Y))) ((mand (mbox_s4 (fellow Z))) ((mand (mbox_s4 (man Z))) ((mand (mbox_s4 (young Z))) ((mand (mbox_s4 ((qmltpeq Y) X2))) ((mand (mbox_s4 ((in X2) X1))) ((mand (mbox_s4 ((qmltpeq Z) X3))) 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