%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SYO044^1 : TPTP v7.5.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 0s % DateTime : Tue Mar 29 00:50:29 EDT 2022 % Result : Theorem 0.70s 0.91s % Output : Proof 0.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYO044^1 : TPTP v7.5.0. Released v4.0.0. % 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.12/0.33 % Computer : n019.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % RAMPerCPU : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % DateTime : Fri Mar 11 08:14:12 EST 2022 % 0.12/0.33 % CPUTime : % 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27' % 0.12/0.35 Python 2.7.5 % 0.40/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 0.40/0.62 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory % 0.40/0.62 FOF formula (<kernel.Constant object at 0x2189bd8>, <kernel.Type object at 0x2189ef0>) of role type named mu_type % 0.40/0.62 Using role type % 0.40/0.62 Declaring mu:Type % 0.40/0.62 FOF formula (<kernel.Constant object at 0x2189dd0>, <kernel.DependentProduct object at 0x2189bd8>) of role type named meq_ind_type % 0.40/0.62 Using role type % 0.40/0.62 Declaring meq_ind:(mu->(mu->(fofType->Prop))) % 0.40/0.62 FOF formula (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) of role definition named meq_ind % 0.40/0.62 A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) % 0.40/0.62 Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)) % 0.40/0.62 FOF formula (<kernel.Constant object at 0x2189e18>, <kernel.DependentProduct object at 0x2189050>) of role type named meq_prop_type % 0.40/0.62 Using role type % 0.40/0.62 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.40/0.62 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 % 0.40/0.62 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)))) % 0.40/0.62 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))) % 0.40/0.62 FOF formula (<kernel.Constant object at 0x218e710>, <kernel.DependentProduct object at 0x2189170>) of role type named mnot_type % 0.40/0.62 Using role type % 0.40/0.62 Declaring mnot:((fofType->Prop)->(fofType->Prop)) % 0.40/0.62 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot % 0.40/0.62 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) % 0.40/0.62 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)) % 0.40/0.62 FOF formula (<kernel.Constant object at 0x218e200>, <kernel.DependentProduct object at 0x2189e18>) of role type named mor_type % 0.40/0.62 Using role type % 0.40/0.62 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.40/0.62 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 % 0.40/0.62 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)))) % 0.40/0.62 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))) % 0.40/0.62 FOF formula (<kernel.Constant object at 0x218e200>, <kernel.DependentProduct object at 0x21898c0>) of role type named mand_type % 0.40/0.62 Using role type % 0.40/0.62 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.40/0.62 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 % 0.40/0.62 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))) % 0.40/0.62 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))) % 0.40/0.62 FOF formula (<kernel.Constant object at 0x218eb00>, <kernel.DependentProduct object at 0x2189fc8>) of role type named mimplies_type % 0.40/0.62 Using role type % 0.40/0.62 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.40/0.62 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 % 0.40/0.62 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))) % 0.40/0.62 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)) % 0.40/0.63 FOF formula (<kernel.Constant object at 0x2189fc8>, <kernel.DependentProduct object at 0x2189bd8>) of role type named mimplied_type % 0.40/0.63 Using role type % 0.40/0.63 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.40/0.63 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 % 0.40/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))) % 0.40/0.63 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)) % 0.40/0.63 FOF formula (<kernel.Constant object at 0x2189bd8>, <kernel.DependentProduct object at 0x2189f80>) of role type named mequiv_type % 0.40/0.63 Using role type % 0.40/0.63 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.40/0.63 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 % 0.40/0.63 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)))) % 0.40/0.63 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))) % 0.40/0.63 FOF formula (<kernel.Constant object at 0x21898c0>, <kernel.DependentProduct object at 0x2186290>) of role type named mxor_type % 0.40/0.63 Using role type % 0.40/0.63 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.40/0.63 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 % 0.40/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))) % 0.40/0.63 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))) % 0.40/0.63 FOF formula (<kernel.Constant object at 0x2189098>, <kernel.DependentProduct object at 0x2186fc8>) of role type named mforall_ind_type % 0.40/0.63 Using role type % 0.40/0.63 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop)) % 0.40/0.63 FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) of role definition named mforall_ind % 0.40/0.63 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) % 0.40/0.63 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))) % 0.40/0.63 FOF formula (<kernel.Constant object at 0x2189098>, <kernel.DependentProduct object at 0x2186248>) of role type named mforall_prop_type % 0.40/0.63 Using role type % 0.40/0.63 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)) % 0.40/0.63 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 % 0.40/0.63 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)))) % 0.40/0.63 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))) % 0.40/0.63 FOF formula (<kernel.Constant object at 0x21898c0>, <kernel.DependentProduct object at 0x2186f80>) of role type named mexists_ind_type % 0.40/0.63 Using role type % 0.40/0.63 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop)) % 0.40/0.63 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 % 0.40/0.63 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))))))) % 0.47/0.63 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2186f80>, <kernel.DependentProduct object at 0x2186248>) of role type named mexists_prop_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)) % 0.47/0.63 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 % 0.47/0.63 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))))))) % 0.47/0.63 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2186cf8>, <kernel.DependentProduct object at 0x2186dd0>) of role type named mtrue_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring mtrue:(fofType->Prop) % 0.47/0.63 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue % 0.47/0.63 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) % 0.47/0.63 Defined: mtrue:=(fun (W:fofType)=> True) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2186e18>, <kernel.DependentProduct object at 0x2186ea8>) of role type named mfalse_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring mfalse:(fofType->Prop) % 0.47/0.63 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse % 0.47/0.63 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue)) % 0.47/0.63 Defined: mfalse:=(mnot mtrue) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2186d88>, <kernel.DependentProduct object at 0x2186e18>) of role type named mbox_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))) % 0.47/0.63 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 % 0.47/0.63 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))))) % 0.47/0.63 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2186cf8>, <kernel.DependentProduct object at 0x2169b90>) of role type named mdia_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))) % 0.47/0.63 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 % 0.47/0.63 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))))) % 0.47/0.63 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2186ea8>, <kernel.DependentProduct object at 0x2169ea8>) of role type named mreflexive_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring mreflexive:((fofType->(fofType->Prop))->Prop) % 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive % 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) % 0.47/0.63 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2186d88>, <kernel.DependentProduct object at 0x2169638>) of role type named msymmetric_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring msymmetric:((fofType->(fofType->Prop))->Prop) % 0.47/0.65 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 % 0.47/0.65 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))))) % 0.47/0.65 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))) % 0.47/0.65 FOF formula (<kernel.Constant object at 0x218b7e8>, <kernel.DependentProduct object at 0x218b518>) of role type named mserial_type % 0.47/0.65 Using role type % 0.47/0.65 Declaring mserial:((fofType->(fofType->Prop))->Prop) % 0.47/0.65 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 % 0.47/0.65 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)))))) % 0.47/0.65 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))) % 0.47/0.65 FOF formula (<kernel.Constant object at 0x218b518>, <kernel.DependentProduct object at 0x218b488>) of role type named mtransitive_type % 0.47/0.65 Using role type % 0.47/0.65 Declaring mtransitive:((fofType->(fofType->Prop))->Prop) % 0.47/0.65 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 % 0.47/0.65 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))))) % 0.47/0.65 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))) % 0.47/0.65 FOF formula (<kernel.Constant object at 0x218b8c0>, <kernel.DependentProduct object at 0x2169c20>) of role type named meuclidean_type % 0.47/0.65 Using role type % 0.47/0.65 Declaring meuclidean:((fofType->(fofType->Prop))->Prop) % 0.47/0.65 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 % 0.47/0.65 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))))) % 0.47/0.65 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))) % 0.47/0.65 FOF formula (<kernel.Constant object at 0x218b7a0>, <kernel.DependentProduct object at 0x2169638>) of role type named mpartially_functional_type % 0.47/0.65 Using role type % 0.47/0.65 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop) % 0.47/0.65 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 % 0.47/0.65 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))))) % 0.47/0.65 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)))) % 0.47/0.65 FOF formula (<kernel.Constant object at 0x218b7a0>, <kernel.DependentProduct object at 0x2169c20>) of role type named mfunctional_type % 0.47/0.65 Using role type % 0.47/0.65 Declaring mfunctional:((fofType->(fofType->Prop))->Prop) % 0.47/0.65 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 % 0.47/0.66 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))))))))) % 0.47/0.66 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)))))))) % 0.47/0.66 FOF formula (<kernel.Constant object at 0x218b7a0>, <kernel.DependentProduct object at 0x2169d88>) of role type named mweakly_dense_type % 0.47/0.66 Using role type % 0.47/0.66 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop) % 0.47/0.66 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 % 0.47/0.66 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))))))))) % 0.47/0.66 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)))))))) % 0.47/0.66 FOF formula (<kernel.Constant object at 0x2169cf8>, <kernel.DependentProduct object at 0x2169d88>) of role type named mweakly_connected_type % 0.47/0.66 Using role type % 0.47/0.66 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop) % 0.47/0.66 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 % 0.47/0.66 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)))))) % 0.47/0.66 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))))) % 0.47/0.66 FOF formula (<kernel.Constant object at 0x2169b90>, <kernel.DependentProduct object at 0x2169d88>) of role type named mweakly_directed_type % 0.47/0.66 Using role type % 0.47/0.66 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop) % 0.47/0.66 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 % 0.47/0.66 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)))))))) % 0.47/0.66 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))))))) % 0.47/0.66 FOF formula (<kernel.Constant object at 0x2169998>, <kernel.DependentProduct object at 0x22ff098>) of role type named mvalid_type % 0.47/0.66 Using role type % 0.47/0.66 Declaring mvalid:((fofType->Prop)->Prop) % 0.47/0.66 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid % 0.47/0.66 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) % 0.47/0.66 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))) % 0.47/0.66 FOF formula (<kernel.Constant object at 0x2169cf8>, <kernel.DependentProduct object at 0x22ff3b0>) of role type named minvalid_type % 0.47/0.66 Using role type % 0.47/0.66 Declaring minvalid:((fofType->Prop)->Prop) % 0.47/0.66 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid % 0.47/0.66 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) % 0.47/0.66 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))) % 0.47/0.66 FOF formula (<kernel.Constant object at 0x22ff4d0>, <kernel.DependentProduct object at 0x22ff638>) of role type named msatisfiable_type % 0.47/0.66 Using role type % 0.47/0.66 Declaring msatisfiable:((fofType->Prop)->Prop) % 0.47/0.66 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable % 0.47/0.66 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) % 0.47/0.66 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))) % 0.47/0.66 FOF formula (<kernel.Constant object at 0x22ff3b0>, <kernel.DependentProduct object at 0x22ff200>) of role type named mcountersatisfiable_type % 0.47/0.66 Using role type % 0.47/0.66 Declaring mcountersatisfiable:((fofType->Prop)->Prop) % 0.47/0.66 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable % 0.47/0.66 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) % 0.47/0.66 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))) % 0.47/0.66 FOF formula (forall (R:(fofType->(fofType->Prop))), (mvalid ((mbox R) mtrue))) of role conjecture named conj % 0.47/0.66 Conjecture to prove = (forall (R:(fofType->(fofType->Prop))), (mvalid ((mbox R) mtrue))):Prop % 0.47/0.66 Parameter mu_DUMMY:mu. % 0.47/0.66 Parameter fofType_DUMMY:fofType. % 0.47/0.66 We need to prove ['(forall (R:(fofType->(fofType->Prop))), (mvalid ((mbox R) mtrue)))'] % 0.47/0.66 Parameter mu:Type. % 0.47/0.66 Parameter fofType:Type. % 0.47/0.66 Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))). % 0.47/0.66 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.47/0.66 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)). % 0.47/0.66 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.47/0.66 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.47/0.66 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.47/0.66 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.47/0.66 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.47/0.66 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.47/0.66 Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)). % 0.47/0.66 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)). % 0.47/0.66 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)). % 0.47/0.66 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)). % 0.47/0.66 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop). % 0.47/0.66 Definition mfalse:=(mnot mtrue):(fofType->Prop). % 0.70/0.91 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))). % 0.70/0.91 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))). % 0.70/0.91 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop). % 0.70/0.91 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop). % 0.70/0.91 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop). % 0.70/0.91 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). % 0.70/0.91 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). % 0.70/0.91 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). % 0.70/0.91 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). % 0.70/0.91 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). % 0.70/0.91 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). % 0.70/0.91 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). % 0.70/0.91 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop). % 0.70/0.91 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop). % 0.70/0.91 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop). % 0.70/0.91 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop). % 0.70/0.91 Trying to prove (forall (R:(fofType->(fofType->Prop))), (mvalid ((mbox R) mtrue))) % 0.70/0.91 Found I:True % 0.70/0.91 Found I as proof of (mtrue V) % 0.70/0.91 Found (or_intror00 I) as proof of ((or (((R W) V)->False)) (mtrue V)) % 0.70/0.91 Found ((or_intror0 (mtrue V)) I) as proof of ((or (((R W) V)->False)) (mtrue V)) % 0.70/0.91 Found (((or_intror (((R W) V)->False)) (mtrue V)) I) as proof of ((or (((R W) V)->False)) (mtrue V)) % 0.70/0.91 Found (fun (V:fofType)=> (((or_intror (((R W) V)->False)) (mtrue V)) I)) as proof of ((or (((R W) V)->False)) (mtrue V)) % 0.70/0.91 Found (fun (V:fofType)=> (((or_intror (((R W) V)->False)) (mtrue V)) I)) as proof of (forall (V:fofType), ((or (((R W) V)->False)) (mtrue V))) % 0.70/0.91 Found (fun (W:fofType) (V:fofType)=> (((or_intror (((R W) V)->False)) (mtrue V)) I)) as proof of (((mbox R) mtrue) W) % 0.70/0.91 Found (fun (R:(fofType->(fofType->Prop))) (W:fofType) (V:fofType)=> (((or_intror (((R W) V)->False)) (mtrue V)) I)) as proof of (mvalid ((mbox R) mtrue)) % 0.70/0.91 Found (fun (R:(fofType->(fofType->Prop))) (W:fofType) (V:fofType)=> (((or_intror (((R W) V)->False)) (mtrue V)) I)) as proof of (forall (R:(fofType->(fofType->Prop))), (mvalid ((mbox R) mtrue))) % 0.70/0.91 Got proof (fun (R:(fofType->(fofType->Prop))) (W:fofType) (V:fofType)=> (((or_intror (((R W) V)->False)) (mtrue V)) I)) % 0.70/0.91 Time elapsed = 0.237919s % 0.70/0.91 node=35 cost=1202.000000 depth=8 % 0.70/0.91 :::::::::::::::::::::: % 0.70/0.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.70/0.91 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.70/0.91 (fun (R:(fofType->(fofType->Prop))) (W:fofType) (V:fofType)=> (((or_intror (((R W) V)->False)) (mtrue V)) I)) % 0.70/0.91 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p %------------------------------------------------------------------------------