%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : LCL719^1 : TPTP v6.1.0. Bugfixed v5.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n095.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 13:26:09 EDT 2014 % Result : Theorem 0.65s % Output : Proof 0.65s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : LCL719^1 : TPTP v6.1.0. Bugfixed v5.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n095.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 10:42:26 CDT 2014 % % CPUTime : 0.65 % Python 2.7.5 % Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory % FOF formula (<kernel.Constant object at 0xea7ea8>, <kernel.Type object at 0xea7bd8>) of role type named mu_type % Using role type % Declaring mu:Type % FOF formula (<kernel.Constant object at 0xea7f38>, <kernel.DependentProduct object at 0xea7ea8>) of role type named meq_ind_type % Using role type % Declaring meq_ind:(mu->(mu->(fofType->Prop))) % FOF formula (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) of role definition named meq_ind % A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) % Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)) % FOF formula (<kernel.Constant object at 0x990d88>, <kernel.DependentProduct object at 0xea7cf8>) 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 0xea7cb0>, <kernel.DependentProduct object at 0xea7bd8>) 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 0xea7290>, <kernel.DependentProduct object at 0xea7ef0>) 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 0xea7bd8>, <kernel.DependentProduct object at 0xacbc20>) 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 0xea7bd8>, <kernel.DependentProduct object at 0xacbdd0>) 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 0xea7bd8>, <kernel.DependentProduct object at 0xacbe60>) 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 0xacbe60>, <kernel.DependentProduct object at 0xacbef0>) 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 0xacbef0>, <kernel.DependentProduct object at 0xacb8c0>) 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 0xacb680>, <kernel.DependentProduct object at 0xacbe60>) of role type named mforall_ind_type % Using role type % Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop)) % FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) of role definition named mforall_ind % A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) % Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))) % FOF formula (<kernel.Constant object at 0xefc7e8>, <kernel.DependentProduct object at 0xacbdd0>) 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 0xefc5f0>, <kernel.DependentProduct object at 0xacb560>) 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 0xacb560>, <kernel.DependentProduct object at 0xacbdd0>) 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 0xacbdd0>, <kernel.DependentProduct object at 0xacbfc8>) 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 0xacbfc8>, <kernel.DependentProduct object at 0xacbc20>) 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 0xacb560>, <kernel.DependentProduct object at 0xacbc20>) 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 0xacbc20>, <kernel.DependentProduct object at 0xacbd40>) 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 0xacbb48>, <kernel.DependentProduct object at 0xac1950>) 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 0xacbb48>, <kernel.DependentProduct object at 0xac1638>) 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 0xacbb48>, <kernel.DependentProduct object at 0xac1950>) 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 0xac1950>, <kernel.DependentProduct object at 0xac17a0>) 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 0xac17a0>, <kernel.DependentProduct object at 0xac18c0>) 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 0xac18c0>, <kernel.DependentProduct object at 0xac1908>) 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 0xac1908>, <kernel.DependentProduct object at 0xac1050>) 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 0xac1050>, <kernel.DependentProduct object at 0xac1a28>) 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 0xac1a28>, <kernel.DependentProduct object at 0xac18c0>) 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 0xac18c0>, <kernel.DependentProduct object at 0xac1e18>) 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 0xac15f0>, <kernel.DependentProduct object at 0xac1cb0>) 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 0xac18c0>, <kernel.DependentProduct object at 0xac10e0>) of role type named minvalid_type % Using role type % Declaring minvalid:((fofType->Prop)->Prop) % FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid % A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) % Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))) % FOF formula (<kernel.Constant object at 0xac1cb0>, <kernel.DependentProduct object at 0xac1098>) 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 0xac10e0>, <kernel.DependentProduct object at 0xac1d40>) of role type named mcountersatisfiable_type % Using role type % Declaring mcountersatisfiable:((fofType->Prop)->Prop) % FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable % A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) % Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))) % Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^1.ax, trying next directory % FOF formula (<kernel.Constant object at 0xea7320>, <kernel.DependentProduct object at 0xea7d40>) of role type named rel_k_type % Using role type % Declaring rel_k:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0xea72d8>, <kernel.DependentProduct object at 0xea7f80>) of role type named mbox_k_type % Using role type % Declaring mbox_k:((fofType->Prop)->(fofType->Prop)) % FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_k) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V))))) of role definition named mbox_k % A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_k) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V))))) % Defined: mbox_k:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V)))) % FOF formula (<kernel.Constant object at 0xea7f80>, <kernel.DependentProduct object at 0xea7bd8>) of role type named mdia_k_type % Using role type % Declaring mdia_k:((fofType->Prop)->(fofType->Prop)) % FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_k) (fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi))))) of role definition named mdia_k % A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_k) (fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi))))) % Defined: mdia_k:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi)))) % FOF formula (<kernel.Constant object at 0xab0b90>, <kernel.DependentProduct object at 0xab0710>) of role type named phi % Using role type % Declaring phi:(fofType->Prop) % FOF formula ((mvalid phi)->(mvalid (mbox_k phi))) of role conjecture named conj % Conjecture to prove = ((mvalid phi)->(mvalid (mbox_k phi))):Prop % Parameter mu_DUMMY:mu. % Parameter fofType_DUMMY:fofType. % We need to prove ['((mvalid phi)->(mvalid (mbox_k phi)))'] % Parameter mu:Type. % Parameter fofType:Type. % Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))). % Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)). % Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)). % Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)). % Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)). % Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)). % Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop). % Definition mfalse:=(mnot mtrue):(fofType->Prop). % Definition mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))). % Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))). % Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop). % Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop). % Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop). % Definition mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))):((fofType->(fofType->Prop))->Prop). % Definition meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))):((fofType->(fofType->Prop))->Prop). % Definition mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))):((fofType->(fofType->Prop))->Prop). % Definition mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))):((fofType->(fofType->Prop))->Prop). % Definition mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))):((fofType->(fofType->Prop))->Prop). % Definition mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))):((fofType->(fofType->Prop))->Prop). % Definition mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))):((fofType->(fofType->Prop))->Prop). % Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop). % Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop). % Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop). % Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop). % Parameter rel_k:(fofType->(fofType->Prop)). % Definition mbox_k:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)). % Definition mdia_k:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi)))):((fofType->Prop)->(fofType->Prop)). % Parameter phi:(fofType->Prop). % Trying to prove ((mvalid phi)->(mvalid (mbox_k phi))) % Found x0:=(x V):(phi V) % Found (x V) as proof of (phi V) % Found (x V) as proof of (phi V) % Found (or_intror00 (x V)) as proof of ((or (((rel_k W) V)->False)) (phi V)) % Found ((or_intror0 (phi V)) (x V)) as proof of ((or (((rel_k W) V)->False)) (phi V)) % Found (((or_intror (((rel_k W) V)->False)) (phi V)) (x V)) as proof of ((or (((rel_k W) V)->False)) (phi V)) % Found (fun (V:fofType)=> (((or_intror (((rel_k W) V)->False)) (phi V)) (x V))) as proof of ((or (((rel_k W) V)->False)) (phi V)) % Found (fun (V:fofType)=> (((or_intror (((rel_k W) V)->False)) (phi V)) (x V))) as proof of (forall (V:fofType), ((or (((rel_k W) V)->False)) (phi V))) % Found (fun (W:fofType) (V:fofType)=> (((or_intror (((rel_k W) V)->False)) (phi V)) (x V))) as proof of ((mbox_k phi) W) % Found (fun (x:(mvalid phi)) (W:fofType) (V:fofType)=> (((or_intror (((rel_k W) V)->False)) (phi V)) (x V))) as proof of (mvalid (mbox_k phi)) % Found (fun (x:(mvalid phi)) (W:fofType) (V:fofType)=> (((or_intror (((rel_k W) V)->False)) (phi V)) (x V))) as proof of ((mvalid phi)->(mvalid (mbox_k phi))) % Got proof (fun (x:(mvalid phi)) (W:fofType) (V:fofType)=> (((or_intror (((rel_k W) V)->False)) (phi V)) (x V))) % Time elapsed = 0.248443s % node=35 cost=1118.000000 depth=9 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:(mvalid phi)) (W:fofType) (V:fofType)=> (((or_intror (((rel_k W) V)->False)) (phi V)) (x V))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------