TSTP Solution File: SYO485^6 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO485^6 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 00:51:53 EDT 2022
% Result : Theorem 1.29s 1.48s
% Output : Proof 1.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO485^6 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % RAMPerCPU : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Sun Mar 13 09:32:57 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.33 Python 2.7.5
% 0.43/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.43/0.61 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b4b8f50e3f8>, <kernel.Type object at 0x2b4b8f50e4d0>) of role type named mu_type
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring mu:Type
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b4b8f50e7e8>, <kernel.DependentProduct object at 0x2b4b8f50e3f8>) of role type named meq_ind_type
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% 0.43/0.61 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
% 0.43/0.61 A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% 0.43/0.61 Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b4b8f50e3f8>, <kernel.DependentProduct object at 0x2b4b8f50eef0>) of role type named meq_prop_type
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.43/0.61 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
% 0.43/0.61 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))))
% 0.43/0.61 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b4b8f50ec20>, <kernel.DependentProduct object at 0x2b4b8f50e5f0>) of role type named mnot_type
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.43/0.61 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% 0.43/0.61 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% 0.43/0.61 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b4b8f50eb00>, <kernel.DependentProduct object at 0x2b4b8f50e5f0>) of role type named mor_type
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.43/0.61 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
% 0.43/0.61 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))))
% 0.43/0.61 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b4b8f50e5f0>, <kernel.DependentProduct object at 0x2b4b8f50ecb0>) of role type named mand_type
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.43/0.61 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
% 0.43/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% 0.43/0.61 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b4b8f50ecb0>, <kernel.DependentProduct object at 0x2b4b8f50e3f8>) of role type named mimplies_type
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.43/0.61 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
% 0.43/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% 0.44/0.62 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% 0.44/0.62 FOF formula (<kernel.Constant object at 0x2b4b8f50e3f8>, <kernel.DependentProduct object at 0x2b4b8f50eb00>) of role type named mimplied_type
% 0.44/0.62 Using role type
% 0.44/0.62 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.44/0.62 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
% 0.44/0.62 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% 0.44/0.62 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% 0.44/0.62 FOF formula (<kernel.Constant object at 0x2b4b8f50e638>, <kernel.DependentProduct object at 0x1b9b488>) of role type named mequiv_type
% 0.44/0.62 Using role type
% 0.44/0.62 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.44/0.62 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
% 0.44/0.62 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))))
% 0.44/0.62 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% 0.44/0.62 FOF formula (<kernel.Constant object at 0x2b4b8f50e638>, <kernel.DependentProduct object at 0x1b9b9e0>) of role type named mxor_type
% 0.44/0.62 Using role type
% 0.44/0.62 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.44/0.62 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
% 0.44/0.62 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% 0.44/0.62 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% 0.44/0.62 FOF formula (<kernel.Constant object at 0x1b9b758>, <kernel.DependentProduct object at 0x1b9b248>) of role type named mforall_ind_type
% 0.44/0.62 Using role type
% 0.44/0.62 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.44/0.62 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
% 0.44/0.62 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% 0.44/0.62 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% 0.44/0.62 FOF formula (<kernel.Constant object at 0x1b9b248>, <kernel.DependentProduct object at 0x1b9ba28>) of role type named mforall_prop_type
% 0.44/0.62 Using role type
% 0.44/0.62 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.44/0.63 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
% 0.44/0.63 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))))
% 0.44/0.63 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1b9bcf8>, <kernel.DependentProduct object at 0x1b9fb48>) of role type named mexists_ind_type
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.44/0.63 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
% 0.44/0.63 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)))))))
% 0.44/0.63 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1b9ba28>, <kernel.DependentProduct object at 0x1b9f3b0>) of role type named mexists_prop_type
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.44/0.63 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
% 0.44/0.63 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)))))))
% 0.44/0.63 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1b9ba28>, <kernel.DependentProduct object at 0x1b9f3b0>) of role type named mtrue_type
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring mtrue:(fofType->Prop)
% 0.44/0.63 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% 0.44/0.63 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% 0.44/0.63 Defined: mtrue:=(fun (W:fofType)=> True)
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1b9ba28>, <kernel.DependentProduct object at 0x1b9fc68>) of role type named mfalse_type
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring mfalse:(fofType->Prop)
% 0.44/0.63 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% 0.44/0.63 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% 0.44/0.63 Defined: mfalse:=(mnot mtrue)
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1b9f5f0>, <kernel.DependentProduct object at 0x1b9f680>) of role type named mbox_type
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.44/0.63 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
% 0.44/0.63 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)))))
% 0.44/0.63 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1b9f680>, <kernel.DependentProduct object at 0x1b9f710>) of role type named mdia_type
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.44/0.63 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
% 0.44/0.63 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)))))
% 0.44/0.63 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1b9f4d0>, <kernel.DependentProduct object at 0x1b9ff80>) of role type named mreflexive_type
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% 0.44/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% 0.44/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% 0.44/0.63 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1b9ff80>, <kernel.DependentProduct object at 0x1b9fc20>) of role type named msymmetric_type
% 0.44/0.65 Using role type
% 0.44/0.65 Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 0.44/0.65 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
% 0.44/0.65 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)))))
% 0.44/0.65 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% 0.44/0.65 FOF formula (<kernel.Constant object at 0x1b9fc20>, <kernel.DependentProduct object at 0x1b9f4d0>) of role type named mserial_type
% 0.44/0.65 Using role type
% 0.44/0.65 Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 0.44/0.65 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
% 0.44/0.65 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))))))
% 0.44/0.65 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% 0.44/0.65 FOF formula (<kernel.Constant object at 0x1b9f4d0>, <kernel.DependentProduct object at 0x1b9ff80>) of role type named mtransitive_type
% 0.44/0.65 Using role type
% 0.44/0.65 Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 0.44/0.65 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
% 0.44/0.65 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)))))
% 0.44/0.65 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% 0.44/0.65 FOF formula (<kernel.Constant object at 0x1b9fc68>, <kernel.DependentProduct object at 0x1b9ff80>) of role type named meuclidean_type
% 0.44/0.65 Using role type
% 0.44/0.65 Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 0.44/0.65 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
% 0.44/0.65 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)))))
% 0.44/0.65 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% 0.44/0.65 FOF formula (<kernel.Constant object at 0x1b9fc20>, <kernel.DependentProduct object at 0x1b9cef0>) of role type named mpartially_functional_type
% 0.44/0.65 Using role type
% 0.44/0.65 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 0.44/0.65 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
% 0.44/0.65 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)))))
% 0.44/0.65 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))))
% 0.44/0.65 FOF formula (<kernel.Constant object at 0x1b9f4d0>, <kernel.DependentProduct object at 0x1b9cb90>) of role type named mfunctional_type
% 0.44/0.65 Using role type
% 0.44/0.65 Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 0.44/0.65 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
% 0.44/0.66 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)))))))))
% 0.44/0.66 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))))))))
% 0.44/0.66 FOF formula (<kernel.Constant object at 0x1b9f4d0>, <kernel.DependentProduct object at 0x1b9c200>) of role type named mweakly_dense_type
% 0.44/0.66 Using role type
% 0.44/0.66 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 0.44/0.66 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
% 0.44/0.66 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)))))))))
% 0.44/0.66 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))))))))
% 0.44/0.66 FOF formula (<kernel.Constant object at 0x1b9fc68>, <kernel.DependentProduct object at 0x1b9ce60>) of role type named mweakly_connected_type
% 0.44/0.66 Using role type
% 0.44/0.66 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 0.44/0.66 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
% 0.44/0.66 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))))))
% 0.44/0.66 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)))))
% 0.44/0.66 FOF formula (<kernel.Constant object at 0x1b9ce60>, <kernel.DependentProduct object at 0x1b9c950>) of role type named mweakly_directed_type
% 0.44/0.66 Using role type
% 0.44/0.66 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 0.44/0.66 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
% 0.44/0.66 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))))))))
% 0.44/0.66 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)))))))
% 0.44/0.66 FOF formula (<kernel.Constant object at 0x1b9c5f0>, <kernel.DependentProduct object at 0x1b9cb00>) of role type named mvalid_type
% 0.44/0.66 Using role type
% 0.44/0.66 Declaring mvalid:((fofType->Prop)->Prop)
% 0.44/0.66 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% 0.44/0.66 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.44/0.66 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.44/0.66 FOF formula (<kernel.Constant object at 0x1b9ce60>, <kernel.DependentProduct object at 0x2b4b87a3b200>) of role type named minvalid_type
% 0.44/0.67 Using role type
% 0.44/0.67 Declaring minvalid:((fofType->Prop)->Prop)
% 0.44/0.67 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% 0.44/0.67 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.44/0.67 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.44/0.67 FOF formula (<kernel.Constant object at 0x1b9c0e0>, <kernel.DependentProduct object at 0x2b4b87a3b5f0>) of role type named msatisfiable_type
% 0.44/0.67 Using role type
% 0.44/0.67 Declaring msatisfiable:((fofType->Prop)->Prop)
% 0.44/0.67 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% 0.44/0.67 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.44/0.67 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.44/0.67 FOF formula (<kernel.Constant object at 0x1b9c200>, <kernel.DependentProduct object at 0x2b4b87a3b5f0>) of role type named mcountersatisfiable_type
% 0.44/0.67 Using role type
% 0.44/0.67 Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% 0.44/0.67 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% 0.44/0.67 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.44/0.67 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.44/0.67 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^6.ax, trying next directory
% 0.44/0.67 FOF formula (<kernel.Constant object at 0x1ba0cb0>, <kernel.DependentProduct object at 0x2b4b8f50e518>) of role type named rel_s5_type
% 0.44/0.67 Using role type
% 0.44/0.67 Declaring rel_s5:(fofType->(fofType->Prop))
% 0.44/0.67 FOF formula (<kernel.Constant object at 0x1ba0cb0>, <kernel.DependentProduct object at 0x2b4b8f50e320>) of role type named mbox_s5_type
% 0.44/0.67 Using role type
% 0.44/0.67 Declaring mbox_s5:((fofType->Prop)->(fofType->Prop))
% 0.44/0.67 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s5) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s5 W) V)->False)) (Phi V))))) of role definition named mbox_s5
% 0.44/0.67 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s5) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s5 W) V)->False)) (Phi V)))))
% 0.44/0.67 Defined: mbox_s5:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s5 W) V)->False)) (Phi V))))
% 0.44/0.67 FOF formula (<kernel.Constant object at 0x2b4b8f5103f8>, <kernel.DependentProduct object at 0x2b4b8f50e6c8>) of role type named mdia_s5_type
% 0.44/0.67 Using role type
% 0.44/0.67 Declaring mdia_s5:((fofType->Prop)->(fofType->Prop))
% 0.44/0.67 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s5) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s5 (mnot Phi))))) of role definition named mdia_s5
% 0.44/0.67 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s5) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s5 (mnot Phi)))))
% 0.44/0.67 Defined: mdia_s5:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s5 (mnot Phi))))
% 0.44/0.67 FOF formula (mreflexive rel_s5) of role axiom named a1
% 0.44/0.67 A new axiom: (mreflexive rel_s5)
% 0.44/0.67 FOF formula (mtransitive rel_s5) of role axiom named a2
% 0.44/0.67 A new axiom: (mtransitive rel_s5)
% 0.44/0.67 FOF formula (msymmetric rel_s5) of role axiom named a3
% 0.44/0.67 A new axiom: (msymmetric rel_s5)
% 0.44/0.67 FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mdia_s5 (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))))))) of role conjecture named prove
% 0.44/0.67 Conjecture to prove = (mvalid (mforall_ind (fun (X:mu)=> (mdia_s5 (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))))))):Prop
% 0.44/0.67 Parameter mu_DUMMY:mu.
% 0.44/0.67 Parameter fofType_DUMMY:fofType.
% 0.44/0.67 We need to prove ['(mvalid (mforall_ind (fun (X:mu)=> (mdia_s5 (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))))))']
% 0.44/0.67 Parameter mu:Type.
% 0.44/0.67 Parameter fofType:Type.
% 0.44/0.67 Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% 0.44/0.67 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.44/0.67 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.44/0.67 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.44/0.67 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.44/0.67 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.44/0.67 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.44/0.67 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.44/0.67 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.44/0.67 Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.44/0.67 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.44/0.67 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.44/0.67 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)).
% 0.44/0.67 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.44/0.67 Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 0.44/0.67 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))).
% 0.44/0.67 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.44/0.67 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% 0.44/0.67 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% 0.44/0.67 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 0.44/0.67 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).
% 0.44/0.67 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).
% 0.44/0.67 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).
% 0.44/0.67 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).
% 0.44/0.67 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).
% 0.44/0.67 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).
% 1.21/1.46 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).
% 1.21/1.46 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 1.21/1.46 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 1.21/1.46 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 1.21/1.46 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 1.21/1.46 Parameter rel_s5:(fofType->(fofType->Prop)).
% 1.21/1.46 Definition mbox_s5:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s5 W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% 1.21/1.46 Definition mdia_s5:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s5 (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% 1.21/1.46 Axiom a1:(mreflexive rel_s5).
% 1.21/1.46 Axiom a2:(mtransitive rel_s5).
% 1.21/1.46 Axiom a3:(msymmetric rel_s5).
% 1.21/1.46 Trying to prove (mvalid (mforall_ind (fun (X:mu)=> (mdia_s5 (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))))))
% 1.21/1.46 Found a10:=(a1 W):((rel_s5 W) W)
% 1.21/1.46 Found (a1 W) as proof of ((rel_s5 W) V)
% 1.21/1.46 Found (a1 W) as proof of ((rel_s5 W) V)
% 1.21/1.46 Found (a1 W) as proof of ((rel_s5 W) V)
% 1.21/1.46 Found (x1 (a1 W)) as proof of False
% 1.21/1.46 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of False
% 1.21/1.46 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s5 W) V)->False)->False)
% 1.21/1.46 Found a10:=(a1 S):((rel_s5 S) S)
% 1.21/1.46 Found (a1 S) as proof of ((rel_s5 S) V)
% 1.21/1.46 Found (a1 S) as proof of ((rel_s5 S) V)
% 1.21/1.46 Found (a1 S) as proof of ((rel_s5 S) V)
% 1.21/1.46 Found (x1 (a1 S)) as proof of False
% 1.21/1.46 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of False
% 1.21/1.46 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s5 S) V)->False)->False)
% 1.21/1.46 Found x3:(P X)
% 1.21/1.46 Instantiate: X0:=X:mu
% 1.21/1.46 Found (fun (x3:(P X))=> x3) as proof of (P X0)
% 1.21/1.46 Found (fun (P:(mu->Prop)) (x3:(P X))=> x3) as proof of ((P X)->(P X0))
% 1.21/1.46 Found (fun (P:(mu->Prop)) (x3:(P X))=> x3) as proof of (((meq_ind X) X0) V)
% 1.21/1.46 Found (x20 (fun (P:(mu->Prop)) (x3:(P X))=> x3)) as proof of False
% 1.21/1.46 Found ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3)) as proof of False
% 1.21/1.46 Found (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) V))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3))) as proof of False
% 1.21/1.46 Found (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) V))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3))) as proof of ((mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))) V)
% 1.21/1.46 Found (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) V))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3)))) as proof of False
% 1.21/1.46 Found (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) V))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) V))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3))))) as proof of False
% 1.21/1.46 Found (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) V))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) V))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3))))) as proof of (((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) V)->False)
% 1.21/1.46 Found ((or_ind00 (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) V))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) V))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3)))))) as proof of False
% 1.21/1.46 Found (((or_ind0 False) (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) V))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) V))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3)))))) as proof of False
% 1.21/1.46 Found ((((fun (P:Prop) (x1:((((rel_s5 W) V)->False)->P)) (x2:(((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) V)->P))=> ((((((or_ind (((rel_s5 W) V)->False)) ((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) V)) P) x1) x2) x0)) False) (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) V))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) V))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3)))))) as proof of False
% 1.29/1.47 Found ((((fun (P:Prop) (x1:((((rel_s5 W) W)->False)->P)) (x2:(((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)->P))=> ((((((or_ind (((rel_s5 W) W)->False)) ((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)) P) x1) x2) (x W))) False) (fun (x1:(((rel_s5 W) W)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) W))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3)))))) as proof of False
% 1.29/1.47 Found (fun (x:((mbox_s5 (mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))))) W))=> ((((fun (P:Prop) (x1:((((rel_s5 W) W)->False)->P)) (x2:(((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)->P))=> ((((((or_ind (((rel_s5 W) W)->False)) ((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)) P) x1) x2) (x W))) False) (fun (x1:(((rel_s5 W) W)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) W))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3))))))) as proof of False
% 1.29/1.47 Found (fun (X:mu) (x:((mbox_s5 (mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))))) W))=> ((((fun (P:Prop) (x1:((((rel_s5 W) W)->False)->P)) (x2:(((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)->P))=> ((((((or_ind (((rel_s5 W) W)->False)) ((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)) P) x1) x2) (x W))) False) (fun (x1:(((rel_s5 W) W)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) W))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3))))))) as proof of (((fun (X:mu)=> (mdia_s5 (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))))) X) W)
% 1.29/1.47 Found (fun (W:fofType) (X:mu) (x:((mbox_s5 (mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))))) W))=> ((((fun (P:Prop) (x1:((((rel_s5 W) W)->False)->P)) (x2:(((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)->P))=> ((((((or_ind (((rel_s5 W) W)->False)) ((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)) P) x1) x2) (x W))) False) (fun (x1:(((rel_s5 W) W)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) W))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3))))))) as proof of ((mforall_ind (fun (X:mu)=> (mdia_s5 (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))))) W)
% 1.29/1.47 Found (fun (W:fofType) (X:mu) (x:((mbox_s5 (mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))))) W))=> ((((fun (P:Prop) (x1:((((rel_s5 W) W)->False)->P)) (x2:(((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)->P))=> ((((((or_ind (((rel_s5 W) W)->False)) ((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)) P) x1) x2) (x W))) False) (fun (x1:(((rel_s5 W) W)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) W))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3))))))) as proof of (mvalid (mforall_ind (fun (X:mu)=> (mdia_s5 (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))))))
% 1.29/1.47 Got proof (fun (W:fofType) (X:mu) (x:((mbox_s5 (mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))))) W))=> ((((fun (P:Prop) (x1:((((rel_s5 W) W)->False)->P)) (x2:(((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)->P))=> ((((((or_ind (((rel_s5 W) W)->False)) ((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)) P) x1) x2) (x W))) False) (fun (x1:(((rel_s5 W) W)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) W))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3)))))))
% 1.29/1.48 Time elapsed = 0.791195s
% 1.29/1.48 node=99 cost=940.000000 depth=17
% 1.29/1.48 ::::::::::::::::::::::
% 1.29/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.29/1.48 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.29/1.48 (fun (W:fofType) (X:mu) (x:((mbox_s5 (mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y))))) W))=> ((((fun (P:Prop) (x1:((((rel_s5 W) W)->False)->P)) (x2:(((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)->P))=> ((((((or_ind (((rel_s5 W) W)->False)) ((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W)) P) x1) x2) (x W))) False) (fun (x1:(((rel_s5 W) W)->False))=> (x1 (a1 W)))) (fun (x1:((mnot (mexists_ind (fun (Y:mu)=> ((meq_ind X) Y)))) W))=> (x1 (fun (x2:((mforall_ind (fun (X0:mu)=> (mnot ((fun (Y:mu)=> ((meq_ind X) Y)) X0)))) W))=> ((x2 X) (fun (P:(mu->Prop)) (x3:(P X))=> x3)))))))
% 1.29/1.48 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------