TSTP Solution File: SET013^7 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET013^7 : TPTP v6.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n101.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 13:29:55 EDT 2014
% Result : Unknown 10.08s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET013^7 : TPTP v6.1.0. Released v5.5.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n101.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:37:16 CDT 2014
% % CPUTime : 10.08
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL015^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x2035c68>, <kernel.Type object at 0x2035f80>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0x20359e0>, <kernel.DependentProduct object at 0x2035c68>) of role type named qmltpeq_type
% Using role type
% Declaring qmltpeq:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1c59f80>, <kernel.DependentProduct object at 0x2034d40>) 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 0x1c59f80>, <kernel.DependentProduct object at 0x2034950>) 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 0x1c59f80>, <kernel.DependentProduct object at 0x2034bd8>) 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 0x2034bd8>, <kernel.DependentProduct object at 0x2034cb0>) 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 0x1b27f38>, <kernel.DependentProduct object at 0x2034cb0>) 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 0x2034f38>, <kernel.DependentProduct object at 0x20349e0>) 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 0x20349e0>, <kernel.DependentProduct object at 0x2034b90>) 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 0x2034830>, <kernel.DependentProduct object at 0x20342d8>) 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 0x20342d8>, <kernel.DependentProduct object at 0x2034758>) 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 0x2034758>, <kernel.DependentProduct object at 0x20346c8>) 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 0x20346c8>, <kernel.DependentProduct object at 0x20349e0>) 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 0x20349e0>, <kernel.DependentProduct object at 0x2034950>) 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 0x2034950>, <kernel.DependentProduct object at 0x2034bd8>) 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 0x2034950>, <kernel.DependentProduct object at 0x1c3e710>) of role type named exists_in_world_type
% Using role type
% Declaring exists_in_world:(mu->(fofType->Prop))
% FOF formula (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))) of role axiom named nonempty_ax
% A new axiom: (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V))))
% FOF formula (<kernel.Constant object at 0x2034950>, <kernel.DependentProduct object at 0x1c3e5a8>) of role type named mforall_ind_type
% Using role type
% Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W))))) of role definition named mforall_ind
% A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W)))))
% Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W))))
% FOF formula (<kernel.Constant object at 0x1c3e878>, <kernel.DependentProduct object at 0x1c3e560>) 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 0x1c3e560>, <kernel.DependentProduct object at 0x1c3e830>) 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 0x1c3e908>, <kernel.DependentProduct object at 0x1c3ec20>) 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 0x1c3ec20>, <kernel.DependentProduct object at 0x1c3eb90>) 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 0x1c3eb90>, <kernel.DependentProduct object at 0x1c3ec68>) 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 0x1c3ec68>, <kernel.DependentProduct object at 0x1c3e7e8>) 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 0x1c3e7e8>, <kernel.DependentProduct object at 0x1c3ef80>) 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 0x1c3ef80>, <kernel.DependentProduct object at 0x1c3ee18>) 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 0x1c3ee18>, <kernel.DependentProduct object at 0x1c3eb90>) 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 0x1c3eb90>, <kernel.DependentProduct object at 0x1c3eb00>) 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 0x1c3eb00>, <kernel.DependentProduct object at 0x1c3edd0>) 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 0x1c3edd0>, <kernel.DependentProduct object at 0x1c3ec20>) 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 0x1c3e560>, <kernel.DependentProduct object at 0x1c3efc8>) 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 0x1c3edd0>, <kernel.DependentProduct object at 0x1c3eb48>) 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 0x1c3efc8>, <kernel.DependentProduct object at 0x2023560>) of role type named mcountersatisfiable_type
% Using role type
% Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% FOF formula (<kernel.Constant object at 0x1c3e560>, <kernel.DependentProduct object at 0x2023248>) of role type named minvalid_type
% Using role type
% Declaring minvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^5.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x20355f0>, <kernel.DependentProduct object at 0x2035cf8>) of role type named rel_s4_type
% Using role type
% Declaring rel_s4:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2035878>, <kernel.DependentProduct object at 0x2035170>) of role type named mbox_s4_type
% Using role type
% Declaring mbox_s4:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))) of role definition named mbox_s4
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))))
% Defined: mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))
% FOF formula (<kernel.Constant object at 0x2013cf8>, <kernel.DependentProduct object at 0x20359e0>) of role type named mdia_s4_type
% Using role type
% Declaring mdia_s4:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))) of role definition named mdia_s4
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))))
% Defined: mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))
% FOF formula (mreflexive rel_s4) of role axiom named a1
% A new axiom: (mreflexive rel_s4)
% FOF formula (mtransitive rel_s4) of role axiom named a2
% A new axiom: (mtransitive rel_s4)
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL015^1.ax, trying next directory
% FOF formula (forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W))) of role axiom named cumulative_ax
% A new axiom: (forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W)))
% FOF formula (<kernel.Constant object at 0x1b24b00>, <kernel.DependentProduct object at 0x2035758>) of role type named subset_type
% Using role type
% Declaring subset:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1b23128>, <kernel.DependentProduct object at 0x2035e18>) of role type named member_type
% Using role type
% Declaring member:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1b24b00>, <kernel.DependentProduct object at 0x2035680>) of role type named equal_set_type
% Using role type
% Declaring equal_set:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1b24b00>, <kernel.DependentProduct object at 0x2035e18>) of role type named power_set_type
% Using role type
% Declaring power_set:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (power_set V1)) V)) of role axiom named existence_of_power_set_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (power_set V1)) V))
% FOF formula (<kernel.Constant object at 0x1c59f38>, <kernel.DependentProduct object at 0x2035758>) of role type named union_type
% Using role type
% Declaring union:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((union V2) V1)) V)) of role axiom named existence_of_union_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((union V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x2035b90>, <kernel.Constant object at 0x2035fc8>) of role type named empty_set_type
% Using role type
% Declaring empty_set:mu
% FOF formula (forall (V:fofType), ((exists_in_world empty_set) V)) of role axiom named existence_of_empty_set_ax
% A new axiom: (forall (V:fofType), ((exists_in_world empty_set) V))
% FOF formula (<kernel.Constant object at 0x2035290>, <kernel.DependentProduct object at 0x2035dd0>) of role type named difference_type
% Using role type
% Declaring difference:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((difference V2) V1)) V)) of role axiom named existence_of_difference_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((difference V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x2035908>, <kernel.DependentProduct object at 0x2035290>) of role type named singleton_type
% Using role type
% Declaring singleton:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (singleton V1)) V)) of role axiom named existence_of_singleton_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (singleton V1)) V))
% FOF formula (<kernel.Constant object at 0x2035758>, <kernel.DependentProduct object at 0x2035b48>) of role type named unordered_pair_type
% Using role type
% Declaring unordered_pair:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((unordered_pair V2) V1)) V)) of role axiom named existence_of_unordered_pair_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((unordered_pair V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x20355a8>, <kernel.DependentProduct object at 0x2035b48>) of role type named sum_type
% Using role type
% Declaring sum:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (sum V1)) V)) of role axiom named existence_of_sum_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (sum V1)) V))
% FOF formula (<kernel.Constant object at 0x2035fc8>, <kernel.DependentProduct object at 0x2035488>) of role type named product_type
% Using role type
% Declaring product:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (product V1)) V)) of role axiom named existence_of_product_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (product V1)) V))
% FOF formula (<kernel.Constant object at 0x2035b48>, <kernel.DependentProduct object at 0x2035ab8>) of role type named intersection_type
% Using role type
% Declaring intersection:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((intersection V2) V1)) V)) of role axiom named existence_of_intersection_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((intersection V2) V1)) V))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((qmltpeq X) X)))) of role axiom named reflexivity
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((qmltpeq X) X))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> ((mimplies ((qmltpeq X) Y)) ((qmltpeq Y) X))))))) of role axiom named symmetry
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> ((mimplies ((qmltpeq X) Y)) ((qmltpeq Y) X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> (mforall_ind (fun (Z:mu)=> ((mimplies ((mand ((qmltpeq X) Y)) ((qmltpeq Y) Z))) ((qmltpeq X) Z))))))))) of role axiom named transitivity
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> (mforall_ind (fun (Z:mu)=> ((mimplies ((mand ((qmltpeq X) Y)) ((qmltpeq Y) Z))) ((qmltpeq X) Z)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((difference A) C)) ((difference B) C)))))))))) of role axiom named difference_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((difference A) C)) ((difference B) C))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((difference C) A)) ((difference C) B)))))))))) of role axiom named difference_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((difference C) A)) ((difference C) B))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((intersection A) C)) ((intersection B) C)))))))))) of role axiom named intersection_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((intersection A) C)) ((intersection B) C))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((intersection C) A)) ((intersection C) B)))))))))) of role axiom named intersection_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((intersection C) A)) ((intersection C) B))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (power_set A)) (power_set B)))))))) of role axiom named power_set_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (power_set A)) (power_set B))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (product A)) (product B)))))))) of role axiom named product_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (product A)) (product B))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (singleton A)) (singleton B)))))))) of role axiom named singleton_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (singleton A)) (singleton B))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (sum A)) (sum B)))))))) of role axiom named sum_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (sum A)) (sum B))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((union A) C)) ((union B) C)))))))))) of role axiom named union_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((union A) C)) ((union B) C))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((union C) A)) ((union C) B)))))))))) of role axiom named union_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((union C) A)) ((union C) B))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((unordered_pair A) C)) ((unordered_pair B) C)))))))))) of role axiom named unordered_pair_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((unordered_pair A) C)) ((unordered_pair B) C))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((unordered_pair C) A)) ((unordered_pair C) B)))))))))) of role axiom named unordered_pair_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((unordered_pair C) A)) ((unordered_pair C) B))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((equal_set A) C))) ((equal_set B) C))))))))) of role axiom named equal_set_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((equal_set A) C))) ((equal_set B) C)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((equal_set C) A))) ((equal_set C) B))))))))) of role axiom named equal_set_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((equal_set C) A))) ((equal_set C) B)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((member A) C))) ((member B) C))))))))) of role axiom named member_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((member A) C))) ((member B) C)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((member C) A))) ((member C) B))))))))) of role axiom named member_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((member C) A))) ((member C) B)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((subset A) C))) ((subset B) C))))))))) of role axiom named subset_substitution_1
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((subset A) C))) ((subset B) C)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((subset C) A))) ((subset C) B))))))))) of role axiom named subset_substitution_2
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((subset C) A))) ((subset C) B)))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((subset A) B)) (mforall_ind (fun (X:mu)=> ((mimplies ((member X) A)) ((member X) B)))))))))) of role axiom named subset
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((subset A) B)) (mforall_ind (fun (X:mu)=> ((mimplies ((member X) A)) ((member X) B))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((equal_set A) B)) ((mand ((subset A) B)) ((subset B) A)))))))) of role axiom named equal_set
% A new axiom: (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((equal_set A) B)) ((mand ((subset A) B)) ((subset B) A))))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (power_set A))) ((subset X) A))))))) of role axiom named power_set
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (power_set A))) ((subset X) A)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((member X) ((intersection A) B))) ((mand ((member X) A)) ((member X) B)))))))))) of role axiom named intersection
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((member X) ((intersection A) B))) ((mand ((member X) A)) ((member X) B))))))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((member X) ((union A) B))) ((mor ((member X) A)) ((member X) B)))))))))) of role axiom named union
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((member X) ((union A) B))) ((mor ((member X) A)) ((member X) B))))))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mnot ((member X) empty_set))))) of role axiom named empty_set
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mnot ((member X) empty_set)))))
% FOF formula (mvalid (mforall_ind (fun (B:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (E:mu)=> ((mequiv ((member B) ((difference E) A))) ((mand ((member B) E)) (mnot ((member B) A))))))))))) of role axiom named difference
% A new axiom: (mvalid (mforall_ind (fun (B:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (E:mu)=> ((mequiv ((member B) ((difference E) A))) ((mand ((member B) E)) (mnot ((member B) A)))))))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (singleton A))) ((qmltpeq X) A))))))) of role axiom named singleton
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (singleton A))) ((qmltpeq X) A)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((member X) ((unordered_pair A) B))) ((mor ((qmltpeq X) A)) ((qmltpeq X) B)))))))))) of role axiom named unordered_pair
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((member X) ((unordered_pair A) B))) ((mor ((qmltpeq X) A)) ((qmltpeq X) B))))))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (sum A))) (mexists_ind (fun (Y:mu)=> ((mand ((member Y) A)) ((member X) Y)))))))))) of role axiom named sum
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (sum A))) (mexists_ind (fun (Y:mu)=> ((mand ((member Y) A)) ((member X) Y))))))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (product A))) (mforall_ind (fun (Y:mu)=> ((mimplies ((member Y) A)) ((member X) Y)))))))))) of role axiom named product
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (product A))) (mforall_ind (fun (Y:mu)=> ((mimplies ((member Y) A)) ((member X) Y))))))))))
% FOF formula (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((equal_set ((intersection A) B)) ((intersection B) A))))))) of role conjecture named thI06
% Conjecture to prove = (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((equal_set ((intersection A) B)) ((intersection B) A))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((equal_set ((intersection A) B)) ((intersection B) A)))))))']
% Parameter mu:Type.
% Parameter fofType:Type.
% Parameter qmltpeq:(mu->(mu->(fofType->Prop))).
% Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% Definition mfalse:=(mnot mtrue):(fofType->Prop).
% Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Parameter exists_in_world:(mu->(fofType->Prop)).
% Axiom nonempty_ax:(forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))).
% Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W)))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% Definition mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))):((fofType->(fofType->Prop))->Prop).
% Definition meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))):((fofType->(fofType->Prop))->Prop).
% Definition mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))):((fofType->(fofType->Prop))->Prop).
% Definition mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))):((fofType->(fofType->Prop))->Prop).
% Definition mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))):((fofType->(fofType->Prop))->Prop).
% Definition mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))):((fofType->(fofType->Prop))->Prop).
% Definition mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))):((fofType->(fofType->Prop))->Prop).
% Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% Parameter rel_s4:(fofType->(fofType->Prop)).
% Definition mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% Definition mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% Axiom a1:(mreflexive rel_s4).
% Axiom a2:(mtransitive rel_s4).
% Axiom cumulative_ax:(forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W))).
% Parameter subset:(mu->(mu->(fofType->Prop))).
% Parameter member:(mu->(mu->(fofType->Prop))).
% Parameter equal_set:(mu->(mu->(fofType->Prop))).
% Parameter power_set:(mu->mu).
% Axiom existence_of_power_set_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (power_set V1)) V)).
% Parameter union:(mu->(mu->mu)).
% Axiom existence_of_union_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((union V2) V1)) V)).
% Parameter empty_set:mu.
% Axiom existence_of_empty_set_ax:(forall (V:fofType), ((exists_in_world empty_set) V)).
% Parameter difference:(mu->(mu->mu)).
% Axiom existence_of_difference_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((difference V2) V1)) V)).
% Parameter singleton:(mu->mu).
% Axiom existence_of_singleton_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (singleton V1)) V)).
% Parameter unordered_pair:(mu->(mu->mu)).
% Axiom existence_of_unordered_pair_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((unordered_pair V2) V1)) V)).
% Parameter sum:(mu->mu).
% Axiom existence_of_sum_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (sum V1)) V)).
% Parameter product:(mu->mu).
% Axiom existence_of_product_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (product V1)) V)).
% Parameter intersection:(mu->(mu->mu)).
% Axiom existence_of_intersection_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((intersection V2) V1)) V)).
% Axiom reflexivity:(mvalid (mforall_ind (fun (X:mu)=> ((qmltpeq X) X)))).
% Axiom symmetry:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> ((mimplies ((qmltpeq X) Y)) ((qmltpeq Y) X))))))).
% Axiom transitivity:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (Y:mu)=> (mforall_ind (fun (Z:mu)=> ((mimplies ((mand ((qmltpeq X) Y)) ((qmltpeq Y) Z))) ((qmltpeq X) Z))))))))).
% Axiom difference_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((difference A) C)) ((difference B) C)))))))))).
% Axiom difference_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((difference C) A)) ((difference C) B)))))))))).
% Axiom intersection_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((intersection A) C)) ((intersection B) C)))))))))).
% Axiom intersection_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((intersection C) A)) ((intersection C) B)))))))))).
% Axiom power_set_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (power_set A)) (power_set B)))))))).
% Axiom product_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (product A)) (product B)))))))).
% Axiom singleton_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (singleton A)) (singleton B)))))))).
% Axiom sum_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq (sum A)) (sum B)))))))).
% Axiom union_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((union A) C)) ((union B) C)))))))))).
% Axiom union_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((union C) A)) ((union C) B)))))))))).
% Axiom unordered_pair_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((unordered_pair A) C)) ((unordered_pair B) C)))))))))).
% Axiom unordered_pair_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((qmltpeq A) B)) ((qmltpeq ((unordered_pair C) A)) ((unordered_pair C) B)))))))))).
% Axiom equal_set_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((equal_set A) C))) ((equal_set B) C))))))))).
% Axiom equal_set_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((equal_set C) A))) ((equal_set C) B))))))))).
% Axiom member_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((member A) C))) ((member B) C))))))))).
% Axiom member_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((member C) A))) ((member C) B))))))))).
% Axiom subset_substitution_1:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((subset A) C))) ((subset B) C))))))))).
% Axiom subset_substitution_2:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> (mforall_ind (fun (C:mu)=> ((mimplies ((mand ((qmltpeq A) B)) ((subset C) A))) ((subset C) B))))))))).
% Axiom subset_TPTP_next:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((subset A) B)) (mforall_ind (fun (X:mu)=> ((mimplies ((member X) A)) ((member X) B)))))))))).
% Axiom equal_set_TPTP_next:(mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((equal_set A) B)) ((mand ((subset A) B)) ((subset B) A)))))))).
% Axiom power_set_TPTP_next:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (power_set A))) ((subset X) A))))))).
% Axiom intersection_TPTP_next:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((member X) ((intersection A) B))) ((mand ((member X) A)) ((member X) B)))))))))).
% Axiom union_TPTP_next:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((member X) ((union A) B))) ((mor ((member X) A)) ((member X) B)))))))))).
% Axiom empty_set_TPTP_next:(mvalid (mforall_ind (fun (X:mu)=> (mnot ((member X) empty_set))))).
% Axiom difference_TPTP_next:(mvalid (mforall_ind (fun (B:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (E:mu)=> ((mequiv ((member B) ((difference E) A))) ((mand ((member B) E)) (mnot ((member B) A))))))))))).
% Axiom singleton_TPTP_next:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (singleton A))) ((qmltpeq X) A))))))).
% Axiom unordered_pair_TPTP_next:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((mequiv ((member X) ((unordered_pair A) B))) ((mor ((qmltpeq X) A)) ((qmltpeq X) B)))))))))).
% Axiom sum_TPTP_next:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (sum A))) (mexists_ind (fun (Y:mu)=> ((mand ((member Y) A)) ((member X) Y)))))))))).
% Axiom product_TPTP_next:(mvalid (mforall_ind (fun (X:mu)=> (mforall_ind (fun (A:mu)=> ((mequiv ((member X) (product A))) (mforall_ind (fun (Y:mu)=> ((mimplies ((member Y) A)) ((member X) Y)))))))))).
% Trying to prove (mvalid (mforall_ind (fun (A:mu)=> (mforall_ind (fun (B:mu)=> ((equal_set ((intersection A) B)) ((intersection B) A)))))))
% % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------