TSTP Solution File: ALG020^7 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ALG020^7 : TPTP v6.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n099.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 13:17:44 EDT 2014
% Result : Timeout 300.07s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : ALG020^7 : TPTP v6.1.0. Released v5.5.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n099.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:35:56 CDT 2014
% % CPUTime : 300.07
% 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 0x165a7e8>, <kernel.Type object at 0x127ef38>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0x165ae18>, <kernel.DependentProduct object at 0x127ebd8>) of role type named qmltpeq_type
% Using role type
% Declaring qmltpeq:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x127ea28>, <kernel.DependentProduct object at 0x127e560>) 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 0x16b83b0>, <kernel.DependentProduct object at 0x127e368>) 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 0x16b83b0>, <kernel.DependentProduct object at 0x127e998>) 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 0x16b83b0>, <kernel.DependentProduct object at 0x127e5a8>) 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 0x16b8320>, <kernel.DependentProduct object at 0x127e368>) 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 0x127e3f8>, <kernel.DependentProduct object at 0x127eab8>) 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 0x127e7e8>, <kernel.DependentProduct object at 0x127e4d0>) 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 0x127e320>, <kernel.DependentProduct object at 0x127e6c8>) 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 0x127e3f8>, <kernel.DependentProduct object at 0x127e6c8>) 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 0x127e560>, <kernel.DependentProduct object at 0x1274710>) 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 0x127e560>, <kernel.DependentProduct object at 0x1274758>) 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 0x127e320>, <kernel.DependentProduct object at 0x1274830>) 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 0x1274830>, <kernel.DependentProduct object at 0x1274518>) 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 0x1274830>, <kernel.DependentProduct object at 0x1274758>) 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 0x1274290>, <kernel.DependentProduct object at 0x12741b8>) 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 0x12746c8>, <kernel.DependentProduct object at 0x1274170>) 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 0x1274170>, <kernel.DependentProduct object at 0x12744d0>) 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 0x12741b8>, <kernel.DependentProduct object at 0x1274c68>) 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 0x1274c68>, <kernel.DependentProduct object at 0x1274bd8>) 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 0x1274bd8>, <kernel.DependentProduct object at 0x1274cb0>) 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 0x1274cb0>, <kernel.DependentProduct object at 0x12747a0>) 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 0x12747a0>, <kernel.DependentProduct object at 0x1274098>) 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 0x1274098>, <kernel.DependentProduct object at 0x1274e60>) 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 0x1274e60>, <kernel.DependentProduct object at 0x1274488>) 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 0x1274488>, <kernel.DependentProduct object at 0x1274878>) 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 0x1274878>, <kernel.DependentProduct object at 0x1274c68>) 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 0x1274c68>, <kernel.DependentProduct object at 0x12746c8>) 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 0x1274170>, <kernel.DependentProduct object at 0x1274b90>) 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 0x1274c68>, <kernel.DependentProduct object at 0x1648050>) 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 0x1274098>, <kernel.DependentProduct object at 0x1648128>) 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 0x1274b90>, <kernel.DependentProduct object at 0x16482d8>) 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 0x165aef0>, <kernel.DependentProduct object at 0x165af80>) of role type named rel_s4_type
% Using role type
% Declaring rel_s4:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x165aea8>, <kernel.DependentProduct object at 0x165afc8>) 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 0x165add0>, <kernel.DependentProduct object at 0x16b8320>) 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 0x165b3b0>, <kernel.DependentProduct object at 0x1263560>) of role type named op2_type
% Using role type
% Declaring op2:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((op2 V2) V1)) V)) of role axiom named existence_of_op2_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((op2 V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x163b128>, <kernel.DependentProduct object at 0x1263ef0>) of role type named op1_type
% Using role type
% Declaring op1:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((op1 V2) V1)) V)) of role axiom named existence_of_op1_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((op1 V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x12638c0>, <kernel.DependentProduct object at 0x1263488>) of role type named j_type
% Using role type
% Declaring j:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (j V1)) V)) of role axiom named existence_of_j_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (j V1)) V))
% FOF formula (<kernel.Constant object at 0x1263488>, <kernel.Constant object at 0x1263758>) of role type named e13_type
% Using role type
% Declaring e13:mu
% FOF formula (forall (V:fofType), ((exists_in_world e13) V)) of role axiom named existence_of_e13_ax
% A new axiom: (forall (V:fofType), ((exists_in_world e13) V))
% FOF formula (<kernel.Constant object at 0x1263cb0>, <kernel.Constant object at 0x1263ef0>) of role type named e12_type
% Using role type
% Declaring e12:mu
% FOF formula (forall (V:fofType), ((exists_in_world e12) V)) of role axiom named existence_of_e12_ax
% A new axiom: (forall (V:fofType), ((exists_in_world e12) V))
% FOF formula (<kernel.Constant object at 0x1263cb0>, <kernel.Constant object at 0x12638c0>) of role type named e11_type
% Using role type
% Declaring e11:mu
% FOF formula (forall (V:fofType), ((exists_in_world e11) V)) of role axiom named existence_of_e11_ax
% A new axiom: (forall (V:fofType), ((exists_in_world e11) V))
% FOF formula (<kernel.Constant object at 0x1263cb0>, <kernel.Constant object at 0x12634d0>) of role type named e23_type
% Using role type
% Declaring e23:mu
% FOF formula (forall (V:fofType), ((exists_in_world e23) V)) of role axiom named existence_of_e23_ax
% A new axiom: (forall (V:fofType), ((exists_in_world e23) V))
% FOF formula (<kernel.Constant object at 0x12634d0>, <kernel.Constant object at 0x1263cb0>) of role type named e22_type
% Using role type
% Declaring e22:mu
% FOF formula (forall (V:fofType), ((exists_in_world e22) V)) of role axiom named existence_of_e22_ax
% A new axiom: (forall (V:fofType), ((exists_in_world e22) V))
% FOF formula (<kernel.Constant object at 0x1263cb0>, <kernel.Constant object at 0x16b83b0>) of role type named e21_type
% Using role type
% Declaring e21:mu
% FOF formula (forall (V:fofType), ((exists_in_world e21) V)) of role axiom named existence_of_e21_ax
% A new axiom: (forall (V:fofType), ((exists_in_world e21) V))
% FOF formula (<kernel.Constant object at 0x1263c20>, <kernel.Constant object at 0x16b83b0>) of role type named e20_type
% Using role type
% Declaring e20:mu
% FOF formula (forall (V:fofType), ((exists_in_world e20) V)) of role axiom named existence_of_e20_ax
% A new axiom: (forall (V:fofType), ((exists_in_world e20) V))
% FOF formula (<kernel.Constant object at 0x16b85a8>, <kernel.Constant object at 0x16b8b48>) of role type named e10_type
% Using role type
% Declaring e10:mu
% FOF formula (forall (V:fofType), ((exists_in_world e10) V)) of role axiom named existence_of_e10_ax
% A new axiom: (forall (V:fofType), ((exists_in_world e10) V))
% FOF formula (<kernel.Constant object at 0x16b85a8>, <kernel.DependentProduct object at 0x165a1b8>) of role type named h_type
% Using role type
% Declaring h:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (h V1)) V)) of role axiom named existence_of_h_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (h V1)) V))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq X) X)))))) of role axiom named reflexivity
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq X) X))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) X))))))))))) of role axiom named symmetry
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) X)))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 (mforall_ind (fun (Z:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) Z)))) (mbox_s4 ((qmltpeq X) Z)))))))))))))) of role axiom named transitivity
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 (mforall_ind (fun (Z:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) Z)))) (mbox_s4 ((qmltpeq X) Z))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (h A)) (h B)))))))))))) of role axiom named h_substitution_1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (h A)) (h B))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (j A)) (j B)))))))))))) of role axiom named j_substitution_1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (j A)) (j B))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op1 A) C)) ((op1 B) C))))))))))))))) of role axiom named op1_substitution_1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op1 A) C)) ((op1 B) C)))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op1 C) A)) ((op1 C) B))))))))))))))) of role axiom named op1_substitution_2
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op1 C) A)) ((op1 C) B)))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op2 A) C)) ((op2 B) C))))))))))))))) of role axiom named op2_substitution_1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op2 A) C)) ((op2 B) C)))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op2 C) A)) ((op2 C) B))))))))))))))) of role axiom named op2_substitution_2
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op2 C) A)) ((op2 C) B)))))))))))))))
% FOF formula (mvalid ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e11))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e12))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e13))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e12))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e13))))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e13)))))))))) of role axiom named ax1
% A new axiom: (mvalid ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e11))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e12))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e13))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e12))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e13))))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e13))))))))))
% FOF formula (mvalid ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e20) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e20) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e20) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e21) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e21) e23))))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq e22) e23)))))))))) of role axiom named ax2
% A new axiom: (mvalid ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e20) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e20) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e20) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e21) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e21) e23))))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq e22) e23))))))))))
% FOF formula (mvalid ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e22))))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e23)))))))))))))))))))) of role axiom named ax3
% A new axiom: (mvalid ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e22))))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e23))))))))))))))))))))
% FOF formula (mvalid ((mand (mbox_s4 ((qmltpeq ((op1 e10) e10)) e10))) ((mand (mbox_s4 ((qmltpeq ((op1 e10) e11)) e11))) ((mand (mbox_s4 ((qmltpeq ((op1 e10) e12)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e10) e13)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e10)) e11))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e11)) e10))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e12)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e13)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e10)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e11)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e12)) e10))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e13)) e11))) ((mand (mbox_s4 ((qmltpeq ((op1 e13) e10)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e13) e11)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e13) e12)) e11))) (mbox_s4 ((qmltpeq ((op1 e13) e13)) e10)))))))))))))))))) of role axiom named ax4
% A new axiom: (mvalid ((mand (mbox_s4 ((qmltpeq ((op1 e10) e10)) e10))) ((mand (mbox_s4 ((qmltpeq ((op1 e10) e11)) e11))) ((mand (mbox_s4 ((qmltpeq ((op1 e10) e12)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e10) e13)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e10)) e11))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e11)) e10))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e12)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e13)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e10)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e11)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e12)) e10))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e13)) e11))) ((mand (mbox_s4 ((qmltpeq ((op1 e13) e10)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e13) e11)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e13) e12)) e11))) (mbox_s4 ((qmltpeq ((op1 e13) e13)) e10))))))))))))))))))
% FOF formula (mvalid ((mand (mbox_s4 ((qmltpeq ((op2 e20) e20)) e20))) ((mand (mbox_s4 ((qmltpeq ((op2 e20) e21)) e21))) ((mand (mbox_s4 ((qmltpeq ((op2 e20) e22)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e20) e23)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e20)) e21))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e21)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e22)) e20))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e23)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e20)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e21)) e20))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e22)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e23)) e21))) ((mand (mbox_s4 ((qmltpeq ((op2 e23) e20)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e23) e21)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e23) e22)) e21))) (mbox_s4 ((qmltpeq ((op2 e23) e23)) e20)))))))))))))))))) of role axiom named ax5
% A new axiom: (mvalid ((mand (mbox_s4 ((qmltpeq ((op2 e20) e20)) e20))) ((mand (mbox_s4 ((qmltpeq ((op2 e20) e21)) e21))) ((mand (mbox_s4 ((qmltpeq ((op2 e20) e22)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e20) e23)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e20)) e21))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e21)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e22)) e20))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e23)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e20)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e21)) e20))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e22)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e23)) e21))) ((mand (mbox_s4 ((qmltpeq ((op2 e23) e20)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e23) e21)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e23) e22)) e21))) (mbox_s4 ((qmltpeq ((op2 e23) e23)) e20))))))))))))))))))
% FOF formula (mvalid (mbox_s4 ((mimplies ((mand ((mor (mbox_s4 ((qmltpeq (h e10)) e20))) ((mor (mbox_s4 ((qmltpeq (h e10)) e21))) ((mor (mbox_s4 ((qmltpeq (h e10)) e22))) (mbox_s4 ((qmltpeq (h e10)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e11)) e20))) ((mor (mbox_s4 ((qmltpeq (h e11)) e21))) ((mor (mbox_s4 ((qmltpeq (h e11)) e22))) (mbox_s4 ((qmltpeq (h e11)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e12)) e20))) ((mor (mbox_s4 ((qmltpeq (h e12)) e21))) ((mor (mbox_s4 ((qmltpeq (h e12)) e22))) (mbox_s4 ((qmltpeq (h e12)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e13)) e20))) ((mor (mbox_s4 ((qmltpeq (h e13)) e21))) ((mor (mbox_s4 ((qmltpeq (h e13)) e22))) (mbox_s4 ((qmltpeq (h e13)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e20)) e10))) ((mor (mbox_s4 ((qmltpeq (j e20)) e11))) ((mor (mbox_s4 ((qmltpeq (j e20)) e12))) (mbox_s4 ((qmltpeq (j e20)) e13)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e21)) e10))) ((mor (mbox_s4 ((qmltpeq (j e21)) e11))) ((mor (mbox_s4 ((qmltpeq (j e21)) e12))) (mbox_s4 ((qmltpeq (j e21)) e13)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e22)) e10))) ((mor (mbox_s4 ((qmltpeq (j e22)) e11))) ((mor (mbox_s4 ((qmltpeq (j e22)) e12))) (mbox_s4 ((qmltpeq (j e22)) e13)))))) ((mor (mbox_s4 ((qmltpeq (j e23)) e10))) ((mor (mbox_s4 ((qmltpeq (j e23)) e11))) ((mor (mbox_s4 ((qmltpeq (j e23)) e12))) (mbox_s4 ((qmltpeq (j e23)) e13))))))))))))) (mbox_s4 (mnot ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e10))) ((op2 (h e10)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e11))) ((op2 (h e10)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e12))) ((op2 (h e10)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e13))) ((op2 (h e10)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e10))) ((op2 (h e11)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e11))) ((op2 (h e11)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e12))) ((op2 (h e11)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e13))) ((op2 (h e11)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e10))) ((op2 (h e12)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e11))) ((op2 (h e12)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e12))) ((op2 (h e12)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e13))) ((op2 (h e12)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e10))) ((op2 (h e13)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e11))) ((op2 (h e13)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e12))) ((op2 (h e13)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e13))) ((op2 (h e13)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e20))) ((op1 (j e20)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e21))) ((op1 (j e20)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e22))) ((op1 (j e20)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e23))) ((op1 (j e20)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e20))) ((op1 (j e21)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e21))) ((op1 (j e21)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e22))) ((op1 (j e21)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e23))) ((op1 (j e21)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e20))) ((op1 (j e22)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e21))) ((op1 (j e22)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e22))) ((op1 (j e22)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e23))) ((op1 (j e22)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e20))) ((op1 (j e23)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e21))) ((op1 (j e23)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e22))) ((op1 (j e23)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e23))) ((op1 (j e23)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (h (j e20))) e20))) ((mand (mbox_s4 ((qmltpeq (h (j e21))) e21))) ((mand (mbox_s4 ((qmltpeq (h (j e22))) e22))) ((mand (mbox_s4 ((qmltpeq (h (j e23))) e23))) ((mand (mbox_s4 ((qmltpeq (j (h e10))) e10))) ((mand (mbox_s4 ((qmltpeq (j (h e11))) e11))) ((mand (mbox_s4 ((qmltpeq (j (h e12))) e12))) (mbox_s4 ((qmltpeq (j (h e13))) e13)))))))))))))))))))))))))))))))))))))))))))))) of role conjecture named co1
% Conjecture to prove = (mvalid (mbox_s4 ((mimplies ((mand ((mor (mbox_s4 ((qmltpeq (h e10)) e20))) ((mor (mbox_s4 ((qmltpeq (h e10)) e21))) ((mor (mbox_s4 ((qmltpeq (h e10)) e22))) (mbox_s4 ((qmltpeq (h e10)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e11)) e20))) ((mor (mbox_s4 ((qmltpeq (h e11)) e21))) ((mor (mbox_s4 ((qmltpeq (h e11)) e22))) (mbox_s4 ((qmltpeq (h e11)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e12)) e20))) ((mor (mbox_s4 ((qmltpeq (h e12)) e21))) ((mor (mbox_s4 ((qmltpeq (h e12)) e22))) (mbox_s4 ((qmltpeq (h e12)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e13)) e20))) ((mor (mbox_s4 ((qmltpeq (h e13)) e21))) ((mor (mbox_s4 ((qmltpeq (h e13)) e22))) (mbox_s4 ((qmltpeq (h e13)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e20)) e10))) ((mor (mbox_s4 ((qmltpeq (j e20)) e11))) ((mor (mbox_s4 ((qmltpeq (j e20)) e12))) (mbox_s4 ((qmltpeq (j e20)) e13)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e21)) e10))) ((mor (mbox_s4 ((qmltpeq (j e21)) e11))) ((mor (mbox_s4 ((qmltpeq (j e21)) e12))) (mbox_s4 ((qmltpeq (j e21)) e13)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e22)) e10))) ((mor (mbox_s4 ((qmltpeq (j e22)) e11))) ((mor (mbox_s4 ((qmltpeq (j e22)) e12))) (mbox_s4 ((qmltpeq (j e22)) e13)))))) ((mor (mbox_s4 ((qmltpeq (j e23)) e10))) ((mor (mbox_s4 ((qmltpeq (j e23)) e11))) ((mor (mbox_s4 ((qmltpeq (j e23)) e12))) (mbox_s4 ((qmltpeq (j e23)) e13))))))))))))) (mbox_s4 (mnot ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e10))) ((op2 (h e10)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e11))) ((op2 (h e10)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e12))) ((op2 (h e10)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e13))) ((op2 (h e10)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e10))) ((op2 (h e11)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e11))) ((op2 (h e11)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e12))) ((op2 (h e11)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e13))) ((op2 (h e11)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e10))) ((op2 (h e12)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e11))) ((op2 (h e12)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e12))) ((op2 (h e12)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e13))) ((op2 (h e12)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e10))) ((op2 (h e13)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e11))) ((op2 (h e13)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e12))) ((op2 (h e13)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e13))) ((op2 (h e13)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e20))) ((op1 (j e20)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e21))) ((op1 (j e20)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e22))) ((op1 (j e20)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e23))) ((op1 (j e20)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e20))) ((op1 (j e21)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e21))) ((op1 (j e21)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e22))) ((op1 (j e21)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e23))) ((op1 (j e21)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e20))) ((op1 (j e22)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e21))) ((op1 (j e22)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e22))) ((op1 (j e22)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e23))) ((op1 (j e22)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e20))) ((op1 (j e23)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e21))) ((op1 (j e23)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e22))) ((op1 (j e23)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e23))) ((op1 (j e23)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (h (j e20))) e20))) ((mand (mbox_s4 ((qmltpeq (h (j e21))) e21))) ((mand (mbox_s4 ((qmltpeq (h (j e22))) e22))) ((mand (mbox_s4 ((qmltpeq (h (j e23))) e23))) ((mand (mbox_s4 ((qmltpeq (j (h e10))) e10))) ((mand (mbox_s4 ((qmltpeq (j (h e11))) e11))) ((mand (mbox_s4 ((qmltpeq (j (h e12))) e12))) (mbox_s4 ((qmltpeq (j (h e13))) e13)))))))))))))))))))))))))))))))))))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(mvalid (mbox_s4 ((mimplies ((mand ((mor (mbox_s4 ((qmltpeq (h e10)) e20))) ((mor (mbox_s4 ((qmltpeq (h e10)) e21))) ((mor (mbox_s4 ((qmltpeq (h e10)) e22))) (mbox_s4 ((qmltpeq (h e10)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e11)) e20))) ((mor (mbox_s4 ((qmltpeq (h e11)) e21))) ((mor (mbox_s4 ((qmltpeq (h e11)) e22))) (mbox_s4 ((qmltpeq (h e11)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e12)) e20))) ((mor (mbox_s4 ((qmltpeq (h e12)) e21))) ((mor (mbox_s4 ((qmltpeq (h e12)) e22))) (mbox_s4 ((qmltpeq (h e12)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e13)) e20))) ((mor (mbox_s4 ((qmltpeq (h e13)) e21))) ((mor (mbox_s4 ((qmltpeq (h e13)) e22))) (mbox_s4 ((qmltpeq (h e13)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e20)) e10))) ((mor (mbox_s4 ((qmltpeq (j e20)) e11))) ((mor (mbox_s4 ((qmltpeq (j e20)) e12))) (mbox_s4 ((qmltpeq (j e20)) e13)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e21)) e10))) ((mor (mbox_s4 ((qmltpeq (j e21)) e11))) ((mor (mbox_s4 ((qmltpeq (j e21)) e12))) (mbox_s4 ((qmltpeq (j e21)) e13)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e22)) e10))) ((mor (mbox_s4 ((qmltpeq (j e22)) e11))) ((mor (mbox_s4 ((qmltpeq (j e22)) e12))) (mbox_s4 ((qmltpeq (j e22)) e13)))))) ((mor (mbox_s4 ((qmltpeq (j e23)) e10))) ((mor (mbox_s4 ((qmltpeq (j e23)) e11))) ((mor (mbox_s4 ((qmltpeq (j e23)) e12))) (mbox_s4 ((qmltpeq (j e23)) e13))))))))))))) (mbox_s4 (mnot ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e10))) ((op2 (h e10)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e11))) ((op2 (h e10)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e12))) ((op2 (h e10)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e13))) ((op2 (h e10)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e10))) ((op2 (h e11)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e11))) ((op2 (h e11)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e12))) ((op2 (h e11)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e13))) ((op2 (h e11)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e10))) ((op2 (h e12)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e11))) ((op2 (h e12)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e12))) ((op2 (h e12)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e13))) ((op2 (h e12)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e10))) ((op2 (h e13)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e11))) ((op2 (h e13)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e12))) ((op2 (h e13)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e13) e13))) ((op2 (h e13)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e20))) ((op1 (j e20)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e21))) ((op1 (j e20)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e22))) ((op1 (j e20)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e20) e23))) ((op1 (j e20)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e20))) ((op1 (j e21)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e21))) ((op1 (j e21)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e22))) ((op1 (j e21)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e21) e23))) ((op1 (j e21)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e20))) ((op1 (j e22)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e21))) ((op1 (j e22)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e22))) ((op1 (j e22)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e22) e23))) ((op1 (j e22)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e20))) ((op1 (j e23)) (j e20))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e21))) ((op1 (j e23)) (j e21))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e22))) ((op1 (j e23)) (j e22))))) ((mand (mbox_s4 ((qmltpeq (j ((op2 e23) e23))) ((op1 (j e23)) (j e23))))) ((mand (mbox_s4 ((qmltpeq (h (j e20))) e20))) ((mand (mbox_s4 ((qmltpeq (h (j e21))) e21))) ((mand (mbox_s4 ((qmltpeq (h (j e22))) e22))) ((mand (mbox_s4 ((qmltpeq (h (j e23))) e23))) ((mand (mbox_s4 ((qmltpeq (j (h e10))) e10))) ((mand (mbox_s4 ((qmltpeq (j (h e11))) e11))) ((mand (mbox_s4 ((qmltpeq (j (h e12))) e12))) (mbox_s4 ((qmltpeq (j (h e13))) e13))))))))))))))))))))))))))))))))))))))))))))))']
% 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 op2:(mu->(mu->mu)).
% Axiom existence_of_op2_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((op2 V2) V1)) V)).
% Parameter op1:(mu->(mu->mu)).
% Axiom existence_of_op1_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((op1 V2) V1)) V)).
% Parameter j:(mu->mu).
% Axiom existence_of_j_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (j V1)) V)).
% Parameter e13:mu.
% Axiom existence_of_e13_ax:(forall (V:fofType), ((exists_in_world e13) V)).
% Parameter e12:mu.
% Axiom existence_of_e12_ax:(forall (V:fofType), ((exists_in_world e12) V)).
% Parameter e11:mu.
% Axiom existence_of_e11_ax:(forall (V:fofType), ((exists_in_world e11) V)).
% Parameter e23:mu.
% Axiom existence_of_e23_ax:(forall (V:fofType), ((exists_in_world e23) V)).
% Parameter e22:mu.
% Axiom existence_of_e22_ax:(forall (V:fofType), ((exists_in_world e22) V)).
% Parameter e21:mu.
% Axiom existence_of_e21_ax:(forall (V:fofType), ((exists_in_world e21) V)).
% Parameter e20:mu.
% Axiom existence_of_e20_ax:(forall (V:fofType), ((exists_in_world e20) V)).
% Parameter e10:mu.
% Axiom existence_of_e10_ax:(forall (V:fofType), ((exists_in_world e10) V)).
% Parameter h:(mu->mu).
% Axiom existence_of_h_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (h V1)) V)).
% Axiom reflexivity:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq X) X)))))).
% Axiom symmetry:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) X))))))))))).
% Axiom transitivity:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 (mforall_ind (fun (Z:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq X) Y))) (mbox_s4 ((qmltpeq Y) Z)))) (mbox_s4 ((qmltpeq X) Z)))))))))))))).
% Axiom h_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (h A)) (h B)))))))))))).
% Axiom j_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (j A)) (j B)))))))))))).
% Axiom op1_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op1 A) C)) ((op1 B) C))))))))))))))).
% Axiom op1_substitution_2:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op1 C) A)) ((op1 C) B))))))))))))))).
% Axiom op2_substitution_1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op2 A) C)) ((op2 B) C))))))))))))))).
% Axiom op2_substitution_2:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((op2 C) A)) ((op2 C) B))))))))))))))).
% Axiom ax1:(mvalid ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e11))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e12))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e13))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e12))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e13))))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e13)))))))))).
% Axiom ax2:(mvalid ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e20) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e20) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e20) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e21) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e21) e23))))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq e22) e23)))))))))).
% Axiom ax3:(mvalid ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e10) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e11) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e22))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e12) e23))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e20))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e21))))) ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e22))))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq e13) e23)))))))))))))))))))).
% Axiom ax4:(mvalid ((mand (mbox_s4 ((qmltpeq ((op1 e10) e10)) e10))) ((mand (mbox_s4 ((qmltpeq ((op1 e10) e11)) e11))) ((mand (mbox_s4 ((qmltpeq ((op1 e10) e12)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e10) e13)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e10)) e11))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e11)) e10))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e12)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e11) e13)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e10)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e11)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e12)) e10))) ((mand (mbox_s4 ((qmltpeq ((op1 e12) e13)) e11))) ((mand (mbox_s4 ((qmltpeq ((op1 e13) e10)) e13))) ((mand (mbox_s4 ((qmltpeq ((op1 e13) e11)) e12))) ((mand (mbox_s4 ((qmltpeq ((op1 e13) e12)) e11))) (mbox_s4 ((qmltpeq ((op1 e13) e13)) e10)))))))))))))))))).
% Axiom ax5:(mvalid ((mand (mbox_s4 ((qmltpeq ((op2 e20) e20)) e20))) ((mand (mbox_s4 ((qmltpeq ((op2 e20) e21)) e21))) ((mand (mbox_s4 ((qmltpeq ((op2 e20) e22)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e20) e23)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e20)) e21))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e21)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e22)) e20))) ((mand (mbox_s4 ((qmltpeq ((op2 e21) e23)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e20)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e21)) e20))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e22)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e22) e23)) e21))) ((mand (mbox_s4 ((qmltpeq ((op2 e23) e20)) e23))) ((mand (mbox_s4 ((qmltpeq ((op2 e23) e21)) e22))) ((mand (mbox_s4 ((qmltpeq ((op2 e23) e22)) e21))) (mbox_s4 ((qmltpeq ((op2 e23) e23)) e20)))))))))))))))))).
% Trying to prove (mvalid (mbox_s4 ((mimplies ((mand ((mor (mbox_s4 ((qmltpeq (h e10)) e20))) ((mor (mbox_s4 ((qmltpeq (h e10)) e21))) ((mor (mbox_s4 ((qmltpeq (h e10)) e22))) (mbox_s4 ((qmltpeq (h e10)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e11)) e20))) ((mor (mbox_s4 ((qmltpeq (h e11)) e21))) ((mor (mbox_s4 ((qmltpeq (h e11)) e22))) (mbox_s4 ((qmltpeq (h e11)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e12)) e20))) ((mor (mbox_s4 ((qmltpeq (h e12)) e21))) ((mor (mbox_s4 ((qmltpeq (h e12)) e22))) (mbox_s4 ((qmltpeq (h e12)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (h e13)) e20))) ((mor (mbox_s4 ((qmltpeq (h e13)) e21))) ((mor (mbox_s4 ((qmltpeq (h e13)) e22))) (mbox_s4 ((qmltpeq (h e13)) e23)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e20)) e10))) ((mor (mbox_s4 ((qmltpeq (j e20)) e11))) ((mor (mbox_s4 ((qmltpeq (j e20)) e12))) (mbox_s4 ((qmltpeq (j e20)) e13)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e21)) e10))) ((mor (mbox_s4 ((qmltpeq (j e21)) e11))) ((mor (mbox_s4 ((qmltpeq (j e21)) e12))) (mbox_s4 ((qmltpeq (j e21)) e13)))))) ((mand ((mor (mbox_s4 ((qmltpeq (j e22)) e10))) ((mor (mbox_s4 ((qmltpeq (j e22)) e11))) ((mor (mbox_s4 ((qmltpeq (j e22)) e12))) (mbox_s4 ((qmltpeq (j e22)) e13)))))) ((mor (mbox_s4 ((qmltpeq (j e23)) e10))) ((mor (mbox_s4 ((qmltpeq (j e23)) e11))) ((mor (mbox_s4 ((qmltpeq (j e23)) e12))) (mbox_s4 ((qmltpeq (j e23)) e13))))))))))))) (mbox_s4 (mnot ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e10))) ((op2 (h e10)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e11))) ((op2 (h e10)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e12))) ((op2 (h e10)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e10) e13))) ((op2 (h e10)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e10))) ((op2 (h e11)) (h e10))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e11))) ((op2 (h e11)) (h e11))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e12))) ((op2 (h e11)) (h e12))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e11) e13))) ((op2 (h e11)) (h e13))))) ((mand (mbox_s4 ((qmltpeq (h ((op1 e12) e10))) ((op2 (h e12)) (h e10))))) ((mand (
% EOF
%------------------------------------------------------------------------------