%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SWV097^7 : TPTP v6.1.0. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n109.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 13:35:23 EDT 2014

% Result   : Theorem 36.47s
% Output   : Proof 36.47s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SWV097^7 : TPTP v6.1.0. Released v5.5.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n109.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 08:08:26 CDT 2014
% % CPUTime  : 36.47 
% 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 0x11c21b8>, <kernel.Type object at 0x11c29e0>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0x11c2200>, <kernel.DependentProduct object at 0x11c21b8>) of role type named qmltpeq_type
% Using role type
% Declaring qmltpeq:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x11c2ef0>, <kernel.DependentProduct object at 0x11c4b90>) 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 0x11c2488>, <kernel.DependentProduct object at 0x11c48c0>) 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 0x11c2488>, <kernel.DependentProduct object at 0x11c4560>) 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 0x11c22d8>, <kernel.DependentProduct object at 0x11c4c68>) 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 0x1221098>, <kernel.DependentProduct object at 0x11c4560>) 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 0x11c4a28>, <kernel.DependentProduct object at 0x11c4200>) 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 0x11c4200>, <kernel.DependentProduct object at 0x11c4560>) 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 0x11c40e0>, <kernel.DependentProduct object at 0x11c4b00>) 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 0x11c4b00>, <kernel.DependentProduct object at 0x11c4b90>) 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 0x11c4b90>, <kernel.DependentProduct object at 0x11c4050>) 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 0x11c4050>, <kernel.DependentProduct object at 0x11c47a0>) 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 0x11c47a0>, <kernel.DependentProduct object at 0x11c4c20>) 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 0x11c4c20>, <kernel.DependentProduct object at 0x11c4290>) 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 0x11c4c20>, <kernel.DependentProduct object at 0xdcc710>) 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 0x11c40e0>, <kernel.DependentProduct object at 0xdcc5f0>) 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 0xdcc950>, <kernel.DependentProduct object at 0xdcc488>) 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 0xdcc488>, <kernel.DependentProduct object at 0xdcc6c8>) 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 0xdcc5f0>, <kernel.DependentProduct object at 0xdccc68>) 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 0xdccc68>, <kernel.DependentProduct object at 0xdccbd8>) 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 0xdccbd8>, <kernel.DependentProduct object at 0xdcccb0>) 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 0xdcccb0>, <kernel.DependentProduct object at 0xdcc878>) 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 0xdcc878>, <kernel.DependentProduct object at 0xdcc4d0>) 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 0xdcc4d0>, <kernel.DependentProduct object at 0xdcce60>) 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 0xdcce60>, <kernel.DependentProduct object at 0xdcc7a0>) 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 0xdcc7a0>, <kernel.DependentProduct object at 0xdcc5a8>) 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 0xdcc5a8>, <kernel.DependentProduct object at 0xdccc68>) 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 0xdccc68>, <kernel.DependentProduct object at 0xdcc950>) 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 0xdcc488>, <kernel.DependentProduct object at 0xdccb90>) 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 0xdccc68>, <kernel.DependentProduct object at 0x11b1050>) 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 0xdcc4d0>, <kernel.DependentProduct object at 0x11b1128>) 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 0xdccb90>, <kernel.DependentProduct object at 0x11b12d8>) 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 0x11c2908>, <kernel.DependentProduct object at 0x11c2cb0>) of role type named rel_s4_type
% Using role type
% Declaring rel_s4:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x11c2680>, <kernel.DependentProduct object at 0x11c2638>) 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 0x11c2638>, <kernel.DependentProduct object at 0x11c2320>) 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 0x11c3758>, <kernel.DependentProduct object at 0xde7bd8>) of role type named true_type
% Using role type
% Declaring true:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x11c3128>, <kernel.DependentProduct object at 0x1223098>) of role type named lt_type
% Using role type
% Declaring lt:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x11c3128>, <kernel.DependentProduct object at 0xf621b8>) of role type named geq_type
% Using role type
% Declaring geq:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x121f5a8>, <kernel.DependentProduct object at 0x11c3128>) of role type named gt_type
% Using role type
% Declaring gt:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x12232d8>, <kernel.DependentProduct object at 0xde7a28>) of role type named leq_type
% Using role type
% Declaring leq:(mu->(mu->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x11c3128>, <kernel.DependentProduct object at 0xcb29e0>) of role type named uniform_int_rnd_type
% Using role type
% Declaring uniform_int_rnd:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((uniform_int_rnd V2) V1)) V)) of role axiom named existence_of_uniform_int_rnd_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((uniform_int_rnd V2) V1)) V))
% FOF formula (<kernel.Constant object at 0xcb2ab8>, <kernel.DependentProduct object at 0xf62290>) of role type named tptp_const_array1_type
% Using role type
% Declaring tptp_const_array1:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_const_array1 V2) V1)) V)) of role axiom named existence_of_tptp_const_array1_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_const_array1 V2) V1)) V))
% FOF formula (<kernel.Constant object at 0xde7a28>, <kernel.DependentProduct object at 0x11c2f38>) of role type named dim_type
% Using role type
% Declaring dim:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((dim V2) V1)) V)) of role axiom named existence_of_dim_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((dim V2) V1)) V))
% FOF formula (<kernel.Constant object at 0xde7bd8>, <kernel.DependentProduct object at 0x11c2f38>) of role type named tptp_const_array2_type
% Using role type
% Declaring tptp_const_array2:(mu->(mu->(mu->mu)))
% FOF formula (forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((tptp_const_array2 V3) V2) V1)) V)) of role axiom named existence_of_tptp_const_array2_ax
% A new axiom: (forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((tptp_const_array2 V3) V2) V1)) V))
% FOF formula (<kernel.Constant object at 0xf621b8>, <kernel.DependentProduct object at 0x11c2bd8>) of role type named inv_type
% Using role type
% Declaring inv:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (inv V1)) V)) of role axiom named existence_of_inv_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (inv V1)) V))
% FOF formula (<kernel.Constant object at 0x11c2d88>, <kernel.DependentProduct object at 0x11c2d40>) of role type named tptp_msub_type
% Using role type
% Declaring tptp_msub:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_msub V2) V1)) V)) of role axiom named existence_of_tptp_msub_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_msub V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x11c2cb0>, <kernel.DependentProduct object at 0x11c2d88>) of role type named trans_type
% Using role type
% Declaring trans:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (trans V1)) V)) of role axiom named existence_of_trans_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (trans V1)) V))
% FOF formula (<kernel.Constant object at 0x11c2cf8>, <kernel.DependentProduct object at 0x11c2368>) of role type named tptp_mmul_type
% Using role type
% Declaring tptp_mmul:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_mmul V2) V1)) V)) of role axiom named existence_of_tptp_mmul_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_mmul V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x11c2680>, <kernel.DependentProduct object at 0x11c2f80>) of role type named tptp_madd_type
% Using role type
% Declaring tptp_madd:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_madd V2) V1)) V)) of role axiom named existence_of_tptp_madd_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_madd V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x11c2368>, <kernel.DependentProduct object at 0x11c22d8>) of role type named sum_type
% Using role type
% Declaring sum:(mu->(mu->(mu->mu)))
% FOF formula (forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((sum V3) V2) V1)) V)) of role axiom named existence_of_sum_ax
% A new axiom: (forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((sum V3) V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x11c27a0>, <kernel.Constant object at 0x11c2cb0>) of role type named tptp_float_0_0_type
% Using role type
% Declaring tptp_float_0_0:mu
% FOF formula (forall (V:fofType), ((exists_in_world tptp_float_0_0) V)) of role axiom named existence_of_tptp_float_0_0_ax
% A new axiom: (forall (V:fofType), ((exists_in_world tptp_float_0_0) V))
% FOF formula (<kernel.Constant object at 0x11c21b8>, <kernel.DependentProduct object at 0x11c2950>) of role type named plus_type
% Using role type
% Declaring plus:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((plus V2) V1)) V)) of role axiom named existence_of_plus_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((plus V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x11c2ea8>, <kernel.DependentProduct object at 0x11c21b8>) of role type named pred_type
% Using role type
% Declaring pred:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (pred V1)) V)) of role axiom named existence_of_pred_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (pred V1)) V))
% FOF formula (<kernel.Constant object at 0x11c22d8>, <kernel.DependentProduct object at 0x11c23b0>) of role type named tptp_update3_type
% Using role type
% Declaring tptp_update3:(mu->(mu->(mu->(mu->mu))))
% FOF formula (forall (V:fofType) (V4:mu) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world ((((tptp_update3 V4) V3) V2) V1)) V)) of role axiom named existence_of_tptp_update3_ax
% A new axiom: (forall (V:fofType) (V4:mu) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world ((((tptp_update3 V4) V3) V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x1221fc8>, <kernel.DependentProduct object at 0x11c2950>) of role type named tptp_update2_type
% Using role type
% Declaring tptp_update2:(mu->(mu->(mu->mu)))
% FOF formula (forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((tptp_update2 V3) V2) V1)) V)) of role axiom named existence_of_tptp_update2_ax
% A new axiom: (forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((tptp_update2 V3) V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x1221d88>, <kernel.Constant object at 0x11c2950>) of role type named def_type
% Using role type
% Declaring def:mu
% FOF formula (forall (V:fofType), ((exists_in_world def) V)) of role axiom named existence_of_def_ax
% A new axiom: (forall (V:fofType), ((exists_in_world def) V))
% FOF formula (<kernel.Constant object at 0x11c2200>, <kernel.Constant object at 0x11c23f8>) of role type named z_defuse_type
% Using role type
% Declaring z_defuse:mu
% FOF formula (forall (V:fofType), ((exists_in_world z_defuse) V)) of role axiom named existence_of_z_defuse_ax
% A new axiom: (forall (V:fofType), ((exists_in_world z_defuse) V))
% FOF formula (<kernel.Constant object at 0x11c2908>, <kernel.DependentProduct object at 0x11c2950>) of role type named minus_type
% Using role type
% Declaring minus:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((minus V2) V1)) V)) of role axiom named existence_of_minus_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((minus V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x11c2908>, <kernel.Constant object at 0x11c20e0>) of role type named pv5_type
% Using role type
% Declaring pv5:mu
% FOF formula (forall (V:fofType), ((exists_in_world pv5) V)) of role axiom named existence_of_pv5_ax
% A new axiom: (forall (V:fofType), ((exists_in_world pv5) V))
% FOF formula (<kernel.Constant object at 0x11c2908>, <kernel.Constant object at 0x11c2950>) of role type named xinit_noise_defuse_type
% Using role type
% Declaring xinit_noise_defuse:mu
% FOF formula (forall (V:fofType), ((exists_in_world xinit_noise_defuse) V)) of role axiom named existence_of_xinit_noise_defuse_ax
% A new axiom: (forall (V:fofType), ((exists_in_world xinit_noise_defuse) V))
% FOF formula (<kernel.Constant object at 0x11c2950>, <kernel.Constant object at 0x11c2908>) of role type named xinit_mean_defuse_type
% Using role type
% Declaring xinit_mean_defuse:mu
% FOF formula (forall (V:fofType), ((exists_in_world xinit_mean_defuse) V)) of role axiom named existence_of_xinit_mean_defuse_ax
% A new axiom: (forall (V:fofType), ((exists_in_world xinit_mean_defuse) V))
% FOF formula (<kernel.Constant object at 0x11c22d8>, <kernel.Constant object at 0x11c4488>) of role type named xinit_defuse_type
% Using role type
% Declaring xinit_defuse:mu
% FOF formula (forall (V:fofType), ((exists_in_world xinit_defuse) V)) of role axiom named existence_of_xinit_defuse_ax
% A new axiom: (forall (V:fofType), ((exists_in_world xinit_defuse) V))
% FOF formula (<kernel.Constant object at 0x11c2908>, <kernel.Constant object at 0x11c4b00>) of role type named u_defuse_type
% Using role type
% Declaring u_defuse:mu
% FOF formula (forall (V:fofType), ((exists_in_world u_defuse) V)) of role axiom named existence_of_u_defuse_ax
% A new axiom: (forall (V:fofType), ((exists_in_world u_defuse) V))
% FOF formula (<kernel.Constant object at 0x11c4830>, <kernel.DependentProduct object at 0x11c4488>) of role type named a_select3_type
% Using role type
% Declaring a_select3:(mu->(mu->(mu->mu)))
% FOF formula (forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((a_select3 V3) V2) V1)) V)) of role axiom named existence_of_a_select3_ax
% A new axiom: (forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((a_select3 V3) V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x11c48c0>, <kernel.Constant object at 0x11c4488>) of role type named sigma_defuse_type
% Using role type
% Declaring sigma_defuse:mu
% FOF formula (forall (V:fofType), ((exists_in_world sigma_defuse) V)) of role axiom named existence_of_sigma_defuse_ax
% A new axiom: (forall (V:fofType), ((exists_in_world sigma_defuse) V))
% FOF formula (<kernel.Constant object at 0x11c43b0>, <kernel.Constant object at 0x11c4290>) of role type named use_type
% Using role type
% Declaring use:mu
% FOF formula (forall (V:fofType), ((exists_in_world use) V)) of role axiom named existence_of_use_ax
% A new axiom: (forall (V:fofType), ((exists_in_world use) V))
% FOF formula (<kernel.Constant object at 0x11c4560>, <kernel.Constant object at 0x11c40e0>) of role type named rho_defuse_type
% Using role type
% Declaring rho_defuse:mu
% FOF formula (forall (V:fofType), ((exists_in_world rho_defuse) V)) of role axiom named existence_of_rho_defuse_ax
% A new axiom: (forall (V:fofType), ((exists_in_world rho_defuse) V))
% FOF formula (<kernel.Constant object at 0x11c4200>, <kernel.DependentProduct object at 0x11c4290>) of role type named a_select2_type
% Using role type
% Declaring a_select2:(mu->(mu->mu))
% FOF formula (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((a_select2 V2) V1)) V)) of role axiom named existence_of_a_select2_ax
% A new axiom: (forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((a_select2 V2) V1)) V))
% FOF formula (<kernel.Constant object at 0x11c4200>, <kernel.Constant object at 0x11c48c0>) of role type named tptp_minus_1_type
% Using role type
% Declaring tptp_minus_1:mu
% FOF formula (forall (V:fofType), ((exists_in_world tptp_minus_1) V)) of role axiom named existence_of_tptp_minus_1_ax
% A new axiom: (forall (V:fofType), ((exists_in_world tptp_minus_1) V))
% FOF formula (<kernel.Constant object at 0x11c48c0>, <kernel.Constant object at 0x11c4200>) of role type named n999_type
% Using role type
% Declaring n999:mu
% FOF formula (forall (V:fofType), ((exists_in_world n999) V)) of role axiom named existence_of_n999_ax
% A new axiom: (forall (V:fofType), ((exists_in_world n999) V))
% FOF formula (<kernel.Constant object at 0x11c4200>, <kernel.Constant object at 0x11c48c0>) of role type named n4_type
% Using role type
% Declaring n4:mu
% FOF formula (forall (V:fofType), ((exists_in_world n4) V)) of role axiom named existence_of_n4_ax
% A new axiom: (forall (V:fofType), ((exists_in_world n4) V))
% FOF formula (<kernel.Constant object at 0x11c48c0>, <kernel.Constant object at 0xdcca70>) of role type named n5_type
% Using role type
% Declaring n5:mu
% FOF formula (forall (V:fofType), ((exists_in_world n5) V)) of role axiom named existence_of_n5_ax
% A new axiom: (forall (V:fofType), ((exists_in_world n5) V))
% FOF formula (<kernel.Constant object at 0x11c4290>, <kernel.Constant object at 0xdcc680>) of role type named n1_type
% Using role type
% Declaring n1:mu
% FOF formula (forall (V:fofType), ((exists_in_world n1) V)) of role axiom named existence_of_n1_ax
% A new axiom: (forall (V:fofType), ((exists_in_world n1) V))
% FOF formula (<kernel.Constant object at 0xdcc758>, <kernel.Constant object at 0xdcc6c8>) of role type named n2_type
% Using role type
% Declaring n2:mu
% FOF formula (forall (V:fofType), ((exists_in_world n2) V)) of role axiom named existence_of_n2_ax
% A new axiom: (forall (V:fofType), ((exists_in_world n2) V))
% FOF formula (<kernel.Constant object at 0xdccb00>, <kernel.Constant object at 0xdcca28>) of role type named n3_type
% Using role type
% Declaring n3:mu
% FOF formula (forall (V:fofType), ((exists_in_world n3) V)) of role axiom named existence_of_n3_ax
% A new axiom: (forall (V:fofType), ((exists_in_world n3) V))
% FOF formula (<kernel.Constant object at 0xdccea8>, <kernel.Constant object at 0xdccd88>) of role type named n0_type
% Using role type
% Declaring n0:mu
% FOF formula (forall (V:fofType), ((exists_in_world n0) V)) of role axiom named existence_of_n0_ax
% A new axiom: (forall (V:fofType), ((exists_in_world n0) V))
% FOF formula (<kernel.Constant object at 0xdcc908>, <kernel.DependentProduct object at 0xdcc7e8>) of role type named succ_type
% Using role type
% Declaring succ:(mu->mu)
% FOF formula (forall (V:fofType) (V1:mu), ((exists_in_world (succ V1)) V)) of role axiom named existence_of_succ_ax
% A new axiom: (forall (V:fofType) (V1:mu), ((exists_in_world (succ 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 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((a_select2 A) C)) ((a_select2 B) C))))))))))))))) of role axiom named a_select2_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 ((a_select2 A) C)) ((a_select2 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 ((a_select2 C) A)) ((a_select2 C) B))))))))))))))) of role axiom named a_select2_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 ((a_select2 C) A)) ((a_select2 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((a_select3 A) C) D)) (((a_select3 B) C) D)))))))))))))))))) of role axiom named a_select3_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((a_select3 A) C) D)) (((a_select3 B) C) D))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((a_select3 C) A) D)) (((a_select3 C) B) D)))))))))))))))))) of role axiom named a_select3_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((a_select3 C) A) D)) (((a_select3 C) B) D))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((a_select3 C) D) A)) (((a_select3 C) D) B)))))))))))))))))) of role axiom named a_select3_substitution_3
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((a_select3 C) D) A)) (((a_select3 C) D) 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 ((dim A) C)) ((dim B) C))))))))))))))) of role axiom named dim_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 ((dim A) C)) ((dim 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 ((dim C) A)) ((dim C) B))))))))))))))) of role axiom named dim_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 ((dim C) A)) ((dim C) 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 (inv A)) (inv B)))))))))))) of role axiom named inv_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 (inv A)) (inv 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 ((minus A) C)) ((minus B) C))))))))))))))) of role axiom named minus_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 ((minus A) C)) ((minus 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 ((minus C) A)) ((minus C) B))))))))))))))) of role axiom named minus_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 ((minus C) A)) ((minus 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 ((plus A) C)) ((plus B) C))))))))))))))) of role axiom named plus_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 ((plus A) C)) ((plus 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 ((plus C) A)) ((plus C) B))))))))))))))) of role axiom named plus_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 ((plus C) A)) ((plus C) 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 (pred A)) (pred B)))))))))))) of role axiom named pred_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 (pred A)) (pred 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 (succ A)) (succ B)))))))))))) of role axiom named succ_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 (succ A)) (succ 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((sum A) C) D)) (((sum B) C) D)))))))))))))))))) of role axiom named sum_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((sum A) C) D)) (((sum B) C) D))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((sum C) A) D)) (((sum C) B) D)))))))))))))))))) of role axiom named sum_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((sum C) A) D)) (((sum C) B) D))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((sum C) D) A)) (((sum C) D) B)))))))))))))))))) of role axiom named sum_substitution_3
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((sum C) D) A)) (((sum C) D) 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 ((tptp_const_array1 A) C)) ((tptp_const_array1 B) C))))))))))))))) of role axiom named tptp_const_array1_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 ((tptp_const_array1 A) C)) ((tptp_const_array1 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 ((tptp_const_array1 C) A)) ((tptp_const_array1 C) B))))))))))))))) of role axiom named tptp_const_array1_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 ((tptp_const_array1 C) A)) ((tptp_const_array1 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_const_array2 A) C) D)) (((tptp_const_array2 B) C) D)))))))))))))))))) of role axiom named tptp_const_array2_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_const_array2 A) C) D)) (((tptp_const_array2 B) C) D))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_const_array2 C) A) D)) (((tptp_const_array2 C) B) D)))))))))))))))))) of role axiom named tptp_const_array2_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_const_array2 C) A) D)) (((tptp_const_array2 C) B) D))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_const_array2 C) D) A)) (((tptp_const_array2 C) D) B)))))))))))))))))) of role axiom named tptp_const_array2_substitution_3
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_const_array2 C) D) A)) (((tptp_const_array2 C) D) 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 ((tptp_madd A) C)) ((tptp_madd B) C))))))))))))))) of role axiom named tptp_madd_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 ((tptp_madd A) C)) ((tptp_madd 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 ((tptp_madd C) A)) ((tptp_madd C) B))))))))))))))) of role axiom named tptp_madd_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 ((tptp_madd C) A)) ((tptp_madd 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 ((tptp_mmul A) C)) ((tptp_mmul B) C))))))))))))))) of role axiom named tptp_mmul_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 ((tptp_mmul A) C)) ((tptp_mmul 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 ((tptp_mmul C) A)) ((tptp_mmul C) B))))))))))))))) of role axiom named tptp_mmul_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 ((tptp_mmul C) A)) ((tptp_mmul 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 ((tptp_msub A) C)) ((tptp_msub B) C))))))))))))))) of role axiom named tptp_msub_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 ((tptp_msub A) C)) ((tptp_msub 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 ((tptp_msub C) A)) ((tptp_msub C) B))))))))))))))) of role axiom named tptp_msub_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 ((tptp_msub C) A)) ((tptp_msub 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_update2 A) C) D)) (((tptp_update2 B) C) D)))))))))))))))))) of role axiom named tptp_update2_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_update2 A) C) D)) (((tptp_update2 B) C) D))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_update2 C) A) D)) (((tptp_update2 C) B) D)))))))))))))))))) of role axiom named tptp_update2_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_update2 C) A) D)) (((tptp_update2 C) B) D))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_update2 C) D) A)) (((tptp_update2 C) D) B)))))))))))))))))) of role axiom named tptp_update2_substitution_3
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_update2 C) D) A)) (((tptp_update2 C) D) 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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 A) C) D) E)) ((((tptp_update3 B) C) D) E))))))))))))))))))))) of role axiom named tptp_update3_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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 A) C) D) E)) ((((tptp_update3 B) C) D) E)))))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 C) A) D) E)) ((((tptp_update3 C) B) D) E))))))))))))))))))))) of role axiom named tptp_update3_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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 C) A) D) E)) ((((tptp_update3 C) B) D) E)))))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 C) D) A) E)) ((((tptp_update3 C) D) B) E))))))))))))))))))))) of role axiom named tptp_update3_substitution_3
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 C) D) A) E)) ((((tptp_update3 C) D) B) E)))))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 C) D) E) A)) ((((tptp_update3 C) D) E) B))))))))))))))))))))) of role axiom named tptp_update3_substitution_4
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 C) D) E) A)) ((((tptp_update3 C) D) E) 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 (trans A)) (trans B)))))))))))) of role axiom named trans_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 (trans A)) (trans 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 ((uniform_int_rnd A) C)) ((uniform_int_rnd B) C))))))))))))))) of role axiom named uniform_int_rnd_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 ((uniform_int_rnd A) C)) ((uniform_int_rnd 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 ((uniform_int_rnd C) A)) ((uniform_int_rnd C) B))))))))))))))) of role axiom named uniform_int_rnd_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 ((uniform_int_rnd C) A)) ((uniform_int_rnd 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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((geq A) C)))) (mbox_s4 ((geq B) C)))))))))))))) of role axiom named geq_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((geq A) C)))) (mbox_s4 ((geq 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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((geq C) A)))) (mbox_s4 ((geq C) B)))))))))))))) of role axiom named geq_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((geq C) A)))) (mbox_s4 ((geq 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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((gt A) C)))) (mbox_s4 ((gt B) C)))))))))))))) of role axiom named gt_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((gt A) C)))) (mbox_s4 ((gt 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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((gt C) A)))) (mbox_s4 ((gt C) B)))))))))))))) of role axiom named gt_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((gt C) A)))) (mbox_s4 ((gt 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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((leq A) C)))) (mbox_s4 ((leq B) C)))))))))))))) of role axiom named leq_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((leq A) C)))) (mbox_s4 ((leq 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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((leq C) A)))) (mbox_s4 ((leq C) B)))))))))))))) of role axiom named leq_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((leq C) A)))) (mbox_s4 ((leq 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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((lt A) C)))) (mbox_s4 ((lt B) C)))))))))))))) of role axiom named lt_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((lt A) C)))) (mbox_s4 ((lt 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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((lt C) A)))) (mbox_s4 ((lt C) B)))))))))))))) of role axiom named lt_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((lt C) A)))) (mbox_s4 ((lt C) B))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mor (mbox_s4 ((gt X) Y))) ((mor (mbox_s4 ((gt Y) X))) (mbox_s4 ((qmltpeq X) Y))))))))))) of role axiom named totality
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mor (mbox_s4 ((gt X) Y))) ((mor (mbox_s4 ((gt Y) X))) (mbox_s4 ((qmltpeq X) Y)))))))))))
% 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 ((gt X) Y))) (mbox_s4 ((gt Y) Z)))) (mbox_s4 ((gt X) Z)))))))))))))) of role axiom named transitivity_gt
% 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 ((gt X) Y))) (mbox_s4 ((gt Y) Z)))) (mbox_s4 ((gt X) Z))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mnot (mbox_s4 ((gt X) X)))))))) of role axiom named irreflexivity_gt
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mnot (mbox_s4 ((gt X) X))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((leq X) X)))))) of role axiom named reflexivity_leq
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((leq X) 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 ((leq X) Y))) (mbox_s4 ((leq Y) Z)))) (mbox_s4 ((leq X) Z)))))))))))))) of role axiom named transitivity_leq
% 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 ((leq X) Y))) (mbox_s4 ((leq Y) Z)))) (mbox_s4 ((leq X) Z))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((lt X) Y))) (mbox_s4 ((gt Y) X))))) (mbox_s4 ((mimplies (mbox_s4 ((gt Y) X))) (mbox_s4 ((lt X) Y)))))))))))) of role axiom named lt_gt
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((lt X) Y))) (mbox_s4 ((gt Y) X))))) (mbox_s4 ((mimplies (mbox_s4 ((gt Y) X))) (mbox_s4 ((lt X) Y))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((geq X) Y))) (mbox_s4 ((leq Y) X))))) (mbox_s4 ((mimplies (mbox_s4 ((leq Y) X))) (mbox_s4 ((geq X) Y)))))))))))) of role axiom named leq_geq
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((geq X) Y))) (mbox_s4 ((leq Y) X))))) (mbox_s4 ((mimplies (mbox_s4 ((leq Y) X))) (mbox_s4 ((geq X) Y))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((gt Y) X))) (mbox_s4 ((leq X) Y))))))))))) of role axiom named leq_gt1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((gt Y) X))) (mbox_s4 ((leq X) Y)))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq X) Y))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq X) Y)))))) (mbox_s4 ((gt Y) X))))))))))) of role axiom named leq_gt2
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq X) Y))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq X) Y)))))) (mbox_s4 ((gt Y) X)))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((leq X) (pred Y)))) (mbox_s4 ((gt Y) X))))) (mbox_s4 ((mimplies (mbox_s4 ((gt Y) X))) (mbox_s4 ((leq X) (pred Y))))))))))))) of role axiom named leq_gt_pred
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((leq X) (pred Y)))) (mbox_s4 ((gt Y) X))))) (mbox_s4 ((mimplies (mbox_s4 ((gt Y) X))) (mbox_s4 ((leq X) (pred Y)))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((gt (succ X)) X)))))) of role axiom named gt_succ
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((gt (succ X)) X))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq X) Y))) (mbox_s4 ((leq X) (succ Y)))))))))))) of role axiom named leq_succ
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq X) Y))) (mbox_s4 ((leq X) (succ Y))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((leq X) Y))) (mbox_s4 ((gt (succ Y)) X))))) (mbox_s4 ((mimplies (mbox_s4 ((gt (succ Y)) X))) (mbox_s4 ((leq X) Y)))))))))))) of role axiom named leq_succ_gt_equiv
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((leq X) Y))) (mbox_s4 ((gt (succ Y)) X))))) (mbox_s4 ((mimplies (mbox_s4 ((gt (succ Y)) X))) (mbox_s4 ((leq X) Y))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq ((uniform_int_rnd C) X)) X))))))))))) of role axiom named uniform_int_rand_ranges_hi
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq ((uniform_int_rnd C) X)) X)))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq n0) ((uniform_int_rnd C) X)))))))))))) of role axiom named uniform_int_rand_ranges_lo
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq n0) ((uniform_int_rnd C) X))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (L:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (Val:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq L) _TPTP_I))) (mbox_s4 ((leq _TPTP_I) U)))) (mbox_s4 ((qmltpeq ((a_select2 ((tptp_const_array1 ((dim L) U)) Val)) _TPTP_I)) Val))))))))))))))))) of role axiom named const_array1_select
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (L:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (Val:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq L) _TPTP_I))) (mbox_s4 ((leq _TPTP_I) U)))) (mbox_s4 ((qmltpeq ((a_select2 ((tptp_const_array1 ((dim L) U)) Val)) _TPTP_I)) Val)))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (L1:mu)=> (mbox_s4 (mforall_ind (fun (U1:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (L2:mu)=> (mbox_s4 (mforall_ind (fun (U2:mu)=> (mbox_s4 (mforall_ind (fun (Val:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq L1) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) U1))) ((mand (mbox_s4 ((leq L2) J))) (mbox_s4 ((leq J) U2)))))) (mbox_s4 ((qmltpeq (((a_select3 (((tptp_const_array2 ((dim L1) U1)) ((dim L2) U2)) Val)) _TPTP_I) J)) Val)))))))))))))))))))))))))) of role axiom named const_array2_select
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (L1:mu)=> (mbox_s4 (mforall_ind (fun (U1:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (L2:mu)=> (mbox_s4 (mforall_ind (fun (U2:mu)=> (mbox_s4 (mforall_ind (fun (Val:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq L1) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) U1))) ((mand (mbox_s4 ((leq L2) J))) (mbox_s4 ((leq J) U2)))))) (mbox_s4 ((qmltpeq (((a_select3 (((tptp_const_array2 ((dim L1) U1)) ((dim L2) U2)) Val)) _TPTP_I) J)) Val))))))))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 (trans A)) _TPTP_I) J)) (((a_select3 (trans A)) J) _TPTP_I)))))))))))))))))))) of role axiom named matrix_symm_trans
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 (trans A)) _TPTP_I) J)) (((a_select3 (trans A)) J) _TPTP_I))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 (inv A)) _TPTP_I) J)) (((a_select3 (inv A)) J) _TPTP_I)))))))))))))))))))) of role axiom named matrix_symm_inv
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 (inv A)) _TPTP_I) J)) (((a_select3 (inv A)) J) _TPTP_I))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (K:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) ((mand (mbox_s4 ((leq J) N))) ((mand (mbox_s4 ((leq n0) K))) (mbox_s4 ((leq K) N)))))))) (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 A) K) K) VAL)) _TPTP_I) J)) (((a_select3 ((((tptp_update3 A) K) K) VAL)) J) _TPTP_I)))))))))))))))))))))))))) of role axiom named matrix_symm_update_diagonal
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (K:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) ((mand (mbox_s4 ((leq J) N))) ((mand (mbox_s4 ((leq n0) K))) (mbox_s4 ((leq K) N)))))))) (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 A) K) K) VAL)) _TPTP_I) J)) (((a_select3 ((((tptp_update3 A) K) K) VAL)) J) _TPTP_I))))))))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I))))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_madd A) B)) _TPTP_I) J)) (((a_select3 ((tptp_madd A) B)) J) _TPTP_I))))))))))))))))))))))) of role axiom named matrix_symm_add
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I))))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_madd A) B)) _TPTP_I) J)) (((a_select3 ((tptp_madd A) B)) J) _TPTP_I)))))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I))))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_msub A) B)) _TPTP_I) J)) (((a_select3 ((tptp_msub A) B)) J) _TPTP_I))))))))))))))))))))))) of role axiom named matrix_symm_sub
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I))))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_msub A) B)) _TPTP_I) J)) (((a_select3 ((tptp_msub A) B)) J) _TPTP_I)))))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) _TPTP_I) J)) (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) J) _TPTP_I))))))))))))))))))))))) of role axiom named matrix_symm_aba1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) _TPTP_I) J)) (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) J) _TPTP_I)))))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 (mforall_ind (fun (M:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) M))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) M)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) _TPTP_I) J)) (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) J) _TPTP_I)))))))))))))))))))))))))) of role axiom named matrix_symm_aba2
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 (mforall_ind (fun (M:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) M))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) M)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) _TPTP_I) J)) (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) J) _TPTP_I))))))))))))))))))))))))))
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 (mforall_ind (fun (M:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) M))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) M)))))) (mbox_s4 ((qmltpeq (((a_select3 D) _TPTP_I) J)) (((a_select3 D) J) _TPTP_I)))))))))))) ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 F) _TPTP_I) J)) (((a_select3 F) J) _TPTP_I)))))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_madd A) ((tptp_mmul B) ((tptp_mmul ((tptp_madd ((tptp_mmul C) ((tptp_mmul D) (trans C)))) ((tptp_mmul E) ((tptp_mmul F) (trans E))))) (trans B))))) _TPTP_I) J)) (((a_select3 ((tptp_madd A) ((tptp_mmul B) ((tptp_mmul ((tptp_madd ((tptp_mmul C) ((tptp_mmul D) (trans C)))) ((tptp_mmul E) ((tptp_mmul F) (trans E))))) (trans B))))) J) _TPTP_I)))))))))))))))))))))))))))))))))))))) of role axiom named matrix_symm_joseph_update
% 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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 (mforall_ind (fun (M:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) M))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) M)))))) (mbox_s4 ((qmltpeq (((a_select3 D) _TPTP_I) J)) (((a_select3 D) J) _TPTP_I)))))))))))) ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 F) _TPTP_I) J)) (((a_select3 F) J) _TPTP_I)))))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_madd A) ((tptp_mmul B) ((tptp_mmul ((tptp_madd ((tptp_mmul C) ((tptp_mmul D) (trans C)))) ((tptp_mmul E) ((tptp_mmul F) (trans E))))) (trans B))))) _TPTP_I) J)) (((a_select3 ((tptp_madd A) ((tptp_mmul B) ((tptp_mmul ((tptp_madd ((tptp_mmul C) ((tptp_mmul D) (trans C)))) ((tptp_mmul E) ((tptp_mmul F) (trans E))))) (trans B))))) J) _TPTP_I))))))))))))))))))))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (Body:mu)=> (mbox_s4 ((qmltpeq (((sum n0) tptp_minus_1) Body)) n0)))))) of role axiom named sum_plus_base
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (Body:mu)=> (mbox_s4 ((qmltpeq (((sum n0) tptp_minus_1) Body)) n0))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (Body:mu)=> (mbox_s4 ((qmltpeq tptp_float_0_0) (((sum n0) tptp_minus_1) Body))))))) of role axiom named sum_plus_base_float
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (Body:mu)=> (mbox_s4 ((qmltpeq tptp_float_0_0) (((sum n0) tptp_minus_1) Body)))))))
% FOF formula (mvalid (mbox_s4 ((qmltpeq (succ tptp_minus_1)) n0))) of role axiom named succ_tptp_minus_1
% A new axiom: (mvalid (mbox_s4 ((qmltpeq (succ tptp_minus_1)) n0)))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n1)) (succ X))))))) of role axiom named succ_plus_1_r
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n1)) (succ X)))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n1) X)) (succ X))))))) of role axiom named succ_plus_1_l
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n1) X)) (succ X)))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n2)) (succ (succ X)))))))) of role axiom named succ_plus_2_r
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n2)) (succ (succ X))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n2) X)) (succ (succ X)))))))) of role axiom named succ_plus_2_l
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n2) X)) (succ (succ X))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n3)) (succ (succ (succ X))))))))) of role axiom named succ_plus_3_r
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n3)) (succ (succ (succ X)))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n3) X)) (succ (succ (succ X))))))))) of role axiom named succ_plus_3_l
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n3) X)) (succ (succ (succ X)))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n4)) (succ (succ (succ (succ X)))))))))) of role axiom named succ_plus_4_r
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n4)) (succ (succ (succ (succ X))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n4) X)) (succ (succ (succ (succ X)))))))))) of role axiom named succ_plus_4_l
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n4) X)) (succ (succ (succ (succ X))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n5)) (succ (succ (succ (succ (succ X))))))))))) of role axiom named succ_plus_5_r
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n5)) (succ (succ (succ (succ (succ X)))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n5) X)) (succ (succ (succ (succ (succ X))))))))))) of role axiom named succ_plus_5_l
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n5) X)) (succ (succ (succ (succ (succ X)))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((minus X) n1)) (pred X))))))) of role axiom named pred_minus_1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((minus X) n1)) (pred X)))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq (pred (succ X))) X)))))) of role axiom named pred_succ
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq (pred (succ X))) X))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq (succ (pred X))) X)))))) of role axiom named succ_pred
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq (succ (pred X))) X))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((leq (succ X)) (succ Y)))) (mbox_s4 ((leq X) Y))))) (mbox_s4 ((mimplies (mbox_s4 ((leq X) Y))) (mbox_s4 ((leq (succ X)) (succ Y))))))))))))) of role axiom named leq_succ_succ
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((leq (succ X)) (succ Y)))) (mbox_s4 ((leq X) Y))))) (mbox_s4 ((mimplies (mbox_s4 ((leq X) Y))) (mbox_s4 ((leq (succ X)) (succ Y)))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq (succ X)) Y))) (mbox_s4 ((gt Y) X))))))))))) of role axiom named leq_succ_gt
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq (succ X)) Y))) (mbox_s4 ((gt Y) X)))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq ((minus X) Y)) X))) (mbox_s4 ((leq n0) Y))))))))))) of role axiom named leq_minus
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq ((minus X) Y)) X))) (mbox_s4 ((leq n0) Y)))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (V:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 X) U) V) VAL)) U) V)) VAL))))))))))))))) of role axiom named sel3_update_1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (V:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 X) U) V) VAL)) U) V)) VAL)))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (V:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 (mforall_ind (fun (VAL2:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq _TPTP_I) U))))) ((mand (mbox_s4 ((qmltpeq J) V))) (mbox_s4 ((qmltpeq (((a_select3 X) U) V)) VAL))))) (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 X) _TPTP_I) J) VAL2)) U) V)) VAL)))))))))))))))))))))))))) of role axiom named sel3_update_2
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (V:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 (mforall_ind (fun (VAL2:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq _TPTP_I) U))))) ((mand (mbox_s4 ((qmltpeq J) V))) (mbox_s4 ((qmltpeq (((a_select3 X) U) V)) VAL))))) (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 X) _TPTP_I) J) VAL2)) U) V)) VAL))))))))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (V:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (I0:mu)=> (mbox_s4 (mforall_ind (fun (J0:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) I0))) ((mand (mbox_s4 ((leq n0) J0))) ((mand (mbox_s4 ((leq I0) U))) (mbox_s4 ((leq J0) V)))))) (mbox_s4 ((qmltpeq (((a_select3 X) I0) J0)) VAL))))))))))) ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) U))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) V))))))) (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 X) U) V) VAL)) _TPTP_I) J)) VAL))))))))))))))))))))))) of role axiom named sel3_update_3
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (V:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (I0:mu)=> (mbox_s4 (mforall_ind (fun (J0:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) I0))) ((mand (mbox_s4 ((leq n0) J0))) ((mand (mbox_s4 ((leq I0) U))) (mbox_s4 ((leq J0) V)))))) (mbox_s4 ((qmltpeq (((a_select3 X) I0) J0)) VAL))))))))))) ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) U))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) V))))))) (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 X) U) V) VAL)) _TPTP_I) J)) VAL)))))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((qmltpeq ((a_select2 (((tptp_update2 X) U) VAL)) U)) VAL)))))))))))) of role axiom named sel2_update_1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((qmltpeq ((a_select2 (((tptp_update2 X) U) VAL)) U)) VAL))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 (mforall_ind (fun (VAL2:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq _TPTP_I) U))))) (mbox_s4 ((qmltpeq ((a_select2 X) U)) VAL)))) (mbox_s4 ((qmltpeq ((a_select2 (((tptp_update2 X) _TPTP_I) VAL2)) U)) VAL)))))))))))))))))))) of role axiom named sel2_update_2
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 (mforall_ind (fun (VAL2:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq _TPTP_I) U))))) (mbox_s4 ((qmltpeq ((a_select2 X) U)) VAL)))) (mbox_s4 ((qmltpeq ((a_select2 (((tptp_update2 X) _TPTP_I) VAL2)) U)) VAL))))))))))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (I0:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) I0))) (mbox_s4 ((leq I0) U)))) (mbox_s4 ((qmltpeq ((a_select2 X) I0)) VAL)))))))) ((mand (mbox_s4 ((leq n0) _TPTP_I))) (mbox_s4 ((leq _TPTP_I) U))))) (mbox_s4 ((qmltpeq ((a_select2 (((tptp_update2 X) U) VAL)) _TPTP_I)) VAL))))))))))))))))) of role axiom named sel2_update_3
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (I0:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) I0))) (mbox_s4 ((leq I0) U)))) (mbox_s4 ((qmltpeq ((a_select2 X) I0)) VAL)))))))) ((mand (mbox_s4 ((leq n0) _TPTP_I))) (mbox_s4 ((leq _TPTP_I) U))))) (mbox_s4 ((qmltpeq ((a_select2 (((tptp_update2 X) U) VAL)) _TPTP_I)) VAL)))))))))))))))))
% FOF formula (mvalid (mbox_s4 true)) of role axiom named ttrue
% A new axiom: (mvalid (mbox_s4 true))
% FOF formula (mvalid (mbox_s4 (mnot (mbox_s4 ((qmltpeq def) use))))) of role axiom named defuse
% A new axiom: (mvalid (mbox_s4 (mnot (mbox_s4 ((qmltpeq def) use)))))
% FOF formula (mvalid (mbox_s4 ((gt n5) n4))) of role axiom named gt_5_4
% A new axiom: (mvalid (mbox_s4 ((gt n5) n4)))
% FOF formula (mvalid (mbox_s4 ((gt n999) n4))) of role axiom named gt_999_4
% A new axiom: (mvalid (mbox_s4 ((gt n999) n4)))
% FOF formula (mvalid (mbox_s4 ((gt n999) n5))) of role axiom named gt_999_5
% A new axiom: (mvalid (mbox_s4 ((gt n999) n5)))
% FOF formula (mvalid (mbox_s4 ((gt n4) tptp_minus_1))) of role axiom named gt_4_tptp_minus_1
% A new axiom: (mvalid (mbox_s4 ((gt n4) tptp_minus_1)))
% FOF formula (mvalid (mbox_s4 ((gt n5) tptp_minus_1))) of role axiom named gt_5_tptp_minus_1
% A new axiom: (mvalid (mbox_s4 ((gt n5) tptp_minus_1)))
% FOF formula (mvalid (mbox_s4 ((gt n999) tptp_minus_1))) of role axiom named gt_999_tptp_minus_1
% A new axiom: (mvalid (mbox_s4 ((gt n999) tptp_minus_1)))
% FOF formula (mvalid (mbox_s4 ((gt n0) tptp_minus_1))) of role axiom named gt_0_tptp_minus_1
% A new axiom: (mvalid (mbox_s4 ((gt n0) tptp_minus_1)))
% FOF formula (mvalid (mbox_s4 ((gt n1) tptp_minus_1))) of role axiom named gt_1_tptp_minus_1
% A new axiom: (mvalid (mbox_s4 ((gt n1) tptp_minus_1)))
% FOF formula (mvalid (mbox_s4 ((gt n2) tptp_minus_1))) of role axiom named gt_2_tptp_minus_1
% A new axiom: (mvalid (mbox_s4 ((gt n2) tptp_minus_1)))
% FOF formula (mvalid (mbox_s4 ((gt n3) tptp_minus_1))) of role axiom named gt_3_tptp_minus_1
% A new axiom: (mvalid (mbox_s4 ((gt n3) tptp_minus_1)))
% FOF formula (mvalid (mbox_s4 ((gt n4) n0))) of role axiom named gt_4_0
% A new axiom: (mvalid (mbox_s4 ((gt n4) n0)))
% FOF formula (mvalid (mbox_s4 ((gt n5) n0))) of role axiom named gt_5_0
% A new axiom: (mvalid (mbox_s4 ((gt n5) n0)))
% FOF formula (mvalid (mbox_s4 ((gt n999) n0))) of role axiom named gt_999_0
% A new axiom: (mvalid (mbox_s4 ((gt n999) n0)))
% FOF formula (mvalid (mbox_s4 ((gt n1) n0))) of role axiom named gt_1_0
% A new axiom: (mvalid (mbox_s4 ((gt n1) n0)))
% FOF formula (mvalid (mbox_s4 ((gt n2) n0))) of role axiom named gt_2_0
% A new axiom: (mvalid (mbox_s4 ((gt n2) n0)))
% FOF formula (mvalid (mbox_s4 ((gt n3) n0))) of role axiom named gt_3_0
% A new axiom: (mvalid (mbox_s4 ((gt n3) n0)))
% FOF formula (mvalid (mbox_s4 ((gt n4) n1))) of role axiom named gt_4_1
% A new axiom: (mvalid (mbox_s4 ((gt n4) n1)))
% FOF formula (mvalid (mbox_s4 ((gt n5) n1))) of role axiom named gt_5_1
% A new axiom: (mvalid (mbox_s4 ((gt n5) n1)))
% FOF formula (mvalid (mbox_s4 ((gt n999) n1))) of role axiom named gt_999_1
% A new axiom: (mvalid (mbox_s4 ((gt n999) n1)))
% FOF formula (mvalid (mbox_s4 ((gt n2) n1))) of role axiom named gt_2_1
% A new axiom: (mvalid (mbox_s4 ((gt n2) n1)))
% FOF formula (mvalid (mbox_s4 ((gt n3) n1))) of role axiom named gt_3_1
% A new axiom: (mvalid (mbox_s4 ((gt n3) n1)))
% FOF formula (mvalid (mbox_s4 ((gt n4) n2))) of role axiom named gt_4_2
% A new axiom: (mvalid (mbox_s4 ((gt n4) n2)))
% FOF formula (mvalid (mbox_s4 ((gt n5) n2))) of role axiom named gt_5_2
% A new axiom: (mvalid (mbox_s4 ((gt n5) n2)))
% FOF formula (mvalid (mbox_s4 ((gt n999) n2))) of role axiom named gt_999_2
% A new axiom: (mvalid (mbox_s4 ((gt n999) n2)))
% FOF formula (mvalid (mbox_s4 ((gt n3) n2))) of role axiom named gt_3_2
% A new axiom: (mvalid (mbox_s4 ((gt n3) n2)))
% FOF formula (mvalid (mbox_s4 ((gt n4) n3))) of role axiom named gt_4_3
% A new axiom: (mvalid (mbox_s4 ((gt n4) n3)))
% FOF formula (mvalid (mbox_s4 ((gt n5) n3))) of role axiom named gt_5_3
% A new axiom: (mvalid (mbox_s4 ((gt n5) n3)))
% FOF formula (mvalid (mbox_s4 ((gt n999) n3))) of role axiom named gt_999_3
% A new axiom: (mvalid (mbox_s4 ((gt n999) n3)))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n4)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) ((mor (mbox_s4 ((qmltpeq X) n2))) ((mor (mbox_s4 ((qmltpeq X) n3))) (mbox_s4 ((qmltpeq X) n4)))))))))))) of role axiom named finite_domain_4
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n4)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) ((mor (mbox_s4 ((qmltpeq X) n2))) ((mor (mbox_s4 ((qmltpeq X) n3))) (mbox_s4 ((qmltpeq X) n4))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n5)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) ((mor (mbox_s4 ((qmltpeq X) n2))) ((mor (mbox_s4 ((qmltpeq X) n3))) ((mor (mbox_s4 ((qmltpeq X) n4))) (mbox_s4 ((qmltpeq X) n5))))))))))))) of role axiom named finite_domain_5
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n5)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) ((mor (mbox_s4 ((qmltpeq X) n2))) ((mor (mbox_s4 ((qmltpeq X) n3))) ((mor (mbox_s4 ((qmltpeq X) n4))) (mbox_s4 ((qmltpeq X) n5)))))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n0)))) (mbox_s4 ((qmltpeq X) n0)))))))) of role axiom named finite_domain_0
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n0)))) (mbox_s4 ((qmltpeq X) n0))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n1)))) ((mor (mbox_s4 ((qmltpeq X) n0))) (mbox_s4 ((qmltpeq X) n1))))))))) of role axiom named finite_domain_1
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n1)))) ((mor (mbox_s4 ((qmltpeq X) n0))) (mbox_s4 ((qmltpeq X) n1)))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n2)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) (mbox_s4 ((qmltpeq X) n2)))))))))) of role axiom named finite_domain_2
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n2)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) (mbox_s4 ((qmltpeq X) n2))))))))))
% FOF formula (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n3)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) ((mor (mbox_s4 ((qmltpeq X) n2))) (mbox_s4 ((qmltpeq X) n3))))))))))) of role axiom named finite_domain_3
% A new axiom: (mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n3)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) ((mor (mbox_s4 ((qmltpeq X) n2))) (mbox_s4 ((qmltpeq X) n3)))))))))))
% FOF formula (mvalid (mbox_s4 ((qmltpeq (succ (succ (succ (succ n0))))) n4))) of role axiom named successor_4
% A new axiom: (mvalid (mbox_s4 ((qmltpeq (succ (succ (succ (succ n0))))) n4)))
% FOF formula (mvalid (mbox_s4 ((qmltpeq (succ (succ (succ (succ (succ n0)))))) n5))) of role axiom named successor_5
% A new axiom: (mvalid (mbox_s4 ((qmltpeq (succ (succ (succ (succ (succ n0)))))) n5)))
% FOF formula (mvalid (mbox_s4 ((qmltpeq (succ n0)) n1))) of role axiom named successor_1
% A new axiom: (mvalid (mbox_s4 ((qmltpeq (succ n0)) n1)))
% FOF formula (mvalid (mbox_s4 ((qmltpeq (succ (succ n0))) n2))) of role axiom named successor_2
% A new axiom: (mvalid (mbox_s4 ((qmltpeq (succ (succ n0))) n2)))
% FOF formula (mvalid (mbox_s4 ((qmltpeq (succ (succ (succ n0)))) n3))) of role axiom named successor_3
% A new axiom: (mvalid (mbox_s4 ((qmltpeq (succ (succ (succ n0)))) n3)))
% FOF formula (mvalid (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use)))))))))))))))))))))))))))))))))))))))))))) of role conjecture named quaternion_ds1_inuse_0009
% Conjecture to prove = (mvalid (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use)))))))))))))))))))))))))))))))))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(mvalid (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))))))']
% 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 true:(fofType->Prop).
% Parameter lt:(mu->(mu->(fofType->Prop))).
% Parameter geq:(mu->(mu->(fofType->Prop))).
% Parameter gt:(mu->(mu->(fofType->Prop))).
% Parameter leq:(mu->(mu->(fofType->Prop))).
% Parameter uniform_int_rnd:(mu->(mu->mu)).
% Axiom existence_of_uniform_int_rnd_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((uniform_int_rnd V2) V1)) V)).
% Parameter tptp_const_array1:(mu->(mu->mu)).
% Axiom existence_of_tptp_const_array1_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_const_array1 V2) V1)) V)).
% Parameter dim:(mu->(mu->mu)).
% Axiom existence_of_dim_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((dim V2) V1)) V)).
% Parameter tptp_const_array2:(mu->(mu->(mu->mu))).
% Axiom existence_of_tptp_const_array2_ax:(forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((tptp_const_array2 V3) V2) V1)) V)).
% Parameter inv:(mu->mu).
% Axiom existence_of_inv_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (inv V1)) V)).
% Parameter tptp_msub:(mu->(mu->mu)).
% Axiom existence_of_tptp_msub_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_msub V2) V1)) V)).
% Parameter trans:(mu->mu).
% Axiom existence_of_trans_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (trans V1)) V)).
% Parameter tptp_mmul:(mu->(mu->mu)).
% Axiom existence_of_tptp_mmul_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_mmul V2) V1)) V)).
% Parameter tptp_madd:(mu->(mu->mu)).
% Axiom existence_of_tptp_madd_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((tptp_madd V2) V1)) V)).
% Parameter sum:(mu->(mu->(mu->mu))).
% Axiom existence_of_sum_ax:(forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((sum V3) V2) V1)) V)).
% Parameter tptp_float_0_0:mu.
% Axiom existence_of_tptp_float_0_0_ax:(forall (V:fofType), ((exists_in_world tptp_float_0_0) V)).
% Parameter plus:(mu->(mu->mu)).
% Axiom existence_of_plus_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((plus V2) V1)) V)).
% Parameter pred:(mu->mu).
% Axiom existence_of_pred_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (pred V1)) V)).
% Parameter tptp_update3:(mu->(mu->(mu->(mu->mu)))).
% Axiom existence_of_tptp_update3_ax:(forall (V:fofType) (V4:mu) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world ((((tptp_update3 V4) V3) V2) V1)) V)).
% Parameter tptp_update2:(mu->(mu->(mu->mu))).
% Axiom existence_of_tptp_update2_ax:(forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((tptp_update2 V3) V2) V1)) V)).
% Parameter def:mu.
% Axiom existence_of_def_ax:(forall (V:fofType), ((exists_in_world def) V)).
% Parameter z_defuse:mu.
% Axiom existence_of_z_defuse_ax:(forall (V:fofType), ((exists_in_world z_defuse) V)).
% Parameter minus:(mu->(mu->mu)).
% Axiom existence_of_minus_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((minus V2) V1)) V)).
% Parameter pv5:mu.
% Axiom existence_of_pv5_ax:(forall (V:fofType), ((exists_in_world pv5) V)).
% Parameter xinit_noise_defuse:mu.
% Axiom existence_of_xinit_noise_defuse_ax:(forall (V:fofType), ((exists_in_world xinit_noise_defuse) V)).
% Parameter xinit_mean_defuse:mu.
% Axiom existence_of_xinit_mean_defuse_ax:(forall (V:fofType), ((exists_in_world xinit_mean_defuse) V)).
% Parameter xinit_defuse:mu.
% Axiom existence_of_xinit_defuse_ax:(forall (V:fofType), ((exists_in_world xinit_defuse) V)).
% Parameter u_defuse:mu.
% Axiom existence_of_u_defuse_ax:(forall (V:fofType), ((exists_in_world u_defuse) V)).
% Parameter a_select3:(mu->(mu->(mu->mu))).
% Axiom existence_of_a_select3_ax:(forall (V:fofType) (V3:mu) (V2:mu) (V1:mu), ((exists_in_world (((a_select3 V3) V2) V1)) V)).
% Parameter sigma_defuse:mu.
% Axiom existence_of_sigma_defuse_ax:(forall (V:fofType), ((exists_in_world sigma_defuse) V)).
% Parameter use:mu.
% Axiom existence_of_use_ax:(forall (V:fofType), ((exists_in_world use) V)).
% Parameter rho_defuse:mu.
% Axiom existence_of_rho_defuse_ax:(forall (V:fofType), ((exists_in_world rho_defuse) V)).
% Parameter a_select2:(mu->(mu->mu)).
% Axiom existence_of_a_select2_ax:(forall (V:fofType) (V2:mu) (V1:mu), ((exists_in_world ((a_select2 V2) V1)) V)).
% Parameter tptp_minus_1:mu.
% Axiom existence_of_tptp_minus_1_ax:(forall (V:fofType), ((exists_in_world tptp_minus_1) V)).
% Parameter n999:mu.
% Axiom existence_of_n999_ax:(forall (V:fofType), ((exists_in_world n999) V)).
% Parameter n4:mu.
% Axiom existence_of_n4_ax:(forall (V:fofType), ((exists_in_world n4) V)).
% Parameter n5:mu.
% Axiom existence_of_n5_ax:(forall (V:fofType), ((exists_in_world n5) V)).
% Parameter n1:mu.
% Axiom existence_of_n1_ax:(forall (V:fofType), ((exists_in_world n1) V)).
% Parameter n2:mu.
% Axiom existence_of_n2_ax:(forall (V:fofType), ((exists_in_world n2) V)).
% Parameter n3:mu.
% Axiom existence_of_n3_ax:(forall (V:fofType), ((exists_in_world n3) V)).
% Parameter n0:mu.
% Axiom existence_of_n0_ax:(forall (V:fofType), ((exists_in_world n0) V)).
% Parameter succ:(mu->mu).
% Axiom existence_of_succ_ax:(forall (V:fofType) (V1:mu), ((exists_in_world (succ 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 a_select2_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 ((a_select2 A) C)) ((a_select2 B) C))))))))))))))).
% Axiom a_select2_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 ((a_select2 C) A)) ((a_select2 C) B))))))))))))))).
% Axiom a_select3_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((a_select3 A) C) D)) (((a_select3 B) C) D)))))))))))))))))).
% Axiom a_select3_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((a_select3 C) A) D)) (((a_select3 C) B) D)))))))))))))))))).
% Axiom a_select3_substitution_3:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((a_select3 C) D) A)) (((a_select3 C) D) B)))))))))))))))))).
% Axiom dim_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 ((dim A) C)) ((dim B) C))))))))))))))).
% Axiom dim_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 ((dim C) A)) ((dim C) B))))))))))))))).
% Axiom inv_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 (inv A)) (inv B)))))))))))).
% Axiom minus_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 ((minus A) C)) ((minus B) C))))))))))))))).
% Axiom minus_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 ((minus C) A)) ((minus C) B))))))))))))))).
% Axiom plus_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 ((plus A) C)) ((plus B) C))))))))))))))).
% Axiom plus_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 ((plus C) A)) ((plus C) B))))))))))))))).
% Axiom pred_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 (pred A)) (pred B)))))))))))).
% Axiom succ_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 (succ A)) (succ B)))))))))))).
% Axiom sum_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((sum A) C) D)) (((sum B) C) D)))))))))))))))))).
% Axiom sum_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((sum C) A) D)) (((sum C) B) D)))))))))))))))))).
% Axiom sum_substitution_3:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((sum C) D) A)) (((sum C) D) B)))))))))))))))))).
% Axiom tptp_const_array1_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 ((tptp_const_array1 A) C)) ((tptp_const_array1 B) C))))))))))))))).
% Axiom tptp_const_array1_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 ((tptp_const_array1 C) A)) ((tptp_const_array1 C) B))))))))))))))).
% Axiom tptp_const_array2_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_const_array2 A) C) D)) (((tptp_const_array2 B) C) D)))))))))))))))))).
% Axiom tptp_const_array2_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_const_array2 C) A) D)) (((tptp_const_array2 C) B) D)))))))))))))))))).
% Axiom tptp_const_array2_substitution_3:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_const_array2 C) D) A)) (((tptp_const_array2 C) D) B)))))))))))))))))).
% Axiom tptp_madd_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 ((tptp_madd A) C)) ((tptp_madd B) C))))))))))))))).
% Axiom tptp_madd_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 ((tptp_madd C) A)) ((tptp_madd C) B))))))))))))))).
% Axiom tptp_mmul_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 ((tptp_mmul A) C)) ((tptp_mmul B) C))))))))))))))).
% Axiom tptp_mmul_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 ((tptp_mmul C) A)) ((tptp_mmul C) B))))))))))))))).
% Axiom tptp_msub_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 ((tptp_msub A) C)) ((tptp_msub B) C))))))))))))))).
% Axiom tptp_msub_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 ((tptp_msub C) A)) ((tptp_msub C) B))))))))))))))).
% Axiom tptp_update2_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_update2 A) C) D)) (((tptp_update2 B) C) D)))))))))))))))))).
% Axiom tptp_update2_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 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_update2 C) A) D)) (((tptp_update2 C) B) D)))))))))))))))))).
% Axiom tptp_update2_substitution_3:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq (((tptp_update2 C) D) A)) (((tptp_update2 C) D) B)))))))))))))))))).
% Axiom tptp_update3_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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 A) C) D) E)) ((((tptp_update3 B) C) D) E))))))))))))))))))))).
% Axiom tptp_update3_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 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 C) A) D) E)) ((((tptp_update3 C) B) D) E))))))))))))))))))))).
% Axiom tptp_update3_substitution_3:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 C) D) A) E)) ((((tptp_update3 C) D) B) E))))))))))))))))))))).
% Axiom tptp_update3_substitution_4:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((qmltpeq ((((tptp_update3 C) D) E) A)) ((((tptp_update3 C) D) E) B))))))))))))))))))))).
% Axiom trans_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 (trans A)) (trans B)))))))))))).
% Axiom uniform_int_rnd_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 ((uniform_int_rnd A) C)) ((uniform_int_rnd B) C))))))))))))))).
% Axiom uniform_int_rnd_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 ((uniform_int_rnd C) A)) ((uniform_int_rnd C) B))))))))))))))).
% Axiom geq_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((geq A) C)))) (mbox_s4 ((geq B) C)))))))))))))).
% Axiom geq_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((geq C) A)))) (mbox_s4 ((geq C) B)))))))))))))).
% Axiom gt_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((gt A) C)))) (mbox_s4 ((gt B) C)))))))))))))).
% Axiom gt_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((gt C) A)))) (mbox_s4 ((gt C) B)))))))))))))).
% Axiom leq_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((leq A) C)))) (mbox_s4 ((leq B) C)))))))))))))).
% Axiom leq_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((leq C) A)))) (mbox_s4 ((leq C) B)))))))))))))).
% Axiom lt_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((lt A) C)))) (mbox_s4 ((lt B) C)))))))))))))).
% Axiom lt_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 ((mand (mbox_s4 ((qmltpeq A) B))) (mbox_s4 ((lt C) A)))) (mbox_s4 ((lt C) B)))))))))))))).
% Axiom totality:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mor (mbox_s4 ((gt X) Y))) ((mor (mbox_s4 ((gt Y) X))) (mbox_s4 ((qmltpeq X) Y))))))))))).
% Axiom transitivity_gt:(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 ((gt X) Y))) (mbox_s4 ((gt Y) Z)))) (mbox_s4 ((gt X) Z)))))))))))))).
% Axiom irreflexivity_gt:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mnot (mbox_s4 ((gt X) X)))))))).
% Axiom reflexivity_leq:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((leq X) X)))))).
% Axiom transitivity_leq:(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 ((leq X) Y))) (mbox_s4 ((leq Y) Z)))) (mbox_s4 ((leq X) Z)))))))))))))).
% Axiom lt_gt:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((lt X) Y))) (mbox_s4 ((gt Y) X))))) (mbox_s4 ((mimplies (mbox_s4 ((gt Y) X))) (mbox_s4 ((lt X) Y)))))))))))).
% Axiom leq_geq:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((geq X) Y))) (mbox_s4 ((leq Y) X))))) (mbox_s4 ((mimplies (mbox_s4 ((leq Y) X))) (mbox_s4 ((geq X) Y)))))))))))).
% Axiom leq_gt1:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((gt Y) X))) (mbox_s4 ((leq X) Y))))))))))).
% Axiom leq_gt2:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq X) Y))) (mbox_s4 (mnot (mbox_s4 ((qmltpeq X) Y)))))) (mbox_s4 ((gt Y) X))))))))))).
% Axiom leq_gt_pred:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((leq X) (pred Y)))) (mbox_s4 ((gt Y) X))))) (mbox_s4 ((mimplies (mbox_s4 ((gt Y) X))) (mbox_s4 ((leq X) (pred Y))))))))))))).
% Axiom gt_succ:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((gt (succ X)) X)))))).
% Axiom leq_succ:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq X) Y))) (mbox_s4 ((leq X) (succ Y)))))))))))).
% Axiom leq_succ_gt_equiv:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((leq X) Y))) (mbox_s4 ((gt (succ Y)) X))))) (mbox_s4 ((mimplies (mbox_s4 ((gt (succ Y)) X))) (mbox_s4 ((leq X) Y)))))))))))).
% Axiom uniform_int_rand_ranges_hi:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq ((uniform_int_rnd C) X)) X))))))))))).
% Axiom uniform_int_rand_ranges_lo:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq n0) ((uniform_int_rnd C) X)))))))))))).
% Axiom const_array1_select:(mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (L:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (Val:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq L) _TPTP_I))) (mbox_s4 ((leq _TPTP_I) U)))) (mbox_s4 ((qmltpeq ((a_select2 ((tptp_const_array1 ((dim L) U)) Val)) _TPTP_I)) Val))))))))))))))))).
% Axiom const_array2_select:(mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (L1:mu)=> (mbox_s4 (mforall_ind (fun (U1:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (L2:mu)=> (mbox_s4 (mforall_ind (fun (U2:mu)=> (mbox_s4 (mforall_ind (fun (Val:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq L1) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) U1))) ((mand (mbox_s4 ((leq L2) J))) (mbox_s4 ((leq J) U2)))))) (mbox_s4 ((qmltpeq (((a_select3 (((tptp_const_array2 ((dim L1) U1)) ((dim L2) U2)) Val)) _TPTP_I) J)) Val)))))))))))))))))))))))))).
% Axiom matrix_symm_trans:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 (trans A)) _TPTP_I) J)) (((a_select3 (trans A)) J) _TPTP_I)))))))))))))))))))).
% Axiom matrix_symm_inv:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 (inv A)) _TPTP_I) J)) (((a_select3 (inv A)) J) _TPTP_I)))))))))))))))))))).
% Axiom matrix_symm_update_diagonal:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (K:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) ((mand (mbox_s4 ((leq J) N))) ((mand (mbox_s4 ((leq n0) K))) (mbox_s4 ((leq K) N)))))))) (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 A) K) K) VAL)) _TPTP_I) J)) (((a_select3 ((((tptp_update3 A) K) K) VAL)) J) _TPTP_I)))))))))))))))))))))))))).
% Axiom matrix_symm_add:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I))))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_madd A) B)) _TPTP_I) J)) (((a_select3 ((tptp_madd A) B)) J) _TPTP_I))))))))))))))))))))))).
% Axiom matrix_symm_sub:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I))))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_msub A) B)) _TPTP_I) J)) (((a_select3 ((tptp_msub A) B)) J) _TPTP_I))))))))))))))))))))))).
% Axiom matrix_symm_aba1:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) _TPTP_I) J)) (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) J) _TPTP_I))))))))))))))))))))))).
% Axiom matrix_symm_aba2:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 (mforall_ind (fun (M:mu)=> (mbox_s4 ((mimplies (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) M))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) M)))))) (mbox_s4 ((qmltpeq (((a_select3 B) _TPTP_I) J)) (((a_select3 B) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) _TPTP_I) J)) (((a_select3 ((tptp_mmul A) ((tptp_mmul B) (trans A)))) J) _TPTP_I)))))))))))))))))))))))))).
% Axiom matrix_symm_joseph_update:(mvalid (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 (mforall_ind (fun (N:mu)=> (mbox_s4 (mforall_ind (fun (M:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) M))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) M)))))) (mbox_s4 ((qmltpeq (((a_select3 D) _TPTP_I) J)) (((a_select3 D) J) _TPTP_I)))))))))))) ((mand (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 A) _TPTP_I) J)) (((a_select3 A) J) _TPTP_I)))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 F) _TPTP_I) J)) (((a_select3 F) J) _TPTP_I)))))))))))))) (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) N))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) N)))))) (mbox_s4 ((qmltpeq (((a_select3 ((tptp_madd A) ((tptp_mmul B) ((tptp_mmul ((tptp_madd ((tptp_mmul C) ((tptp_mmul D) (trans C)))) ((tptp_mmul E) ((tptp_mmul F) (trans E))))) (trans B))))) _TPTP_I) J)) (((a_select3 ((tptp_madd A) ((tptp_mmul B) ((tptp_mmul ((tptp_madd ((tptp_mmul C) ((tptp_mmul D) (trans C)))) ((tptp_mmul E) ((tptp_mmul F) (trans E))))) (trans B))))) J) _TPTP_I)))))))))))))))))))))))))))))))))))))).
% Axiom sum_plus_base:(mvalid (mbox_s4 (mforall_ind (fun (Body:mu)=> (mbox_s4 ((qmltpeq (((sum n0) tptp_minus_1) Body)) n0)))))).
% Axiom sum_plus_base_float:(mvalid (mbox_s4 (mforall_ind (fun (Body:mu)=> (mbox_s4 ((qmltpeq tptp_float_0_0) (((sum n0) tptp_minus_1) Body))))))).
% Axiom succ_tptp_minus_1:(mvalid (mbox_s4 ((qmltpeq (succ tptp_minus_1)) n0))).
% Axiom succ_plus_1_r:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n1)) (succ X))))))).
% Axiom succ_plus_1_l:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n1) X)) (succ X))))))).
% Axiom succ_plus_2_r:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n2)) (succ (succ X)))))))).
% Axiom succ_plus_2_l:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n2) X)) (succ (succ X)))))))).
% Axiom succ_plus_3_r:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n3)) (succ (succ (succ X))))))))).
% Axiom succ_plus_3_l:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n3) X)) (succ (succ (succ X))))))))).
% Axiom succ_plus_4_r:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n4)) (succ (succ (succ (succ X)))))))))).
% Axiom succ_plus_4_l:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n4) X)) (succ (succ (succ (succ X)))))))))).
% Axiom succ_plus_5_r:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus X) n5)) (succ (succ (succ (succ (succ X))))))))))).
% Axiom succ_plus_5_l:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((plus n5) X)) (succ (succ (succ (succ (succ X))))))))))).
% Axiom pred_minus_1:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq ((minus X) n1)) (pred X))))))).
% Axiom pred_succ:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq (pred (succ X))) X)))))).
% Axiom succ_pred:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((qmltpeq (succ (pred X))) X)))))).
% Axiom leq_succ_succ:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> ((mand (mbox_s4 ((mimplies (mbox_s4 ((leq (succ X)) (succ Y)))) (mbox_s4 ((leq X) Y))))) (mbox_s4 ((mimplies (mbox_s4 ((leq X) Y))) (mbox_s4 ((leq (succ X)) (succ Y))))))))))))).
% Axiom leq_succ_gt:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq (succ X)) Y))) (mbox_s4 ((gt Y) X))))))))))).
% Axiom leq_minus:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (Y:mu)=> (mbox_s4 ((mimplies (mbox_s4 ((leq ((minus X) Y)) X))) (mbox_s4 ((leq n0) Y))))))))))).
% Axiom sel3_update_1:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (V:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 X) U) V) VAL)) U) V)) VAL))))))))))))))).
% Axiom sel3_update_2:(mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (V:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 (mforall_ind (fun (VAL2:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq _TPTP_I) U))))) ((mand (mbox_s4 ((qmltpeq J) V))) (mbox_s4 ((qmltpeq (((a_select3 X) U) V)) VAL))))) (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 X) _TPTP_I) J) VAL2)) U) V)) VAL)))))))))))))))))))))))))).
% Axiom sel3_update_3:(mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (J:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (V:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (I0:mu)=> (mbox_s4 (mforall_ind (fun (J0:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) I0))) ((mand (mbox_s4 ((leq n0) J0))) ((mand (mbox_s4 ((leq I0) U))) (mbox_s4 ((leq J0) V)))))) (mbox_s4 ((qmltpeq (((a_select3 X) I0) J0)) VAL))))))))))) ((mand (mbox_s4 ((leq n0) _TPTP_I))) ((mand (mbox_s4 ((leq _TPTP_I) U))) ((mand (mbox_s4 ((leq n0) J))) (mbox_s4 ((leq J) V))))))) (mbox_s4 ((qmltpeq (((a_select3 ((((tptp_update3 X) U) V) VAL)) _TPTP_I) J)) VAL))))))))))))))))))))))).
% Axiom sel2_update_1:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((qmltpeq ((a_select2 (((tptp_update2 X) U) VAL)) U)) VAL)))))))))))).
% Axiom sel2_update_2:(mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 (mforall_ind (fun (VAL2:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mnot (mbox_s4 ((qmltpeq _TPTP_I) U))))) (mbox_s4 ((qmltpeq ((a_select2 X) U)) VAL)))) (mbox_s4 ((qmltpeq ((a_select2 (((tptp_update2 X) _TPTP_I) VAL2)) U)) VAL)))))))))))))))))))).
% Axiom sel2_update_3:(mvalid (mbox_s4 (mforall_ind (fun (_TPTP_I:mu)=> (mbox_s4 (mforall_ind (fun (U:mu)=> (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (mforall_ind (fun (VAL:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 (mforall_ind (fun (I0:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) I0))) (mbox_s4 ((leq I0) U)))) (mbox_s4 ((qmltpeq ((a_select2 X) I0)) VAL)))))))) ((mand (mbox_s4 ((leq n0) _TPTP_I))) (mbox_s4 ((leq _TPTP_I) U))))) (mbox_s4 ((qmltpeq ((a_select2 (((tptp_update2 X) U) VAL)) _TPTP_I)) VAL))))))))))))))))).
% Axiom ttrue:(mvalid (mbox_s4 true)).
% Axiom defuse:(mvalid (mbox_s4 (mnot (mbox_s4 ((qmltpeq def) use))))).
% Axiom gt_5_4:(mvalid (mbox_s4 ((gt n5) n4))).
% Axiom gt_999_4:(mvalid (mbox_s4 ((gt n999) n4))).
% Axiom gt_999_5:(mvalid (mbox_s4 ((gt n999) n5))).
% Axiom gt_4_tptp_minus_1:(mvalid (mbox_s4 ((gt n4) tptp_minus_1))).
% Axiom gt_5_tptp_minus_1:(mvalid (mbox_s4 ((gt n5) tptp_minus_1))).
% Axiom gt_999_tptp_minus_1:(mvalid (mbox_s4 ((gt n999) tptp_minus_1))).
% Axiom gt_0_tptp_minus_1:(mvalid (mbox_s4 ((gt n0) tptp_minus_1))).
% Axiom gt_1_tptp_minus_1:(mvalid (mbox_s4 ((gt n1) tptp_minus_1))).
% Axiom gt_2_tptp_minus_1:(mvalid (mbox_s4 ((gt n2) tptp_minus_1))).
% Axiom gt_3_tptp_minus_1:(mvalid (mbox_s4 ((gt n3) tptp_minus_1))).
% Axiom gt_4_0:(mvalid (mbox_s4 ((gt n4) n0))).
% Axiom gt_5_0:(mvalid (mbox_s4 ((gt n5) n0))).
% Axiom gt_999_0:(mvalid (mbox_s4 ((gt n999) n0))).
% Axiom gt_1_0:(mvalid (mbox_s4 ((gt n1) n0))).
% Axiom gt_2_0:(mvalid (mbox_s4 ((gt n2) n0))).
% Axiom gt_3_0:(mvalid (mbox_s4 ((gt n3) n0))).
% Axiom gt_4_1:(mvalid (mbox_s4 ((gt n4) n1))).
% Axiom gt_5_1:(mvalid (mbox_s4 ((gt n5) n1))).
% Axiom gt_999_1:(mvalid (mbox_s4 ((gt n999) n1))).
% Axiom gt_2_1:(mvalid (mbox_s4 ((gt n2) n1))).
% Axiom gt_3_1:(mvalid (mbox_s4 ((gt n3) n1))).
% Axiom gt_4_2:(mvalid (mbox_s4 ((gt n4) n2))).
% Axiom gt_5_2:(mvalid (mbox_s4 ((gt n5) n2))).
% Axiom gt_999_2:(mvalid (mbox_s4 ((gt n999) n2))).
% Axiom gt_3_2:(mvalid (mbox_s4 ((gt n3) n2))).
% Axiom gt_4_3:(mvalid (mbox_s4 ((gt n4) n3))).
% Axiom gt_5_3:(mvalid (mbox_s4 ((gt n5) n3))).
% Axiom gt_999_3:(mvalid (mbox_s4 ((gt n999) n3))).
% Axiom finite_domain_4:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n4)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) ((mor (mbox_s4 ((qmltpeq X) n2))) ((mor (mbox_s4 ((qmltpeq X) n3))) (mbox_s4 ((qmltpeq X) n4)))))))))))).
% Axiom finite_domain_5:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n5)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) ((mor (mbox_s4 ((qmltpeq X) n2))) ((mor (mbox_s4 ((qmltpeq X) n3))) ((mor (mbox_s4 ((qmltpeq X) n4))) (mbox_s4 ((qmltpeq X) n5))))))))))))).
% Axiom finite_domain_0:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n0)))) (mbox_s4 ((qmltpeq X) n0)))))))).
% Axiom finite_domain_1:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n1)))) ((mor (mbox_s4 ((qmltpeq X) n0))) (mbox_s4 ((qmltpeq X) n1))))))))).
% Axiom finite_domain_2:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n2)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) (mbox_s4 ((qmltpeq X) n2)))))))))).
% Axiom finite_domain_3:(mvalid (mbox_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq X) n3)))) ((mor (mbox_s4 ((qmltpeq X) n0))) ((mor (mbox_s4 ((qmltpeq X) n1))) ((mor (mbox_s4 ((qmltpeq X) n2))) (mbox_s4 ((qmltpeq X) n3))))))))))).
% Axiom successor_4:(mvalid (mbox_s4 ((qmltpeq (succ (succ (succ (succ n0))))) n4))).
% Axiom successor_5:(mvalid (mbox_s4 ((qmltpeq (succ (succ (succ (succ (succ n0)))))) n5))).
% Axiom successor_1:(mvalid (mbox_s4 ((qmltpeq (succ n0)) n1))).
% Axiom successor_2:(mvalid (mbox_s4 ((qmltpeq (succ (succ n0))) n2))).
% Axiom successor_3:(mvalid (mbox_s4 ((qmltpeq (succ (succ (succ n0)))) n3))).
% Trying to prove (mvalid (mbox_s4 ((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))))))
% Found classic0:=(classic (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V)):((or (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V)) (not (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V)))
% Found (classic (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V)) as proof of ((or (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 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G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V)) ((mnot ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) V))
% Found (classic (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V)) as proof of ((or (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 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use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) V))
% Found (or_comm_i00 (classic (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand 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((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V))) as proof of ((or ((mnot ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand 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% Found ((or_comm_i0 ((mnot ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 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% Found (((or_comm_i (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 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use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V))) as proof of ((or ((mnot ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 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((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V))
% Found (((or_comm_i (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 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% Found (((or_comm_i (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 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% Found (or_intror00 (((or_comm_i (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand 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% Found ((or_intror0 (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand 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rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) V)) (classic (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq 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((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V)))) as proof of ((or (((rel_s4 W) V)->False)) (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq 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((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use)))))))))))))))))))))))))))))))))))))))))) V))
% Found (((or_intror (((rel_s4 W) V)->False)) (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 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(mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand 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((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand 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use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 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(mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) V)) (classic (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) 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% Found (fun (V:fofType)=> (((or_intror (((rel_s4 W) V)->False)) (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq 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use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 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n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 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(mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V))))) as proof of ((or (((rel_s4 W) V)->False)) (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 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% Found (fun (V:fofType)=> (((or_intror (((rel_s4 W) V)->False)) (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq 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use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 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((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V)) ((mnot ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 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(mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use))))))))))))))))))))))))))))))))))))))))) V))))) as proof of (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 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((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use)))))))))))))))))))))))))))))))))))))))))) V)))
% Found (fun (W:fofType) (V:fofType)=> (((or_intror (((rel_s4 W) V)->False)) (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (A:mu)=> (mbox_s4 (mforall_ind (fun (B:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) A))) ((mand (mbox_s4 ((leq n0) B))) ((mand (mbox_s4 ((leq A) n2))) (mbox_s4 ((leq B) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) A) B)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) A) B)) use)))))))))))) (mbox_s4 (mforall_ind (fun (C:mu)=> (mbox_s4 (mforall_ind (fun (D:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) C))) ((mand (mbox_s4 ((leq n0) D))) ((mand (mbox_s4 ((leq C) n2))) (mbox_s4 ((leq D) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) C) D)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) C) D)) use)))))))))))))))))))))))))))))))))))))))))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_noise_defuse) n5)) use))) ((mand (mbox_s4 ((leq n0) pv5))) ((mand (mbox_s4 ((leq pv5) ((minus n999) n1)))) ((mand (mbox_s4 (mforall_ind (fun (E:mu)=> (mbox_s4 (mforall_ind (fun (F:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) E))) ((mand (mbox_s4 ((leq n0) F))) ((mand (mbox_s4 ((leq E) n2))) (mbox_s4 ((leq F) pv5)))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) E) F)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) E) F)) use)))))))))))) (mbox_s4 (mforall_ind (fun (G:mu)=> (mbox_s4 (mforall_ind (fun (H:mu)=> (mbox_s4 ((mimplies ((mand (mbox_s4 ((leq n0) G))) ((mand (mbox_s4 ((leq n0) H))) ((mand (mbox_s4 ((leq G) n2))) (mbox_s4 ((leq H) ((minus pv5) n1))))))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) G) H)) use))) (mbox_s4 ((qmltpeq (((a_select3 z_defuse) G) H)) use)))))))))))))))))))))))))))))))))))))))))) V)) (((or_comm_i (((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 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n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_mean_defuse) n0)) use))) ((mand (mbox_s4 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% Found (fun (W:fofType) (V:fofType)=> (((or_intror (((rel_s4 W) V)->False)) (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand (mbox_s4 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% Got proof (fun (W:fofType) (V:fofType)=> (((or_intror (((rel_s4 W) V)->False)) (((mimplies ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 rho_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n1)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n2)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n4)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 sigma_defuse) n5)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n0) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n1) n0)) use))) ((mand (mbox_s4 ((qmltpeq (((a_select3 u_defuse) n2) n0)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n3)) use))) ((mand (mbox_s4 ((qmltpeq ((a_select2 xinit_defuse) n4)) use))) ((mand 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% Time elapsed = 35.335060s
% node=85 cost=11838.000000 depth=13
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------