TSTP Solution File: AGT030^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : AGT030^1 : TPTP v6.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n117.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:17:41 EDT 2014
% Result : Timeout 300.06s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : AGT030^1 : TPTP v6.1.0. Released v5.2.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n117.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:47:56 CDT 2014
% % CPUTime : 300.06
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x2034ea8>, <kernel.Type object at 0x2271e60>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0x2034c68>, <kernel.DependentProduct object at 0x1e258c0>) of role type named meq_ind_type
% Using role type
% Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% FOF formula (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) of role definition named meq_ind
% A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% FOF formula (<kernel.Constant object at 0x2034c68>, <kernel.DependentProduct object at 0x2271f38>) 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 0x2271e60>, <kernel.DependentProduct object at 0x1e40cb0>) 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 0x2271e60>, <kernel.DependentProduct object at 0x1e405a8>) 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 0x1e405a8>, <kernel.DependentProduct object at 0x1e40b90>) 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 0x1e40b90>, <kernel.DependentProduct object at 0x1e403b0>) 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 0x1e403b0>, <kernel.DependentProduct object at 0x1e40320>) 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 0x1e40320>, <kernel.DependentProduct object at 0x1e40bd8>) 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 0x1e40bd8>, <kernel.DependentProduct object at 0x1e40f80>) 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 0x1e40758>, <kernel.DependentProduct object at 0x1e40e60>) of role type named mforall_ind_type
% Using role type
% Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) of role definition named mforall_ind
% A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% FOF formula (<kernel.Constant object at 0x1e40e60>, <kernel.DependentProduct object at 0x1e409e0>) 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 0x2035248>, <kernel.DependentProduct object at 0x20353b0>) 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 0x2035b00>, <kernel.DependentProduct object at 0x1e40bd8>) 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 0x2035ab8>, <kernel.DependentProduct object at 0x1e40bd8>) 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 0x2035ab8>, <kernel.DependentProduct object at 0x1e40bd8>) 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 0x2035248>, <kernel.DependentProduct object at 0x1e40bd8>) 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 0x1e405a8>, <kernel.DependentProduct object at 0x1e40320>) 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 0x1e40e60>, <kernel.DependentProduct object at 0x1e36950>) 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 0x1e40e60>, <kernel.DependentProduct object at 0x1e36710>) 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 0x1e40320>, <kernel.DependentProduct object at 0x1e36950>) 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 0x1e36950>, <kernel.DependentProduct object at 0x1e366c8>) 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 0x1e366c8>, <kernel.DependentProduct object at 0x1e36830>) 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 0x1e36830>, <kernel.DependentProduct object at 0x1e368c0>) 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 0x1e368c0>, <kernel.DependentProduct object at 0x1e369e0>) 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 0x1e369e0>, <kernel.DependentProduct object at 0x1e36a70>) 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 0x1e36a70>, <kernel.DependentProduct object at 0x1e36830>) 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 0x1e36830>, <kernel.DependentProduct object at 0x1e36e60>) 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 0x1e36908>, <kernel.DependentProduct object at 0x1e36cf8>) 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 0x1e36830>, <kernel.DependentProduct object at 0x1e36050>) of role type named minvalid_type
% Using role type
% Declaring minvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% FOF formula (<kernel.Constant object at 0x1e36cf8>, <kernel.DependentProduct object at 0x1e360e0>) 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 0x1e36050>, <kernel.DependentProduct object at 0x1e36d88>) 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 0x1e25ab8>, <kernel.DependentProduct object at 0x1e25dd0>) of role type named r1
% Using role type
% Declaring r1:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e25830>, <kernel.DependentProduct object at 0x1e25710>) of role type named r2
% Using role type
% Declaring r2:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e25518>, <kernel.DependentProduct object at 0x1e25ab8>) of role type named r3
% Using role type
% Declaring r3:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e25ef0>, <kernel.DependentProduct object at 0x1e25830>) of role type named r4
% Using role type
% Declaring r4:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e25b48>, <kernel.DependentProduct object at 0x1e25518>) of role type named r5
% Using role type
% Declaring r5:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e25dd0>, <kernel.Constant object at 0x1e25518>) of role type named john
% Using role type
% Declaring john:mu
% FOF formula (<kernel.Constant object at 0x1e25ef0>, <kernel.Constant object at 0x1e25518>) of role type named tom
% Using role type
% Declaring tom:mu
% FOF formula (<kernel.Constant object at 0x1e25b48>, <kernel.Constant object at 0x1e25518>) of role type named peter
% Using role type
% Declaring peter:mu
% FOF formula (<kernel.Constant object at 0x1e25dd0>, <kernel.Constant object at 0x1e25518>) of role type named mike
% Using role type
% Declaring mike:mu
% FOF formula (<kernel.Constant object at 0x1e25ef0>, <kernel.DependentProduct object at 0x1e25b48>) of role type named good_in_maths
% Using role type
% Declaring good_in_maths:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e257a0>, <kernel.DependentProduct object at 0x2034248>) of role type named maths_teacher
% Using role type
% Declaring maths_teacher:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e25518>, <kernel.DependentProduct object at 0x20341b8>) of role type named mathematician
% Using role type
% Declaring mathematician:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e25638>, <kernel.DependentProduct object at 0x20343f8>) of role type named maths_student
% Using role type
% Declaring maths_student:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e257a0>, <kernel.DependentProduct object at 0x20343f8>) of role type named good_in_physics
% Using role type
% Declaring good_in_physics:(mu->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1e25518>, <kernel.DependentProduct object at 0x20343f8>) of role type named physics_student
% Using role type
% Declaring physics_student:(mu->(fofType->Prop))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mimplies (maths_teacher X)) ((mbox r4) (good_in_maths X)))))) of role axiom named axiom_r1
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mimplies (maths_teacher X)) ((mbox r4) (good_in_maths X))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r1) (mathematician X))) ((mbox r1) (good_in_maths X))))))) of role axiom named axiom_r2_1
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r1) (mathematician X))) ((mbox r1) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r2) (mathematician X))) ((mbox r2) (good_in_maths X))))))) of role axiom named axiom_r2_2
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r2) (mathematician X))) ((mbox r2) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r3) (mathematician X))) ((mbox r3) (good_in_maths X))))))) of role axiom named axiom_r2_3
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r3) (mathematician X))) ((mbox r3) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r4) (mathematician X))) ((mbox r4) (good_in_maths X))))))) of role axiom named axiom_r2_4
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r4) (mathematician X))) ((mbox r4) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r5) (mathematician X))) ((mbox r5) (good_in_maths X))))))) of role axiom named axiom_r2_5
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r5) (mathematician X))) ((mbox r5) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r1) (good_in_maths X))))))) of role axiom named axiom_r3_1
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r1) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r2) (good_in_maths X))))))) of role axiom named axiom_r3_2
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r2) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r3) (good_in_maths X))))))) of role axiom named axiom_r3_3
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r3) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r4) (good_in_maths X))))))) of role axiom named axiom_r3_4
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r4) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r5) (good_in_maths X))))))) of role axiom named axiom_r3_5
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r5) (good_in_maths X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r1) (good_in_physics X))))))) of role axiom named axiom_r4_1
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r1) (good_in_physics X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r2) (good_in_physics X))))))) of role axiom named axiom_r4_2
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r2) (good_in_physics X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r3) (good_in_physics X))))))) of role axiom named axiom_r4_3
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r3) (good_in_physics X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r4) (good_in_physics X))))))) of role axiom named axiom_r4_4
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r4) (good_in_physics X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r5) (good_in_physics X))))))) of role axiom named axiom_r4_5
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r5) (good_in_physics X)))))))
% FOF formula (mvalid (mforall_ind (fun (X:mu)=> ((mbox r2) ((mimplies (good_in_physics X)) ((mdia r2) (good_in_maths X))))))) of role axiom named axiom_r5
% A new axiom: (mvalid (mforall_ind (fun (X:mu)=> ((mbox r2) ((mimplies (good_in_physics X)) ((mdia r2) (good_in_maths X)))))))
% FOF formula (mvalid (maths_teacher john)) of role axiom named axiom_a6
% A new axiom: (mvalid (maths_teacher john))
% FOF formula (mvalid ((mbox r2) (mathematician tom))) of role axiom named axiom_a7
% A new axiom: (mvalid ((mbox r2) (mathematician tom)))
% FOF formula (mvalid ((mbox r5) (maths_student peter))) of role axiom named axiom_a8
% A new axiom: (mvalid ((mbox r5) (maths_student peter)))
% FOF formula (mvalid ((mbox r5) (physics_student mike))) of role axiom named axiom_a9
% A new axiom: (mvalid ((mbox r5) (physics_student mike)))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) (mnot ((mbox r1) (mnot Phi))))))) of role axiom named axiom_D_for_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) (mnot ((mbox r1) (mnot Phi)))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) (mnot ((mbox r2) (mnot Phi))))))) of role axiom named axiom_D_for_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) (mnot ((mbox r2) (mnot Phi)))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) (mnot ((mbox r3) (mnot Phi))))))) of role axiom named axiom_D_for_r3
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) (mnot ((mbox r3) (mnot Phi)))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) (mnot ((mbox r4) (mnot Phi))))))) of role axiom named axiom_D_for_r4
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) (mnot ((mbox r4) (mnot Phi)))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) (mnot ((mbox r5) (mnot Phi))))))) of role axiom named axiom_D_for_r5
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) (mnot ((mbox r5) (mnot Phi)))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r1) Phi))))) of role axiom named axiom_I_for_r2_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r1) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r1) Phi))))) of role axiom named axiom_I_for_r3_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r1) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r1) Phi))))) of role axiom named axiom_I_for_r4_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r1) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r1) Phi))))) of role axiom named axiom_I_for_r45r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r1) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r2) Phi))))) of role axiom named axiom_I_for_r3_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r2) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r2) Phi))))) of role axiom named axiom_I_for_r4_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r2) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r2) Phi))))) of role axiom named axiom_I_for_r5_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r2) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r3) Phi))))) of role axiom named axiom_I_for_r4_r3
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r3) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r3) Phi))))) of role axiom named axiom_I_for_r5_r3
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r3) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r4) Phi))))) of role axiom named axiom_I_for_r5_r4
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r4) Phi)))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r1) ((mbox r1) Phi)))))) of role axiom named axiom_4s_for_r1_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r1) ((mbox r1) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r2) ((mbox r1) Phi)))))) of role axiom named axiom_4s_for_r1_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r2) ((mbox r1) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r3) ((mbox r1) Phi)))))) of role axiom named axiom_4s_for_r1_r3
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r3) ((mbox r1) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r4) ((mbox r1) Phi)))))) of role axiom named axiom_4s_for_r1_r4
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r4) ((mbox r1) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r5) ((mbox r1) Phi)))))) of role axiom named axiom_4s_for_r1_r5
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r5) ((mbox r1) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r1) ((mbox r2) Phi)))))) of role axiom named axiom_4s_for_r2_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r1) ((mbox r2) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r2) ((mbox r2) Phi)))))) of role axiom named axiom_4s_for_r2_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r2) ((mbox r2) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r3) ((mbox r2) Phi)))))) of role axiom named axiom_4s_for_r2_r3
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r3) ((mbox r2) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r4) ((mbox r2) Phi)))))) of role axiom named axiom_4s_for_r2_r4
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r4) ((mbox r2) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r5) ((mbox r2) Phi)))))) of role axiom named axiom_4s_for_r2_r5
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r5) ((mbox r2) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r1) ((mbox r3) Phi)))))) of role axiom named axiom_4s_for_r3_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r1) ((mbox r3) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r2) ((mbox r3) Phi)))))) of role axiom named axiom_4s_for_r3_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r2) ((mbox r3) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r3) ((mbox r3) Phi)))))) of role axiom named axiom_4s_for_r3_r3
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r3) ((mbox r3) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r4) ((mbox r3) Phi)))))) of role axiom named axiom_4s_for_r3_r4
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r4) ((mbox r3) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r5) ((mbox r3) Phi)))))) of role axiom named axiom_4s_for_r3_r5
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r5) ((mbox r3) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r1) ((mbox r4) Phi)))))) of role axiom named axiom_4s_for_r4_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r1) ((mbox r4) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r2) ((mbox r4) Phi)))))) of role axiom named axiom_4s_for_r4_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r2) ((mbox r4) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r3) ((mbox r4) Phi)))))) of role axiom named axiom_4s_for_r4_r3
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r3) ((mbox r4) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r4) ((mbox r4) Phi)))))) of role axiom named axiom_4s_for_r4_r4
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r4) ((mbox r4) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r5) ((mbox r4) Phi)))))) of role axiom named axiom_4s_for_r4_r5
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r5) ((mbox r4) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r1) ((mbox r5) Phi)))))) of role axiom named axiom_4s_for_r5_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r1) ((mbox r5) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r2) ((mbox r5) Phi)))))) of role axiom named axiom_4s_for_r5_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r2) ((mbox r5) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r3) ((mbox r5) Phi)))))) of role axiom named axiom_4s_for_r5_r3
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r3) ((mbox r5) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r4) ((mbox r5) Phi)))))) of role axiom named axiom_4s_for_r5_r4
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r4) ((mbox r5) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r5) ((mbox r5) Phi)))))) of role axiom named axiom_4s_for_r5_r5
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r5) ((mbox r5) Phi))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r1) Phi))) ((mbox r1) (mnot ((mbox r1) Phi))))))) of role axiom named axiom_5_for_r1
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r1) Phi))) ((mbox r1) (mnot ((mbox r1) Phi)))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r2) Phi))) ((mbox r2) (mnot ((mbox r2) Phi))))))) of role axiom named axiom_5_for_r2
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r2) Phi))) ((mbox r2) (mnot ((mbox r2) Phi)))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r3) Phi))) ((mbox r3) (mnot ((mbox r3) Phi))))))) of role axiom named axiom_5_for_r3
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r3) Phi))) ((mbox r3) (mnot ((mbox r3) Phi)))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r4) Phi))) ((mbox r4) (mnot ((mbox r4) Phi))))))) of role axiom named axiom_5_for_r4
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r4) Phi))) ((mbox r4) (mnot ((mbox r4) Phi)))))))
% FOF formula (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r5) Phi))) ((mbox r5) (mnot ((mbox r5) Phi))))))) of role axiom named axiom_5_for_r5
% A new axiom: (mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r5) Phi))) ((mbox r5) (mnot ((mbox r5) Phi)))))))
% FOF formula (mvalid (mexists_ind (fun (X:mu)=> ((mdia r1) (good_in_maths X))))) of role conjecture named conj
% Conjecture to prove = (mvalid (mexists_ind (fun (X:mu)=> ((mdia r1) (good_in_maths X))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(mvalid (mexists_ind (fun (X:mu)=> ((mdia r1) (good_in_maths X)))))']
% Parameter mu:Type.
% Parameter fofType:Type.
% Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% Definition mfalse:=(mnot mtrue):(fofType->Prop).
% Definition mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% Definition mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))):((fofType->(fofType->Prop))->Prop).
% Definition meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))):((fofType->(fofType->Prop))->Prop).
% Definition mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))):((fofType->(fofType->Prop))->Prop).
% Definition mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))):((fofType->(fofType->Prop))->Prop).
% Definition mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))):((fofType->(fofType->Prop))->Prop).
% Definition mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))):((fofType->(fofType->Prop))->Prop).
% Definition mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))):((fofType->(fofType->Prop))->Prop).
% Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% Parameter r1:(fofType->(fofType->Prop)).
% Parameter r2:(fofType->(fofType->Prop)).
% Parameter r3:(fofType->(fofType->Prop)).
% Parameter r4:(fofType->(fofType->Prop)).
% Parameter r5:(fofType->(fofType->Prop)).
% Parameter john:mu.
% Parameter tom:mu.
% Parameter peter:mu.
% Parameter mike:mu.
% Parameter good_in_maths:(mu->(fofType->Prop)).
% Parameter maths_teacher:(mu->(fofType->Prop)).
% Parameter mathematician:(mu->(fofType->Prop)).
% Parameter maths_student:(mu->(fofType->Prop)).
% Parameter good_in_physics:(mu->(fofType->Prop)).
% Parameter physics_student:(mu->(fofType->Prop)).
% Axiom axiom_r1:(mvalid (mforall_ind (fun (X:mu)=> ((mimplies (maths_teacher X)) ((mbox r4) (good_in_maths X)))))).
% Axiom axiom_r2_1:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r1) (mathematician X))) ((mbox r1) (good_in_maths X))))))).
% Axiom axiom_r2_2:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r2) (mathematician X))) ((mbox r2) (good_in_maths X))))))).
% Axiom axiom_r2_3:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r3) (mathematician X))) ((mbox r3) (good_in_maths X))))))).
% Axiom axiom_r2_4:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r4) (mathematician X))) ((mbox r4) (good_in_maths X))))))).
% Axiom axiom_r2_5:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r5) ((mimplies ((mbox r5) (mathematician X))) ((mbox r5) (good_in_maths X))))))).
% Axiom axiom_r3_1:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r1) (good_in_maths X))))))).
% Axiom axiom_r3_2:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r2) (good_in_maths X))))))).
% Axiom axiom_r3_3:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r3) (good_in_maths X))))))).
% Axiom axiom_r3_4:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r4) (good_in_maths X))))))).
% Axiom axiom_r3_5:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (maths_student X)) ((mdia r5) (good_in_maths X))))))).
% Axiom axiom_r4_1:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r1) (good_in_physics X))))))).
% Axiom axiom_r4_2:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r2) (good_in_physics X))))))).
% Axiom axiom_r4_3:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r3) (good_in_physics X))))))).
% Axiom axiom_r4_4:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r4) (good_in_physics X))))))).
% Axiom axiom_r4_5:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r3) ((mimplies (physics_student X)) ((mdia r5) (good_in_physics X))))))).
% Axiom axiom_r5:(mvalid (mforall_ind (fun (X:mu)=> ((mbox r2) ((mimplies (good_in_physics X)) ((mdia r2) (good_in_maths X))))))).
% Axiom axiom_a6:(mvalid (maths_teacher john)).
% Axiom axiom_a7:(mvalid ((mbox r2) (mathematician tom))).
% Axiom axiom_a8:(mvalid ((mbox r5) (maths_student peter))).
% Axiom axiom_a9:(mvalid ((mbox r5) (physics_student mike))).
% Axiom axiom_D_for_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) (mnot ((mbox r1) (mnot Phi))))))).
% Axiom axiom_D_for_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) (mnot ((mbox r2) (mnot Phi))))))).
% Axiom axiom_D_for_r3:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) (mnot ((mbox r3) (mnot Phi))))))).
% Axiom axiom_D_for_r4:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) (mnot ((mbox r4) (mnot Phi))))))).
% Axiom axiom_D_for_r5:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) (mnot ((mbox r5) (mnot Phi))))))).
% Axiom axiom_I_for_r2_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r1) Phi))))).
% Axiom axiom_I_for_r3_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r1) Phi))))).
% Axiom axiom_I_for_r4_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r1) Phi))))).
% Axiom axiom_I_for_r45r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r1) Phi))))).
% Axiom axiom_I_for_r3_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r2) Phi))))).
% Axiom axiom_I_for_r4_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r2) Phi))))).
% Axiom axiom_I_for_r5_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r2) Phi))))).
% Axiom axiom_I_for_r4_r3:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r3) Phi))))).
% Axiom axiom_I_for_r5_r3:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r3) Phi))))).
% Axiom axiom_I_for_r5_r4:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r4) Phi))))).
% Axiom axiom_4s_for_r1_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r1) ((mbox r1) Phi)))))).
% Axiom axiom_4s_for_r1_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r2) ((mbox r1) Phi)))))).
% Axiom axiom_4s_for_r1_r3:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r3) ((mbox r1) Phi)))))).
% Axiom axiom_4s_for_r1_r4:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r4) ((mbox r1) Phi)))))).
% Axiom axiom_4s_for_r1_r5:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r1) Phi)) ((mbox r5) ((mbox r1) Phi)))))).
% Axiom axiom_4s_for_r2_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r1) ((mbox r2) Phi)))))).
% Axiom axiom_4s_for_r2_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r2) ((mbox r2) Phi)))))).
% Axiom axiom_4s_for_r2_r3:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r3) ((mbox r2) Phi)))))).
% Axiom axiom_4s_for_r2_r4:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r4) ((mbox r2) Phi)))))).
% Axiom axiom_4s_for_r2_r5:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r2) Phi)) ((mbox r5) ((mbox r2) Phi)))))).
% Axiom axiom_4s_for_r3_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r1) ((mbox r3) Phi)))))).
% Axiom axiom_4s_for_r3_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r2) ((mbox r3) Phi)))))).
% Axiom axiom_4s_for_r3_r3:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r3) ((mbox r3) Phi)))))).
% Axiom axiom_4s_for_r3_r4:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r4) ((mbox r3) Phi)))))).
% Axiom axiom_4s_for_r3_r5:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r3) Phi)) ((mbox r5) ((mbox r3) Phi)))))).
% Axiom axiom_4s_for_r4_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r1) ((mbox r4) Phi)))))).
% Axiom axiom_4s_for_r4_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r2) ((mbox r4) Phi)))))).
% Axiom axiom_4s_for_r4_r3:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r3) ((mbox r4) Phi)))))).
% Axiom axiom_4s_for_r4_r4:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r4) ((mbox r4) Phi)))))).
% Axiom axiom_4s_for_r4_r5:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r4) Phi)) ((mbox r5) ((mbox r4) Phi)))))).
% Axiom axiom_4s_for_r5_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r1) ((mbox r5) Phi)))))).
% Axiom axiom_4s_for_r5_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r2) ((mbox r5) Phi)))))).
% Axiom axiom_4s_for_r5_r3:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r3) ((mbox r5) Phi)))))).
% Axiom axiom_4s_for_r5_r4:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r4) ((mbox r5) Phi)))))).
% Axiom axiom_4s_for_r5_r5:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies ((mbox r5) Phi)) ((mbox r5) ((mbox r5) Phi)))))).
% Axiom axiom_5_for_r1:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r1) Phi))) ((mbox r1) (mnot ((mbox r1) Phi))))))).
% Axiom axiom_5_for_r2:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r2) Phi))) ((mbox r2) (mnot ((mbox r2) Phi))))))).
% Axiom axiom_5_for_r3:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r3) Phi))) ((mbox r3) (mnot ((mbox r3) Phi))))))).
% Axiom axiom_5_for_r4:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r4) Phi))) ((mbox r4) (mnot ((mbox r4) Phi))))))).
% Axiom axiom_5_for_r5:(mvalid (mforall_prop (fun (Phi:(fofType->Prop))=> ((mimplies (mnot ((mbox r5) Phi))) ((mbox r5) (mnot ((mbox r5) Phi))))))).
% Trying to prove (mvalid (mexists_ind (fun (X:mu)=> ((mdia r1) (good_in_maths X)))))
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x20:False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x20:False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x20:False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x20:False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x20:False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x20:False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x20:False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x3:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of False
% Found (fun (x3:((mnot (good_in_maths X)) V0))=> x20) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x50:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x50) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x50) as proof of (((mdia r1) (good_in_maths X1)) W)
% Found x50:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x50) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x50) as proof of (((mdia r1) (good_in_maths X1)) W)
% Found x40:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x40) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x40) as proof of (((mdia r1) (good_in_maths X1)) W)
% Found x40:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x40) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x40) as proof of (((mdia r1) (good_in_maths X1)) W)
% Found x30:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x30) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x30) as proof of (((mdia r1) (good_in_maths X1)) W)
% Found x50:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x50) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x50) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X1)))) W)
% Found x50:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x50) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x50) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X1)))) W)
% Found x20:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x20) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x20) as proof of (((mdia r1) (good_in_maths X1)) W)
% Found x40:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x40) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x40) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X1)))) W)
% Found x40:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x40) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x40) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X1)))) W)
% Found x30:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x30) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x30) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X1)))) W)
% Found x20:False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x20) as proof of False
% Found (fun (x6:(((mbox r1) (mnot (good_in_maths X1))) W))=> x20) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X1)))) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x30:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x40:False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of ((((r1 W) V0)->False)->False)
% Found x40:False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x40) as proof of False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x40) as proof of (((mnot (good_in_maths X0)) V0)->False)
% Found x40:False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x40) as proof of False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x40) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x40:False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x40) as proof of False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x40) as proof of (((mnot (good_in_maths X0)) V0)->False)
% Found x40:False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of ((((r1 W) V0)->False)->False)
% Found x40:False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of ((((r1 W) V0)->False)->False)
% Found x40:False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x40) as proof of False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x40) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x40:False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x30) as proof of False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x30) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x30:False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x30) as proof of False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x30) as proof of (((mnot (good_in_maths X0)) V0)->False)
% Found x30:False
% Found (fun (x5:(((r1 W) V0)->False))=> x30) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x30) as proof of ((((r1 W) V0)->False)->False)
% Found x30:False
% Found (fun (x5:(((r1 W) V0)->False))=> x30) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x30) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x40:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x40:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((((mbox r1) (mnot (good_in_maths X0))) W)->False)
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:((mnot (good_in_maths X)) V0)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found (fun (x4:((mnot (good_in_maths X)) V0)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mnot (good_in_maths X)) V0)->(((mdia r1) (good_in_maths X0)) W))
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((r1 W) V0)->False)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found (fun (x4:(((r1 W) V0)->False)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((((r1 W) V0)->False)->(((mdia r1) (good_in_maths X0)) W))
% Found x20:False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x20) as proof of False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x20) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x20:False
% Found (fun (x5:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x5:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x20) as proof of False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x20) as proof of (((mnot (good_in_maths X0)) V0)->False)
% Found x40:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x40:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:((mnot (good_in_maths X)) V0)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found (fun (x4:((mnot (good_in_maths X)) V0)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mnot (good_in_maths X)) V0)->(((mdia r1) (good_in_maths X0)) W))
% Found x20:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x4:(((r1 W) V0)->False)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found (fun (x4:(((r1 W) V0)->False)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of ((((r1 W) V0)->False)->(((mdia r1) (good_in_maths X0)) W))
% Found x40:False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x40) as proof of False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x40) as proof of (((mnot (good_in_maths X0)) V0)->False)
% Found x40:False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x40) as proof of False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x40) as proof of (((mnot (good_in_maths X0)) V0)->False)
% Found x40:False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of ((((r1 W) V0)->False)->False)
% Found x40:False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x40) as proof of False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x40) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x40:False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of ((((r1 W) V0)->False)->False)
% Found x40:False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of ((((r1 W) V0)->False)->False)
% Found x40:False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x40) as proof of False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x40) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x40:False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x40) as proof of ((((r1 W) V0)->False)->False)
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x20:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x20) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mdia r1) (good_in_maths X0)) W)
% Found x30:False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x30) as proof of False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x30) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x30:False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x30) as proof of False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x30) as proof of (((mnot (good_in_maths X0)) V0)->False)
% Found x30:False
% Found (fun (x5:(((r1 W) V0)->False))=> x30) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x30) as proof of ((((r1 W) V0)->False)->False)
% Found x30:False
% Found (fun (x5:(((r1 W) V0)->False))=> x30) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x30) as proof of ((((r1 W) V0)->False)->False)
% Found x40:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x40:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x40) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:((mnot (good_in_maths X)) V0)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found (fun (x4:((mnot (good_in_maths X)) V0)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of (((mnot (good_in_maths X)) V0)->((mnot ((mbox r1) (mnot (good_in_maths X0)))) W))
% Found x30:False
% Found (fun (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of False
% Found (fun (x4:(((r1 W) V0)->False)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((mnot ((mbox r1) (mnot (good_in_maths X0)))) W)
% Found (fun (x4:(((r1 W) V0)->False)) (x5:(((mbox r1) (mnot (good_in_maths X0))) W))=> x30) as proof of ((((r1 W) V0)->False)->((mnot ((mbox r1) (mnot (good_in_maths X0)))) W))
% Found x20:False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x20) as proof of False
% Found (fun (x5:((mnot (good_in_maths X)) V0))=> x20) as proof of (((mnot (good_in_maths X)) V0)->False)
% Found x20:False
% Found (fun (x5:(((r1 W) V0)->False))=> x20) as proof of False
% Found (fun (x5:(((r1 W) V0)->False))=> x20) as proof of ((((r1 W) V0)->False)->False)
% Found x20:False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x20) as proof of False
% Found (fun (x5:((mnot (good_in_maths X0)) V0))=> x20) as proof of (((mnot (good_in_maths X0)) V0)->False)
% Found
% EOF
%------------------------------------------------------------------------------