TSTP Solution File: SYO072^4.002 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO072^4.002 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:50:35 EDT 2022
% Result : Timeout 300.01s 300.55s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO072^4.002 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 11 13:55:27 EST 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.35 Python 2.7.5
% 0.47/0.63 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.47/0.63 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL010^0.ax, trying next directory
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ae41685e9e0>, <kernel.DependentProduct object at 0x2ae41685e908>) of role type named irel_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring irel:(fofType->(fofType->Prop))
% 0.47/0.63 FOF formula (forall (X:fofType), ((irel X) X)) of role axiom named refl_axiom
% 0.47/0.63 A new axiom: (forall (X:fofType), ((irel X) X))
% 0.47/0.63 FOF formula (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((irel X) Y)) ((irel Y) Z))->((irel X) Z))) of role axiom named trans_axiom
% 0.47/0.63 A new axiom: (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((irel X) Y)) ((irel Y) Z))->((irel X) Z)))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ae41685ea28>, <kernel.DependentProduct object at 0x2ae41685e5f0>) of role type named mnot_decl_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.47/0.63 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))) of role definition named mnot
% 0.47/0.63 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)))
% 0.47/0.63 Defined: mnot:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ae41685e830>, <kernel.DependentProduct object at 0x2ae41685e4d0>) of role type named mor_decl_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.63 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))) of role definition named mor
% 0.47/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))))
% 0.47/0.63 Defined: mor:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ae41685ea28>, <kernel.DependentProduct object at 0x2ae41685e680>) of role type named mand_decl_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.63 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))) of role definition named mand
% 0.47/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))))
% 0.47/0.63 Defined: mand:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ae41685e830>, <kernel.DependentProduct object at 0x2ae41685e3b0>) of role type named mimplies_decl_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.63 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V))) of role definition named mimplies
% 0.47/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V)))
% 0.47/0.63 Defined: mimplies:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ae41685e830>, <kernel.DependentProduct object at 0x2ae41685e878>) of role type named mbox_s4_decl_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mbox_s4:((fofType->Prop)->(fofType->Prop))
% 0.47/0.63 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y))))) of role definition named mbox_s4
% 0.47/0.63 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y)))))
% 0.47/0.63 Defined: mbox_s4:=(fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ae41685e878>, <kernel.DependentProduct object at 0x2ae41685e248>) of role type named iatom_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring iatom:((fofType->Prop)->(fofType->Prop))
% 0.47/0.64 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) iatom) (fun (P:(fofType->Prop))=> P)) of role definition named iatom
% 0.47/0.64 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) iatom) (fun (P:(fofType->Prop))=> P))
% 0.47/0.64 Defined: iatom:=(fun (P:(fofType->Prop))=> P)
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2ae41685e830>, <kernel.DependentProduct object at 0x2ae41685e368>) of role type named inot_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring inot:((fofType->Prop)->(fofType->Prop))
% 0.47/0.64 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) inot) (fun (P:(fofType->Prop))=> (mnot (mbox_s4 P)))) of role definition named inot
% 0.47/0.64 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) inot) (fun (P:(fofType->Prop))=> (mnot (mbox_s4 P))))
% 0.47/0.64 Defined: inot:=(fun (P:(fofType->Prop))=> (mnot (mbox_s4 P)))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2ae41685e878>, <kernel.DependentProduct object at 0x2ae41685e518>) of role type named itrue_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring itrue:(fofType->Prop)
% 0.47/0.64 FOF formula (((eq (fofType->Prop)) itrue) (fun (W:fofType)=> True)) of role definition named itrue
% 0.47/0.64 A new definition: (((eq (fofType->Prop)) itrue) (fun (W:fofType)=> True))
% 0.47/0.64 Defined: itrue:=(fun (W:fofType)=> True)
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2ae41685e050>, <kernel.DependentProduct object at 0x1700c20>) of role type named ifalse_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring ifalse:(fofType->Prop)
% 0.47/0.64 FOF formula (((eq (fofType->Prop)) ifalse) (inot itrue)) of role definition named ifalse
% 0.47/0.64 A new definition: (((eq (fofType->Prop)) ifalse) (inot itrue))
% 0.47/0.64 Defined: ifalse:=(inot itrue)
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2ae41685e488>, <kernel.DependentProduct object at 0x1700638>) of role type named iand_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring iand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.64 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iand) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q))) of role definition named iand
% 0.47/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iand) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q)))
% 0.47/0.64 Defined: iand:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2ae41685e830>, <kernel.DependentProduct object at 0x1700908>) of role type named ior_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring ior:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.64 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) ior) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mor (mbox_s4 P)) (mbox_s4 Q)))) of role definition named ior
% 0.47/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) ior) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mor (mbox_s4 P)) (mbox_s4 Q))))
% 0.47/0.64 Defined: ior:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mor (mbox_s4 P)) (mbox_s4 Q)))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x1700ab8>, <kernel.DependentProduct object at 0x1700a28>) of role type named iimplies_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring iimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.64 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iimplies) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mimplies (mbox_s4 P)) (mbox_s4 Q)))) of role definition named iimplies
% 0.47/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iimplies) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mimplies (mbox_s4 P)) (mbox_s4 Q))))
% 0.47/0.64 Defined: iimplies:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mimplies (mbox_s4 P)) (mbox_s4 Q)))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x17009e0>, <kernel.DependentProduct object at 0x1726710>) of role type named iimplied_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring iimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.64 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iimplied) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P))) of role definition named iimplied
% 0.47/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iimplied) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P)))
% 0.47/0.65 Defined: iimplied:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x1700a28>, <kernel.DependentProduct object at 0x17267a0>) of role type named iequiv_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring iequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iequiv) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iand ((iimplies P) Q)) ((iimplies Q) P)))) of role definition named iequiv
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iequiv) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iand ((iimplies P) Q)) ((iimplies Q) P))))
% 0.47/0.65 Defined: iequiv:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iand ((iimplies P) Q)) ((iimplies Q) P)))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x1726200>, <kernel.DependentProduct object at 0x17267e8>) of role type named ixor_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring ixor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) ixor) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> (inot ((iequiv P) Q)))) of role definition named ixor
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) ixor) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> (inot ((iequiv P) Q))))
% 0.47/0.65 Defined: ixor:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> (inot ((iequiv P) Q)))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x17266c8>, <kernel.DependentProduct object at 0x1726488>) of role type named ivalid_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring ivalid:((fofType->Prop)->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) ivalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named ivalid
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) ivalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.47/0.65 Defined: ivalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x1726200>, <kernel.DependentProduct object at 0x2ae41685c1b8>) of role type named isatisfiable_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring isatisfiable:((fofType->Prop)->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) isatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named isatisfiable
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) isatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.47/0.65 Defined: isatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x1726f80>, <kernel.DependentProduct object at 0x2ae41685c1b8>) of role type named icountersatisfiable_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring icountersatisfiable:((fofType->Prop)->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) icountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named icountersatisfiable
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) icountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.47/0.65 Defined: icountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2ae41685c200>, <kernel.DependentProduct object at 0x2ae41685c440>) of role type named iinvalid_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring iinvalid:((fofType->Prop)->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) iinvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named iinvalid
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) iinvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.47/0.65 Defined: iinvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x17232d8>, <kernel.DependentProduct object at 0x2ae41e32c908>) of role type named o11_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring o11:(fofType->Prop)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x1723878>, <kernel.DependentProduct object at 0x2ae41e32cf38>) of role type named o12_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring o12:(fofType->Prop)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x17235a8>, <kernel.DependentProduct object at 0x2ae41e32cbd8>) of role type named o21_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring o21:(fofType->Prop)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x17232d8>, <kernel.DependentProduct object at 0x2ae41e32cd88>) of role type named o22_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring o22:(fofType->Prop)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x17235a8>, <kernel.DependentProduct object at 0x2ae41e32c8c0>) of role type named o31_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring o31:(fofType->Prop)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x1723878>, <kernel.DependentProduct object at 0x2ae41e32ce18>) of role type named o32_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring o32:(fofType->Prop)
% 0.47/0.65 FOF formula (ivalid ((ior (iatom o11)) (inot (inot (iatom o12))))) of role axiom named axiom1
% 0.47/0.65 A new axiom: (ivalid ((ior (iatom o11)) (inot (inot (iatom o12)))))
% 0.47/0.65 FOF formula (ivalid ((ior (iatom o21)) (inot (inot (iatom o22))))) of role axiom named axiom2
% 0.47/0.65 A new axiom: (ivalid ((ior (iatom o21)) (inot (inot (iatom o22)))))
% 0.47/0.65 FOF formula (ivalid ((ior (iatom o31)) (inot (inot (iatom o32))))) of role axiom named axiom3
% 0.47/0.65 A new axiom: (ivalid ((ior (iatom o31)) (inot (inot (iatom o32)))))
% 0.47/0.65 FOF formula (ivalid ((ior ((iand (iatom o11)) (iatom o21))) ((ior ((iand (iatom o11)) (iatom o31))) ((ior ((iand (iatom o21)) (iatom o31))) ((ior ((iand (iatom o12)) (iatom o22))) ((ior ((iand (iatom o12)) (iatom o32))) ((iand (iatom o22)) (iatom o32)))))))) of role conjecture named con
% 0.47/0.65 Conjecture to prove = (ivalid ((ior ((iand (iatom o11)) (iatom o21))) ((ior ((iand (iatom o11)) (iatom o31))) ((ior ((iand (iatom o21)) (iatom o31))) ((ior ((iand (iatom o12)) (iatom o22))) ((ior ((iand (iatom o12)) (iatom o32))) ((iand (iatom o22)) (iatom o32)))))))):Prop
% 0.47/0.65 Parameter fofType_DUMMY:fofType.
% 0.47/0.65 We need to prove ['(ivalid ((ior ((iand (iatom o11)) (iatom o21))) ((ior ((iand (iatom o11)) (iatom o31))) ((ior ((iand (iatom o21)) (iatom o31))) ((ior ((iand (iatom o12)) (iatom o22))) ((ior ((iand (iatom o12)) (iatom o32))) ((iand (iatom o22)) (iatom o32))))))))']
% 0.47/0.65 Parameter fofType:Type.
% 0.47/0.65 Parameter irel:(fofType->(fofType->Prop)).
% 0.47/0.65 Axiom refl_axiom:(forall (X:fofType), ((irel X) X)).
% 0.47/0.65 Axiom trans_axiom:(forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((irel X) Y)) ((irel Y) Z))->((irel X) Z))).
% 0.47/0.65 Definition mnot:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.47/0.65 Definition mor:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mand:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mimplies:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mbox_s4:=(fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y)))):((fofType->Prop)->(fofType->Prop)).
% 0.47/0.65 Definition iatom:=(fun (P:(fofType->Prop))=> P):((fofType->Prop)->(fofType->Prop)).
% 0.47/0.65 Definition inot:=(fun (P:(fofType->Prop))=> (mnot (mbox_s4 P))):((fofType->Prop)->(fofType->Prop)).
% 0.47/0.65 Definition itrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.47/0.65 Definition ifalse:=(inot itrue):(fofType->Prop).
% 0.47/0.65 Definition iand:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition ior:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mor (mbox_s4 P)) (mbox_s4 Q))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition iimplies:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mimplies (mbox_s4 P)) (mbox_s4 Q))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition iimplied:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition iequiv:=(fun (P:(fofType->Prop)) (Q:(fofTy
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