TSTP Solution File: SYO060^4 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO060^4 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 00:50:31 EDT 2022
% Result : Theorem 0.60s 0.82s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SYO060^4 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % RAMPerCPU : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Fri Mar 11 11:24:20 EST 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.33 Python 2.7.5
% 0.42/0.60 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.42/0.60 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL010^0.ax, trying next directory
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1c4fc20>, <kernel.DependentProduct object at 0x1c4fb48>) of role type named irel_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring irel:(fofType->(fofType->Prop))
% 0.42/0.60 FOF formula (forall (X:fofType), ((irel X) X)) of role axiom named refl_axiom
% 0.42/0.60 A new axiom: (forall (X:fofType), ((irel X) X))
% 0.42/0.60 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
% 0.42/0.60 A new axiom: (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((irel X) Y)) ((irel Y) Z))->((irel X) Z)))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1c4fc68>, <kernel.DependentProduct object at 0x1c4f8c0>) of role type named mnot_decl_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.42/0.60 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))) of role definition named mnot
% 0.42/0.60 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)))
% 0.42/0.60 Defined: mnot:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1c4fa70>, <kernel.DependentProduct object at 0x1c4f710>) of role type named mor_decl_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.60 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
% 0.42/0.60 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))))
% 0.42/0.60 Defined: mor:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1c4fc68>, <kernel.DependentProduct object at 0x1c4f950>) of role type named mand_decl_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.60 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
% 0.42/0.60 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))))
% 0.42/0.60 Defined: mand:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1c4fa70>, <kernel.DependentProduct object at 0x1c4f5f0>) of role type named mimplies_decl_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.60 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
% 0.42/0.60 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V)))
% 0.42/0.60 Defined: mimplies:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1c4fa70>, <kernel.DependentProduct object at 0x1c4fab8>) of role type named mbox_s4_decl_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mbox_s4:((fofType->Prop)->(fofType->Prop))
% 0.42/0.60 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
% 0.42/0.60 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y)))))
% 0.42/0.60 Defined: mbox_s4:=(fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y))))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1c4f0e0>, <kernel.DependentProduct object at 0x1c4f320>) of role type named iatom_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring iatom:((fofType->Prop)->(fofType->Prop))
% 0.42/0.61 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) iatom) (fun (P:(fofType->Prop))=> P)) of role definition named iatom
% 0.42/0.61 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) iatom) (fun (P:(fofType->Prop))=> P))
% 0.42/0.61 Defined: iatom:=(fun (P:(fofType->Prop))=> P)
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1c4f2d8>, <kernel.DependentProduct object at 0x1c4f128>) of role type named inot_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring inot:((fofType->Prop)->(fofType->Prop))
% 0.42/0.61 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) inot) (fun (P:(fofType->Prop))=> (mnot (mbox_s4 P)))) of role definition named inot
% 0.42/0.61 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) inot) (fun (P:(fofType->Prop))=> (mnot (mbox_s4 P))))
% 0.42/0.61 Defined: inot:=(fun (P:(fofType->Prop))=> (mnot (mbox_s4 P)))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1c4f0e0>, <kernel.DependentProduct object at 0x1c4f290>) of role type named itrue_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring itrue:(fofType->Prop)
% 0.42/0.61 FOF formula (((eq (fofType->Prop)) itrue) (fun (W:fofType)=> True)) of role definition named itrue
% 0.42/0.61 A new definition: (((eq (fofType->Prop)) itrue) (fun (W:fofType)=> True))
% 0.42/0.61 Defined: itrue:=(fun (W:fofType)=> True)
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1c4f290>, <kernel.DependentProduct object at 0x1c4fd88>) of role type named ifalse_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring ifalse:(fofType->Prop)
% 0.42/0.61 FOF formula (((eq (fofType->Prop)) ifalse) (inot itrue)) of role definition named ifalse
% 0.42/0.61 A new definition: (((eq (fofType->Prop)) ifalse) (inot itrue))
% 0.42/0.61 Defined: ifalse:=(inot itrue)
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1c4f128>, <kernel.DependentProduct object at 0x1c4f6c8>) of role type named iand_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring iand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.61 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
% 0.42/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iand) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q)))
% 0.42/0.61 Defined: iand:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1d833f8>, <kernel.DependentProduct object at 0x1c4f1b8>) of role type named ior_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring ior:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.61 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
% 0.42/0.61 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))))
% 0.42/0.61 Defined: ior:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mor (mbox_s4 P)) (mbox_s4 Q)))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1c4f1b8>, <kernel.DependentProduct object at 0x1c4f098>) of role type named iimplies_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring iimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.61 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
% 0.42/0.61 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))))
% 0.42/0.61 Defined: iimplies:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mimplies (mbox_s4 P)) (mbox_s4 Q)))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1adfe60>, <kernel.DependentProduct object at 0x1c4f050>) of role type named iimplied_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring iimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.61 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
% 0.42/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iimplied) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P)))
% 0.42/0.61 Defined: iimplied:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1ae7d40>, <kernel.DependentProduct object at 0x1c4f1b8>) of role type named iequiv_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring iequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.62 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
% 0.42/0.62 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))))
% 0.42/0.62 Defined: iequiv:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iand ((iimplies P) Q)) ((iimplies Q) P)))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1c4f1b8>, <kernel.DependentProduct object at 0x1c4f098>) of role type named ixor_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring ixor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.62 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
% 0.42/0.62 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) ixor) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> (inot ((iequiv P) Q))))
% 0.42/0.62 Defined: ixor:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> (inot ((iequiv P) Q)))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1c4f128>, <kernel.DependentProduct object at 0x1c58170>) of role type named ivalid_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring ivalid:((fofType->Prop)->Prop)
% 0.42/0.62 FOF formula (((eq ((fofType->Prop)->Prop)) ivalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named ivalid
% 0.42/0.62 A new definition: (((eq ((fofType->Prop)->Prop)) ivalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.42/0.62 Defined: ivalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1c4f3f8>, <kernel.DependentProduct object at 0x1c58128>) of role type named isatisfiable_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring isatisfiable:((fofType->Prop)->Prop)
% 0.42/0.62 FOF formula (((eq ((fofType->Prop)->Prop)) isatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named isatisfiable
% 0.42/0.62 A new definition: (((eq ((fofType->Prop)->Prop)) isatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.42/0.62 Defined: isatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1c58128>, <kernel.DependentProduct object at 0x1c582d8>) of role type named icountersatisfiable_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring icountersatisfiable:((fofType->Prop)->Prop)
% 0.42/0.62 FOF formula (((eq ((fofType->Prop)->Prop)) icountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named icountersatisfiable
% 0.42/0.62 A new definition: (((eq ((fofType->Prop)->Prop)) icountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.42/0.62 Defined: icountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1c58050>, <kernel.DependentProduct object at 0x1c58518>) of role type named iinvalid_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring iinvalid:((fofType->Prop)->Prop)
% 0.42/0.62 FOF formula (((eq ((fofType->Prop)->Prop)) iinvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named iinvalid
% 0.42/0.62 A new definition: (((eq ((fofType->Prop)->Prop)) iinvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.42/0.62 Defined: iinvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1ae4ab8>, <kernel.DependentProduct object at 0x2b5f21cd34d0>) of role type named a_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring a:(fofType->Prop)
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1ae4a70>, <kernel.DependentProduct object at 0x2b5f21cd3878>) of role type named b_type
% 0.42/0.62 Using role type
% 0.60/0.82 Declaring b:(fofType->Prop)
% 0.60/0.82 FOF formula (ivalid ((ior (inot (iatom a))) (inot (iatom b)))) of role axiom named axiom1
% 0.60/0.82 A new axiom: (ivalid ((ior (inot (iatom a))) (inot (iatom b))))
% 0.60/0.82 FOF formula (ivalid ((ior (inot (iatom b))) (inot (iatom a)))) of role conjecture named con
% 0.60/0.82 Conjecture to prove = (ivalid ((ior (inot (iatom b))) (inot (iatom a)))):Prop
% 0.60/0.82 Parameter fofType_DUMMY:fofType.
% 0.60/0.82 We need to prove ['(ivalid ((ior (inot (iatom b))) (inot (iatom a))))']
% 0.60/0.82 Parameter fofType:Type.
% 0.60/0.82 Parameter irel:(fofType->(fofType->Prop)).
% 0.60/0.82 Axiom refl_axiom:(forall (X:fofType), ((irel X) X)).
% 0.60/0.82 Axiom trans_axiom:(forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((irel X) Y)) ((irel Y) Z))->((irel X) Z))).
% 0.60/0.82 Definition mnot:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.60/0.82 Definition mor:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.60/0.82 Definition mand:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.60/0.82 Definition mimplies:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.60/0.82 Definition mbox_s4:=(fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y)))):((fofType->Prop)->(fofType->Prop)).
% 0.60/0.82 Definition iatom:=(fun (P:(fofType->Prop))=> P):((fofType->Prop)->(fofType->Prop)).
% 0.60/0.82 Definition inot:=(fun (P:(fofType->Prop))=> (mnot (mbox_s4 P))):((fofType->Prop)->(fofType->Prop)).
% 0.60/0.82 Definition itrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.60/0.82 Definition ifalse:=(inot itrue):(fofType->Prop).
% 0.60/0.82 Definition iand:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.60/0.82 Definition ior:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mor (mbox_s4 P)) (mbox_s4 Q))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.60/0.82 Definition iimplies:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mimplies (mbox_s4 P)) (mbox_s4 Q))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.60/0.82 Definition iimplied:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.60/0.82 Definition iequiv:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iand ((iimplies P) Q)) ((iimplies Q) P))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.60/0.82 Definition ixor:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> (inot ((iequiv P) Q))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.60/0.82 Definition ivalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 0.60/0.82 Definition isatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 0.60/0.82 Definition icountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 0.60/0.82 Definition iinvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 0.60/0.82 Parameter a:(fofType->Prop).
% 0.60/0.82 Parameter b:(fofType->Prop).
% 0.60/0.82 Axiom axiom1:(ivalid ((ior (inot (iatom a))) (inot (iatom b)))).
% 0.60/0.82 Trying to prove (ivalid ((ior (inot (iatom b))) (inot (iatom a))))
% 0.60/0.82 Found axiom10:=(axiom1 W):(((ior (inot (iatom a))) (inot (iatom b))) W)
% 0.60/0.82 Found (axiom1 W) as proof of ((or ((mbox_s4 (inot (iatom a))) W)) ((mbox_s4 (inot (iatom b))) W))
% 0.60/0.82 Found (axiom1 W) as proof of ((or ((mbox_s4 (inot (iatom a))) W)) ((mbox_s4 (inot (iatom b))) W))
% 0.60/0.82 Found (or_comm_i00 (axiom1 W)) as proof of ((or ((mbox_s4 (inot (iatom b))) W)) ((mbox_s4 (inot (iatom a))) W))
% 0.60/0.82 Found ((or_comm_i0 ((mbox_s4 (inot (iatom b))) W)) (axiom1 W)) as proof of ((or ((mbox_s4 (inot (iatom b))) W)) ((mbox_s4 (inot (iatom a))) W))
% 0.60/0.82 Found (((or_comm_i ((mbox_s4 (inot (iatom a))) W)) ((mbox_s4 (inot (iatom b))) W)) (axiom1 W)) as proof of ((or ((mbox_s4 (inot (iatom b))) W)) ((mbox_s4 (inot (iatom a))) W))
% 0.60/0.82 Found (((or_comm_i ((mbox_s4 (inot (iatom a))) W)) ((mbox_s4 (inot (iatom b))) W)) (axiom1 W)) as proof of ((or ((mbox_s4 (inot (iatom b))) W)) ((mbox_s4 (inot (iatom a))) W))
% 0.60/0.82 Found (fun (W:fofType)=> (((or_comm_i ((mbox_s4 (inot (iatom a))) W)) ((mbox_s4 (inot (iatom b))) W)) (axiom1 W))) as proof of (((ior (inot (iatom b))) (inot (iatom a))) W)
% 0.60/0.82 Found (fun (W:fofType)=> (((or_comm_i ((mbox_s4 (inot (iatom a))) W)) ((mbox_s4 (inot (iatom b))) W)) (axiom1 W))) as proof of (ivalid ((ior (inot (iatom b))) (inot (iatom a))))
% 0.60/0.82 Got proof (fun (W:fofType)=> (((or_comm_i ((mbox_s4 (inot (iatom a))) W)) ((mbox_s4 (inot (iatom b))) W)) (axiom1 W)))
% 0.60/0.82 Time elapsed = 0.192730s
% 0.60/0.82 node=30 cost=1085.000000 depth=7
% 0.60/0.82 ::::::::::::::::::::::
% 0.60/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.82 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.82 (fun (W:fofType)=> (((or_comm_i ((mbox_s4 (inot (iatom a))) W)) ((mbox_s4 (inot (iatom b))) W)) (axiom1 W)))
% 0.60/0.82 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------