%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SYO061^4 : TPTP v7.5.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p % Computer : n007.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 00:50:32 EDT 2022 % Result : Theorem 0.48s 0.64s % Output : Proof 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SYO061^4 : TPTP v7.5.0. Released v4.0.0. % 0.00/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.12/0.33 % Computer : n007.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 10:59:45 EST 2022 % 0.12/0.33 % CPUTime : % 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27' % 0.19/0.34 Python 2.7.5 % 0.43/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/'] % 0.43/0.61 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL010^0.ax, trying next directory % 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b57fa72a8c0>, <kernel.DependentProduct object at 0x2b57fa72a7e8>) of role type named irel_type % 0.43/0.61 Using role type % 0.43/0.61 Declaring irel:(fofType->(fofType->Prop)) % 0.43/0.61 FOF formula (forall (X:fofType), ((irel X) X)) of role axiom named refl_axiom % 0.43/0.61 A new axiom: (forall (X:fofType), ((irel X) X)) % 0.43/0.61 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 % 0.43/0.61 A new axiom: (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((irel X) Y)) ((irel Y) Z))->((irel X) Z))) % 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b57fa72a908>, <kernel.DependentProduct object at 0x2b57fa72a4d0>) of role type named mnot_decl_type % 0.43/0.61 Using role type % 0.43/0.61 Declaring mnot:((fofType->Prop)->(fofType->Prop)) % 0.43/0.61 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))) of role definition named mnot % 0.43/0.61 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))) % 0.43/0.61 Defined: mnot:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)) % 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b57fa72a680>, <kernel.DependentProduct object at 0x2b57fa72a3b0>) of role type named mor_decl_type % 0.43/0.61 Using role type % 0.43/0.61 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.43/0.61 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 % 0.43/0.61 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)))) % 0.43/0.61 Defined: mor:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))) % 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b57fa72a908>, <kernel.DependentProduct object at 0x2b57fa72a560>) of role type named mand_decl_type % 0.43/0.61 Using role type % 0.43/0.61 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.43/0.61 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 % 0.43/0.61 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)))) % 0.43/0.61 Defined: mand:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))) % 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b57fa72a680>, <kernel.DependentProduct object at 0x2b57fa72a290>) of role type named mimplies_decl_type % 0.43/0.61 Using role type % 0.43/0.61 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.43/0.61 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 % 0.43/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V))) % 0.43/0.61 Defined: mimplies:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V)) % 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b57fa72a680>, <kernel.DependentProduct object at 0x2b57fa72a368>) of role type named mbox_s4_decl_type % 0.43/0.61 Using role type % 0.43/0.61 Declaring mbox_s4:((fofType->Prop)->(fofType->Prop)) % 0.43/0.61 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 % 0.43/0.61 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y))))) % 0.43/0.61 Defined: mbox_s4:=(fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y)))) % 0.43/0.61 FOF formula (<kernel.Constant object at 0x2b57fa72a908>, <kernel.DependentProduct object at 0x2b57fa72a248>) of role type named iatom_type % 0.43/0.62 Using role type % 0.43/0.62 Declaring iatom:((fofType->Prop)->(fofType->Prop)) % 0.43/0.62 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) iatom) (fun (P:(fofType->Prop))=> P)) of role definition named iatom % 0.43/0.62 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) iatom) (fun (P:(fofType->Prop))=> P)) % 0.43/0.62 Defined: iatom:=(fun (P:(fofType->Prop))=> P) % 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b57fa72a320>, <kernel.DependentProduct object at 0x2b57fa72a3f8>) of role type named inot_type % 0.43/0.62 Using role type % 0.43/0.62 Declaring inot:((fofType->Prop)->(fofType->Prop)) % 0.43/0.62 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) inot) (fun (P:(fofType->Prop))=> (mnot (mbox_s4 P)))) of role definition named inot % 0.43/0.62 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) inot) (fun (P:(fofType->Prop))=> (mnot (mbox_s4 P)))) % 0.43/0.62 Defined: inot:=(fun (P:(fofType->Prop))=> (mnot (mbox_s4 P))) % 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b57fa72a908>, <kernel.DependentProduct object at 0x2b58021fb998>) of role type named itrue_type % 0.43/0.62 Using role type % 0.43/0.62 Declaring itrue:(fofType->Prop) % 0.43/0.62 FOF formula (((eq (fofType->Prop)) itrue) (fun (W:fofType)=> True)) of role definition named itrue % 0.43/0.62 A new definition: (((eq (fofType->Prop)) itrue) (fun (W:fofType)=> True)) % 0.43/0.62 Defined: itrue:=(fun (W:fofType)=> True) % 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b57fa72a320>, <kernel.DependentProduct object at 0x2b58021fb440>) of role type named ifalse_type % 0.43/0.62 Using role type % 0.43/0.62 Declaring ifalse:(fofType->Prop) % 0.43/0.62 FOF formula (((eq (fofType->Prop)) ifalse) (inot itrue)) of role definition named ifalse % 0.43/0.62 A new definition: (((eq (fofType->Prop)) ifalse) (inot itrue)) % 0.43/0.62 Defined: ifalse:=(inot itrue) % 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b57fa72a2d8>, <kernel.DependentProduct object at 0x2b58021fb7a0>) of role type named iand_type % 0.43/0.62 Using role type % 0.43/0.62 Declaring iand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.43/0.62 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 % 0.43/0.62 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iand) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q))) % 0.43/0.62 Defined: iand:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q)) % 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b58021fb638>, <kernel.DependentProduct object at 0x2b58021fbef0>) of role type named ior_type % 0.43/0.62 Using role type % 0.43/0.62 Declaring ior:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.43/0.62 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 % 0.43/0.62 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)))) % 0.43/0.62 Defined: ior:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mor (mbox_s4 P)) (mbox_s4 Q))) % 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b58021fb638>, <kernel.DependentProduct object at 0x2b58021fb830>) of role type named iimplies_type % 0.43/0.62 Using role type % 0.43/0.62 Declaring iimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.43/0.62 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 % 0.43/0.62 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)))) % 0.43/0.62 Defined: iimplies:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mimplies (mbox_s4 P)) (mbox_s4 Q))) % 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b58021fb3b0>, <kernel.DependentProduct object at 0x2b58021fb440>) of role type named iimplied_type % 0.43/0.62 Using role type % 0.43/0.62 Declaring iimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.43/0.62 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 % 0.43/0.62 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) iimplied) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P))) % 0.47/0.63 Defined: iimplied:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P)) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b58021fb3b0>, <kernel.DependentProduct object at 0x1c05320>) of role type named iequiv_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring iequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.47/0.63 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 % 0.47/0.63 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)))) % 0.47/0.63 Defined: iequiv:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iand ((iimplies P) Q)) ((iimplies Q) P))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b58021fb0e0>, <kernel.DependentProduct object at 0x1c053b0>) of role type named ixor_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring ixor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop))) % 0.47/0.63 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 % 0.47/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) ixor) (fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> (inot ((iequiv P) Q)))) % 0.47/0.63 Defined: ixor:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> (inot ((iequiv P) Q))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x1c05cf8>, <kernel.DependentProduct object at 0x1c05200>) of role type named ivalid_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring ivalid:((fofType->Prop)->Prop) % 0.47/0.63 FOF formula (((eq ((fofType->Prop)->Prop)) ivalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named ivalid % 0.47/0.63 A new definition: (((eq ((fofType->Prop)->Prop)) ivalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) % 0.47/0.63 Defined: ivalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x1c05320>, <kernel.DependentProduct object at 0x2b57fa728128>) of role type named isatisfiable_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring isatisfiable:((fofType->Prop)->Prop) % 0.47/0.63 FOF formula (((eq ((fofType->Prop)->Prop)) isatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named isatisfiable % 0.47/0.63 A new definition: (((eq ((fofType->Prop)->Prop)) isatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) % 0.47/0.63 Defined: isatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x1c059e0>, <kernel.DependentProduct object at 0x2b57fa728128>) of role type named icountersatisfiable_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring icountersatisfiable:((fofType->Prop)->Prop) % 0.47/0.63 FOF formula (((eq ((fofType->Prop)->Prop)) icountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named icountersatisfiable % 0.47/0.63 A new definition: (((eq ((fofType->Prop)->Prop)) icountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) % 0.47/0.63 Defined: icountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b57fa728320>, <kernel.DependentProduct object at 0x2b57fa7283f8>) of role type named iinvalid_type % 0.47/0.63 Using role type % 0.47/0.63 Declaring iinvalid:((fofType->Prop)->Prop) % 0.47/0.63 FOF formula (((eq ((fofType->Prop)->Prop)) iinvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named iinvalid % 0.47/0.63 A new definition: (((eq ((fofType->Prop)->Prop)) iinvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) % 0.47/0.63 Defined: iinvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))) % 0.47/0.63 FOF formula (<kernel.Constant object at 0x1c025a8>, <kernel.DependentProduct object at 0x1bdfb48>) of role type named a_type % 0.47/0.63 Using role type % 0.48/0.64 Declaring a:(fofType->Prop) % 0.48/0.64 FOF formula (<kernel.Constant object at 0x1c02d88>, <kernel.DependentProduct object at 0x1bdf5a8>) of role type named b_type % 0.48/0.64 Using role type % 0.48/0.64 Declaring b:(fofType->Prop) % 0.48/0.64 FOF formula (ivalid ((iimplies (iatom a)) (iatom b))) of role axiom named axiom1 % 0.48/0.64 A new axiom: (ivalid ((iimplies (iatom a)) (iatom b))) % 0.48/0.64 FOF formula (ivalid ((iimplies (iatom a)) (iatom b))) of role conjecture named con % 0.48/0.64 Conjecture to prove = (ivalid ((iimplies (iatom a)) (iatom b))):Prop % 0.48/0.64 Parameter fofType_DUMMY:fofType. % 0.48/0.64 We need to prove ['(ivalid ((iimplies (iatom a)) (iatom b)))'] % 0.48/0.64 Parameter fofType:Type. % 0.48/0.64 Parameter irel:(fofType->(fofType->Prop)). % 0.48/0.64 Axiom refl_axiom:(forall (X:fofType), ((irel X) X)). % 0.48/0.64 Axiom trans_axiom:(forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((irel X) Y)) ((irel Y) Z))->((irel X) Z))). % 0.48/0.64 Definition mnot:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)):((fofType->Prop)->(fofType->Prop)). % 0.48/0.64 Definition mor:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.48/0.64 Definition mand:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.48/0.64 Definition mimplies:=(fun (U:(fofType->Prop)) (V:(fofType->Prop))=> ((mor (mnot U)) V)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.48/0.64 Definition mbox_s4:=(fun (P:(fofType->Prop)) (X:fofType)=> (forall (Y:fofType), (((irel X) Y)->(P Y)))):((fofType->Prop)->(fofType->Prop)). % 0.48/0.64 Definition iatom:=(fun (P:(fofType->Prop))=> P):((fofType->Prop)->(fofType->Prop)). % 0.48/0.64 Definition inot:=(fun (P:(fofType->Prop))=> (mnot (mbox_s4 P))):((fofType->Prop)->(fofType->Prop)). % 0.48/0.64 Definition itrue:=(fun (W:fofType)=> True):(fofType->Prop). % 0.48/0.64 Definition ifalse:=(inot itrue):(fofType->Prop). % 0.48/0.64 Definition iand:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mand P) Q)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.48/0.64 Definition ior:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mor (mbox_s4 P)) (mbox_s4 Q))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.48/0.64 Definition iimplies:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((mimplies (mbox_s4 P)) (mbox_s4 Q))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.48/0.64 Definition iimplied:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iimplies Q) P)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.48/0.64 Definition iequiv:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> ((iand ((iimplies P) Q)) ((iimplies Q) P))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.48/0.64 Definition ixor:=(fun (P:(fofType->Prop)) (Q:(fofType->Prop))=> (inot ((iequiv P) Q))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))). % 0.48/0.64 Definition ivalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop). % 0.48/0.64 Definition isatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop). % 0.48/0.64 Definition icountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop). % 0.48/0.64 Definition iinvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop). % 0.48/0.64 Parameter a:(fofType->Prop). % 0.48/0.64 Parameter b:(fofType->Prop). % 0.48/0.64 Axiom axiom1:(ivalid ((iimplies (iatom a)) (iatom b))). % 0.48/0.64 Trying to prove (ivalid ((iimplies (iatom a)) (iatom b))) % 0.48/0.64 Found axiom1:(ivalid ((iimplies (iatom a)) (iatom b))) % 0.48/0.64 Found axiom1 as proof of (ivalid ((iimplies (iatom a)) (iatom b))) % 0.48/0.64 Got proof axiom1 % 0.48/0.64 Time elapsed = 0.001852s % 0.48/0.64 node=0 cost=0.000000 depth=0 % 0.48/0.64 :::::::::::::::::::::: % 0.48/0.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.48/0.64 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.48/0.64 axiom1 % 0.48/0.64 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p %------------------------------------------------------------------------------