%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SYO237^5 : TPTP v7.5.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n004.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 00:50:59 EDT 2022 % Result : Theorem 0.90s 1.08s % Output : Proof 0.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYO237^5 : TPTP v7.5.0. Released v4.0.0. % 0.06/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.13/0.33 % Computer : n004.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % RAMPerCPU : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % DateTime : Fri Mar 11 20:35:25 EST 2022 % 0.13/0.33 % CPUTime : % 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27' % 0.13/0.34 Python 2.7.5 % 0.90/1.07 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 0.90/1.07 FOF formula (<kernel.Constant object at 0x18cf950>, <kernel.DependentProduct object at 0x18cfd88>) of role type named g % 0.90/1.07 Using role type % 0.90/1.07 Declaring g:(fofType->fofType) % 0.90/1.07 FOF formula (<kernel.Constant object at 0x18cf6c8>, <kernel.DependentProduct object at 0x18cf908>) of role type named p % 0.90/1.07 Using role type % 0.90/1.07 Declaring p:((fofType->fofType)->Prop) % 0.90/1.07 FOF formula (<kernel.Constant object at 0x18cf950>, <kernel.Single object at 0x18cf098>) of role type named x % 0.90/1.07 Using role type % 0.90/1.07 Declaring x:fofType % 0.90/1.07 FOF formula (<kernel.Constant object at 0x18cf758>, <kernel.DependentProduct object at 0x1b6bd88>) of role type named q % 0.90/1.07 Using role type % 0.90/1.07 Declaring q:(fofType->Prop) % 0.90/1.07 FOF formula (<kernel.Constant object at 0x18cf098>, <kernel.DependentProduct object at 0x1b6be18>) of role type named f % 0.90/1.07 Using role type % 0.90/1.07 Declaring f:(fofType->fofType) % 0.90/1.07 FOF formula ((forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0)))->((p (fun (Xx0:fofType)=> (f Xx0)))->((q x)->(p (fun (Xx0:fofType)=> (g Xx0)))))) of role conjecture named cTHM508 % 0.90/1.07 Conjecture to prove = ((forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0)))->((p (fun (Xx0:fofType)=> (f Xx0)))->((q x)->(p (fun (Xx0:fofType)=> (g Xx0)))))):Prop % 0.90/1.07 We need to prove ['((forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0)))->((p (fun (Xx0:fofType)=> (f Xx0)))->((q x)->(p (fun (Xx0:fofType)=> (g Xx0))))))'] % 0.90/1.07 Parameter fofType:Type. % 0.90/1.07 Parameter g:(fofType->fofType). % 0.90/1.07 Parameter p:((fofType->fofType)->Prop). % 0.90/1.07 Parameter x:fofType. % 0.90/1.07 Parameter q:(fofType->Prop). % 0.90/1.07 Parameter f:(fofType->fofType). % 0.90/1.07 Trying to prove ((forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0)))->((p (fun (Xx0:fofType)=> (f Xx0)))->((q x)->(p (fun (Xx0:fofType)=> (g Xx0)))))) % 0.90/1.07 Found x00:(p (fun (Xx0:fofType)=> (f Xx0))) % 0.90/1.07 Instantiate: b:=(fun (Xx0:fofType)=> (f Xx0)):(fofType->fofType) % 0.90/1.07 Found x00 as proof of (P b) % 0.90/1.07 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx0:fofType)=> (g Xx0))):(((eq (fofType->fofType)) (fun (Xx0:fofType)=> (g Xx0))) (fun (x:fofType)=> (g x))) % 0.90/1.07 Found (eta_expansion_dep00 (fun (Xx0:fofType)=> (g Xx0))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (g Xx0))) b) % 0.90/1.07 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (Xx0:fofType)=> (g Xx0))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (g Xx0))) b) % 0.90/1.07 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (Xx0:fofType)=> (g Xx0))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (g Xx0))) b) % 0.90/1.07 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (Xx0:fofType)=> (g Xx0))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (g Xx0))) b) % 0.90/1.07 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (Xx0:fofType)=> (g Xx0))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (g Xx0))) b) % 0.90/1.07 Found x00:(p (fun (Xx0:fofType)=> (f Xx0))) % 0.90/1.07 Instantiate: f0:=(fun (Xx0:fofType)=> (f Xx0)):(fofType->fofType) % 0.90/1.07 Found x00 as proof of (P f0) % 0.90/1.07 Found x0:(forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0))) % 0.90/1.07 Instantiate: f0:=f:(fofType->fofType) % 0.90/1.07 Found x0 as proof of (forall (x:fofType), (((eq fofType) (f0 x)) (g x))) % 0.90/1.07 Found x0:(forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0))) % 0.90/1.07 Found x0 as proof of (forall (x:fofType), (((eq fofType) (f0 x)) (g x))) % 0.90/1.07 Found ((functional_extensionality00000 x0) x00) as proof of (p (fun (Xx0:fofType)=> (g Xx0))) % 0.90/1.07 Found ((functional_extensionality00000 x0) x00) as proof of (p (fun (Xx0:fofType)=> (g Xx0))) % 0.90/1.07 Found (((fun (x2:(forall (x:fofType), (((eq fofType) (f0 x)) (g x))))=> ((functional_extensionality0000 x2) p)) x0) x00) as proof of (p (fun (Xx0:fofType)=> (g Xx0))) % 0.90/1.07 Found (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> (((functional_extensionality000 (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00) as proof of (p (fun (Xx0:fofType)=> (g Xx0))) % 0.90/1.07 Found (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> ((((fun (f0:(fofType->fofType))=> ((functional_extensionality00 f0) (fun (Xx0:fofType)=> (g Xx0)))) (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00) as proof of (p (fun (Xx0:fofType)=> (g Xx0))) % 0.90/1.08 Found (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> ((((fun (f0:(fofType->fofType))=> (((functional_extensionality0 fofType) f0) (fun (Xx0:fofType)=> (g Xx0)))) (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00) as proof of (p (fun (Xx0:fofType)=> (g Xx0))) % 0.90/1.08 Found (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> ((((fun (f0:(fofType->fofType))=> ((((functional_extensionality fofType) fofType) f0) (fun (Xx0:fofType)=> (g Xx0)))) (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00) as proof of (p (fun (Xx0:fofType)=> (g Xx0))) % 0.90/1.08 Found (fun (x1:(q x))=> (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> ((((fun (f0:(fofType->fofType))=> ((((functional_extensionality fofType) fofType) f0) (fun (Xx0:fofType)=> (g Xx0)))) (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00)) as proof of (p (fun (Xx0:fofType)=> (g Xx0))) % 0.90/1.08 Found (fun (x00:(p (fun (Xx0:fofType)=> (f Xx0)))) (x1:(q x))=> (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> ((((fun (f0:(fofType->fofType))=> ((((functional_extensionality fofType) fofType) f0) (fun (Xx0:fofType)=> (g Xx0)))) (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00)) as proof of ((q x)->(p (fun (Xx0:fofType)=> (g Xx0)))) % 0.90/1.08 Found (fun (x0:(forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0)))) (x00:(p (fun (Xx0:fofType)=> (f Xx0)))) (x1:(q x))=> (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> ((((fun (f0:(fofType->fofType))=> ((((functional_extensionality fofType) fofType) f0) (fun (Xx0:fofType)=> (g Xx0)))) (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00)) as proof of ((p (fun (Xx0:fofType)=> (f Xx0)))->((q x)->(p (fun (Xx0:fofType)=> (g Xx0))))) % 0.90/1.08 Found (fun (x0:(forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0)))) (x00:(p (fun (Xx0:fofType)=> (f Xx0)))) (x1:(q x))=> (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> ((((fun (f0:(fofType->fofType))=> ((((functional_extensionality fofType) fofType) f0) (fun (Xx0:fofType)=> (g Xx0)))) (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00)) as proof of ((forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0)))->((p (fun (Xx0:fofType)=> (f Xx0)))->((q x)->(p (fun (Xx0:fofType)=> (g Xx0)))))) % 0.90/1.08 Got proof (fun (x0:(forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0)))) (x00:(p (fun (Xx0:fofType)=> (f Xx0)))) (x1:(q x))=> (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> ((((fun (f0:(fofType->fofType))=> ((((functional_extensionality fofType) fofType) f0) (fun (Xx0:fofType)=> (g Xx0)))) (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00)) % 0.90/1.08 Time elapsed = 0.453227s % 0.90/1.08 node=130 cost=976.000000 depth=11 % 0.90/1.08 :::::::::::::::::::::: % 0.90/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.90/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.90/1.08 (fun (x0:(forall (Xx0:fofType), (((eq fofType) (f Xx0)) (g Xx0)))) (x00:(p (fun (Xx0:fofType)=> (f Xx0)))) (x1:(q x))=> (((fun (x2:(forall (x:fofType), (((eq fofType) ((fun (Xx0:fofType)=> (f Xx0)) x)) (g x))))=> ((((fun (f0:(fofType->fofType))=> ((((functional_extensionality fofType) fofType) f0) (fun (Xx0:fofType)=> (g Xx0)))) (fun (Xx0:fofType)=> (f Xx0))) x2) p)) x0) x00)) % 0.90/1.08 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p 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