TSTP Solution File: SYO237^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% 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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