TSTP Solution File: SYO238^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO238^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 5.02s 5.19s
% Output : Proof 5.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYO238^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n010.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 20:35:37 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'
% 0.11/0.34 Python 2.7.5
% 2.56/2.79 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 2.56/2.79 FOF formula (<kernel.Constant object at 0x21151b8>, <kernel.Sort object at 0x2b0cc5b65638>) of role type named cB
% 2.56/2.79 Using role type
% 2.56/2.79 Declaring cB:Prop
% 2.56/2.79 FOF formula (<kernel.Constant object at 0x2115878>, <kernel.Constant object at 0x2115638>) of role type named x
% 2.56/2.79 Using role type
% 2.56/2.79 Declaring x:fofType
% 2.56/2.79 FOF formula (<kernel.Constant object at 0x2115248>, <kernel.DependentProduct object at 0x2282e18>) of role type named cP
% 2.56/2.79 Using role type
% 2.56/2.79 Declaring cP:(fofType->Prop)
% 2.56/2.79 FOF formula (<kernel.Constant object at 0x2119320>, <kernel.DependentProduct object at 0x2282f80>) of role type named f
% 2.56/2.79 Using role type
% 2.56/2.79 Declaring f:(fofType->fofType)
% 2.56/2.79 FOF formula ((True->(forall (Xx0:fofType), (((eq fofType) (f Xx0)) Xx0)))->(((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)->((cP x)->cB))) of role conjecture named cADDHYP5
% 2.56/2.79 Conjecture to prove = ((True->(forall (Xx0:fofType), (((eq fofType) (f Xx0)) Xx0)))->(((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)->((cP x)->cB))):Prop
% 2.56/2.79 We need to prove ['((True->(forall (Xx0:fofType), (((eq fofType) (f Xx0)) Xx0)))->(((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)->((cP x)->cB)))']
% 2.56/2.79 Parameter cB:Prop.
% 2.56/2.79 Parameter fofType:Type.
% 2.56/2.79 Parameter x:fofType.
% 2.56/2.79 Parameter cP:(fofType->Prop).
% 2.56/2.79 Parameter f:(fofType->fofType).
% 2.56/2.79 Trying to prove ((True->(forall (Xx0:fofType), (((eq fofType) (f Xx0)) Xx0)))->(((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)->((cP x)->cB)))
% 2.56/2.79 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx0:fofType)=> (f (f Xx0))))->(P (fun (x:fofType)=> (f (f x)))))
% 2.56/2.79 Found (eta_expansion000 P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found ((eta_expansion00 (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found (((eta_expansion0 fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found ((((eta_expansion fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found ((((eta_expansion fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx0:fofType)=> (f (f Xx0))))->(P (fun (x:fofType)=> (f (f x)))))
% 2.56/2.79 Found (eta_expansion000 P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found ((eta_expansion00 (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found (((eta_expansion0 fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found ((((eta_expansion fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found ((((eta_expansion fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx0:fofType)=> (f (f Xx0))))->(P (fun (x:fofType)=> (f (f x)))))
% 2.56/2.79 Found (eta_expansion000 P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found ((eta_expansion00 (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found (((eta_expansion0 fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found ((((eta_expansion fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found ((((eta_expansion fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) P) as proof of (P0 (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found eq_ref00:=(eq_ref0 (fun (Xx0:fofType)=> (f (f Xx0)))):(((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> (f (f Xx0))))
% 2.56/2.79 Found (eq_ref0 (fun (Xx0:fofType)=> (f (f Xx0)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) b)
% 2.56/2.79 Found ((eq_ref (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) b)
% 5.02/5.18 Found ((eq_ref (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) b)
% 5.02/5.18 Found ((eq_ref (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) b)
% 5.02/5.18 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 5.02/5.18 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found x000:cB
% 5.02/5.18 Found (fun (x1:(cP x))=> x000) as proof of cB
% 5.02/5.18 Found (fun (x1:(cP x))=> x000) as proof of ((cP x)->cB)
% 5.02/5.18 Found eq_ref000:=(eq_ref00 P):((P (fun (Xx0:fofType)=> Xx0))->(P (fun (Xx0:fofType)=> Xx0)))
% 5.02/5.18 Found (eq_ref00 P) as proof of (P0 (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found ((eq_ref0 (fun (Xx0:fofType)=> Xx0)) P) as proof of (P0 (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found (((eq_ref (fofType->fofType)) (fun (Xx0:fofType)=> Xx0)) P) as proof of (P0 (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found (((eq_ref (fofType->fofType)) (fun (Xx0:fofType)=> Xx0)) P) as proof of (P0 (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx0:fofType)=> Xx0))->(P (fun (x:fofType)=> x)))
% 5.02/5.18 Found (eta_expansion000 P) as proof of (P0 (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found ((eta_expansion00 (fun (Xx0:fofType)=> Xx0)) P) as proof of (P0 (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found (((eta_expansion0 fofType) (fun (Xx0:fofType)=> Xx0)) P) as proof of (P0 (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found ((((eta_expansion fofType) fofType) (fun (Xx0:fofType)=> Xx0)) P) as proof of (P0 (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found ((((eta_expansion fofType) fofType) (fun (Xx0:fofType)=> Xx0)) P) as proof of (P0 (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found x02000:=(x0200 x3):(P (f x2))
% 5.02/5.18 Found (x0200 x3) as proof of (P (f x2))
% 5.02/5.18 Found ((x020 P) x3) as proof of (P (f x2))
% 5.02/5.18 Found (((x02 (f x2)) P) x3) as proof of (P (f x2))
% 5.02/5.18 Found ((((x0 I) (f x2)) P) x3) as proof of (P (f x2))
% 5.02/5.18 Found ((((x0 I) (f x2)) P) x3) as proof of (P (f x2))
% 5.02/5.18 Found (x0100 ((((x0 I) (f x2)) P) x3)) as proof of (P x2)
% 5.02/5.18 Found ((x010 P) ((((x0 I) (f x2)) P) x3)) as proof of (P x2)
% 5.02/5.18 Found (((x01 I) P) ((((x0 I) (f x2)) P) x3)) as proof of (P x2)
% 5.02/5.18 Found ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)) as proof of (P x2)
% 5.02/5.18 Found (fun (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3))) as proof of (P x2)
% 5.02/5.18 Found (fun (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3))) as proof of ((P (f (f x2)))->(P x2))
% 5.02/5.18 Found (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3))) as proof of (((eq fofType) (f (f x2))) x2)
% 5.02/5.18 Found (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3))) as proof of (forall (x:fofType), (((eq fofType) (f (f x))) x))
% 5.02/5.18 Found (functional_extensionality0000 (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found ((functional_extensionality000 (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.18 Found (((functional_extensionality00 (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.19 Found ((((functional_extensionality0 fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.19 Found (((((functional_extensionality fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.19 Found (((((functional_extensionality fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))) as proof of (((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))
% 5.02/5.19 Found (x00 (((((functional_extensionality fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3))))) as proof of cB
% 5.02/5.19 Found (fun (x1:(cP x))=> (x00 (((((functional_extensionality fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))))) as proof of cB
% 5.02/5.19 Found (fun (x00:((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)) (x1:(cP x))=> (x00 (((((functional_extensionality fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))))) as proof of ((cP x)->cB)
% 5.02/5.19 Found (fun (x0:(True->(forall (Xx0:fofType), (((eq fofType) (f Xx0)) Xx0)))) (x00:((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)) (x1:(cP x))=> (x00 (((((functional_extensionality fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))))) as proof of (((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)->((cP x)->cB))
% 5.02/5.19 Found (fun (x0:(True->(forall (Xx0:fofType), (((eq fofType) (f Xx0)) Xx0)))) (x00:((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)) (x1:(cP x))=> (x00 (((((functional_extensionality fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3)))))) as proof of ((True->(forall (Xx0:fofType), (((eq fofType) (f Xx0)) Xx0)))->(((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)->((cP x)->cB)))
% 5.02/5.19 Got proof (fun (x0:(True->(forall (Xx0:fofType), (((eq fofType) (f Xx0)) Xx0)))) (x00:((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)) (x1:(cP x))=> (x00 (((((functional_extensionality fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3))))))
% 5.02/5.19 Time elapsed = 4.583648s
% 5.02/5.19 node=1136 cost=605.000000 depth=23
% 5.02/5.19 ::::::::::::::::::::::
% 5.02/5.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.02/5.19 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.02/5.19 (fun (x0:(True->(forall (Xx0:fofType), (((eq fofType) (f Xx0)) Xx0)))) (x00:((((eq (fofType->fofType)) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0))->cB)) (x1:(cP x))=> (x00 (((((functional_extensionality fofType) fofType) (fun (Xx0:fofType)=> (f (f Xx0)))) (fun (Xx0:fofType)=> Xx0)) (fun (x2:fofType) (P:(fofType->Prop)) (x3:(P (f (f x2))))=> ((((fun (x4:True)=> ((x0 x4) x2)) I) P) ((((x0 I) (f x2)) P) x3))))))
% 5.06/5.23 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------