TSTP Solution File: SYO008^1 by cocATP---0.2.0
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- Process Solution
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% File : cocATP---0.2.0
% Problem : SYO008^1 : TPTP v7.5.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 00:50:23 EDT 2022
% Result : Theorem 0.51s 0.70s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO008^1 : TPTP v7.5.0. Released v3.7.0.
% 0.03/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n013.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 : Thu Mar 10 23:41:07 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
% 0.51/0.70 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.51/0.70 FOF formula (<kernel.Constant object at 0x1866f38>, <kernel.DependentProduct object at 0x1866908>) of role type named leibeq1_type
% 0.51/0.70 Using role type
% 0.51/0.70 Declaring leibeq1:(fofType->(fofType->Prop))
% 0.51/0.70 FOF formula (((eq (fofType->(fofType->Prop))) leibeq1) (fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V))))) of role definition named leibeq1
% 0.51/0.70 A new definition: (((eq (fofType->(fofType->Prop))) leibeq1) (fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V)))))
% 0.51/0.70 Defined: leibeq1:=(fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V))))
% 0.51/0.70 FOF formula (<kernel.Constant object at 0x1866f38>, <kernel.DependentProduct object at 0x18667a0>) of role type named leibeq2_type
% 0.51/0.70 Using role type
% 0.51/0.70 Declaring leibeq2:((fofType->fofType)->((fofType->fofType)->Prop))
% 0.51/0.70 FOF formula (((eq ((fofType->fofType)->((fofType->fofType)->Prop))) leibeq2) (fun (X:(fofType->fofType)) (Y:(fofType->fofType))=> (forall (P:((fofType->fofType)->Prop)), ((P X)->(P Y))))) of role definition named leibeq2
% 0.51/0.70 A new definition: (((eq ((fofType->fofType)->((fofType->fofType)->Prop))) leibeq2) (fun (X:(fofType->fofType)) (Y:(fofType->fofType))=> (forall (P:((fofType->fofType)->Prop)), ((P X)->(P Y)))))
% 0.51/0.70 Defined: leibeq2:=(fun (X:(fofType->fofType)) (Y:(fofType->fofType))=> (forall (P:((fofType->fofType)->Prop)), ((P X)->(P Y))))
% 0.51/0.70 FOF formula (forall (F:(fofType->fofType)) (G:(fofType->fofType)), ((forall (X:fofType), ((leibeq1 (F X)) (G X)))->((leibeq2 F) G))) of role conjecture named conj
% 0.51/0.70 Conjecture to prove = (forall (F:(fofType->fofType)) (G:(fofType->fofType)), ((forall (X:fofType), ((leibeq1 (F X)) (G X)))->((leibeq2 F) G))):Prop
% 0.51/0.70 Parameter fofType_DUMMY:fofType.
% 0.51/0.70 We need to prove ['(forall (F:(fofType->fofType)) (G:(fofType->fofType)), ((forall (X:fofType), ((leibeq1 (F X)) (G X)))->((leibeq2 F) G)))']
% 0.51/0.70 Parameter fofType:Type.
% 0.51/0.70 Definition leibeq1:=(fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V)))):(fofType->(fofType->Prop)).
% 0.51/0.70 Definition leibeq2:=(fun (X:(fofType->fofType)) (Y:(fofType->fofType))=> (forall (P:((fofType->fofType)->Prop)), ((P X)->(P Y)))):((fofType->fofType)->((fofType->fofType)->Prop)).
% 0.51/0.70 Trying to prove (forall (F:(fofType->fofType)) (G:(fofType->fofType)), ((forall (X:fofType), ((leibeq1 (F X)) (G X)))->((leibeq2 F) G)))
% 0.51/0.70 Found functional_extensionality_dep00:=(functional_extensionality_dep0 (fun (x1:fofType)=> fofType)):(forall (f:(fofType->fofType)) (g:(fofType->fofType)), ((forall (x:fofType), (((eq fofType) (f x)) (g x)))->(((eq (fofType->fofType)) f) g)))
% 0.51/0.70 Found (functional_extensionality_dep0 (fun (x1:fofType)=> fofType)) as proof of (forall (F:(fofType->fofType)) (G:(fofType->fofType)), ((forall (X:fofType), ((leibeq1 (F X)) (G X)))->(((eq (fofType->fofType)) F) G)))
% 0.51/0.70 Found ((functional_extensionality_dep fofType) (fun (x1:fofType)=> fofType)) as proof of (forall (F:(fofType->fofType)) (G:(fofType->fofType)), ((forall (X:fofType), ((leibeq1 (F X)) (G X)))->(((eq (fofType->fofType)) F) G)))
% 0.51/0.70 Found ((functional_extensionality_dep fofType) (fun (x1:fofType)=> fofType)) as proof of (forall (F:(fofType->fofType)) (G:(fofType->fofType)), ((forall (X:fofType), ((leibeq1 (F X)) (G X)))->(((eq (fofType->fofType)) F) G)))
% 0.51/0.70 Found ((functional_extensionality_dep fofType) (fun (x1:fofType)=> fofType)) as proof of (forall (F:(fofType->fofType)) (G:(fofType->fofType)), ((forall (X:fofType), ((leibeq1 (F X)) (G X)))->((leibeq2 F) G)))
% 0.51/0.70 Got proof ((functional_extensionality_dep fofType) (fun (x1:fofType)=> fofType))
% 0.51/0.70 Time elapsed = 0.087318s
% 0.51/0.70 node=13 cost=-108.000000 depth=3
% 0.51/0.70 ::::::::::::::::::::::
% 0.51/0.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.70 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.70 ((functional_extensionality_dep fofType) (fun (x1:fofType)=> fofType))
% 0.51/0.70 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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