TSTP Solution File: SYO005^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO005^1 : TPTP v7.5.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n022.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 00:50:22 EDT 2022
% Result : Theorem 0.55s 0.72s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO005^1 : TPTP v7.5.0. Released v3.7.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Fri Mar 11 09:13:12 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.55/0.72 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.55/0.72 FOF formula (<kernel.Constant object at 0x2ace7d747ab8>, <kernel.DependentProduct object at 0x10f9998>) of role type named leibeq1_type
% 0.55/0.72 Using role type
% 0.55/0.72 Declaring leibeq1:(fofType->(fofType->Prop))
% 0.55/0.72 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
% 0.55/0.72 A new definition: (((eq (fofType->(fofType->Prop))) leibeq1) (fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V)))))
% 0.55/0.72 Defined: leibeq1:=(fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V))))
% 0.55/0.72 FOF formula (<kernel.Constant object at 0x2ace7d747ab8>, <kernel.DependentProduct object at 0x10f9a28>) of role type named leibeq2_type
% 0.55/0.72 Using role type
% 0.55/0.72 Declaring leibeq2:((fofType->fofType)->((fofType->fofType)->Prop))
% 0.55/0.72 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
% 0.55/0.72 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)))))
% 0.55/0.72 Defined: leibeq2:=(fun (X:(fofType->fofType)) (Y:(fofType->fofType))=> (forall (P:((fofType->fofType)->Prop)), ((P X)->(P Y))))
% 0.55/0.72 FOF formula (forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((leibeq2 F) G)->(forall (X:fofType), ((leibeq1 (F X)) (G X))))) of role conjecture named conj
% 0.55/0.72 Conjecture to prove = (forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((leibeq2 F) G)->(forall (X:fofType), ((leibeq1 (F X)) (G X))))):Prop
% 0.55/0.72 Parameter fofType_DUMMY:fofType.
% 0.55/0.72 We need to prove ['(forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((leibeq2 F) G)->(forall (X:fofType), ((leibeq1 (F X)) (G X)))))']
% 0.55/0.72 Parameter fofType:Type.
% 0.55/0.72 Definition leibeq1:=(fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V)))):(fofType->(fofType->Prop)).
% 0.55/0.72 Definition leibeq2:=(fun (X:(fofType->fofType)) (Y:(fofType->fofType))=> (forall (P:((fofType->fofType)->Prop)), ((P X)->(P Y)))):((fofType->fofType)->((fofType->fofType)->Prop)).
% 0.55/0.72 Trying to prove (forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((leibeq2 F) G)->(forall (X:fofType), ((leibeq1 (F X)) (G X)))))
% 0.55/0.72 Found x0:=(x (fun (x0:(fofType->fofType))=> (Q (x0 X)))):((Q (F X))->(Q (G X)))
% 0.55/0.72 Found (x (fun (x0:(fofType->fofType))=> (Q (x0 X)))) as proof of ((Q (F X))->(Q (G X)))
% 0.55/0.72 Found (fun (Q:(fofType->Prop))=> (x (fun (x0:(fofType->fofType))=> (Q (x0 X))))) as proof of ((Q (F X))->(Q (G X)))
% 0.55/0.72 Found (fun (X:fofType) (Q:(fofType->Prop))=> (x (fun (x0:(fofType->fofType))=> (Q (x0 X))))) as proof of ((leibeq1 (F X)) (G X))
% 0.55/0.72 Found (fun (x:((leibeq2 F) G)) (X:fofType) (Q:(fofType->Prop))=> (x (fun (x0:(fofType->fofType))=> (Q (x0 X))))) as proof of (forall (X:fofType), ((leibeq1 (F X)) (G X)))
% 0.55/0.72 Found (fun (G:(fofType->fofType)) (x:((leibeq2 F) G)) (X:fofType) (Q:(fofType->Prop))=> (x (fun (x0:(fofType->fofType))=> (Q (x0 X))))) as proof of (((leibeq2 F) G)->(forall (X:fofType), ((leibeq1 (F X)) (G X))))
% 0.55/0.72 Found (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (x:((leibeq2 F) G)) (X:fofType) (Q:(fofType->Prop))=> (x (fun (x0:(fofType->fofType))=> (Q (x0 X))))) as proof of (forall (G:(fofType->fofType)), (((leibeq2 F) G)->(forall (X:fofType), ((leibeq1 (F X)) (G X)))))
% 0.55/0.72 Found (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (x:((leibeq2 F) G)) (X:fofType) (Q:(fofType->Prop))=> (x (fun (x0:(fofType->fofType))=> (Q (x0 X))))) as proof of (forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((leibeq2 F) G)->(forall (X:fofType), ((leibeq1 (F X)) (G X)))))
% 0.55/0.72 Got proof (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (x:((leibeq2 F) G)) (X:fofType) (Q:(fofType->Prop))=> (x (fun (x0:(fofType->fofType))=> (Q (x0 X)))))
% 0.55/0.72 Time elapsed = 0.094889s
% 0.55/0.72 node=11 cost=-67.000000 depth=6
% 0.55/0.72 ::::::::::::::::::::::
% 0.55/0.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.73 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.73 (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (x:((leibeq2 F) G)) (X:fofType) (Q:(fofType->Prop))=> (x (fun (x0:(fofType->fofType))=> (Q (x0 X)))))
% 0.55/0.73 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------