TSTP Solution File: SEU510^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU510^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n094.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:32:20 EDT 2014
% Result : Theorem 0.87s
% Output : Proof 0.87s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU510^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n094.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 10:27:16 CDT 2014
% % CPUTime : 0.87
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x244cd40>, <kernel.DependentProduct object at 0x244cb48>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2886488>, <kernel.Single object at 0x244ccb0>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x244cb48>, <kernel.DependentProduct object at 0x244cd88>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x244c5f0>, <kernel.Sort object at 0x2317098>) of role type named dsetconstrI_type
% Using role type
% Declaring dsetconstrI:Prop
% FOF formula (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named dsetconstrI
% A new definition: (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Defined: dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% FOF formula (<kernel.Constant object at 0x2829ab8>, <kernel.Sort object at 0x2317098>) of role type named emptysetE_type
% Using role type
% Declaring emptysetE:Prop
% FOF formula (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))) of role definition named emptysetE
% A new definition: (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))))
% Defined: emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))
% FOF formula (<kernel.Constant object at 0x2829ab8>, <kernel.DependentProduct object at 0x244ccb0>) of role type named nonempty_type
% Using role type
% Declaring nonempty:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))) of role definition named nonempty
% A new definition: (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))))
% Defined: nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))
% FOF formula (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))) of role conjecture named nonemptyI
% Conjecture to prove = (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))):Prop
% We need to prove ['(dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))):Prop.
% Definition emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))):Prop.
% Definition nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))):(fofType->Prop).
% Trying to prove (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))
% Found x2:(Xphi Xx)
% Instantiate: Xx0:=Xx:fofType
% Found x2 as proof of (Xphi Xx0)
% Found x1:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x1 as proof of ((in Xx0) A)
% Found ((x400 x1) x2) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (((x40 Xx0) x1) x2) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found ((((x4 Xphi) Xx0) x1) x2) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (((((x A) Xphi) Xx0) x1) x2) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (((((x A) Xphi) Xx0) x1) x2) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (x30 (((((x A) Xphi) Xx0) x1) x2)) as proof of ((in Xx0) emptyset)
% Found ((x3 (in Xx0)) (((((x A) Xphi) Xx0) x1) x2)) as proof of ((in Xx0) emptyset)
% Found ((x3 (in Xx0)) (((((x A) Xphi) Xx0) x1) x2)) as proof of ((in Xx0) emptyset)
% Found (x000 ((x3 (in Xx0)) (((((x A) Xphi) Xx0) x1) x2))) as proof of False
% Found (x000 ((x3 (in Xx0)) (((((x A) Xphi) Xx0) x1) x2))) as proof of False
% Found ((fun (x4:((in Xx0) emptyset))=> ((x00 x4) False)) ((x3 (in Xx0)) (((((x A) Xphi) Xx0) x1) x2))) as proof of False
% Found ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2))) as proof of False
% Found (fun (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2)))) as proof of False
% Found (fun (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2)))) as proof of (nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (fun (x1:((in Xx) A)) (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2)))) as proof of ((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))
% Found (fun (Xx:fofType) (x1:((in Xx) A)) (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2)))) as proof of (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))
% Found (fun (Xphi:(fofType->Prop)) (Xx:fofType) (x1:((in Xx) A)) (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2)))) as proof of (forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% Found (fun (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x1:((in Xx) A)) (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2)))) as proof of (forall (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% Found (fun (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x1:((in Xx) A)) (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2)))) as proof of (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% Found (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x1:((in Xx) A)) (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2)))) as proof of (emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Found (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x1:((in Xx) A)) (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2)))) as proof of (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))
% Got proof (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x1:((in Xx) A)) (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2))))
% Time elapsed = 0.543184s
% node=95 cost=1019.000000 depth=21
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x1:((in Xx) A)) (x2:(Xphi Xx)) (x3:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((fun (x4:((in Xx) emptyset))=> (((x0 Xx) x4) False)) ((x3 (in Xx)) (((((x A) Xphi) Xx) x1) x2))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------