TSTP Solution File: SEU685^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU685^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n189.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 13:32:48 EDT 2014
% Result : Theorem 0.67s
% Output : Proof 0.67s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU685^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n189.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 11:10:31 CDT 2014
% % CPUTime : 0.67
% 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 0x1d8fea8>, <kernel.DependentProduct object at 0x1d8fb00>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x21b2f38>, <kernel.Single object at 0x1d8fc20>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x1d8fb00>, <kernel.DependentProduct object at 0x1d8fbd8>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1d8fc68>, <kernel.DependentProduct object at 0x1d8ffc8>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x1d8fab8>, <kernel.DependentProduct object at 0x1d8fb00>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1d8fef0>, <kernel.DependentProduct object at 0x1d8fc68>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1d8ff38>, <kernel.DependentProduct object at 0x1d8fab8>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1d8fbd8>, <kernel.DependentProduct object at 0x1d8f8c0>) of role type named singleton_type
% Using role type
% Declaring singleton:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) of role definition named singleton
% A new definition: (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))))
% Defined: singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))
% FOF formula (<kernel.Constant object at 0x1d8f8c0>, <kernel.DependentProduct object at 0x1d8fa70>) of role type named ex1_type
% Using role type
% Declaring ex1:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named ex1
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Defined: ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% FOF formula (<kernel.Constant object at 0x1d8fa70>, <kernel.DependentProduct object at 0x1d8f710>) of role type named breln_type
% Using role type
% Declaring breln:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))) of role definition named breln
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))))
% Defined: breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))
% FOF formula (<kernel.Constant object at 0x1d8f710>, <kernel.DependentProduct object at 0x1d8f998>) of role type named func_type
% Using role type
% Declaring func:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))) of role definition named func
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))))
% Defined: func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))
% FOF formula (<kernel.Constant object at 0x1d8f998>, <kernel.DependentProduct object at 0x1d8f680>) of role type named funcSet_type
% Using role type
% Declaring funcSet:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1d8f638>, <kernel.DependentProduct object at 0x1d8fdd0>) of role type named ap_type
% Using role type
% Declaring ap:(fofType->(fofType->(fofType->(fofType->fofType))))
% FOF formula (<kernel.Constant object at 0x1d8f710>, <kernel.Sort object at 0x1c58248>) of role type named infuncsetfunc_type
% Using role type
% Declaring infuncsetfunc:Prop
% FOF formula (((eq Prop) infuncsetfunc) (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))) of role definition named infuncsetfunc
% A new definition: (((eq Prop) infuncsetfunc) (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))))
% Defined: infuncsetfunc:=(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))
% FOF formula (<kernel.Constant object at 0x1d8f7a0>, <kernel.Sort object at 0x1c58248>) of role type named funcGraphProp1_type
% Using role type
% Declaring funcGraphProp1:Prop
% FOF formula (((eq Prop) funcGraphProp1) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))) of role definition named funcGraphProp1
% A new definition: (((eq Prop) funcGraphProp1) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf))))))
% Defined: funcGraphProp1:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))
% FOF formula (infuncsetfunc->(funcGraphProp1->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf))))))) of role conjecture named funcGraphProp3
% Conjecture to prove = (infuncsetfunc->(funcGraphProp1->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf))))))):Prop
% We need to prove ['(infuncsetfunc->(funcGraphProp1->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Parameter subset:(fofType->(fofType->Prop)).
% Parameter kpair:(fofType->(fofType->fofType)).
% Parameter cartprod:(fofType->(fofType->fofType)).
% Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop).
% Definition ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))):(fofType->((fofType->Prop)->Prop)).
% Definition breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))):(fofType->(fofType->(fofType->Prop))).
% Definition func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))):(fofType->(fofType->(fofType->Prop))).
% Parameter funcSet:(fofType->(fofType->fofType)).
% Parameter ap:(fofType->(fofType->(fofType->(fofType->fofType)))).
% Definition infuncsetfunc:=(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))):Prop.
% Definition funcGraphProp1:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf))))):Prop.
% Trying to prove (infuncsetfunc->(funcGraphProp1->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))))
% Found x2000:=(x200 x1):(((func A) B) Xf)
% Found (x200 x1) as proof of (((func A) B) Xf)
% Found ((x20 Xf) x1) as proof of (((func A) B) Xf)
% Found (((x2 B) Xf) x1) as proof of (((func A) B) Xf)
% Found ((((x A) B) Xf) x1) as proof of (((func A) B) Xf)
% Found ((((x A) B) Xf) x1) as proof of (((func A) B) Xf)
% Found (x0000 ((((x A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))
% Found ((x000 Xf) ((((x A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))
% Found (((x00 B) Xf) ((((x A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))
% Found ((((x0 A) B) Xf) ((((x A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))
% Found (fun (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))
% Found (fun (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf))))
% Found (fun (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (forall (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))
% Found (fun (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (forall (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))
% Found (fun (x0:funcGraphProp1) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))
% Found (fun (x:infuncsetfunc) (x0:funcGraphProp1) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (funcGraphProp1->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf))))))
% Found (fun (x:infuncsetfunc) (x0:funcGraphProp1) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (infuncsetfunc->(funcGraphProp1->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((kpair Xx) ((((ap A) B) Xf) Xx))) Xf)))))))
% Got proof (fun (x:infuncsetfunc) (x0:funcGraphProp1) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1)))
% Time elapsed = 0.315680s
% node=27 cost=226.000000 depth=15
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:infuncsetfunc) (x0:funcGraphProp1) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------