TSTP Solution File: SEU780^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU780^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n190.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 13:33:06 EDT 2014
% Result : Theorem 0.74s
% Output : Proof 0.74s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU780^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n190.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 11:27:11 CDT 2014
% % CPUTime : 0.74
% 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 0x2aa8710>, <kernel.DependentProduct object at 0x2859488>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2aa8c68>, <kernel.DependentProduct object at 0x2859488>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2aaf7a0>, <kernel.DependentProduct object at 0x2859758>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x2aa8c68>, <kernel.DependentProduct object at 0x2859170>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x2aa8c68>, <kernel.DependentProduct object at 0x2859d40>) 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 0x2859d40>, <kernel.DependentProduct object at 0x2859128>) of role type named dpsetconstr_type
% Using role type
% Declaring dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType)))
% FOF formula (<kernel.Constant object at 0x2859758>, <kernel.Sort object at 0x253fc68>) of role type named dpsetconstrER_type
% Using role type
% Declaring dpsetconstrER:Prop
% FOF formula (((eq Prop) dpsetconstrER) (forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((Xphi Xx) Xy)))) of role definition named dpsetconstrER
% A new definition: (((eq Prop) dpsetconstrER) (forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((Xphi Xx) Xy))))
% Defined: dpsetconstrER:=(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((Xphi Xx) Xy)))
% FOF formula (<kernel.Constant object at 0x2859488>, <kernel.DependentProduct object at 0x2859050>) of role type named breln1_type
% Using role type
% Declaring breln1:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) breln1) (fun (A:fofType) (R:fofType)=> (((breln A) A) R))) of role definition named breln1
% A new definition: (((eq (fofType->(fofType->Prop))) breln1) (fun (A:fofType) (R:fofType)=> (((breln A) A) R)))
% Defined: breln1:=(fun (A:fofType) (R:fofType)=> (((breln A) A) R))
% FOF formula (<kernel.Constant object at 0x2859050>, <kernel.DependentProduct object at 0x2859cb0>) of role type named breln1compset_type
% Using role type
% Declaring breln1compset:(fofType->(fofType->(fofType->fofType)))
% FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) breln1compset) (fun (A:fofType) (R:fofType) (S:fofType)=> (((dpsetconstr A) A) (fun (Xx:fofType) (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))) of role definition named breln1compset
% A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) breln1compset) (fun (A:fofType) (R:fofType) (S:fofType)=> (((dpsetconstr A) A) (fun (Xx:fofType) (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))
% Defined: breln1compset:=(fun (A:fofType) (R:fofType) (S:fofType)=> (((dpsetconstr A) A) (fun (Xx:fofType) (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))
% FOF formula (dpsetconstrER->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))))))))) of role conjecture named breln1compE
% Conjecture to prove = (dpsetconstrER->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(dpsetconstrER->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter subset:(fofType->(fofType->Prop)).
% Parameter kpair:(fofType->(fofType->fofType)).
% Parameter cartprod:(fofType->(fofType->fofType)).
% Definition breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))):(fofType->(fofType->(fofType->Prop))).
% Parameter dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType))).
% Definition dpsetconstrER:=(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((Xphi Xx) Xy))):Prop.
% Definition breln1:=(fun (A:fofType) (R:fofType)=> (((breln A) A) R)):(fofType->(fofType->Prop)).
% Definition breln1compset:=(fun (A:fofType) (R:fofType) (S:fofType)=> (((dpsetconstr A) A) (fun (Xx:fofType) (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))):(fofType->(fofType->(fofType->fofType))).
% Trying to prove (dpsetconstrER->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))))))))
% Found x40000:=(x4000 Xy):(((in ((kpair Xx) Xy)) (((dpsetconstr A) A) (fun (Xz:fofType) (Xu:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xz) Xz0)) R))) ((in ((kpair Xz0) Xu)) S)))))))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))
% Found (x4000 Xy) as proof of (((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))
% Found ((x400 Xx) Xy) as proof of (((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))
% Found (((x40 (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy) as proof of (((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))
% Found ((((x4 A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy) as proof of (((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))
% Found (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy) as proof of (((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))
% Found (fun (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))
% Found (fun (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))
% Found (fun (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))
% Found (fun (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))
% Found (fun (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))))
% Found (fun (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))))
% Found (fun (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))))))
% Found (fun (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))))))
% Found (fun (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (forall (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))))))))
% Found (fun (x:dpsetconstrER) (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))))))))
% Found (fun (x:dpsetconstrER) (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy)) as proof of (dpsetconstrER->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))))))))
% Got proof (fun (x:dpsetconstrER) (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy))
% Time elapsed = 0.383691s
% node=20 cost=-363.000000 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:dpsetconstrER) (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A))=> (((((x A) A) (fun (x8:fofType) (x70:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair x8) Xz)) R))) ((in ((kpair Xz) x70)) S)))))) Xx) Xy))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------