%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------