%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU737^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n180.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 13:32:58 EDT 2014 % Result : Theorem 1.11s % Output : Proof 1.11s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU737^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n180.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 11:20:41 CDT 2014 % % CPUTime : 1.11 % 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 0x1e85440>, <kernel.DependentProduct object at 0x1e85c68>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x2242320>, <kernel.DependentProduct object at 0x1e853f8>) of role type named powerset_type % Using role type % Declaring powerset:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x1e85bd8>, <kernel.DependentProduct object at 0x1e85368>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1e855f0>, <kernel.DependentProduct object at 0x1e85440>) of role type named setminus_type % Using role type % Declaring setminus:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x1e85cf8>, <kernel.Sort object at 0x2118878>) of role type named complementT_lem_type % Using role type % Declaring complementT_lem:Prop % FOF formula (((eq Prop) complementT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A))))) of role definition named complementT_lem % A new definition: (((eq Prop) complementT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A))))) % Defined: complementT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A)))) % FOF formula (<kernel.Constant object at 0x1e855a8>, <kernel.Sort object at 0x2118878>) of role type named subsetTI_type % Using role type % Declaring subsetTI:Prop % FOF formula (((eq Prop) subsetTI) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) Y))))->((subset X) Y))))))) of role definition named subsetTI % A new definition: (((eq Prop) subsetTI) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) Y))))->((subset X) Y))))))) % Defined: subsetTI:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) Y))))->((subset X) Y)))))) % FOF formula (<kernel.Constant object at 0x1e85908>, <kernel.Sort object at 0x2118878>) of role type named contraSubsetComplement_type % Using role type % Declaring contraSubsetComplement:Prop % FOF formula (((eq Prop) contraSubsetComplement) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))))))))) of role definition named contraSubsetComplement % A new definition: (((eq Prop) contraSubsetComplement) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))))))))) % Defined: contraSubsetComplement:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X)))))))))) % FOF formula (complementT_lem->(subsetTI->(contraSubsetComplement->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X)))))))))) of role conjecture named complementTcontraSubset % Conjecture to prove = (complementT_lem->(subsetTI->(contraSubsetComplement->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X)))))))))):Prop % Parameter fofType_DUMMY:fofType. % We need to prove ['(complementT_lem->(subsetTI->(contraSubsetComplement->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X))))))))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % Parameter powerset:(fofType->fofType). % Parameter subset:(fofType->(fofType->Prop)). % Parameter setminus:(fofType->(fofType->fofType)). % Definition complementT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A)))):Prop. % Definition subsetTI:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) Y))))->((subset X) Y)))))):Prop. % Definition contraSubsetComplement:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X)))))))))):Prop. % Trying to prove (complementT_lem->(subsetTI->(contraSubsetComplement->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X)))))))))) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x500:=(x50 x2):((in ((setminus A) X)) (powerset A)) % Found (x50 x2) as proof of ((in ((setminus A) X)) (powerset A)) % Found ((x5 X) x2) as proof of ((in ((setminus A) X)) (powerset A)) % Found (((x A) X) x2) as proof of ((in ((setminus A) X)) (powerset A)) % Found (((x A) X) x2) as proof of ((in ((setminus A) X)) (powerset A)) % Found x1000000:=(x100000 x4):(forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))) % Found (x100000 x4) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))) % Found ((x10000 x3) x4) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))) % Found (((x1000 Y) x3) x4) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))) % Found ((((x100 x2) Y) x3) x4) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))) % Found (((((x10 X) x2) Y) x3) x4) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))) % Found ((((((x1 A) X) x2) Y) x3) x4) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))) % Found ((((((x1 A) X) x2) Y) x3) x4) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) ((setminus A) X))))) % Found (((x0000 x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4)) as proof of ((subset Y) ((setminus A) X)) % Found ((((x000 A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4)) as proof of ((subset Y) ((setminus A) X)) % Found (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> (((x00 A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4)) as proof of ((subset Y) ((setminus A) X)) % Found (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4)) as proof of ((subset Y) ((setminus A) X)) % Found (fun (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of ((subset Y) ((setminus A) X)) % Found (fun (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of (((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X))) % Found (fun (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X)))) % Found (fun (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of (forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X))))) % Found (fun (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X)))))) % Found (fun (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of (forall (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X))))))) % Found (fun (x1:contraSubsetComplement) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X))))))) % Found (fun (x0:subsetTI) (x1:contraSubsetComplement) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of (contraSubsetComplement->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X)))))))) % Found (fun (x:complementT_lem) (x0:subsetTI) (x1:contraSubsetComplement) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of (subsetTI->(contraSubsetComplement->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X))))))))) % Found (fun (x:complementT_lem) (x0:subsetTI) (x1:contraSubsetComplement) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) as proof of (complementT_lem->(subsetTI->(contraSubsetComplement->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((subset X) ((setminus A) Y))->((subset Y) ((setminus A) X)))))))))) % Got proof (fun (x:complementT_lem) (x0:subsetTI) (x1:contraSubsetComplement) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) % Time elapsed = 0.777766s % node=121 cost=896.000000 depth=20 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:complementT_lem) (x0:subsetTI) (x1:contraSubsetComplement) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (x4:((subset X) ((setminus A) Y)))=> (((((fun (A0:fofType) (x5:((in Y) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) Y)) A0) x5) ((setminus A) X))) A) x3) (((x A) X) x2)) ((((((x1 A) X) x2) Y) x3) x4))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------