%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU817^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n090.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 13:33:13 EDT 2014 % Result : Theorem 0.75s % Output : Proof 0.75s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU817^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n090.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 11:33:21 CDT 2014 % % CPUTime : 0.75 % 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 0x27c93b0>, <kernel.DependentProduct object at 0x2aa08c0>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x27c9488>, <kernel.Single object at 0x27c9dd0>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0x27c9ef0>, <kernel.DependentProduct object at 0x2691710>) of role type named powerset_type % Using role type % Declaring powerset:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x27c9518>, <kernel.DependentProduct object at 0x2691dd0>) 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 (<kernel.Constant object at 0x27c9ef0>, <kernel.DependentProduct object at 0x2691710>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x27c9518>, <kernel.Sort object at 0x26923f8>) of role type named subsetE_type % Using role type % Declaring subsetE:Prop % FOF formula (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))) of role definition named subsetE % A new definition: (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))) % Defined: subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))) % FOF formula (<kernel.Constant object at 0x27c9518>, <kernel.DependentProduct object at 0x2691dd0>) of role type named transitiveset_type % Using role type % Declaring transitiveset:(fofType->Prop) % FOF formula (((eq (fofType->Prop)) transitiveset) (fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A))))) of role definition named transitiveset % A new definition: (((eq (fofType->Prop)) transitiveset) (fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A))))) % Defined: transitiveset:=(fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A)))) % FOF formula (<kernel.Constant object at 0x27c9ab8>, <kernel.DependentProduct object at 0x2a9f248>) of role type named stricttotalorderedByIn_type % Using role type % Declaring stricttotalorderedByIn:(fofType->Prop) % FOF formula (((eq (fofType->Prop)) stricttotalorderedByIn) (fun (A:fofType)=> ((and ((and (forall (Xx:fofType), (((in Xx) A)->(forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->(((and ((in Xx) X)) ((in X) Y))->((in Xx) Y))))))))) (forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->((or ((or (((eq fofType) X) Y)) ((in X) Y))) ((in Y) X)))))))) (forall (X:fofType), (((in X) A)->(((in X) X)->False)))))) of role definition named stricttotalorderedByIn % A new definition: (((eq (fofType->Prop)) stricttotalorderedByIn) (fun (A:fofType)=> ((and ((and (forall (Xx:fofType), (((in Xx) A)->(forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->(((and ((in Xx) X)) ((in X) Y))->((in Xx) Y))))))))) (forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->((or ((or (((eq fofType) X) Y)) ((in X) Y))) ((in Y) X)))))))) (forall (X:fofType), (((in X) A)->(((in X) X)->False)))))) % Defined: stricttotalorderedByIn:=(fun (A:fofType)=> ((and ((and (forall (Xx:fofType), (((in Xx) A)->(forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->(((and ((in Xx) X)) ((in X) Y))->((in Xx) Y))))))))) (forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->((or ((or (((eq fofType) X) Y)) ((in X) Y))) ((in Y) X)))))))) (forall (X:fofType), (((in X) A)->(((in X) X)->False))))) % FOF formula (<kernel.Constant object at 0x2697290>, <kernel.DependentProduct object at 0x2a9fa70>) of role type named wellorderedByIn_type % Using role type % Declaring wellorderedByIn:(fofType->Prop) % FOF formula (((eq (fofType->Prop)) wellorderedByIn) (fun (A:fofType)=> ((and (stricttotalorderedByIn A)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Y:fofType), (((in Y) X)->((or (((eq fofType) Xx) Y)) ((in Xx) Y))))))))))))) of role definition named wellorderedByIn % A new definition: (((eq (fofType->Prop)) wellorderedByIn) (fun (A:fofType)=> ((and (stricttotalorderedByIn A)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Y:fofType), (((in Y) X)->((or (((eq fofType) Xx) Y)) ((in Xx) Y))))))))))))) % Defined: wellorderedByIn:=(fun (A:fofType)=> ((and (stricttotalorderedByIn A)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Y:fofType), (((in Y) X)->((or (((eq fofType) Xx) Y)) ((in Xx) Y)))))))))))) % FOF formula (<kernel.Constant object at 0x2a802d8>, <kernel.DependentProduct object at 0x2691200>) of role type named ordinal_type % Using role type % Declaring ordinal:(fofType->Prop) % FOF formula (((eq (fofType->Prop)) ordinal) (fun (Xx:fofType)=> ((and (transitiveset Xx)) (wellorderedByIn Xx)))) of role definition named ordinal % A new definition: (((eq (fofType->Prop)) ordinal) (fun (Xx:fofType)=> ((and (transitiveset Xx)) (wellorderedByIn Xx)))) % Defined: ordinal:=(fun (Xx:fofType)=> ((and (transitiveset Xx)) (wellorderedByIn Xx))) % FOF formula (subsetE->(forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X))))))) of role conjecture named ordinalTransSet % Conjecture to prove = (subsetE->(forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X))))))):Prop % We need to prove ['(subsetE->(forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X)))))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % Parameter emptyset:fofType. % Parameter powerset:(fofType->fofType). % Definition nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))):(fofType->Prop). % Parameter subset:(fofType->(fofType->Prop)). % Definition subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))):Prop. % Definition transitiveset:=(fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A)))):(fofType->Prop). % Definition stricttotalorderedByIn:=(fun (A:fofType)=> ((and ((and (forall (Xx:fofType), (((in Xx) A)->(forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->(((and ((in Xx) X)) ((in X) Y))->((in Xx) Y))))))))) (forall (X:fofType), (((in X) A)->(forall (Y:fofType), (((in Y) A)->((or ((or (((eq fofType) X) Y)) ((in X) Y))) ((in Y) X)))))))) (forall (X:fofType), (((in X) A)->(((in X) X)->False))))):(fofType->Prop). % Definition wellorderedByIn:=(fun (A:fofType)=> ((and (stricttotalorderedByIn A)) (forall (X:fofType), (((in X) (powerset A))->((nonempty X)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) X)) (forall (Y:fofType), (((in Y) X)->((or (((eq fofType) Xx) Y)) ((in Xx) Y)))))))))))):(fofType->Prop). % Definition ordinal:=(fun (Xx:fofType)=> ((and (transitiveset Xx)) (wellorderedByIn Xx))):(fofType->Prop). % Trying to prove (subsetE->(forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X))))))) % Found x300:=(x30 x1):((subset A) X) % Found (x30 x1) as proof of ((subset A) X) % Found ((x3 A) x1) as proof of ((subset A) X) % Found (fun (x4:(wellorderedByIn X))=> ((x3 A) x1)) as proof of ((subset A) X) % Found (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1)) as proof of ((wellorderedByIn X)->((subset A) X)) % Found (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1)) as proof of ((transitiveset X)->((wellorderedByIn X)->((subset A) X))) % Found (and_rect00 (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))) as proof of ((subset A) X) % Found ((and_rect0 ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))) as proof of ((subset A) X) % Found (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))) as proof of ((subset A) X) % Found (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))) as proof of ((subset A) X) % Found (x200 (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1)))) as proof of (((in Xx) A)->((in Xx) X)) % Found ((x20 Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1)))) as proof of (((in Xx) A)->((in Xx) X)) % Found (((x2 X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1)))) as proof of (((in Xx) A)->((in Xx) X)) % Found ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1)))) as proof of (((in Xx) A)->((in Xx) X)) % Found (fun (x1:((in A) X))=> ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))))) as proof of (((in Xx) A)->((in Xx) X)) % Found (fun (A:fofType) (x1:((in A) X))=> ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))))) as proof of (((in A) X)->(((in Xx) A)->((in Xx) X))) % Found (fun (Xx:fofType) (A:fofType) (x1:((in A) X))=> ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))))) as proof of (forall (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X)))) % Found (fun (x0:(ordinal X)) (Xx:fofType) (A:fofType) (x1:((in A) X))=> ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))))) as proof of (forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X)))) % Found (fun (X:fofType) (x0:(ordinal X)) (Xx:fofType) (A:fofType) (x1:((in A) X))=> ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))))) as proof of ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X))))) % Found (fun (x:subsetE) (X:fofType) (x0:(ordinal X)) (Xx:fofType) (A:fofType) (x1:((in A) X))=> ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))))) as proof of (forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X)))))) % Found (fun (x:subsetE) (X:fofType) (x0:(ordinal X)) (Xx:fofType) (A:fofType) (x1:((in A) X))=> ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))))) as proof of (subsetE->(forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X))))))) % Got proof (fun (x:subsetE) (X:fofType) (x0:(ordinal X)) (Xx:fofType) (A:fofType) (x1:((in A) X))=> ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))))) % Time elapsed = 0.406223s % node=45 cost=380.000000 depth=19 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:subsetE) (X:fofType) (x0:(ordinal X)) (Xx:fofType) (A:fofType) (x1:((in A) X))=> ((((x A) X) Xx) (((fun (P:Type) (x3:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x3) x0)) ((subset A) X)) (fun (x3:(transitiveset X)) (x4:(wellorderedByIn X))=> ((x3 A) x1))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------