%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU818^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n098.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 0.60s % Output : Proof 0.60s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU818^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n098.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 11:33:26 CDT 2014 % % CPUTime : 0.60 % 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 0xb8a7a0>, <kernel.DependentProduct object at 0xb8aa70>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0xd6d368>, <kernel.Single object at 0xb8ac68>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0xb8aa70>, <kernel.DependentProduct object at 0xb8a440>) of role type named powerset_type % Using role type % Declaring powerset:(fofType->fofType) % FOF formula (<kernel.Constant object at 0xb8ab90>, <kernel.DependentProduct object at 0xb8ad40>) 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 0xb8ad40>, <kernel.DependentProduct object at 0xb8a368>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0xb8a488>, <kernel.Sort object at 0xa4fea8>) of role type named subsetI1_type % Using role type % Declaring subsetI1:Prop % FOF formula (((eq Prop) subsetI1) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))) of role definition named subsetI1 % A new definition: (((eq Prop) subsetI1) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))) % Defined: subsetI1:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))) % FOF formula (<kernel.Constant object at 0xb8ab90>, <kernel.DependentProduct object at 0xb8add0>) 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 0xb8add0>, <kernel.DependentProduct object at 0xb8aa28>) 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 0xb8aa28>, <kernel.DependentProduct object at 0xb8a488>) 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 0xb8a488>, <kernel.DependentProduct object at 0xb8ab90>) 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 (<kernel.Constant object at 0xb8ab90>, <kernel.Sort object at 0xa4fea8>) of role type named ordinalTransSet_type % Using role type % Declaring ordinalTransSet:Prop % FOF formula (((eq Prop) ordinalTransSet) (forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X))))))) of role definition named ordinalTransSet % A new definition: (((eq Prop) ordinalTransSet) (forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X))))))) % Defined: ordinalTransSet:=(forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X)))))) % FOF formula (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) X))))))) of role conjecture named ordinalTransSet1 % Conjecture to prove = (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) X))))))):Prop % We need to prove ['(subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) 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 subsetI1:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) 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). % Definition ordinalTransSet:=(forall (X:fofType), ((ordinal X)->(forall (Xx:fofType) (A:fofType), (((in A) X)->(((in Xx) A)->((in Xx) X)))))):Prop. % Trying to prove (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) X))))))) % Found x2:(transitiveset X) % Found (fun (x3:(wellorderedByIn X))=> x2) as proof of (transitiveset X) % Found (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2) as proof of ((wellorderedByIn X)->(transitiveset X)) % Found (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2) as proof of ((transitiveset X)->((wellorderedByIn X)->(transitiveset X))) % Found (and_rect00 (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2)) as proof of (transitiveset X) % Found ((and_rect0 (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2)) as proof of (transitiveset X) % Found (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2)) as proof of (transitiveset X) % Found (fun (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (transitiveset X) % Found (fun (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of ((ordinal X)->(transitiveset X)) % Found (fun (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (forall (X:fofType), ((ordinal X)->(transitiveset X))) % Found (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (ordinalTransSet->(forall (X:fofType), ((ordinal X)->(transitiveset X)))) % Found (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(transitiveset X))))) % Found (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) as proof of (subsetI1->(ordinalTransSet->(forall (X:fofType), ((ordinal X)->(forall (A:fofType), (((in A) X)->((subset A) X))))))) % Got proof (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) % Time elapsed = 0.254000s % node=42 cost=144.000000 depth=11 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:subsetI1) (x0:ordinalTransSet) (X:fofType) (x1:(ordinal X))=> (((fun (P:Type) (x2:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x2) x1)) (transitiveset X)) (fun (x2:(transitiveset X)) (x3:(wellorderedByIn X))=> x2))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------