%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU816^2 : 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 5.91s % Output : Proof 5.91s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU816^2 : 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 11:33:11 CDT 2014 % % CPUTime : 5.91 % 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 0x19fc6c8>, <kernel.DependentProduct object at 0x19fce18>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x19fd2d8>, <kernel.Single object at 0x19fc638>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0x19fce18>, <kernel.DependentProduct object at 0x19fc3b0>) of role type named powerset_type % Using role type % Declaring powerset:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x19fc710>, <kernel.DependentProduct object at 0x19fc248>) 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 0x19fc248>, <kernel.DependentProduct object at 0x19fc170>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x19fc3f8>, <kernel.DependentProduct object at 0x19fc638>) of role type named binintersect_type % Using role type % Declaring binintersect:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x19fc710>, <kernel.DependentProduct object at 0x19fc680>) 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 0x19fc680>, <kernel.Sort object at 0x16df7e8>) of role type named binintTransitive_type % Using role type % Declaring binintTransitive:Prop % FOF formula (((eq Prop) binintTransitive) (forall (X:fofType), ((transitiveset X)->(forall (Y:fofType), ((transitiveset Y)->(transitiveset ((binintersect X) Y))))))) of role definition named binintTransitive % A new definition: (((eq Prop) binintTransitive) (forall (X:fofType), ((transitiveset X)->(forall (Y:fofType), ((transitiveset Y)->(transitiveset ((binintersect X) Y))))))) % Defined: binintTransitive:=(forall (X:fofType), ((transitiveset X)->(forall (Y:fofType), ((transitiveset Y)->(transitiveset ((binintersect X) Y)))))) % FOF formula (<kernel.Constant object at 0x19fc518>, <kernel.DependentProduct object at 0x19fc878>) 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 0x19fc680>, <kernel.DependentProduct object at 0x19fb2d8>) 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 0x19fc518>, <kernel.DependentProduct object at 0x19fbef0>) 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 (binintTransitive->(forall (X:fofType), ((ordinal X)->(forall (Y:fofType), ((ordinal Y)->(transitiveset ((binintersect X) Y))))))) of role conjecture named ordinalMinLem1 % Conjecture to prove = (binintTransitive->(forall (X:fofType), ((ordinal X)->(forall (Y:fofType), ((ordinal Y)->(transitiveset ((binintersect X) Y))))))):Prop % We need to prove ['(binintTransitive->(forall (X:fofType), ((ordinal X)->(forall (Y:fofType), ((ordinal Y)->(transitiveset ((binintersect X) Y)))))))'] % 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)). % Parameter binintersect:(fofType->(fofType->fofType)). % Definition transitiveset:=(fun (A:fofType)=> (forall (X:fofType), (((in X) A)->((subset X) A)))):(fofType->Prop). % Definition binintTransitive:=(forall (X:fofType), ((transitiveset X)->(forall (Y:fofType), ((transitiveset Y)->(transitiveset ((binintersect X) Y)))))):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 (binintTransitive->(forall (X:fofType), ((ordinal X)->(forall (Y:fofType), ((ordinal Y)->(transitiveset ((binintersect X) Y))))))) % Found x2:(transitiveset Y) % Found x2 as proof of (transitiveset Y) % Found x2:(transitiveset X) % Found x2 as proof of (transitiveset X) % Found x2:((in X0) ((binintersect X) Y)) % Found x2 as proof of ((in X0) ((binintersect X) Y)) % Found x6000:=(x600 x2):(transitiveset ((binintersect X) Y)) % Found (x600 x2) as proof of (transitiveset ((binintersect X) Y)) % Found ((x60 Y) x2) as proof of (transitiveset ((binintersect X) Y)) % Found (((x6 x4) Y) x2) as proof of (transitiveset ((binintersect X) Y)) % Found ((((x X) x4) Y) x2) as proof of (transitiveset ((binintersect X) Y)) % Found (fun (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)) as proof of (transitiveset ((binintersect X) Y)) % Found (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)) as proof of ((wellorderedByIn X)->(transitiveset ((binintersect X) Y))) % Found (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)) as proof of ((transitiveset X)->((wellorderedByIn X)->(transitiveset ((binintersect X) Y)))) % Found (and_rect10 (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2))) as proof of (transitiveset ((binintersect X) Y)) % Found ((and_rect1 (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2))) as proof of (transitiveset ((binintersect X) Y)) % Found (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2))) as proof of (transitiveset ((binintersect X) Y)) % Found (fun (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))) as proof of (transitiveset ((binintersect X) Y)) % Found (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))) as proof of ((wellorderedByIn Y)->(transitiveset ((binintersect X) Y))) % Found (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))) as proof of ((transitiveset Y)->((wellorderedByIn Y)->(transitiveset ((binintersect X) Y)))) % Found (and_rect00 (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2))))) as proof of (transitiveset ((binintersect X) Y)) % Found ((and_rect0 (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2))))) as proof of (transitiveset ((binintersect X) Y)) % Found (((fun (P:Type) (x2:((transitiveset Y)->((wellorderedByIn Y)->P)))=> (((((and_rect (transitiveset Y)) (wellorderedByIn Y)) P) x2) x1)) (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2))))) as proof of (transitiveset ((binintersect X) Y)) % Found (fun (x1:(ordinal Y))=> (((fun (P:Type) (x2:((transitiveset Y)->((wellorderedByIn Y)->P)))=> (((((and_rect (transitiveset Y)) (wellorderedByIn Y)) P) x2) x1)) (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))))) as proof of (transitiveset ((binintersect X) Y)) % Found (fun (Y:fofType) (x1:(ordinal Y))=> (((fun (P:Type) (x2:((transitiveset Y)->((wellorderedByIn Y)->P)))=> (((((and_rect (transitiveset Y)) (wellorderedByIn Y)) P) x2) x1)) (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))))) as proof of ((ordinal Y)->(transitiveset ((binintersect X) Y))) % Found (fun (x0:(ordinal X)) (Y:fofType) (x1:(ordinal Y))=> (((fun (P:Type) (x2:((transitiveset Y)->((wellorderedByIn Y)->P)))=> (((((and_rect (transitiveset Y)) (wellorderedByIn Y)) P) x2) x1)) (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))))) as proof of (forall (Y:fofType), ((ordinal Y)->(transitiveset ((binintersect X) Y)))) % Found (fun (X:fofType) (x0:(ordinal X)) (Y:fofType) (x1:(ordinal Y))=> (((fun (P:Type) (x2:((transitiveset Y)->((wellorderedByIn Y)->P)))=> (((((and_rect (transitiveset Y)) (wellorderedByIn Y)) P) x2) x1)) (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))))) as proof of ((ordinal X)->(forall (Y:fofType), ((ordinal Y)->(transitiveset ((binintersect X) Y))))) % Found (fun (x:binintTransitive) (X:fofType) (x0:(ordinal X)) (Y:fofType) (x1:(ordinal Y))=> (((fun (P:Type) (x2:((transitiveset Y)->((wellorderedByIn Y)->P)))=> (((((and_rect (transitiveset Y)) (wellorderedByIn Y)) P) x2) x1)) (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))))) as proof of (forall (X:fofType), ((ordinal X)->(forall (Y:fofType), ((ordinal Y)->(transitiveset ((binintersect X) Y)))))) % Found (fun (x:binintTransitive) (X:fofType) (x0:(ordinal X)) (Y:fofType) (x1:(ordinal Y))=> (((fun (P:Type) (x2:((transitiveset Y)->((wellorderedByIn Y)->P)))=> (((((and_rect (transitiveset Y)) (wellorderedByIn Y)) P) x2) x1)) (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))))) as proof of (binintTransitive->(forall (X:fofType), ((ordinal X)->(forall (Y:fofType), ((ordinal Y)->(transitiveset ((binintersect X) Y))))))) % Got proof (fun (x:binintTransitive) (X:fofType) (x0:(ordinal X)) (Y:fofType) (x1:(ordinal Y))=> (((fun (P:Type) (x2:((transitiveset Y)->((wellorderedByIn Y)->P)))=> (((((and_rect (transitiveset Y)) (wellorderedByIn Y)) P) x2) x1)) (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))))) % Time elapsed = 5.511593s % node=587 cost=448.000000 depth=21 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:binintTransitive) (X:fofType) (x0:(ordinal X)) (Y:fofType) (x1:(ordinal Y))=> (((fun (P:Type) (x2:((transitiveset Y)->((wellorderedByIn Y)->P)))=> (((((and_rect (transitiveset Y)) (wellorderedByIn Y)) P) x2) x1)) (transitiveset ((binintersect X) Y))) (fun (x2:(transitiveset Y)) (x3:(wellorderedByIn Y))=> (((fun (P:Type) (x4:((transitiveset X)->((wellorderedByIn X)->P)))=> (((((and_rect (transitiveset X)) (wellorderedByIn X)) P) x4) x0)) (transitiveset ((binintersect X) Y))) (fun (x4:(transitiveset X)) (x5:(wellorderedByIn X))=> ((((x X) x4) Y) x2)))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------