%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU672^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n093.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 13:32:46 EDT 2014 % Result : Theorem 0.57s % Output : Proof 0.57s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU672^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n093.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 11:07:26 CDT 2014 % % CPUTime : 0.57 % 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 0x1c8eb90>, <kernel.DependentProduct object at 0x1c8e7e8>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1e6c560>, <kernel.Single object at 0x1c8e680>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0x1c8e7e8>, <kernel.DependentProduct object at 0x1c8ef38>) of role type named setadjoin_type % Using role type % Declaring setadjoin:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x1c8edd0>, <kernel.DependentProduct object at 0x1c8e710>) of role type named dsetconstr_type % Using role type % Declaring dsetconstr:(fofType->((fofType->Prop)->fofType)) % FOF formula (<kernel.Constant object at 0x1c8ec20>, <kernel.DependentProduct object at 0x1c8e7e8>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1c8e9e0>, <kernel.DependentProduct object at 0x1c8edd0>) of role type named kpair_type % Using role type % Declaring kpair:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x1c8e830>, <kernel.DependentProduct object at 0x1c8ec20>) of role type named cartprod_type % Using role type % Declaring cartprod:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x1c8ef38>, <kernel.DependentProduct object at 0x1c8e488>) of role type named singleton_type % Using role type % Declaring singleton:(fofType->Prop) % FOF formula (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) of role definition named singleton % A new definition: (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) % Defined: singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))) % FOF formula (<kernel.Constant object at 0x1c8e488>, <kernel.DependentProduct object at 0x1c8e7a0>) of role type named ex1_type % Using role type % Declaring ex1:(fofType->((fofType->Prop)->Prop)) % FOF formula (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named ex1 % A new definition: (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))) % Defined: ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) % FOF formula (<kernel.Constant object at 0x1c8e7a0>, <kernel.DependentProduct object at 0x1c8ec20>) 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 0x1b74e18>, <kernel.DependentProduct object at 0x1c8edd0>) of role type named func_type % Using role type % Declaring func:(fofType->(fofType->(fofType->Prop))) % FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))) of role definition named func % A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))) % Defined: func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))) % FOF formula (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))))) of role conjecture named funcImageSingleton % Conjecture to prove = (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))))):Prop % We need to prove ['(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % Parameter emptyset:fofType. % Parameter setadjoin:(fofType->(fofType->fofType)). % Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)). % Parameter subset:(fofType->(fofType->Prop)). % Parameter kpair:(fofType->(fofType->fofType)). % Parameter cartprod:(fofType->(fofType->fofType)). % Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop). % Definition ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))):(fofType->((fofType->Prop)->Prop)). % Definition breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))):(fofType->(fofType->(fofType->Prop))). % Definition func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))):(fofType->(fofType->(fofType->Prop))). % Trying to prove (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))))) % Found x200:=(x20 x0):((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))) % Found (x20 x0) as proof of (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))) % Found ((x2 Xx) x0) as proof of (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))) % Found (fun (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)) as proof of (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))) % Found (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)) as proof of ((forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf)))))->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) % Found (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)) as proof of ((((breln A) B) Xf)->((forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf)))))->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) % Found (and_rect00 (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0))) as proof of (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))) % Found ((and_rect0 (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0))) as proof of (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))) % Found (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0))) as proof of (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))) % Found (fun (x0:((in Xx) A))=> (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)))) as proof of (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))) % Found (fun (Xx:fofType) (x0:((in Xx) A))=> (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)))) as proof of (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) % Found (fun (x:(((func A) B) Xf)) (Xx:fofType) (x0:((in Xx) A))=> (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)))) as proof of (forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) % Found (fun (Xf:fofType) (x:(((func A) B) Xf)) (Xx:fofType) (x0:((in Xx) A))=> (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)))) as proof of ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))) % Found (fun (B:fofType) (Xf:fofType) (x:(((func A) B) Xf)) (Xx:fofType) (x0:((in Xx) A))=> (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)))) as proof of (forall (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))))) % Found (fun (A:fofType) (B:fofType) (Xf:fofType) (x:(((func A) B) Xf)) (Xx:fofType) (x0:((in Xx) A))=> (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)))) as proof of (forall (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))))) % Found (fun (A:fofType) (B:fofType) (Xf:fofType) (x:(((func A) B) Xf)) (Xx:fofType) (x0:((in Xx) A))=> (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)))) as proof of (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))))) % Got proof (fun (A:fofType) (B:fofType) (Xf:fofType) (x:(((func A) B) Xf)) (Xx:fofType) (x0:((in Xx) A))=> (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)))) % Time elapsed = 0.232932s % node=21 cost=193.000000 depth=14 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (A:fofType) (B:fofType) (Xf:fofType) (x:(((func A) B) Xf)) (Xx:fofType) (x0:((in Xx) A))=> (((fun (P:Type) (x1:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x1) x)) (singleton ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) (fun (x1:(((breln A) B) Xf)) (x2:(forall (Xx0:fofType), (((in Xx0) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx0) Xy)) Xf))))))=> ((x2 Xx) x0)))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------