%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU688^2 : 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 13:32:49 EDT 2014 % Result : Theorem 1.26s % Output : Proof 1.26s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU688^2 : 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 11:11:31 CDT 2014 % % CPUTime : 1.26 % 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 0x16c4050>, <kernel.DependentProduct object at 0x16c40e0>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x1501518>, <kernel.Single object at 0x16c4170>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0x16c40e0>, <kernel.DependentProduct object at 0x16c43f8>) of role type named setadjoin_type % Using role type % Declaring setadjoin:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x16c42d8>, <kernel.DependentProduct object at 0x16e49e0>) of role type named dsetconstr_type % Using role type % Declaring dsetconstr:(fofType->((fofType->Prop)->fofType)) % FOF formula (<kernel.Constant object at 0x16c4170>, <kernel.DependentProduct object at 0x16e4bd8>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x16c4488>, <kernel.DependentProduct object at 0x16e4bd8>) of role type named kpair_type % Using role type % Declaring kpair:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x16c40e0>, <kernel.DependentProduct object at 0x16e4bd8>) of role type named cartprod_type % Using role type % Declaring cartprod:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x16c4488>, <kernel.DependentProduct object at 0x16e49e0>) 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 0x16e4440>, <kernel.DependentProduct object at 0x16c40e0>) 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 0x16e4440>, <kernel.DependentProduct object at 0x16c4560>) 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 0x16c4560>, <kernel.DependentProduct object at 0x16e4098>) 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 (<kernel.Constant object at 0x16c4170>, <kernel.DependentProduct object at 0x16e28c0>) of role type named funcSet_type % Using role type % Declaring funcSet:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x16e49e0>, <kernel.DependentProduct object at 0x16e28c0>) of role type named ap_type % Using role type % Declaring ap:(fofType->(fofType->(fofType->(fofType->fofType)))) % FOF formula (<kernel.Constant object at 0x16e4098>, <kernel.Sort object at 0x1794d88>) of role type named infuncsetfunc_type % Using role type % Declaring infuncsetfunc:Prop % FOF formula (((eq Prop) infuncsetfunc) (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))) of role definition named infuncsetfunc % A new definition: (((eq Prop) infuncsetfunc) (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))) % Defined: infuncsetfunc:=(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))) % FOF formula (<kernel.Constant object at 0x16e49e0>, <kernel.Sort object at 0x1794d88>) of role type named funcGraphProp2_type % Using role type % Declaring funcGraphProp2:Prop % FOF formula (((eq Prop) funcGraphProp2) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))) of role definition named funcGraphProp2 % A new definition: (((eq Prop) funcGraphProp2) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))) % Defined: funcGraphProp2:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))) % FOF formula (infuncsetfunc->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))))) of role conjecture named funcGraphProp4 % Conjecture to prove = (infuncsetfunc->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))))):Prop % We need to prove ['(infuncsetfunc->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))))'] % 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))). % Parameter funcSet:(fofType->(fofType->fofType)). % Parameter ap:(fofType->(fofType->(fofType->(fofType->fofType)))). % Definition infuncsetfunc:=(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))):Prop. % Definition funcGraphProp2:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))):Prop. % Trying to prove (infuncsetfunc->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))))) % Found x2000:=(x200 x1):(((func A) B) Xf) % Found (x200 x1) as proof of (((func A) B) Xf) % Found ((x20 Xf) x1) as proof of (((func A) B) Xf) % Found (((x2 B) Xf) x1) as proof of (((func A) B) Xf) % Found ((((x A) B) Xf) x1) as proof of (((func A) B) Xf) % Found ((((x A) B) Xf) x1) as proof of (((func A) B) Xf) % Found (x0000 ((((x A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))) % Found ((x000 Xf) ((((x A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))) % Found (((x00 B) Xf) ((((x A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))) % Found ((((x0 A) B) Xf) ((((x A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))) % Found (fun (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))) % Found (fun (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))) % Found (fun (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (forall (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))) % Found (fun (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (forall (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))) % Found (fun (x0:funcGraphProp2) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))) % Found (fun (x:infuncsetfunc) (x0:funcGraphProp2) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))) % Found (fun (x:infuncsetfunc) (x0:funcGraphProp2) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) as proof of (infuncsetfunc->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))))) % Got proof (fun (x:infuncsetfunc) (x0:funcGraphProp2) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) % Time elapsed = 0.887211s % node=62 cost=226.000000 depth=15 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:infuncsetfunc) (x0:funcGraphProp2) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x0 A) B) Xf) ((((x A) B) Xf) x1))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------