%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU676^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n102.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 13:32:47 EDT 2014 % Result : Theorem 0.69s % Output : Proof 0.69s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU676^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n102.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 11:08:21 CDT 2014 % % CPUTime : 0.69 % 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 0x913a70>, <kernel.DependentProduct object at 0x913b90>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0xd50320>, <kernel.Single object at 0x913cf8>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0x913b90>, <kernel.DependentProduct object at 0x913dd0>) of role type named setadjoin_type % Using role type % Declaring setadjoin:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x913a28>, <kernel.DependentProduct object at 0x913cb0>) of role type named powerset_type % Using role type % Declaring powerset:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x913c68>, <kernel.DependentProduct object at 0x9134d0>) of role type named setunion_type % Using role type % Declaring setunion:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x913d88>, <kernel.DependentProduct object at 0x9137a0>) of role type named dsetconstr_type % Using role type % Declaring dsetconstr:(fofType->((fofType->Prop)->fofType)) % FOF formula (<kernel.Constant object at 0x913dd0>, <kernel.DependentProduct object at 0x913c68>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x913cb0>, <kernel.DependentProduct object at 0x913d88>) of role type named kpair_type % Using role type % Declaring kpair:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x913a28>, <kernel.DependentProduct object at 0x913dd0>) of role type named cartprod_type % Using role type % Declaring cartprod:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x9134d0>, <kernel.DependentProduct object at 0x913368>) 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 0x913368>, <kernel.DependentProduct object at 0x913f80>) 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 0x913f80>, <kernel.DependentProduct object at 0x913b00>) 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 0x9134d0>, <kernel.DependentProduct object at 0x913368>) 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 0x913c68>, <kernel.DependentProduct object at 0xcf27a0>) of role type named funcSet_type % Using role type % Declaring funcSet:(fofType->(fofType->fofType)) % FOF formula (((eq (fofType->(fofType->fofType))) funcSet) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf))))) of role definition named funcSet % A new definition: (((eq (fofType->(fofType->fofType))) funcSet) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf))))) % Defined: funcSet:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf)))) % FOF formula (<kernel.Constant object at 0x913f80>, <kernel.DependentProduct object at 0xcf2680>) of role type named ap_type % Using role type % Declaring ap:(fofType->(fofType->(fofType->(fofType->fofType)))) % FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) ap) (fun (A:fofType) (B:fofType) (Xf:fofType) (Xx:fofType)=> (setunion ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) of role definition named ap % A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) ap) (fun (A:fofType) (B:fofType) (Xf:fofType) (Xx:fofType)=> (setunion ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) % Defined: ap:=(fun (A:fofType) (B:fofType) (Xf:fofType) (Xx:fofType)=> (setunion ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))) % FOF formula (<kernel.Constant object at 0x913f80>, <kernel.Sort object at 0xbaac68>) of role type named app_type % Using role type % Declaring app:Prop % FOF formula (((eq Prop) app) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))))) of role definition named app % A new definition: (((eq Prop) app) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))))) % Defined: app:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))) % FOF formula (<kernel.Constant object at 0x913f80>, <kernel.Sort object at 0xbaac68>) 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 (app->(infuncsetfunc->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))))) of role conjecture named ap2p % Conjecture to prove = (app->(infuncsetfunc->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))))):Prop % We need to prove ['(app->(infuncsetfunc->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % Parameter emptyset:fofType. % Parameter setadjoin:(fofType->(fofType->fofType)). % Parameter powerset:(fofType->fofType). % Parameter setunion:(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))). % Definition funcSet:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf)))):(fofType->(fofType->fofType)). % Definition ap:=(fun (A:fofType) (B:fofType) (Xf:fofType) (Xx:fofType)=> (setunion ((dsetconstr B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))):(fofType->(fofType->(fofType->(fofType->fofType)))). % Definition app:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))):Prop. % Definition infuncsetfunc:=(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))):Prop. % Trying to prove (app->(infuncsetfunc->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))))) % Found x00000:=(x0000 x1):(((func A) B) Xf) % Found (x0000 x1) as proof of (((func A) B) Xf) % Found ((x000 Xf) x1) as proof of (((func A) B) Xf) % Found (((x00 B) Xf) x1) as proof of (((func A) B) Xf) % Found ((((x0 A) B) Xf) x1) as proof of (((func A) B) Xf) % Found ((((x0 A) B) Xf) x1) as proof of (((func A) B) Xf) % Found (x200 ((((x0 A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))) % Found ((x20 Xf) ((((x0 A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))) % Found (((x2 B) Xf) ((((x0 A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))) % Found ((((x A) B) Xf) ((((x0 A) B) Xf) x1)) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))) % Found (fun (x1:((in Xf) ((funcSet A) B)))=> ((((x A) B) Xf) ((((x0 A) B) Xf) x1))) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))) % Found (fun (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x A) B) Xf) ((((x0 A) B) Xf) x1))) as proof of (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))) % Found (fun (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x A) B) Xf) ((((x0 A) B) Xf) x1))) as proof of (forall (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))) % Found (fun (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x A) B) Xf) ((((x0 A) B) Xf) x1))) as proof of (forall (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))) % Found (fun (x0:infuncsetfunc) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x A) B) Xf) ((((x0 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)->((in ((((ap A) B) Xf) Xx)) B))))) % Found (fun (x:app) (x0:infuncsetfunc) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x A) B) Xf) ((((x0 A) B) Xf) x1))) as proof of (infuncsetfunc->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))))) % Found (fun (x:app) (x0:infuncsetfunc) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x A) B) Xf) ((((x0 A) B) Xf) x1))) as proof of (app->(infuncsetfunc->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))))) % Got proof (fun (x:app) (x0:infuncsetfunc) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x A) B) Xf) ((((x0 A) B) Xf) x1))) % Time elapsed = 0.326710s % node=25 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:app) (x0:infuncsetfunc) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B)))=> ((((x A) B) Xf) ((((x0 A) B) Xf) x1))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------