%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU679^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n092.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 0.46s % Output : Proof 0.46s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU679^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n092.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 11:08:51 CDT 2014 % % CPUTime : 0.46 % 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 0x214a8c0>, <kernel.DependentProduct object at 0x214a5f0>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x2002cb0>, <kernel.Single object at 0x214ab00>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0x214a5f0>, <kernel.DependentProduct object at 0x214a170>) of role type named setadjoin_type % Using role type % Declaring setadjoin:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x214a128>, <kernel.DependentProduct object at 0x214a560>) of role type named dsetconstr_type % Using role type % Declaring dsetconstr:(fofType->((fofType->Prop)->fofType)) % FOF formula (<kernel.Constant object at 0x214afc8>, <kernel.DependentProduct object at 0x214a5f0>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x214a2d8>, <kernel.DependentProduct object at 0x214a128>) of role type named kpair_type % Using role type % Declaring kpair:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x214ac20>, <kernel.DependentProduct object at 0x214afc8>) of role type named cartprod_type % Using role type % Declaring cartprod:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x214a170>, <kernel.DependentProduct object at 0x214ab90>) 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 0x214ab90>, <kernel.DependentProduct object at 0x214a758>) 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 0x214a758>, <kernel.DependentProduct object at 0x214ae18>) 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 0x214acb0>, <kernel.DependentProduct object at 0x214a3b0>) of role type named dpsetconstr_type % Using role type % Declaring dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType))) % FOF formula (<kernel.Constant object at 0x214afc8>, <kernel.DependentProduct object at 0x214a128>) 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 0x214a560>, <kernel.Sort object at 0x1c391b8>) of role type named lamProp_type % Using role type % Declaring lamProp:Prop % FOF formula (((eq Prop) lamProp) (forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy))))))) of role definition named lamProp % A new definition: (((eq Prop) lamProp) (forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy))))))) % Defined: lamProp:=(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy)))))) % FOF formula (<kernel.Constant object at 0x214acb0>, <kernel.DependentProduct object at 0x214a908>) of role type named lam_type % Using role type % Declaring lam:(fofType->(fofType->((fofType->fofType)->fofType))) % FOF formula (((eq (fofType->(fofType->((fofType->fofType)->fofType)))) lam) (fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy))))) of role definition named lam % A new definition: (((eq (fofType->(fofType->((fofType->fofType)->fofType)))) lam) (fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy))))) % Defined: lam:=(fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy)))) % FOF formula (lamProp->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx))))))) of role conjecture named lamp % Conjecture to prove = (lamProp->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx))))))):Prop % We need to prove ['(lamProp->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx)))))))'] % 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))). % Parameter dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType))). % 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 lamProp:=(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy)))))):Prop. % Definition lam:=(fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy)))):(fofType->(fofType->((fofType->fofType)->fofType))). % Trying to prove (lamProp->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx))))))) % Found x:lamProp % Found (fun (x:lamProp)=> x) as proof of (forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx)))))) % Found (fun (x:lamProp)=> x) as proof of (lamProp->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx))))))) % Got proof (fun (x:lamProp)=> x) % Time elapsed = 0.104247s % node=1 cost=3.000000 depth=1 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:lamProp)=> x) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------