%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU705^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n117.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 13:32:52 EDT 2014 % Result : Theorem 0.84s % Output : Proof 0.84s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU705^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n117.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 11:15:26 CDT 2014 % % CPUTime : 0.84 % 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 0x251de60>, <kernel.DependentProduct object at 0x251d560>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x28da5f0>, <kernel.Single object at 0x251df80>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0x251d560>, <kernel.DependentProduct object at 0x251df38>) of role type named setadjoin_type % Using role type % Declaring setadjoin:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x251d518>, <kernel.DependentProduct object at 0x251dc20>) of role type named setunion_type % Using role type % Declaring setunion:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x251ddd0>, <kernel.DependentProduct object at 0x251d440>) of role type named dsetconstr_type % Using role type % Declaring dsetconstr:(fofType->((fofType->Prop)->fofType)) % FOF formula (<kernel.Constant object at 0x251dbd8>, <kernel.DependentProduct object at 0x251d518>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x251df38>, <kernel.Sort object at 0x23e5ea8>) of role type named subsetE_type % Using role type % Declaring subsetE:Prop % FOF formula (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))) of role definition named subsetE % A new definition: (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))) % Defined: subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))) % FOF formula (<kernel.Constant object at 0x251d560>, <kernel.Sort object at 0x23e5ea8>) of role type named sepSubset_type % Using role type % Declaring sepSubset:Prop % FOF formula (((eq Prop) sepSubset) (forall (A:fofType) (Xphi:(fofType->Prop)), ((subset ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) A))) of role definition named sepSubset % A new definition: (((eq Prop) sepSubset) (forall (A:fofType) (Xphi:(fofType->Prop)), ((subset ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) A))) % Defined: sepSubset:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((subset ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) A)) % FOF formula (<kernel.Constant object at 0x251d5f0>, <kernel.DependentProduct object at 0x251d440>) 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 0x251d440>, <kernel.Sort object at 0x23e5ea8>) of role type named theprop_type % Using role type % Declaring theprop:Prop % FOF formula (((eq Prop) theprop) (forall (X:fofType), ((singleton X)->((in (setunion X)) X)))) of role definition named theprop % A new definition: (((eq Prop) theprop) (forall (X:fofType), ((singleton X)->((in (setunion X)) X)))) % Defined: theprop:=(forall (X:fofType), ((singleton X)->((in (setunion X)) X))) % FOF formula (<kernel.Constant object at 0x251d4d0>, <kernel.Sort object at 0x23e5ea8>) of role type named ifSingleton_type % Using role type % Declaring ifSingleton:Prop % FOF formula (((eq Prop) ifSingleton) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))) of role definition named ifSingleton % A new definition: (((eq Prop) ifSingleton) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))) % Defined: ifSingleton:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))) % FOF formula (<kernel.Constant object at 0x251ddd0>, <kernel.DependentProduct object at 0x251d560>) of role type named if_type % Using role type % Declaring if:(fofType->(Prop->(fofType->(fofType->fofType)))) % FOF formula (((eq (fofType->(Prop->(fofType->(fofType->fofType))))) if) (fun (A:fofType) (Xphi:Prop) (Xx:fofType) (Xy:fofType)=> (setunion ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))) of role definition named if % A new definition: (((eq (fofType->(Prop->(fofType->(fofType->fofType))))) if) (fun (A:fofType) (Xphi:Prop) (Xx:fofType) (Xy:fofType)=> (setunion ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))) % Defined: if:=(fun (A:fofType) (Xphi:Prop) (Xx:fofType) (Xy:fofType)=> (setunion ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) % FOF formula (subsetE->(sepSubset->(theprop->(ifSingleton->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A))))))))) of role conjecture named ifp % Conjecture to prove = (subsetE->(sepSubset->(theprop->(ifSingleton->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A))))))))):Prop % We need to prove ['(subsetE->(sepSubset->(theprop->(ifSingleton->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A)))))))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % Parameter emptyset:fofType. % Parameter setadjoin:(fofType->(fofType->fofType)). % Parameter setunion:(fofType->fofType). % Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)). % Parameter subset:(fofType->(fofType->Prop)). % Definition subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))):Prop. % Definition sepSubset:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((subset ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) A)):Prop. % Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop). % Definition theprop:=(forall (X:fofType), ((singleton X)->((in (setunion X)) X))):Prop. % Definition ifSingleton:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))):Prop. % Definition if:=(fun (A:fofType) (Xphi:Prop) (Xx:fofType) (Xy:fofType)=> (setunion ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))):(fofType->(Prop->(fofType->(fofType->fofType)))). % Trying to prove (subsetE->(sepSubset->(theprop->(ifSingleton->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A))))))))) % Found x2000000:=(x200000 x4):(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) % Found (x200000 x4) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) % Found ((x20000 Xy) x4) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) % Found (((x2000 x3) Xy) x4) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) % Found ((((x200 Xx) x3) Xy) x4) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) % Found (((((x20 Xphi) Xx) x3) Xy) x4) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) % Found ((((((x2 A) Xphi) Xx) x3) Xy) x4) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) % Found ((((((x2 A) Xphi) Xx) x3) Xy) x4) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) % Found (x10 ((((((x2 A) Xphi) Xx) x3) Xy) x4)) as proof of ((in ((((if A) Xphi) Xx) Xy)) A0) % Found ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)) as proof of ((in ((((if A) Xphi) Xx) Xy)) A0) % Found ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)) as proof of ((in ((((if A) Xphi) Xx) Xy)) A0) % Found ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)) as proof of ((in ((((if A) Xphi) Xx) Xy)) A0) % Found x000:=(x00 (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy))))):((subset ((dsetconstr A) (fun (Xx0:fofType)=> ((or ((and Xphi) (((eq fofType) Xx0) Xx))) ((and (Xphi->False)) (((eq fofType) Xx0) Xy)))))) A) % Found (x00 (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy))))) as proof of ((subset A0) A) % Found ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy))))) as proof of ((subset A0) A) % Found ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy))))) as proof of ((subset A0) A) % Found ((x500 ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4))) as proof of ((in ((((if A) Xphi) Xx) Xy)) A) % Found (((x50 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4))) as proof of ((in ((((if A) Xphi) Xx) Xy)) A) % Found ((((fun (A0:fofType)=> ((x5 A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4))) as proof of ((in ((((if A) Xphi) Xx) Xy)) A) % Found ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4))) as proof of ((in ((((if A) Xphi) Xx) Xy)) A) % Found (fun (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of ((in ((((if A) Xphi) Xx) Xy)) A) % Found (fun (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A)) % Found (fun (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A))) % Found (fun (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A)))) % Found (fun (Xphi:Prop) (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A))))) % Found (fun (A:fofType) (Xphi:Prop) (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (forall (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A))))) % Found (fun (x2:ifSingleton) (A:fofType) (Xphi:Prop) (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A))))) % Found (fun (x1:theprop) (x2:ifSingleton) (A:fofType) (Xphi:Prop) (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (ifSingleton->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A)))))) % Found (fun (x0:sepSubset) (x1:theprop) (x2:ifSingleton) (A:fofType) (Xphi:Prop) (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (theprop->(ifSingleton->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A))))))) % Found (fun (x:subsetE) (x0:sepSubset) (x1:theprop) (x2:ifSingleton) (A:fofType) (Xphi:Prop) (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (sepSubset->(theprop->(ifSingleton->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A)))))))) % Found (fun (x:subsetE) (x0:sepSubset) (x1:theprop) (x2:ifSingleton) (A:fofType) (Xphi:Prop) (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) as proof of (subsetE->(sepSubset->(theprop->(ifSingleton->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((in ((((if A) Xphi) Xx) Xy)) A))))))))) % Got proof (fun (x:subsetE) (x0:sepSubset) (x1:theprop) (x2:ifSingleton) (A:fofType) (Xphi:Prop) (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) % Time elapsed = 0.500729s % node=64 cost=274.000000 depth=17 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:subsetE) (x0:sepSubset) (x1:theprop) (x2:ifSingleton) (A:fofType) (Xphi:Prop) (Xx:fofType) (x3:((in Xx) A)) (Xy:fofType) (x4:((in Xy) A))=> ((((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x A0) A)) A0) ((((if A) Xphi) Xx) Xy))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((x0 A) (fun (x7:fofType)=> ((or ((and Xphi) (((eq fofType) x7) Xx))) ((and (Xphi->False)) (((eq fofType) x7) Xy)))))) ((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((((((x2 A) Xphi) Xx) x3) Xy) x4)))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------