%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU534^2 : 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 13:32:24 EDT 2014 % Result : Theorem 4.68s % Output : Proof 4.68s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU534^2 : 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 10:32:51 CDT 2014 % % CPUTime : 4.68 % 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 0xf0fa70>, <kernel.DependentProduct object at 0xf0f950>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x12cc098>, <kernel.Single object at 0xf0f908>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0xf0f950>, <kernel.DependentProduct object at 0xf0fbd8>) of role type named dsetconstr_type % Using role type % Declaring dsetconstr:(fofType->((fofType->Prop)->fofType)) % FOF formula (<kernel.Constant object at 0xf0fb90>, <kernel.Sort object at 0xdd5518>) of role type named dsetconstrI_type % Using role type % Declaring dsetconstrI:Prop % FOF formula (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named dsetconstrI % A new definition: (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) % Defined: dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))) % FOF formula (<kernel.Constant object at 0xf0f998>, <kernel.Sort object at 0xdd5518>) of role type named emptysetE_type % Using role type % Declaring emptysetE:Prop % FOF formula (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))) of role definition named emptysetE % A new definition: (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))) % Defined: emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))) % FOF formula (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))))) of role conjecture named emptyE1 % Conjecture to prove = (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))))):Prop % We need to prove ['(dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % Parameter emptyset:fofType. % Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)). % Definition dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))):Prop. % Definition emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))):Prop. % Trying to prove (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))))) % Found x500:=(x50 x3):(((in x3) A)->((Xphi x3)->((in x3) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))) % Found (x50 x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))) % Found ((x5 Xphi) x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))) % Found (((x A) Xphi) x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))) % Found (((x A) Xphi) x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))) % Found (((x A) Xphi) x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))) % Found (x20 (((x A) Xphi) x3)) as proof of (((in x3) A)->((Xphi x3)->((in Xx) emptyset))) % Found ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)) as proof of (((in x3) A)->((Xphi x3)->((in Xx) emptyset))) % Found ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)) as proof of (((in x3) A)->((Xphi x3)->((in Xx) emptyset))) % Found (and_rect00 ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3))) as proof of ((in Xx) emptyset) % Found ((and_rect0 ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3))) as proof of ((in Xx) emptyset) % Found (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3))) as proof of ((in Xx) emptyset) % Found (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3))) as proof of ((in Xx) emptyset) % Found (x000 (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)))) as proof of False % Found (x000 (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)))) as proof of False % Found ((fun (x5:((in Xx) emptyset))=> ((x00 x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)))) as proof of False % Found ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))) as proof of False % Found (fun (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))) as proof of False % Found (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))) as proof of (((and ((in x3) A)) (Xphi x3))->False) % Found (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))) as proof of (forall (x:fofType), (((and ((in x) A)) (Xphi x))->False)) % Found (ex_ind00 (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))))) as proof of False % Found ((ex_ind0 False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))))) as proof of False % Found (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))))) as proof of False % Found (fun (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of False % Found (fun (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of ((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False) % Found (fun (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)) % Found (fun (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))) % Found (fun (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))) % Found (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)))) % Found (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))))) % Got proof (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) % Time elapsed = 4.322874s % node=675 cost=968.000000 depth=28 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------