%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU755^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n096.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 13:33:01 EDT 2014 % Result : Theorem 19.50s % Output : Proof 19.50s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU755^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n096.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 11:23:41 CDT 2014 % % CPUTime : 19.50 % 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 0xac4878>, <kernel.DependentProduct object at 0xac4d88>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0xe81488>, <kernel.DependentProduct object at 0xac43f8>) of role type named powerset_type % Using role type % Declaring powerset:(fofType->fofType) % FOF formula (<kernel.Constant object at 0xac44d0>, <kernel.DependentProduct object at 0xac4ab8>) of role type named binunion_type % Using role type % Declaring binunion:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0xac4a70>, <kernel.DependentProduct object at 0xac4878>) of role type named setminus_type % Using role type % Declaring setminus:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0xac4ea8>, <kernel.Sort object at 0x98f098>) of role type named setminusI_type % Using role type % Declaring setminusI:Prop % FOF formula (((eq Prop) setminusI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B)))))) of role definition named setminusI % A new definition: (((eq Prop) setminusI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B)))))) % Defined: setminusI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B))))) % FOF formula (<kernel.Constant object at 0xac4f38>, <kernel.Sort object at 0x98f098>) of role type named setminusER_type % Using role type % Declaring setminusER:Prop % FOF formula (((eq Prop) setminusER) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False)))) of role definition named setminusER % A new definition: (((eq Prop) setminusER) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False)))) % Defined: setminusER:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False))) % FOF formula (<kernel.Constant object at 0xac4b48>, <kernel.Sort object at 0x98f098>) of role type named binunionTEcontra_type % Using role type % Declaring binunionTEcontra:Prop % FOF formula (((eq Prop) binunionTEcontra) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->((((in Xx) X)->False)->((((in Xx) Y)->False)->(((in Xx) ((binunion X) Y))->False)))))))))) of role definition named binunionTEcontra % A new definition: (((eq Prop) binunionTEcontra) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->((((in Xx) X)->False)->((((in Xx) Y)->False)->(((in Xx) ((binunion X) Y))->False)))))))))) % Defined: binunionTEcontra:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->((((in Xx) X)->False)->((((in Xx) Y)->False)->(((in Xx) ((binunion X) Y))->False))))))))) % FOF formula (setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))))) of role conjecture named demorgan2b2 % Conjecture to prove = (setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))))):Prop % Parameter fofType_DUMMY:fofType. % We need to prove ['(setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))))))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % Parameter powerset:(fofType->fofType). % Parameter binunion:(fofType->(fofType->fofType)). % Parameter setminus:(fofType->(fofType->fofType)). % Definition setminusI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B))))):Prop. % Definition setminusER:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False))):Prop. % Definition binunionTEcontra:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->((((in Xx) X)->False)->((((in Xx) Y)->False)->(((in Xx) ((binunion X) Y))->False))))))))):Prop. % Trying to prove (setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))))) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x6:((in Xx) ((setminus A) Y)) % Found x6 as proof of ((in Xx) ((setminus A) Y)) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x2:((in X) (powerset A)) % Found x2 as proof of ((in X) (powerset A)) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x8:((in Xx) ((binunion X) Y)) % Found x8 as proof of ((in Xx) ((binunion X) Y)) % Found x5:((in Xx) ((setminus A) X)) % Found x5 as proof of ((in Xx) ((setminus A) X)) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x2:((in X) (powerset A)) % Found x2 as proof of ((in X) (powerset A)) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x8:((in Xx) ((binunion X) Y)) % Found x8 as proof of ((in Xx) ((binunion X) Y)) % Found x5:((in Xx) ((setminus A) X)) % Found x5 as proof of ((in Xx) ((setminus A) X)) % Found x6:((in Xx) ((setminus A) Y)) % Found x6 as proof of ((in Xx) ((setminus A) Y)) % Found x2:((in X) (powerset A)) % Found x2 as proof of ((in X) (powerset A)) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x5:((in Xx) ((setminus A) X)) % Found x5 as proof of ((in Xx) ((setminus A) X)) % Found x6:((in Xx) ((setminus A) Y)) % Found x6 as proof of ((in Xx) ((setminus A) Y)) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x6:((in Xx) ((setminus A) Y)) % Found x6 as proof of ((in Xx) ((setminus A) Y)) % Found x4:((in Xx) A) % Found x4 as proof of ((in Xx) A) % Found x2:((in X) (powerset A)) % Found x2 as proof of ((in X) (powerset A)) % Found x3:((in Y) (powerset A)) % Found x3 as proof of ((in Y) (powerset A)) % Found x5:((in Xx) ((setminus A) X)) % Found x5 as proof of ((in Xx) ((setminus A) X)) % Found x00000:=(x0000 x6):(((in Xx) Y)->False) % Found (x0000 x6) as proof of (((in Xx) Y)->False) % Found ((x000 A) x6) as proof of (((in Xx) Y)->False) % Found (((fun (A0:fofType)=> ((x00 A0) Xx)) A) x6) as proof of (((in Xx) Y)->False) % Found (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6) as proof of (((in Xx) Y)->False) % Found (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6) as proof of (((in Xx) Y)->False) % Found x00000:=(x0000 x5):(((in Xx) X)->False) % Found (x0000 x5) as proof of (((in Xx) X)->False) % Found ((x000 A) x5) as proof of (((in Xx) X)->False) % Found (((fun (A0:fofType)=> ((x00 A0) Xx)) A) x5) as proof of (((in Xx) X)->False) % Found (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5) as proof of (((in Xx) X)->False) % Found (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5) as proof of (((in Xx) X)->False) % Found (((((x1000 x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)) as proof of False % Found ((((((x100 A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)) as proof of False % Found (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> (((((((x10 A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)) as proof of False % Found (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)) as proof of False % Found (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))) as proof of False % Found (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))) as proof of (((in Xx) ((binunion X) Y))->False) % Found ((x700 x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))) as proof of ((in Xx) ((setminus A) ((binunion X) Y))) % Found (((x70 Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))) as proof of ((in Xx) ((setminus A) ((binunion X) Y))) % Found ((((x7 ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))) as proof of ((in Xx) ((setminus A) ((binunion X) Y))) % Found (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6)))) as proof of ((in Xx) ((setminus A) ((binunion X) Y))) % Found (fun (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of ((in Xx) ((setminus A) ((binunion X) Y))) % Found (fun (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))) % Found (fun (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))) % Found (fun (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))) % Found (fun (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))) % Found (fun (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))) % Found (fun (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))) % Found (fun (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))) % Found (fun (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (forall (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))))) % Found (fun (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))))) % Found (fun (x0:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))) % Found (fun (x:setminusI) (x0:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y))))))))))))) % Found (fun (x:setminusI) (x0:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) as proof of (setminusI->(setminusER->(binunionTEcontra->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) X))->(((in Xx) ((setminus A) Y))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))))) % Got proof (fun (x:setminusI) (x0:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) % Time elapsed = 19.047652s % node=3357 cost=1466.000000 depth=27 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:setminusI) (x0:setminusER) (x1:binunionTEcontra) (A:fofType) (X:fofType) (x2:((in X) (powerset A))) (Y:fofType) (x3:((in Y) (powerset A))) (Xx:fofType) (x4:((in Xx) A)) (x5:((in Xx) ((setminus A) X))) (x6:((in Xx) ((setminus A) Y)))=> (((((x A) ((binunion X) Y)) Xx) x4) (fun (x8:((in Xx) ((binunion X) Y)))=> (((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x100:((in Y) (powerset A0))) (x11:((in Xx) A0)) (x12:(((in Xx) X)->False)) (x13:(((in Xx) Y)->False))=> ((((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((((x1 A0) X) x9) Y) x10) Xx)) A0) x9) x100) x11) x12) x13) x8)) A) x2) x3) x4) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) X)) A0) Xx)) A) x5)) (((fun (A0:fofType)=> (((fun (A0:fofType)=> ((x0 A0) Y)) A0) Xx)) A) x6))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------