%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : NUM416^1 : TPTP v7.0.0. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p % Computer : n135.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32218.625MB % OS : Linux 3.10.0-693.2.2.el7.x86_64 % CPULimit : 300s % DateTime : Mon Jan 8 13:10:42 EST 2018 % Result : Theorem 2.48s % Output : Proof 2.48s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : NUM416^1 : TPTP v7.0.0. Released v3.6.0. % 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.03/0.23 % Computer : n135.star.cs.uiowa.edu % 0.03/0.23 % Model : x86_64 x86_64 % 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % 0.03/0.23 % Memory : 32218.625MB % 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 % 0.03/0.23 % CPULimit : 300 % 0.03/0.23 % DateTime : Fri Jan 5 02:54:15 CST 2018 % 0.03/0.23 % CPUTime : % 0.08/0.28 Python 2.7.13 % 0.29/0.76 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/'] % 0.29/0.76 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM006^0.ax, trying next directory % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07c3c68>, <kernel.DependentProduct object at 0x2b10f0aaa098>) of role type named zero % 0.29/0.76 Using role type % 0.29/0.76 Declaring zero:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f0aaabd8>, <kernel.DependentProduct object at 0x2b10f07c3c68>) of role type named one % 0.29/0.76 Using role type % 0.29/0.76 Declaring one:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f0b60710>, <kernel.DependentProduct object at 0x2b10f07bd368>) of role type named two % 0.29/0.76 Using role type % 0.29/0.76 Declaring two:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f0aaabd8>, <kernel.DependentProduct object at 0x2b10f07bd908>) of role type named three % 0.29/0.76 Using role type % 0.29/0.76 Declaring three:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f0aaabd8>, <kernel.DependentProduct object at 0x2b10f07bd638>) of role type named four % 0.29/0.76 Using role type % 0.29/0.76 Declaring four:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07c3830>, <kernel.DependentProduct object at 0x2b10f07bd200>) of role type named five % 0.29/0.76 Using role type % 0.29/0.76 Declaring five:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07c3c68>, <kernel.DependentProduct object at 0x2b10f07bd908>) of role type named six % 0.29/0.76 Using role type % 0.29/0.76 Declaring six:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07c3830>, <kernel.DependentProduct object at 0x2b10f07bd200>) of role type named seven % 0.29/0.76 Using role type % 0.29/0.76 Declaring seven:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07c3830>, <kernel.DependentProduct object at 0x2b10f07bd908>) of role type named eight % 0.29/0.76 Using role type % 0.29/0.76 Declaring eight:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07bdab8>, <kernel.DependentProduct object at 0x2b10f07bd200>) of role type named nine % 0.29/0.76 Using role type % 0.29/0.76 Declaring nine:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07bda70>, <kernel.DependentProduct object at 0x2b10f07bd908>) of role type named ten % 0.29/0.76 Using role type % 0.29/0.76 Declaring ten:((fofType->fofType)->(fofType->fofType)) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07bd8c0>, <kernel.DependentProduct object at 0x2b10f07bd518>) of role type named succ % 0.29/0.76 Using role type % 0.29/0.76 Declaring succ:(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07bd098>, <kernel.DependentProduct object at 0x2b10f07bd320>) of role type named plus % 0.29/0.76 Using role type % 0.29/0.76 Declaring plus:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) % 0.29/0.76 FOF formula (<kernel.Constant object at 0x2b10f07c70e0>, <kernel.DependentProduct object at 0x2b10f07bdab8>) of role type named mult % 0.29/0.76 Using role type % 0.29/0.76 Declaring mult:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) % 0.29/0.76 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y)) of role definition named zero_ax % 0.29/0.76 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y)) % 0.29/0.76 Defined: zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y) % 0.29/0.76 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))) of role definition named one_ax % 0.29/0.76 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))) % 0.29/0.76 Defined: one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)) % 0.29/0.76 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))) of role definition named two_ax % 0.29/0.78 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))) % 0.29/0.78 Defined: two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))) % 0.29/0.78 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))) of role definition named three_ax % 0.29/0.78 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))) % 0.29/0.78 Defined: three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))) % 0.29/0.78 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))) of role definition named four_ax % 0.29/0.78 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))) % 0.29/0.78 Defined: four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))) % 0.29/0.78 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))) of role definition named five_ax % 0.29/0.78 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))) % 0.29/0.78 Defined: five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))) % 0.29/0.78 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))) of role definition named six_ax % 0.29/0.78 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))) % 0.29/0.78 Defined: six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))) % 0.29/0.78 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))) of role definition named seven_ax % 0.29/0.78 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))) % 0.29/0.78 Defined: seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))) % 0.29/0.78 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))) of role definition named eight_ax % 0.29/0.78 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))) % 0.29/0.78 Defined: eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))) % 0.29/0.78 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) nine) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))) of role definition named nine_ax % 0.29/0.78 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) nine) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))) % 0.29/0.78 Defined: nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))) % 0.29/0.78 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) ten) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))) of role definition named ten_ax % 0.29/0.78 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) ten) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))) % 0.29/0.78 Defined: ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))) % 0.29/0.78 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) succ) (fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))) of role definition named succ_ax % 0.29/0.78 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) succ) (fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))) % 0.29/0.78 Defined: succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y))) % 0.29/0.78 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) plus) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))) of role definition named plus_ax % 0.29/0.78 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) plus) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))) % 0.29/0.78 Defined: plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y))) % 0.29/0.78 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) mult) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))) of role definition named mult_ax % 0.29/0.78 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) mult) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))) % 0.29/0.78 Defined: mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y)) % 0.29/0.78 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ten) ((mult ten) ten))) ((mult ((plus ten) ten)) ((mult five) ten))) of role conjecture named thm % 0.29/0.78 Conjecture to prove = (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ten) ((mult ten) ten))) ((mult ((plus ten) ten)) ((mult five) ten))):Prop % 0.29/0.78 Parameter fofType_DUMMY:fofType. % 0.29/0.78 We need to prove ['(((eq ((fofType->fofType)->(fofType->fofType))) ((mult ten) ((mult ten) ten))) ((mult ((plus ten) ten)) ((mult five) ten)))'] % 0.29/0.78 Parameter fofType:Type. % 0.29/0.78 Definition zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))):((fofType->fofType)->(fofType->fofType)). % 0.29/0.78 Definition succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y))):(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))). % 0.29/0.78 Definition plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y))):(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))). % 0.29/0.78 Definition mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y)):(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))). % 2.48/2.91 Trying to prove (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ten) ((mult ten) ten))) ((mult ((plus ten) ten)) ((mult five) ten))) % 2.48/2.91 Found eta_expansion000:=(eta_expansion00 ((mult ten) ((mult ten) ten))):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult ten) ((mult ten) ten))) (fun (x:(fofType->fofType))=> (((mult ten) ((mult ten) ten)) x))) % 2.48/2.91 Found (eta_expansion00 ((mult ten) ((mult ten) ten))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ten) ((mult ten) ten))) ((mult ((plus ten) ten)) ((mult five) ten))) % 2.48/2.91 Found ((eta_expansion0 (fofType->fofType)) ((mult ten) ((mult ten) ten))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ten) ((mult ten) ten))) ((mult ((plus ten) ten)) ((mult five) ten))) % 2.48/2.91 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult ten) ((mult ten) ten))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ten) ((mult ten) ten))) ((mult ((plus ten) ten)) ((mult five) ten))) % 2.48/2.91 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult ten) ((mult ten) ten))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ten) ((mult ten) ten))) ((mult ((plus ten) ten)) ((mult five) ten))) % 2.48/2.91 Got proof (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult ten) ((mult ten) ten))) % 2.48/2.91 Time elapsed = 2.080427s % 2.48/2.91 node=12 cost=-276.000000 depth=3 % 2.48/2.91:::::::::::::::::::::: % 2.48/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 2.48/2.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p % 2.48/2.91 (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult ten) ((mult ten) ten))) % 2.48/2.91 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p %------------------------------------------------------------------------------