TSTP Solution File: NUM417^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM417^1 : TPTP v7.0.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n142.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 6.23s
% Output : Proof 6.23s
% 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 : NUM417^1 : TPTP v7.0.0. Released v3.6.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n142.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 02:54:14 CST 2018
% 0.02/0.23 % CPUTime :
% 0.08/0.27 Python 2.7.13
% 0.28/0.71 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.28/0.71 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM006^0.ax, trying next directory
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446fb48>, <kernel.DependentProduct object at 0x2b1d7446f170>) of role type named zero
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring zero:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d74449e18>, <kernel.DependentProduct object at 0x2b1d7446fc20>) of role type named one
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring one:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446f5f0>, <kernel.DependentProduct object at 0x2b1d7446f170>) of role type named two
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring two:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446f1b8>, <kernel.DependentProduct object at 0x2b1d7446fc20>) of role type named three
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring three:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d739fc050>, <kernel.DependentProduct object at 0x2b1d7446f950>) of role type named four
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring four:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446f998>, <kernel.DependentProduct object at 0x2b1d7446fb48>) of role type named five
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring five:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d744643f8>, <kernel.DependentProduct object at 0x2b1d7446fcb0>) of role type named six
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring six:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d73da3950>, <kernel.DependentProduct object at 0x2b1d7446fc20>) of role type named seven
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring seven:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446fef0>, <kernel.DependentProduct object at 0x2b1d7446fcb0>) of role type named eight
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring eight:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446ff38>, <kernel.DependentProduct object at 0x2b1d7446fc20>) of role type named nine
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring nine:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446f170>, <kernel.DependentProduct object at 0x2b1d7446fb48>) of role type named ten
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring ten:((fofType->fofType)->(fofType->fofType))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446fcb0>, <kernel.DependentProduct object at 0x2b1d7446ff38>) of role type named succ
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring succ:(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446fc20>, <kernel.DependentProduct object at 0x2b1d739f4098>) of role type named plus
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring plus:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.28/0.71 FOF formula (<kernel.Constant object at 0x2b1d7446fb48>, <kernel.DependentProduct object at 0x2b1d739f4758>) of role type named mult
% 0.28/0.71 Using role type
% 0.28/0.71 Declaring mult:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.28/0.71 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y)) of role definition named zero_ax
% 0.28/0.71 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y))
% 0.28/0.71 Defined: zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y)
% 0.28/0.71 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))) of role definition named one_ax
% 0.28/0.71 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)))
% 0.28/0.71 Defined: one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))
% 0.28/0.71 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))) of role definition named two_ax
% 0.36/0.73 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))))
% 0.36/0.73 Defined: two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))
% 0.36/0.73 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))) of role definition named three_ax
% 0.36/0.73 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))))
% 0.36/0.73 Defined: three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))
% 0.36/0.73 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
% 0.36/0.73 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))))
% 0.36/0.73 Defined: four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))
% 0.36/0.73 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
% 0.36/0.73 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))))
% 0.36/0.73 Defined: five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))
% 0.36/0.73 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
% 0.36/0.73 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))))
% 0.36/0.73 Defined: six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))
% 0.36/0.73 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
% 0.36/0.73 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))))
% 0.36/0.73 Defined: seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))
% 0.36/0.73 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
% 0.36/0.73 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))))
% 0.36/0.73 Defined: eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))
% 0.36/0.73 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
% 0.36/0.73 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)))))))))))
% 0.36/0.73 Defined: nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))
% 0.36/0.73 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
% 0.36/0.73 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))))))))))))
% 0.36/0.73 Defined: ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))
% 0.36/0.73 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
% 0.36/0.73 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))))
% 0.36/0.73 Defined: succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))
% 0.36/0.73 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
% 0.36/0.73 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))))
% 0.36/0.73 Defined: plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))
% 0.36/0.73 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
% 0.36/0.73 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)))
% 0.36/0.73 Defined: mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))
% 0.36/0.73 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ((mult ten) ten)) ((mult ten) ten))) ((mult ((mult ((mult ten) ten)) ten)) ten)) of role conjecture named thm
% 0.36/0.73 Conjecture to prove = (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ((mult ten) ten)) ((mult ten) ten))) ((mult ((mult ((mult ten) ten)) ten)) ten)):Prop
% 0.36/0.73 Parameter fofType_DUMMY:fofType.
% 0.36/0.73 We need to prove ['(((eq ((fofType->fofType)->(fofType->fofType))) ((mult ((mult ten) ten)) ((mult ten) ten))) ((mult ((mult ((mult ten) ten)) ten)) ten))']
% 0.36/0.73 Parameter fofType:Type.
% 0.36/0.73 Definition zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 Definition ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.73 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))).
% 0.36/0.73 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)))).
% 0.36/0.73 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)))).
% 6.23/6.61 Trying to prove (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ((mult ten) ten)) ((mult ten) ten))) ((mult ((mult ((mult ten) ten)) ten)) ten))
% 6.23/6.61 Found eta_expansion000:=(eta_expansion00 ((mult ((mult ten) ten)) ((mult ten) ten))):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult ((mult ten) ten)) ((mult ten) ten))) (fun (x:(fofType->fofType))=> (((mult ((mult ten) ten)) ((mult ten) ten)) x)))
% 6.23/6.61 Found (eta_expansion00 ((mult ((mult ten) ten)) ((mult ten) ten))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ((mult ten) ten)) ((mult ten) ten))) ((mult ((mult ((mult ten) ten)) ten)) ten))
% 6.23/6.61 Found ((eta_expansion0 (fofType->fofType)) ((mult ((mult ten) ten)) ((mult ten) ten))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ((mult ten) ten)) ((mult ten) ten))) ((mult ((mult ((mult ten) ten)) ten)) ten))
% 6.23/6.61 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult ((mult ten) ten)) ((mult ten) ten))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ((mult ten) ten)) ((mult ten) ten))) ((mult ((mult ((mult ten) ten)) ten)) ten))
% 6.23/6.61 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult ((mult ten) ten)) ((mult ten) ten))) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult ((mult ten) ten)) ((mult ten) ten))) ((mult ((mult ((mult ten) ten)) ten)) ten))
% 6.23/6.61 Got proof (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult ((mult ten) ten)) ((mult ten) ten)))
% 6.23/6.61 Time elapsed = 5.787990s
% 6.23/6.61 node=12 cost=-278.000000 depth=3
% 6.23/6.61::::::::::::::::::::::
% 6.23/6.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.23/6.61 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.23/6.61 (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult ((mult ten) ten)) ((mult ten) ten)))
% 6.23/6.61 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------