TSTP Solution File: NUM636^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM636^2 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n068.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 13:11:14 EST 2018
% Result : Theorem 2.16s
% Output : Proof 2.16s
% 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 : NUM636^2 : TPTP v7.0.0. Released v3.7.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.24 % Computer : n068.star.cs.uiowa.edu
% 0.03/0.24 % Model : x86_64 x86_64
% 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.24 % Memory : 32218.625MB
% 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.24 % CPULimit : 300
% 0.03/0.24 % DateTime : Fri Jan 5 11:15:30 CST 2018
% 0.03/0.24 % CPUTime :
% 0.08/0.27 Python 2.7.13
% 2.16/2.54 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 2.16/2.54 FOF formula (<kernel.Constant object at 0x2b69b611eef0>, <kernel.Constant object at 0x2b69b611e098>) of role type named one_type
% 2.16/2.54 Using role type
% 2.16/2.54 Declaring one:fofType
% 2.16/2.54 FOF formula (<kernel.Constant object at 0x2b69b56a6ea8>, <kernel.DependentProduct object at 0x2b69b611cb90>) of role type named succ_type
% 2.16/2.54 Using role type
% 2.16/2.54 Declaring succ:(fofType->fofType)
% 2.16/2.54 FOF formula (forall (X:fofType), (not (((eq fofType) (succ X)) one))) of role axiom named one_is_first
% 2.16/2.54 A new axiom: (forall (X:fofType), (not (((eq fofType) (succ X)) one)))
% 2.16/2.54 FOF formula (forall (X:fofType) (Y:fofType), ((((eq fofType) (succ X)) (succ Y))->(((eq fofType) X) Y))) of role axiom named succ_injective
% 2.16/2.54 A new axiom: (forall (X:fofType) (Y:fofType), ((((eq fofType) (succ X)) (succ Y))->(((eq fofType) X) Y)))
% 2.16/2.54 FOF formula (forall (M:(fofType->Prop)), (((and (M one)) (forall (X:fofType), ((M X)->(M (succ X)))))->(forall (Y:fofType), (M Y)))) of role axiom named induction
% 2.16/2.54 A new axiom: (forall (M:(fofType->Prop)), (((and (M one)) (forall (X:fofType), ((M X)->(M (succ X)))))->(forall (Y:fofType), (M Y))))
% 2.16/2.54 FOF formula (forall (X:fofType), (not (((eq fofType) (succ X)) X))) of role conjecture named satz2
% 2.16/2.54 Conjecture to prove = (forall (X:fofType), (not (((eq fofType) (succ X)) X))):Prop
% 2.16/2.54 We need to prove ['(forall (X:fofType), (not (((eq fofType) (succ X)) X)))']
% 2.16/2.54 Parameter fofType:Type.
% 2.16/2.54 Parameter one:fofType.
% 2.16/2.54 Parameter succ:(fofType->fofType).
% 2.16/2.54 Axiom one_is_first:(forall (X:fofType), (not (((eq fofType) (succ X)) one))).
% 2.16/2.54 Axiom succ_injective:(forall (X:fofType) (Y:fofType), ((((eq fofType) (succ X)) (succ Y))->(((eq fofType) X) Y))).
% 2.16/2.54 Axiom induction:(forall (M:(fofType->Prop)), (((and (M one)) (forall (X:fofType), ((M X)->(M (succ X)))))->(forall (Y:fofType), (M Y)))).
% 2.16/2.54 Trying to prove (forall (X:fofType), (not (((eq fofType) (succ X)) X)))
% 2.16/2.54 Found one_is_first0:=(one_is_first one):(not (((eq fofType) (succ one)) one))
% 2.16/2.54 Found (one_is_first one) as proof of (not (((eq fofType) (succ one)) one))
% 2.16/2.54 Found (one_is_first one) as proof of (not (((eq fofType) (succ one)) one))
% 2.16/2.54 Found succ_injective000:=(succ_injective00 x0):(((eq fofType) (succ X0)) X0)
% 2.16/2.54 Found (succ_injective00 x0) as proof of (((eq fofType) (succ X0)) X0)
% 2.16/2.54 Found ((succ_injective0 X0) x0) as proof of (((eq fofType) (succ X0)) X0)
% 2.16/2.54 Found (((succ_injective (succ X0)) X0) x0) as proof of (((eq fofType) (succ X0)) X0)
% 2.16/2.54 Found (((succ_injective (succ X0)) X0) x0) as proof of (((eq fofType) (succ X0)) X0)
% 2.16/2.54 Found (x (((succ_injective (succ X0)) X0) x0)) as proof of False
% 2.16/2.54 Found (fun (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0))) as proof of False
% 2.16/2.54 Found (fun (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0))) as proof of (not (((eq fofType) (succ (succ X0))) (succ X0)))
% 2.16/2.54 Found (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0))) as proof of ((not (((eq fofType) (succ X0)) X0))->(not (((eq fofType) (succ (succ X0))) (succ X0))))
% 2.16/2.54 Found (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0))) as proof of (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X)))))
% 2.16/2.54 Found ((conj00 (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0)))) as proof of ((and (not (((eq fofType) (succ one)) one))) (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X))))))
% 2.16/2.54 Found (((conj0 (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0)))) as proof of ((and (not (((eq fofType) (succ one)) one))) (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X))))))
% 2.16/2.55 Found ((((conj (not (((eq fofType) (succ one)) one))) (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0)))) as proof of ((and (not (((eq fofType) (succ one)) one))) (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X))))))
% 2.16/2.55 Found ((((conj (not (((eq fofType) (succ one)) one))) (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0)))) as proof of ((and (not (((eq fofType) (succ one)) one))) (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X))))))
% 2.16/2.55 Found (induction00 ((((conj (not (((eq fofType) (succ one)) one))) (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0))))) as proof of (not (((eq fofType) (succ X)) X))
% 2.16/2.55 Found ((induction0 (fun (x0:fofType)=> (not (((eq fofType) (succ x0)) x0)))) ((((conj (not (((eq fofType) (succ one)) one))) (forall (X:fofType), ((not (((eq fofType) (succ X)) X))->(not (((eq fofType) (succ (succ X))) (succ X)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0))))) as proof of (not (((eq fofType) (succ X)) X))
% 2.16/2.55 Found (((fun (M:(fofType->Prop)) (x:((and (M one)) (forall (X:fofType), ((M X)->(M (succ X))))))=> (((induction M) x) X)) (fun (x0:fofType)=> (not (((eq fofType) (succ x0)) x0)))) ((((conj (not (((eq fofType) (succ one)) one))) (forall (X0:fofType), ((not (((eq fofType) (succ X0)) X0))->(not (((eq fofType) (succ (succ X0))) (succ X0)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0))))) as proof of (not (((eq fofType) (succ X)) X))
% 2.16/2.55 Found (fun (X:fofType)=> (((fun (M:(fofType->Prop)) (x:((and (M one)) (forall (X:fofType), ((M X)->(M (succ X))))))=> (((induction M) x) X)) (fun (x0:fofType)=> (not (((eq fofType) (succ x0)) x0)))) ((((conj (not (((eq fofType) (succ one)) one))) (forall (X0:fofType), ((not (((eq fofType) (succ X0)) X0))->(not (((eq fofType) (succ (succ X0))) (succ X0)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0)))))) as proof of (not (((eq fofType) (succ X)) X))
% 2.16/2.55 Found (fun (X:fofType)=> (((fun (M:(fofType->Prop)) (x:((and (M one)) (forall (X:fofType), ((M X)->(M (succ X))))))=> (((induction M) x) X)) (fun (x0:fofType)=> (not (((eq fofType) (succ x0)) x0)))) ((((conj (not (((eq fofType) (succ one)) one))) (forall (X0:fofType), ((not (((eq fofType) (succ X0)) X0))->(not (((eq fofType) (succ (succ X0))) (succ X0)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0)))))) as proof of (forall (X:fofType), (not (((eq fofType) (succ X)) X)))
% 2.16/2.55 Got proof (fun (X:fofType)=> (((fun (M:(fofType->Prop)) (x:((and (M one)) (forall (X:fofType), ((M X)->(M (succ X))))))=> (((induction M) x) X)) (fun (x0:fofType)=> (not (((eq fofType) (succ x0)) x0)))) ((((conj (not (((eq fofType) (succ one)) one))) (forall (X0:fofType), ((not (((eq fofType) (succ X0)) X0))->(not (((eq fofType) (succ (succ X0))) (succ X0)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0))))))
% 2.16/2.56 Time elapsed = 1.820267s
% 2.16/2.56 node=322 cost=341.000000 depth=17
% 2.16/2.56::::::::::::::::::::::
% 2.16/2.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.16/2.56 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.16/2.56 (fun (X:fofType)=> (((fun (M:(fofType->Prop)) (x:((and (M one)) (forall (X:fofType), ((M X)->(M (succ X))))))=> (((induction M) x) X)) (fun (x0:fofType)=> (not (((eq fofType) (succ x0)) x0)))) ((((conj (not (((eq fofType) (succ one)) one))) (forall (X0:fofType), ((not (((eq fofType) (succ X0)) X0))->(not (((eq fofType) (succ (succ X0))) (succ X0)))))) (one_is_first one)) (fun (X0:fofType) (x:(not (((eq fofType) (succ X0)) X0))) (x0:(((eq fofType) (succ (succ X0))) (succ X0)))=> (x (((succ_injective (succ X0)) X0) x0))))))
% 2.16/2.56 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------