TSTP Solution File: PUZ121^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : PUZ121^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n123.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 2.6.32-504.8.1.el6.x86_64
% CPULimit : 300s
% DateTime : Wed May 6 14:22:31 EDT 2015
% Result : Unknown 231.64s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ121^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.01/1.06 % Computer : n123.star.cs.uiowa.edu
% 0.01/1.06 % Model : x86_64 x86_64
% 0.01/1.06 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.01/1.06 % Memory : 32286.75MB
% 0.01/1.06 % OS : Linux 2.6.32-504.8.1.el6.x86_64
% 0.01/1.06 % CPULimit : 300
% 0.01/1.06 % DateTime : Thu Apr 16 11:47:32 CDT 2015
% 0.01/1.06 % CPUTime :
% 0.01/1.08 Python 2.7.5
% 0.04/1.39 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.04/1.39 FOF formula (<kernel.Constant object at 0x1e3ba70>, <kernel.Constant object at 0x1e3b368>) of role type named c1_type
% 0.04/1.39 Using role type
% 0.04/1.39 Declaring c1:fofType
% 0.04/1.39 FOF formula (<kernel.Constant object at 0x1e3bcb0>, <kernel.DependentProduct object at 0x1cd6e18>) of role type named s_type
% 0.04/1.39 Using role type
% 0.04/1.39 Declaring s:(fofType->fofType)
% 0.04/1.39 FOF formula (<kernel.Constant object at 0x1e44f38>, <kernel.DependentProduct object at 0x1cd6ea8>) of role type named cCKB_BLACK_type
% 0.04/1.39 Using role type
% 0.04/1.39 Declaring cCKB_BLACK:(fofType->(fofType->Prop))
% 0.04/1.39 FOF formula (<kernel.Constant object at 0x1e3b368>, <kernel.DependentProduct object at 0x1cd6560>) of role type named cCKB_EVEN_type
% 0.04/1.39 Using role type
% 0.04/1.39 Declaring cCKB_EVEN:(fofType->Prop)
% 0.04/1.39 FOF formula (<kernel.Constant object at 0x1e3b128>, <kernel.DependentProduct object at 0x1cd65a8>) of role type named cCKB_ODD_type
% 0.04/1.39 Using role type
% 0.04/1.39 Declaring cCKB_ODD:(fofType->Prop)
% 0.04/1.39 FOF formula (((eq (fofType->Prop)) cCKB_EVEN) (fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) (s c1))) (((eq fofType) Xx) (s (s (s c1)))))) (((eq fofType) Xx) (s (s (s (s (s c1)))))))) (((eq fofType) Xx) (s (s (s (s (s (s (s c1))))))))))) of role definition named cCKB_EVEN_def
% 0.04/1.39 A new definition: (((eq (fofType->Prop)) cCKB_EVEN) (fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) (s c1))) (((eq fofType) Xx) (s (s (s c1)))))) (((eq fofType) Xx) (s (s (s (s (s c1)))))))) (((eq fofType) Xx) (s (s (s (s (s (s (s c1)))))))))))
% 0.04/1.39 Defined: cCKB_EVEN:=(fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) (s c1))) (((eq fofType) Xx) (s (s (s c1)))))) (((eq fofType) Xx) (s (s (s (s (s c1)))))))) (((eq fofType) Xx) (s (s (s (s (s (s (s c1))))))))))
% 0.04/1.39 FOF formula (((eq (fofType->Prop)) cCKB_ODD) (fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) c1)) (((eq fofType) Xx) (s (s c1))))) (((eq fofType) Xx) (s (s (s (s c1))))))) (((eq fofType) Xx) (s (s (s (s (s (s c1)))))))))) of role definition named cCKB_ODD_def
% 0.04/1.39 A new definition: (((eq (fofType->Prop)) cCKB_ODD) (fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) c1)) (((eq fofType) Xx) (s (s c1))))) (((eq fofType) Xx) (s (s (s (s c1))))))) (((eq fofType) Xx) (s (s (s (s (s (s c1))))))))))
% 0.04/1.39 Defined: cCKB_ODD:=(fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) c1)) (((eq fofType) Xx) (s (s c1))))) (((eq fofType) Xx) (s (s (s (s c1))))))) (((eq fofType) Xx) (s (s (s (s (s (s c1)))))))))
% 0.04/1.39 FOF formula (((eq (fofType->(fofType->Prop))) cCKB_BLACK) (fun (Xu:fofType) (Xv:fofType)=> ((or ((and (cCKB_ODD Xu)) (cCKB_ODD Xv))) ((and (cCKB_EVEN Xu)) (cCKB_EVEN Xv))))) of role definition named cCKB_BLACK_def
% 0.04/1.39 A new definition: (((eq (fofType->(fofType->Prop))) cCKB_BLACK) (fun (Xu:fofType) (Xv:fofType)=> ((or ((and (cCKB_ODD Xu)) (cCKB_ODD Xv))) ((and (cCKB_EVEN Xu)) (cCKB_EVEN Xv)))))
% 0.04/1.39 Defined: cCKB_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> ((or ((and (cCKB_ODD Xu)) (cCKB_ODD Xv))) ((and (cCKB_EVEN Xu)) (cCKB_EVEN Xv))))
% 0.04/1.39 FOF formula (forall (Xu:fofType) (Xv:fofType), (((cCKB_BLACK Xu) Xv)->((and ((and ((cCKB_BLACK (s Xu)) (s Xv))) ((cCKB_BLACK Xu) (s (s Xv))))) ((cCKB_BLACK (s (s Xu))) Xv)))) of role conjecture named cCKB_L11000
% 0.04/1.39 Conjecture to prove = (forall (Xu:fofType) (Xv:fofType), (((cCKB_BLACK Xu) Xv)->((and ((and ((cCKB_BLACK (s Xu)) (s Xv))) ((cCKB_BLACK Xu) (s (s Xv))))) ((cCKB_BLACK (s (s Xu))) Xv)))):Prop
% 0.04/1.39 We need to prove ['(forall (Xu:fofType) (Xv:fofType), (((cCKB_BLACK Xu) Xv)->((and ((and ((cCKB_BLACK (s Xu)) (s Xv))) ((cCKB_BLACK Xu) (s (s Xv))))) ((cCKB_BLACK (s (s Xu))) Xv))))']
% 0.04/1.39 Parameter fofType:Type.
% 0.04/1.39 Parameter c1:fofType.
% 0.04/1.39 Parameter s:(fofType->fofType).
% 0.04/1.39 Definition cCKB_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> ((or ((and (cCKB_ODD Xu)) (cCKB_ODD Xv))) ((and (cCKB_EVEN Xu)) (cCKB_EVEN Xv)))):(fofType->(fofType->Prop)).
% 0.04/1.39 Definition cCKB_EVEN:=(fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) (s c1))) (((eq fofType) Xx) (s (s (s c1)))))) (((eq fofType) Xx) (s (s (s (s (s c1)))))))) (((eq fofType) Xx) (s (s (s (s (s (s (s c1)))))))))):(fofType->Prop).
% 0.04/1.39 Definition cCKB_ODD:=(fun (Xx:fofType)=> ((or ((or ((or (((eq fofType) Xx) c1)) (((eq fofType) Xx) (s (s c1))))) (((eq fofType) Xx) (s (s (s (s c1))))))) (((eq fofType) Xx) (s (s (s (s (s (s c1))))))))):(fofType->Prop).
% 123.12/124.30 Trying to prove (forall (Xu:fofType) (Xv:fofType), (((cCKB_BLACK Xu) Xv)->((and ((and ((cCKB_BLACK (s Xu)) (s Xv))) ((cCKB_BLACK Xu) (s (s Xv))))) ((cCKB_BLACK (s (s Xu))) Xv))))
% 123.12/124.30 Found eq_ref00:=(eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)):(((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) ((cCKB_BLACK (s (s Xu))) Xv))
% 123.12/124.30 Found (eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found eq_ref00:=(eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)):(((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) ((cCKB_BLACK (s (s Xu))) Xv))
% 123.12/124.30 Found (eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found eq_ref00:=(eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)):(((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) ((cCKB_BLACK (s (s Xu))) Xv))
% 123.12/124.30 Found (eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found eq_ref00:=(eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)):(((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) ((cCKB_BLACK (s (s Xu))) Xv))
% 123.12/124.30 Found (eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found eq_ref00:=(eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)):(((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) ((cCKB_BLACK (s (s Xu))) Xv))
% 123.12/124.30 Found (eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found eq_ref00:=(eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)):(((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) ((cCKB_BLACK (s (s Xu))) Xv))
% 123.12/124.30 Found (eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found eq_ref00:=(eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)):(((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) ((cCKB_BLACK (s (s Xu))) Xv))
% 123.12/124.30 Found (eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 123.12/124.30 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 231.64/232.78 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 231.64/232.78 Found eq_ref00:=(eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)):(((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) ((cCKB_BLACK (s (s Xu))) Xv))
% 231.64/232.78 Found (eq_ref0 ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 231.64/232.78 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 231.64/232.78 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 231.64/232.78 Found ((eq_ref Prop) ((cCKB_BLACK (s (s Xu))) Xv)) as proof of (((eq Prop) ((cCKB_BLACK (s (s Xu))) Xv)) b)
% 231.64/232.78 Found x2:(cCKB_EVEN Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_EVEN Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_ODD Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_ODD Xv)
% 231.64/232.78 Found x2:(cCKB_EVEN Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_EVEN Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_ODD Xv)
% 231.64/232.78 Found x2:(cCKB_EVEN Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_EVEN Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_ODD Xv)
% 231.64/232.78 Found x2:(cCKB_EVEN Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_EVEN Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_ODD Xv)
% 231.64/232.78 Found x2:(cCKB_EVEN Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_EVEN Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_ODD Xv)
% 231.64/232.78 Found x2:(cCKB_EVEN Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_EVEN Xv)
% 231.64/232.78 Found x2:(cCKB_EVEN Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_EVEN Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_ODD Xv)
% 231.64/232.78 Found x2:(cCKB_EVEN Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_EVEN Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_ODD Xv)
% 231.64/232.78 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 231.64/232.78 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 231.64/232.78 Found or_comm_i as proof of b
% 231.64/232.78 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 231.64/232.78 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 231.64/232.78 Found or_comm_i as proof of b
% 231.64/232.78 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 231.64/232.78 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 231.64/232.78 Found or_comm_i as proof of b
% 231.64/232.78 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 231.64/232.78 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 231.64/232.78 Found or_comm_i as proof of b
% 231.64/232.78 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 231.64/232.78 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 231.64/232.78 Found or_comm_i as proof of b
% 231.64/232.78 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 231.64/232.78 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 231.64/232.78 Found or_comm_i as proof of b
% 231.64/232.78 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 231.64/232.78 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 231.64/232.78 Found or_comm_i as proof of b
% 231.64/232.78 Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 231.64/232.78 Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% 231.64/232.78 Found or_comm_i as proof of b
% 231.64/232.78 Found x2:(cCKB_EVEN Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_EVEN Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 as proof of (cCKB_ODD Xv)
% 231.64/232.78 Found x2:(cCKB_ODD Xv)
% 231.64/232.78 Found x2 a
%------------------------------------------------------------------------------