TSTP Solution File: SET014^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET014^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n184.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 13:29:55 EDT 2014
% Result : Theorem 0.54s
% Output : Proof 0.54s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET014^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n184.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 07:40:11 CDT 2014
% % CPUTime : 0.54
% 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 0x2288638>, <kernel.Type object at 0x22889e0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->(forall (Xx:a), (((or (X Xx)) (Y Xx))->(Z Xx))))) of role conjecture named cBOOL_PROP_32_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->(forall (Xx:a), (((or (X Xx)) (Y Xx))->(Z Xx))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->(forall (Xx:a), (((or (X Xx)) (Y Xx))->(Z Xx)))))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->(forall (Xx:a), (((or (X Xx)) (Y Xx))->(Z Xx)))))
% Found x10:=(x1 Xx):((X Xx)->(Z Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Z Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Z Xx))
% Found x20:=(x2 Xx):((Y Xx)->(Z Xx))
% Found (x2 Xx) as proof of ((Y Xx)->(Z Xx))
% Found (x2 Xx) as proof of ((Y Xx)->(Z Xx))
% Found ((or_ind00 (x1 Xx)) (x2 Xx)) as proof of (Z Xx)
% Found (((or_ind0 (Z Xx)) (x1 Xx)) (x2 Xx)) as proof of (Z Xx)
% Found ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)) as proof of (Z Xx)
% Found (fun (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))) as proof of (Z Xx)
% Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))) as proof of ((forall (Xx0:a), ((Y Xx0)->(Z Xx0)))->(Z Xx))
% Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))) as proof of ((forall (Xx0:a), ((X Xx0)->(Z Xx0)))->((forall (Xx0:a), ((Y Xx0)->(Z Xx0)))->(Z Xx)))
% Found (and_rect00 (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))) as proof of (Z Xx)
% Found ((and_rect0 (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))) as proof of (Z Xx)
% Found (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))) as proof of (Z Xx)
% Found (fun (x0:((or (X Xx)) (Y Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (Z Xx)
% Found (fun (Xx:a) (x0:((or (X Xx)) (Y Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (((or (X Xx)) (Y Xx))->(Z Xx))
% Found (fun (x:((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))) (Xx:a) (x0:((or (X Xx)) (Y Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (forall (Xx:a), (((or (X Xx)) (Y Xx))->(Z Xx)))
% Found (fun (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))) (Xx:a) (x0:((or (X Xx)) (Y Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->(forall (Xx:a), (((or (X Xx)) (Y Xx))->(Z Xx))))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))) (Xx:a) (x0:((or (X Xx)) (Y Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (forall (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->(forall (Xx:a), (((or (X Xx)) (Y Xx))->(Z Xx)))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))) (Xx:a) (x0:((or (X Xx)) (Y Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->(forall (Xx:a), (((or (X Xx)) (Y Xx))->(Z Xx)))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))) (Xx:a) (x0:((or (X Xx)) (Y Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->(forall (Xx:a), (((or (X Xx)) (Y Xx))->(Z Xx)))))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))) (Xx:a) (x0:((or (X Xx)) (Y Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))))
% Time elapsed = 0.222027s
% node=44 cost=202.000000 depth=17
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx))))) (Xx:a) (x0:((or (X Xx)) (Y Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Z Xx)))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Z Xx)))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Z Xx0)))) (x2:(forall (Xx0:a), ((Y Xx0)->(Z Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Y Xx)->P))=> ((((((or_ind (X Xx)) (Y Xx)) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------