TSTP Solution File: SET201^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET201^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n186.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 13:30:22 EDT 2014
% Result : Theorem 0.87s
% Output : Proof 0.87s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET201^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n186.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 09:25:21 CDT 2014
% % CPUTime : 0.87
% 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 0x1e307e8>, <kernel.Type object at 0x1e30200>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1919b90>, <kernel.DependentProduct object at 0x1e30128>) of role type named cV
% Using role type
% Declaring cV:(a->Prop)
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))))) of role conjecture named cBOOL_PROP_41_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV 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)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx))))))']
% Parameter a:Type.
% Parameter cV:(a->Prop).
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx))))))
% Found x200:=(x20 x4):(cV Xx)
% Found (x20 x4) as proof of (cV Xx)
% Found ((x2 Xx) x4) as proof of (cV Xx)
% Found ((x2 Xx) x4) as proof of (cV Xx)
% Found x100:=(x10 x3):(Y Xx)
% Found (x10 x3) as proof of (Y Xx)
% Found ((x1 Xx) x3) as proof of (Y Xx)
% Found ((x1 Xx) x3) as proof of (Y Xx)
% Found ((conj00 ((x1 Xx) x3)) ((x2 Xx) x4)) as proof of ((and (Y Xx)) (cV Xx))
% Found (((conj0 (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)) as proof of ((and (Y Xx)) (cV Xx))
% Found ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)) as proof of ((and (Y Xx)) (cV Xx))
% Found (fun (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))) as proof of ((and (Y Xx)) (cV Xx))
% Found (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))) as proof of ((Z Xx)->((and (Y Xx)) (cV Xx)))
% Found (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))) as proof of ((X Xx)->((Z Xx)->((and (Y Xx)) (cV Xx))))
% Found (and_rect10 (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))) as proof of ((and (Y Xx)) (cV Xx))
% Found ((and_rect1 ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))) as proof of ((and (Y Xx)) (cV Xx))
% Found (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))) as proof of ((and (Y Xx)) (cV Xx))
% Found (fun (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))) as proof of ((and (Y Xx)) (cV Xx))
% Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))) as proof of ((forall (Xx0:a), ((Z Xx0)->(cV Xx0)))->((and (Y Xx)) (cV Xx)))
% Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))) as proof of ((forall (Xx0:a), ((X Xx0)->(Y Xx0)))->((forall (Xx0:a), ((Z Xx0)->(cV Xx0)))->((and (Y Xx)) (cV Xx))))
% Found (and_rect00 (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))))) as proof of ((and (Y Xx)) (cV Xx))
% Found ((and_rect0 ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))))) as proof of ((and (Y Xx)) (cV Xx))
% Found (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))))) as proof of ((and (Y Xx)) (cV Xx))
% Found (fun (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of ((and (Y Xx)) (cV Xx))
% Found (fun (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))
% Found (fun (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx))))
% Found (fun (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx)))))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (forall (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4))))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))->(forall (Xx:a), (((and (X Xx)) (Z Xx))->((and (Y Xx)) (cV Xx))))))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))))))
% Time elapsed = 0.545291s
% node=114 cost=568.000000 depth=24
% ::::::::::::::::::::::
% % 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)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx))))) (Xx:a) (x0:((and (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(cV Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(cV Xx)))) P) x1) x)) ((and (Y Xx)) (cV Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(cV Xx0))))=> (((fun (P:Type) (x3:((X Xx)->((Z Xx)->P)))=> (((((and_rect (X Xx)) (Z Xx)) P) x3) x0)) ((and (Y Xx)) (cV Xx))) (fun (x3:(X Xx)) (x4:(Z Xx))=> ((((conj (Y Xx)) (cV Xx)) ((x1 Xx) x3)) ((x2 Xx) x4)))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------