TSTP Solution File: SEV271^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV271^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n096.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 13:33:58 EDT 2014
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV271^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n096.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 08:41:11 CDT 2014
% % CPUTime : 300.02
% 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 0x1a86710>, <kernel.Type object at 0x1a86ef0>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x1c645f0>, <kernel.Type object at 0x1a86dd0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (S:((b->Prop)->Prop)) (T:((a->Prop)->Prop)), (((and ((and ((and ((and ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->(T R)))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->(T R))))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->(T Xx)))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S0:(a->Prop))=> ((and (K S0)) (S0 Xx)))))))->(T R))))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S0:(a->Prop)), (((and ((and (T Y)) (T Z))) (((eq (a->Prop)) S0) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->(T S0))))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx:b)=> False))->(S R))))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx:b)=> (False->False)))->(S R))))) (forall (K:((b->Prop)->Prop)) (R:(b->Prop)), (((and (forall (Xx:(b->Prop)), ((K Xx)->(S Xx)))) (((eq (b->Prop)) R) (fun (Xx:b)=> ((ex (b->Prop)) (fun (S0:(b->Prop))=> ((and (K S0)) (S0 Xx)))))))->(S R))))) (forall (Y:(b->Prop)) (Z:(b->Prop)) (S0:(b->Prop)), (((and ((and (S Y)) (S Z))) (((eq (b->Prop)) S0) (fun (Xx:b)=> ((and (Y Xx)) (Z Xx)))))->(S S0))))->(forall (F:(b->a)), ((iff (forall (X:(a->Prop)), ((T X)->(forall (Y:(b->Prop)), ((((eq (b->Prop)) Y) (fun (Xb:b)=> (X (F Xb))))->(S Y)))))) (forall (X:(b->Prop)) (Xx:a), (((ex b) (fun (Xt:b)=> ((and (forall (S0:(b->Prop)), (((and (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx0:b)=> ((S0 Xx0)->False)))->(S R))))->(S0 Xt)))) (((eq a) Xx) (F Xt)))))->(forall (S0:(a->Prop)), (((and (forall (Xx0:a), (((ex b) (fun (Xt:b)=> ((and (X Xt)) (((eq a) Xx0) (F Xt)))))->(S0 Xx0)))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx0:a)=> ((S0 Xx0)->False)))->(T R))))->(S0 Xx))))))))) of role conjecture named cCLOSURE_THM2_pme
% Conjecture to prove = (forall (S:((b->Prop)->Prop)) (T:((a->Prop)->Prop)), (((and ((and ((and ((and ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->(T R)))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->(T R))))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->(T Xx)))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S0:(a->Prop))=> ((and (K S0)) (S0 Xx)))))))->(T R))))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S0:(a->Prop)), (((and ((and (T Y)) (T Z))) (((eq (a->Prop)) S0) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->(T S0))))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx:b)=> False))->(S R))))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx:b)=> (False->False)))->(S R))))) (forall (K:((b->Prop)->Prop)) (R:(b->Prop)), (((and (forall (Xx:(b->Prop)), ((K Xx)->(S Xx)))) (((eq (b->Prop)) R) (fun (Xx:b)=> ((ex (b->Prop)) (fun (S0:(b->Prop))=> ((and (K S0)) (S0 Xx)))))))->(S R))))) (forall (Y:(b->Prop)) (Z:(b->Prop)) (S0:(b->Prop)), (((and ((and (S Y)) (S Z))) (((eq (b->Prop)) S0) (fun (Xx:b)=> ((and (Y Xx)) (Z Xx)))))->(S S0))))->(forall (F:(b->a)), ((iff (forall (X:(a->Prop)), ((T X)->(forall (Y:(b->Prop)), ((((eq (b->Prop)) Y) (fun (Xb:b)=> (X (F Xb))))->(S Y)))))) (forall (X:(b->Prop)) (Xx:a), (((ex b) (fun (Xt:b)=> ((and (forall (S0:(b->Prop)), (((and (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx0:b)=> ((S0 Xx0)->False)))->(S R))))->(S0 Xt)))) (((eq a) Xx) (F Xt)))))->(forall (S0:(a->Prop)), (((and (forall (Xx0:a), (((ex b) (fun (Xt:b)=> ((and (X Xt)) (((eq a) Xx0) (F Xt)))))->(S0 Xx0)))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx0:a)=> ((S0 Xx0)->False)))->(T R))))->(S0 Xx))))))))):Prop
% Parameter b_DUMMY:b.
% Parameter a_DUMMY:a.
% We need to prove ['(forall (S:((b->Prop)->Prop)) (T:((a->Prop)->Prop)), (((and ((and ((and ((and ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->(T R)))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->(T R))))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->(T Xx)))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S0:(a->Prop))=> ((and (K S0)) (S0 Xx)))))))->(T R))))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S0:(a->Prop)), (((and ((and (T Y)) (T Z))) (((eq (a->Prop)) S0) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->(T S0))))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx:b)=> False))->(S R))))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx:b)=> (False->False)))->(S R))))) (forall (K:((b->Prop)->Prop)) (R:(b->Prop)), (((and (forall (Xx:(b->Prop)), ((K Xx)->(S Xx)))) (((eq (b->Prop)) R) (fun (Xx:b)=> ((ex (b->Prop)) (fun (S0:(b->Prop))=> ((and (K S0)) (S0 Xx)))))))->(S R))))) (forall (Y:(b->Prop)) (Z:(b->Prop)) (S0:(b->Prop)), (((and ((and (S Y)) (S Z))) (((eq (b->Prop)) S0) (fun (Xx:b)=> ((and (Y Xx)) (Z Xx)))))->(S S0))))->(forall (F:(b->a)), ((iff (forall (X:(a->Prop)), ((T X)->(forall (Y:(b->Prop)), ((((eq (b->Prop)) Y) (fun (Xb:b)=> (X (F Xb))))->(S Y)))))) (forall (X:(b->Prop)) (Xx:a), (((ex b) (fun (Xt:b)=> ((and (forall (S0:(b->Prop)), (((and (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx0:b)=> ((S0 Xx0)->False)))->(S R))))->(S0 Xt)))) (((eq a) Xx) (F Xt)))))->(forall (S0:(a->Prop)), (((and (forall (Xx0:a), (((ex b) (fun (Xt:b)=> ((and (X Xt)) (((eq a) Xx0) (F Xt)))))->(S0 Xx0)))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx0:a)=> ((S0 Xx0)->False)))->(T R))))->(S0 Xx)))))))))']
% Parameter b:Type.
% Parameter a:Type.
% Trying to prove (forall (S:((b->Prop)->Prop)) (T:((a->Prop)->Prop)), (((and ((and ((and ((and ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->(T R)))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->(T R))))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->(T Xx)))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S0:(a->Prop))=> ((and (K S0)) (S0 Xx)))))))->(T R))))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S0:(a->Prop)), (((and ((and (T Y)) (T Z))) (((eq (a->Prop)) S0) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->(T S0))))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx:b)=> False))->(S R))))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx:b)=> (False->False)))->(S R))))) (forall (K:((b->Prop)->Prop)) (R:(b->Prop)), (((and (forall (Xx:(b->Prop)), ((K Xx)->(S Xx)))) (((eq (b->Prop)) R) (fun (Xx:b)=> ((ex (b->Prop)) (fun (S0:(b->Prop))=> ((and (K S0)) (S0 Xx)))))))->(S R))))) (forall (Y:(b->Prop)) (Z:(b->Prop)) (S0:(b->Prop)), (((and ((and (S Y)) (S Z))) (((eq (b->Prop)) S0) (fun (Xx:b)=> ((and (Y Xx)) (Z Xx)))))->(S S0))))->(forall (F:(b->a)), ((iff (forall (X:(a->Prop)), ((T X)->(forall (Y:(b->Prop)), ((((eq (b->Prop)) Y) (fun (Xb:b)=> (X (F Xb))))->(S Y)))))) (forall (X:(b->Prop)) (Xx:a), (((ex b) (fun (Xt:b)=> ((and (forall (S0:(b->Prop)), (((and (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) (forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx0:b)=> ((S0 Xx0)->False)))->(S R))))->(S0 Xt)))) (((eq a) Xx) (F Xt)))))->(forall (S0:(a->Prop)), (((and (forall (Xx0:a), (((ex b) (fun (Xt:b)=> ((and (X Xt)) (((eq a) Xx0) (F Xt)))))->(S0 Xx0)))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx0:a)=> ((S0 Xx0)->False)))->(T R))))->(S0 Xx)))))))))
% Found x2:(((eq (b->Prop)) Y) (fun (Xb:b)=> (X (F Xb))))
% Instantiate: b0:=(fun (Xb:b)=> (X (F Xb))):(b->Prop)
% Found x2 as proof of (((eq (b->Prop)) Y) b0)
% Found eq_ref000:=(eq_ref00 K):((K Xx)->(K Xx))
% Found (eq_ref00 K) as proof of ((K Xx)->(S Xx))
% Found ((eq_ref0 Xx) K) as proof of ((K Xx)->(S Xx))
% Found (((eq_ref (b->Prop)) Xx) K) as proof of ((K Xx)->(S Xx))
% Found (((eq_ref (b->Prop)) Xx) K) as proof of ((K Xx)->(S Xx))
% Found (fun (Xx:(b->Prop))=> (((eq_ref (b->Prop)) Xx) K)) as proof of ((K Xx)->(S Xx))
% Found (fun (Xx:(b->Prop))=> (((eq_ref (b->Prop)) Xx) K)) as proof of (forall (Xx:(b->Prop)), ((K Xx)->(S Xx)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x5:(forall (R:(b->Prop)), ((((eq (b->Prop)) R) (fun (Xx:b)=> (False->False)))->(S R)))
% Instantiate: K:=(fun (x10:(b->Prop))=> (((eq (b->Prop)) x10) (fun (Xx:b)=> (False->False)))):((b->Prop)->Prop)
% Found x5 as proof of (forall (Xx:(b->Prop)), ((K Xx)->(S Xx)))
% Found x2:(((eq (b->Prop)) Y) (fun (Xb:b)=> (X (F Xb))))
% Instantiate: b0:=(fun (Xb:b)=> (X (F Xb))):(b->Prop)
% Found x2 as proof of (((eq (b->Prop)) Y) b0)
% Found x4:(((eq (b->Prop)) Y) (fun (Xb:b)=> (X (F Xb))))
% Instantiate: b0:=(fun (Xb:b)=> (X (F Xb))):(b->Prop)
% Found x4 as proof of (((eq (b->Prop)) Y) b0)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (Y x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (Y x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (Y x3))
% Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (Y x3))
% Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (Y x)))
% Found x8:(((eq (b->Prop)) Y) (fun (Xb:b)=> (X (F Xb))))
% Instantiate: b0:=(fun (Xb:b)=> (X (F Xb))):(b->Prop)
% Found x8 as proof of (((eq (b->Prop)) Y) b0)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (Y x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (Y x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (Y x3))
% Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (Y x3))
% Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (Y x)))
% Found eta_expansion000:=(eta_expansion00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq (b->Prop)) b0) (fun (Xx:b)=> (False->False)))
% Found ((eta_expansion0 Prop) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx:b)=> (False->False)))
% Found (((eta_expansion b) Prop) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx:b)=> (False->False)))
% Found (((eta_expansion b) Prop) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx:b)=> (False->False)))
% Found (((eta_expansion b) Prop) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx:b)=> (False->False)))
% Found x60:=(x6 (fun (x7:(b->Prop))=> (K Xx))):((K Xx)->(K Xx))
% Found (x6 (fun (x7:(b->Prop))=> (K Xx))) as proof of ((K Xx)->(S Xx))
% Found (x6 (fun (x7:(b->Prop))=> (K Xx))) as proof of ((K Xx)->(S Xx))
% Found (fun (Xx:(b->Prop))=> (x6 (fun (x7:(b->Prop))=> (K Xx)))) as proof of ((K Xx)->(S Xx))
% Found (fun (Xx:(b->Prop))=> (x6 (fun (x7:(b->Prop))=> (K Xx)))) as proof of (forall (Xx:(b->Prop)), ((K Xx)->(S Xx)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x40:=(x4 (fun (x7:(b->Prop))=> (K Xx))):((K Xx)->(K Xx))
% Found (x4 (fun (x7:(b->Prop))=> (K Xx))) as proof of ((K Xx)->(S Xx))
% Found (x4 (fun (x7:(b->Prop))=> (K Xx))) as proof of ((K Xx)->(S Xx))
% Found (fun (Xx:(b->Prop))=> (x4 (fun (x7:(b->Prop))=> (K Xx)))) as proof of ((K Xx)->(S Xx))
% Found (fun (Xx:(b->Prop))=> (x4 (fun (x7:(b->Prop))=> (K Xx)))) as proof of (forall (Xx:(b->Prop)), ((K Xx)->(S Xx)))
% Found x60:=(x6 (fun (x7:(b->Prop))=> (K Xx))):((K Xx)->(K Xx))
% Found (x6 (fun (x7:(b->Prop))=> (K Xx))) as proof of ((K Xx)->(S Xx))
% Found (x6 (fun (x7:(b->Prop))=> (K Xx))) as proof of ((K Xx)->(S Xx))
% Found (fun (Xx:(b->Prop))=> (x6 (fun (
% EOF
%------------------------------------------------------------------------------