TSTP Solution File: SEV258^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV258^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n113.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 13:33:57 EDT 2014
% Result : Theorem 1.68s
% Output : Proof 1.68s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV258^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n113.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 08:38:36 CDT 2014
% % CPUTime : 1.68
% 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 0x1fd84d0>, <kernel.Type object at 0x1fd82d8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))) of role conjecture named cDISCRETE_TOPOLOGY_pme
% Conjecture to prove = ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True)))']
% Parameter a:Type.
% Trying to prove ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True)))
% Found I:True
% Found (fun (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of True
% Found (fun (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True)
% Found (fun (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of (forall (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of (forall (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))
% Found I:True
% Found (fun (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of True
% Found (fun (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True)
% Found (fun (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of (forall (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of (forall (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))
% Found I:True
% Found (fun (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I) as proof of True
% Found (fun (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I) as proof of (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)
% Found (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I) as proof of (forall (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))
% Found (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I) as proof of (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))
% Found I:True
% Found (fun (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I) as proof of True
% Found (fun (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I) as proof of (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)
% Found (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I) as proof of (forall (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))
% Found (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I) as proof of (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))
% Found I:True
% Found (fun (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I) as proof of True
% Found (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I) as proof of ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True)
% Found (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I) as proof of (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))
% Found I:True
% Found (fun (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I) as proof of True
% Found (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I) as proof of ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)
% Found (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I) as proof of (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))
% Found ((conj20 (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I)) as proof of ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))
% Found (((conj2 (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I)) as proof of ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))
% Found ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I)) as proof of ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))
% Found ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I)) as proof of ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))
% Found ((conj10 ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I)) as proof of ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))
% Found (((conj1 (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))) ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I)) as proof of ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))
% Found ((((conj ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))) ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I)) as proof of ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))
% Found ((((conj ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))) ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I)) as proof of ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))
% Found ((conj00 ((((conj ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))) ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I))) (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I)) as proof of ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True)))
% Found (((conj0 (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))) ((((conj ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))) ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I))) (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I)) as proof of ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True)))
% Found ((((conj ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))) ((((conj ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))) ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I))) (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I)) as proof of ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True)))
% Found ((((conj ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))) ((((conj ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))) ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I))) (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I)) as proof of ((and ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True)))
% Got proof ((((conj ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))) ((((conj ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))) ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I))) (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I))
% Time elapsed = 1.364471s
% node=106 cost=384.000000 depth=14
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% ((((conj ((and ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True)))) (forall (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)), (((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx)))))->True))) ((((conj ((and (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True)))) (forall (K:((a->Prop)->Prop)) (R:(a->Prop)), (((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx)))))))->True))) ((((conj (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> False))->True))) (forall (R:(a->Prop)), ((((eq (a->Prop)) R) (fun (Xx:a)=> (False->False)))->True))) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> False)))=> I)) (fun (R:(a->Prop)) (x:(((eq (a->Prop)) R) (fun (Xx:a)=> (False->False))))=> I))) (fun (K:((a->Prop)->Prop)) (R:(a->Prop)) (x:((and (forall (Xx:(a->Prop)), ((K Xx)->True))) (((eq (a->Prop)) R) (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))=> I))) (fun (Y:(a->Prop)) (Z:(a->Prop)) (S:(a->Prop)) (x:((and ((and True) True)) (((eq (a->Prop)) S) (fun (Xx:a)=> ((and (Y Xx)) (Z Xx))))))=> I))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------