TSTP Solution File: SET625^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET625^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n188.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 13:30:53 EDT 2014
% Result : Theorem 1.80s
% Output : Proof 1.80s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET625^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n188.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 10:25:41 CDT 2014
% % CPUTime : 1.80
% 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 0x10ae8c0>, <kernel.Type object at 0x10ae6c8>) 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 ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))))) of role conjecture named cBOOL_PROP_101_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))))
% Found x4:(X x2)
% Instantiate: x6:=x2:a
% Found x4 as proof of (X x6)
% Found x5:(X x3)
% Instantiate: x2:=x3:a
% Found x5 as proof of (X x2)
% Found x5:(X x2)
% Instantiate: x4:=x2:a
% Found x5 as proof of (X x4)
% Found x5:(X x3)
% Instantiate: x0:=x3:a
% Found x5 as proof of (X x0)
% Found x100:=(x10 x5):(Z x6)
% Found (x10 x5) as proof of (Z x6)
% Found ((x1 x6) x5) as proof of (Z x6)
% Found ((x1 x6) x5) as proof of (Z x6)
% Found ((conj00 x4) ((x1 x6) x5)) as proof of ((and (X x6)) (Z x6))
% Found (((conj0 (Z x6)) x4) ((x1 x6) x5)) as proof of ((and (X x6)) (Z x6))
% Found ((((conj (X x6)) (Z x6)) x4) ((x1 x6) x5)) as proof of ((and (X x6)) (Z x6))
% Found ((((conj (X x6)) (Z x6)) x4) ((x1 x6) x5)) as proof of ((and (X x6)) (Z x6))
% Found (ex_intro000 ((((conj (X x6)) (Z x6)) x4) ((x1 x6) x5))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found ((ex_intro00 x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (((ex_intro0 (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (fun (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))) as proof of ((Y x2)->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))))
% Found (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))) as proof of ((X x2)->((Y x2)->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))))
% Found (and_rect10 (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found ((and_rect1 ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (fun (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))) as proof of (((and (X x2)) (Y x2))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))))
% Found (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))) as proof of (forall (x:a), (((and (X x)) (Y x))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))))
% Found (ex_ind00 (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found ((ex_ind0 ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (((fun (P:Prop) (x2:(forall (x:a), (((and (X x)) (Y x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (fun (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x:a), (((and (X x)) (Y x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x:a), (((and (X x)) (Y x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))))) as proof of ((forall (Xx:a), ((Y Xx)->(Z Xx)))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))))
% Found (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x:a), (((and (X x)) (Y x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))))) as proof of (((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))))
% Found (and_rect00 (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x:a), (((and (X x)) (Y x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found ((and_rect0 ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x:a), (((and (X x)) (Y x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (((fun (P:Type) (x0:(((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x0:a), (((and (X x0)) (Y x0))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (fun (x:((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))))=> (((fun (P:Type) (x0:(((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x0:a), (((and (X x0)) (Y x0))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))
% Found (fun (Z:(a->Prop)) (x:((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))))=> (((fun (P:Type) (x0:(((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x0:a), (((and (X x0)) (Y x0))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))))))) as proof of (((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (x:((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))))=> (((fun (P:Type) (x0:(((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x0:a), (((and (X x0)) (Y x0))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))))))) as proof of (forall (Z:(a->Prop)), (((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))))=> (((fun (P:Type) (x0:(((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x0:a), (((and (X x0)) (Y x0))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))))))) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))))=> (((fun (P:Type) (x0:(((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x0:a), (((and (X x0)) (Y x0))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5)))))))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))))=> (((fun (P:Type) (x0:(((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x0:a), (((and (X x0)) (Y x0))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))))))))
% Time elapsed = 1.473413s
% node=205 cost=1001.000000 depth=33
% ::::::::::::::::::::::
% % 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 ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))))=> (((fun (P:Type) (x0:(((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))->((forall (Xx:a), ((Y Xx)->(Z Xx)))->P)))=> (((((and_rect ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (forall (Xx:a), ((Y Xx)->(Z Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x0:((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (x1:(forall (Xx:a), ((Y Xx)->(Z Xx))))=> (((fun (P:Prop) (x2:(forall (x0:a), (((and (X x0)) (Y x0))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) P) x2) x0)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x2:a) (x3:((and (X x2)) (Y x2)))=> (((fun (P:Type) (x4:((X x2)->((Y x2)->P)))=> (((((and_rect (X x2)) (Y x2)) P) x4) x3)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx))))) (fun (x4:(X x2)) (x5:(Y x2))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Z Xx)))) x2) ((((conj (X x2)) (Z x2)) x4) ((x1 x2) x5))))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------