%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU885^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n092.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 13:33:20 EDT 2014

% Result   : Theorem 9.52s
% Output   : Proof 9.52s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU885^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.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 11:40:41 CDT 2014
% % CPUTime  : 9.52 
% 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 0x2663320>, <kernel.Type object at 0x2a3eb90>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x2a9cdd0>, <kernel.Type object at 0x2a3eb48>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x2663320>, <kernel.DependentProduct object at 0x2a3e7e8>) of role type named cF
% Using role type
% Declaring cF:(b->a)
% FOF formula (<kernel.Constant object at 0x2663320>, <kernel.DependentProduct object at 0x2a3ea28>) of role type named cV
% Using role type
% Declaring cV:(b->Prop)
% FOF formula (<kernel.Constant object at 0x2a3ec20>, <kernel.DependentProduct object at 0x2a3e950>) of role type named cU
% Using role type
% Declaring cU:(b->Prop)
% FOF formula ((forall (Xx:b), ((cU Xx)->(cV Xx)))->(forall (Xx:a), (((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))))) of role conjecture named cTHM30A_pme
% Conjecture to prove = ((forall (Xx:b), ((cU Xx)->(cV Xx)))->(forall (Xx:a), (((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))))):Prop
% Parameter b_DUMMY:b.
% Parameter a_DUMMY:a.
% We need to prove ['((forall (Xx:b), ((cU Xx)->(cV Xx)))->(forall (Xx:a), (((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))))))']
% Parameter b:Type.
% Parameter a:Type.
% Parameter cF:(b->a).
% Parameter cV:(b->Prop).
% Parameter cU:(b->Prop).
% Trying to prove ((forall (Xx:b), ((cU Xx)->(cV Xx)))->(forall (Xx:a), (((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))))))
% Found eta_expansion0000:=(eta_expansion000 (ex b)):(((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (x:b)=> ((and (cU x)) (((eq a) Xx) (cF x))))))
% Found (eta_expansion000 (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((eta_expansion00 (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found (((eta_expansion0 Prop) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((((eta_expansion b) Prop) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((((eta_expansion b) Prop) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found eq_ref000:=(eq_ref00 (ex b)):(((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))))
% Found (eq_ref00 (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((eq_ref0 (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found (((eq_ref (b->Prop)) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found (((eq_ref (b->Prop)) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 (ex b)):(((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (x:b)=> ((and (cU x)) (((eq a) Xx) (cF x))))))
% Found (eta_expansion_dep000 (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((eta_expansion_dep00 (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found (((eta_expansion_dep0 (fun (x1:b)=> Prop)) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((((eta_expansion_dep b) (fun (x1:b)=> Prop)) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((((eta_expansion_dep b) (fun (x1:b)=> Prop)) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) (ex b)) as proof of (P (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))
% Found x4:(((eq a) Xx) (cF x1))
% Instantiate: x5:=x1:b
% Found x4 as proof of (((eq a) Xx) (cF x5))
% Found x3:(cU x1)
% Instantiate: x5:=x1:b
% Found x3 as proof of (cU x5)
% Found (x6 x3) as proof of (cV x5)
% Found ((x x5) x3) as proof of (cV x5)
% Found ((x x5) x3) as proof of (cV x5)
% Found ((conj00 ((x x5) x3)) x4) as proof of ((and (cV x5)) (((eq a) Xx) (cF x5)))
% Found (((conj0 (((eq a) Xx) (cF x5))) ((x x5) x3)) x4) as proof of ((and (cV x5)) (((eq a) Xx) (cF x5)))
% Found ((((conj (cV x5)) (((eq a) Xx) (cF x5))) ((x x5) x3)) x4) as proof of ((and (cV x5)) (((eq a) Xx) (cF x5)))
% Found ((((conj (cV x5)) (((eq a) Xx) (cF x5))) ((x x5) x3)) x4) as proof of ((and (cV x5)) (((eq a) Xx) (cF x5)))
% Found (ex_intro000 ((((conj (cV x5)) (((eq a) Xx) (cF x5))) ((x x5) x3)) x4)) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((ex_intro00 x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found (((ex_intro0 (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found (fun (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))) as proof of ((((eq a) Xx) (cF x1))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))))
% Found (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))) as proof of ((cU x1)->((((eq a) Xx) (cF x1))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))))
% Found (and_rect00 (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)))) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((and_rect0 ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)))) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)))) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found (fun (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))))) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))))) as proof of (((and (cU x1)) (((eq a) Xx) (cF x1)))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))))
% Found (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))))) as proof of (forall (x:b), (((and (cU x)) (((eq a) Xx) (cF x)))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))))
% Found (ex_ind00 (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)))))) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found ((ex_ind0 ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)))))) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found (((fun (P:Prop) (x1:(forall (x:b), (((and (cU x)) (((eq a) Xx) (cF x)))->P)))=> (((((ex_ind b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) P) x1) x0)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)))))) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found (fun (x0:((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))))=> (((fun (P:Prop) (x1:(forall (x:b), (((and (cU x)) (((eq a) Xx) (cF x)))->P)))=> (((((ex_ind b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) P) x1) x0)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))))))) as proof of ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))
% Found (fun (Xx:a) (x0:((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))))=> (((fun (P:Prop) (x1:(forall (x:b), (((and (cU x)) (((eq a) Xx) (cF x)))->P)))=> (((((ex_ind b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) P) x1) x0)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))))))) as proof of (((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))))
% Found (fun (x:(forall (Xx:b), ((cU Xx)->(cV Xx)))) (Xx:a) (x0:((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))))=> (((fun (P:Prop) (x1:(forall (x:b), (((and (cU x)) (((eq a) Xx) (cF x)))->P)))=> (((((ex_ind b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) P) x1) x0)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))))))) as proof of (forall (Xx:a), (((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))))
% Found (fun (x:(forall (Xx:b), ((cU Xx)->(cV Xx)))) (Xx:a) (x0:((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))))=> (((fun (P:Prop) (x1:(forall (x:b), (((and (cU x)) (((eq a) Xx) (cF x)))->P)))=> (((((ex_ind b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) P) x1) x0)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4))))))) as proof of ((forall (Xx:b), ((cU Xx)->(cV Xx)))->(forall (Xx:a), (((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt)))))->((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))))))
% Got proof (fun (x:(forall (Xx:b), ((cU Xx)->(cV Xx)))) (Xx:a) (x0:((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))))=> (((fun (P:Prop) (x1:(forall (x:b), (((and (cU x)) (((eq a) Xx) (cF x)))->P)))=> (((((ex_ind b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) P) x1) x0)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)))))))
% Time elapsed = 9.133072s
% node=1238 cost=769.000000 depth=27
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:(forall (Xx:b), ((cU Xx)->(cV Xx)))) (Xx:a) (x0:((ex b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))))=> (((fun (P:Prop) (x1:(forall (x:b), (((and (cU x)) (((eq a) Xx) (cF x)))->P)))=> (((((ex_ind b) (fun (Xt:b)=> ((and (cU Xt)) (((eq a) Xx) (cF Xt))))) P) x1) x0)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x1:b) (x2:((and (cU x1)) (((eq a) Xx) (cF x1))))=> (((fun (P:Type) (x3:((cU x1)->((((eq a) Xx) (cF x1))->P)))=> (((((and_rect (cU x1)) (((eq a) Xx) (cF x1))) P) x3) x2)) ((ex b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt)))))) (fun (x3:(cU x1)) (x4:(((eq a) Xx) (cF x1)))=> ((((ex_intro b) (fun (Xt:b)=> ((and (cV Xt)) (((eq a) Xx) (cF Xt))))) x1) ((((conj (cV x1)) (((eq a) Xx) (cF x1))) ((x x1) x3)) x4)))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------