%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU790^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n109.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 13:33:08 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU790^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n109.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 11:29:11 CDT 2014
% % CPUTime  : 300.09 
% 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 0x2762cb0>, <kernel.DependentProduct object at 0x2627170>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2762a28>, <kernel.DependentProduct object at 0x2627170>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2762cb0>, <kernel.Sort object at 0x2628d88>) of role type named setextsub_type
% Using role type
% Declaring setextsub:Prop
% FOF formula (((eq Prop) setextsub) (forall (A:fofType) (B:fofType), (((subset A) B)->(((subset B) A)->(((eq fofType) A) B))))) of role definition named setextsub
% A new definition: (((eq Prop) setextsub) (forall (A:fofType) (B:fofType), (((subset A) B)->(((subset B) A)->(((eq fofType) A) B)))))
% Defined: setextsub:=(forall (A:fofType) (B:fofType), (((subset A) B)->(((subset B) A)->(((eq fofType) A) B))))
% FOF formula (<kernel.Constant object at 0x2762cb0>, <kernel.DependentProduct object at 0x2627950>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x2762cb0>, <kernel.DependentProduct object at 0x2627d40>) of role type named breln1_type
% Using role type
% Declaring breln1:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2627908>, <kernel.Sort object at 0x2628d88>) of role type named subbreln1_type
% Using role type
% Declaring subbreln1:Prop
% FOF formula (((eq Prop) subbreln1) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xx) Xy)) S))))))->((subset R) S))))))) of role definition named subbreln1
% A new definition: (((eq Prop) subbreln1) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xx) Xy)) S))))))->((subset R) S)))))))
% Defined: subbreln1:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xx) Xy)) S))))))->((subset R) S))))))
% FOF formula (<kernel.Constant object at 0x2b9c998>, <kernel.DependentProduct object at 0x2627a70>) of role type named breln1invset_type
% Using role type
% Declaring breln1invset:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x2b9ce60>, <kernel.Sort object at 0x2628d88>) of role type named breln1invprop_type
% Using role type
% Declaring breln1invprop:Prop
% FOF formula (((eq Prop) breln1invprop) (forall (A:fofType) (R:fofType), (((breln1 A) R)->((breln1 A) ((breln1invset A) R))))) of role definition named breln1invprop
% A new definition: (((eq Prop) breln1invprop) (forall (A:fofType) (R:fofType), (((breln1 A) R)->((breln1 A) ((breln1invset A) R)))))
% Defined: breln1invprop:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->((breln1 A) ((breln1invset A) R))))
% FOF formula (<kernel.Constant object at 0x26266c8>, <kernel.Sort object at 0x2628d88>) of role type named breln1invI_type
% Using role type
% Declaring breln1invI:Prop
% FOF formula (((eq Prop) breln1invI) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xy) Xx)) ((breln1invset A) R)))))))))) of role definition named breln1invI
% A new definition: (((eq Prop) breln1invI) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xy) Xx)) ((breln1invset A) R))))))))))
% Defined: breln1invI:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xy) Xx)) ((breln1invset A) R)))))))))
% FOF formula (<kernel.Constant object at 0x2626dd0>, <kernel.Sort object at 0x2628d88>) of role type named breln1invE_type
% Using role type
% Declaring breln1invE:Prop
% FOF formula (((eq Prop) breln1invE) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xy) Xx)) ((breln1invset A) R))->((in ((kpair Xx) Xy)) R))))))))) of role definition named breln1invE
% A new definition: (((eq Prop) breln1invE) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xy) Xx)) ((breln1invset A) R))->((in ((kpair Xx) Xy)) R)))))))))
% Defined: breln1invE:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xy) Xx)) ((breln1invset A) R))->((in ((kpair Xx) Xy)) R))))))))
% FOF formula (<kernel.Constant object at 0x26279e0>, <kernel.DependentProduct object at 0x2627a70>) of role type named breln1compset_type
% Using role type
% Declaring breln1compset:(fofType->(fofType->(fofType->fofType)))
% FOF formula (<kernel.Constant object at 0x2627830>, <kernel.Sort object at 0x2628d88>) of role type named breln1compprop_type
% Using role type
% Declaring breln1compprop:Prop
% FOF formula (((eq Prop) breln1compprop) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((breln1 A) (((breln1compset A) R) S))))))) of role definition named breln1compprop
% A new definition: (((eq Prop) breln1compprop) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((breln1 A) (((breln1compset A) R) S)))))))
% Defined: breln1compprop:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((breln1 A) (((breln1compset A) R) S))))))
% FOF formula (<kernel.Constant object at 0x2627830>, <kernel.Sort object at 0x2628d88>) of role type named breln1compI_type
% Using role type
% Declaring breln1compI:Prop
% FOF formula (((eq Prop) breln1compI) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))))))))))) of role definition named breln1compI
% A new definition: (((eq Prop) breln1compI) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))))))))))))
% Defined: breln1compI:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))))))))))
% FOF formula (<kernel.Constant object at 0x2627830>, <kernel.Sort object at 0x2628d88>) of role type named breln1compE_type
% Using role type
% Declaring breln1compE:Prop
% FOF formula (((eq Prop) breln1compE) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))))))))) of role definition named breln1compE
% A new definition: (((eq Prop) breln1compE) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))))))))
% Defined: breln1compE:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))))))))
% FOF formula (setextsub->(subbreln1->(breln1invprop->(breln1invI->(breln1invE->(breln1compprop->(breln1compI->(breln1compE->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))))))))))))) of role conjecture named woz2W
% Conjecture to prove = (setextsub->(subbreln1->(breln1invprop->(breln1invI->(breln1invE->(breln1compprop->(breln1compI->(breln1compE->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(setextsub->(subbreln1->(breln1invprop->(breln1invI->(breln1invE->(breln1compprop->(breln1compI->(breln1compE->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter subset:(fofType->(fofType->Prop)).
% Definition setextsub:=(forall (A:fofType) (B:fofType), (((subset A) B)->(((subset B) A)->(((eq fofType) A) B)))):Prop.
% Parameter kpair:(fofType->(fofType->fofType)).
% Parameter breln1:(fofType->(fofType->Prop)).
% Definition subbreln1:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xx) Xy)) S))))))->((subset R) S)))))):Prop.
% Parameter breln1invset:(fofType->(fofType->fofType)).
% Definition breln1invprop:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->((breln1 A) ((breln1invset A) R)))):Prop.
% Definition breln1invI:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) R)->((in ((kpair Xy) Xx)) ((breln1invset A) R))))))))):Prop.
% Definition breln1invE:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xy) Xx)) ((breln1invset A) R))->((in ((kpair Xx) Xy)) R)))))))):Prop.
% Parameter breln1compset:(fofType->(fofType->(fofType->fofType))).
% Definition breln1compprop:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((breln1 A) (((breln1compset A) R) S)))))):Prop.
% Definition breln1compI:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))))))))))):Prop.
% Definition breln1compE:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(((in ((kpair Xx) Xy)) (((breln1compset A) R) S))->((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))))))):Prop.
% Trying to prove (setextsub->(subbreln1->(breln1invprop->(breln1invI->(breln1invE->(breln1compprop->(breln1compI->(breln1compE->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))))))))))))))
% Found x100:(P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x100:(P ((breln1invset A) (((breln1compset A) R) S))))=> x100) as proof of (P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x100:(P ((breln1invset A) (((breln1compset A) R) S))))=> x100) as proof of (P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found x90:(P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x90:(P ((breln1invset A) (((breln1compset A) R) S))))=> x90) as proof of (P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x90:(P ((breln1invset A) (((breln1compset A) R) S))))=> x90) as proof of (P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x9:(P ((breln1invset A) (((breln1compset A) R) S)))
% Instantiate: b:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x9:(P ((breln1invset A) (((breln1compset A) R) S)))
% Instantiate: A0:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found x9 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x9:(P0 b)
% Instantiate: b:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found (fun (x9:(P0 b))=> x9) as proof of (P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b))=> x9) as proof of ((P0 b)->(P0 ((breln1invset A) (((breln1compset A) R) S))))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b))=> x9) as proof of (P b)
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: b:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x90:(P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x90:(P ((breln1invset A) (((breln1compset A) R) S))))=> x90) as proof of (P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x90:(P ((breln1invset A) (((breln1compset A) R) S))))=> x90) as proof of (P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: A0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found x100:(P b)
% Found (fun (x100:(P b))=> x100) as proof of (P b)
% Found (fun (x100:(P b))=> x100) as proof of (P0 b)
% Found x90:(P b)
% Found (fun (x90:(P b))=> x90) as proof of (P b)
% Found (fun (x90:(P b))=> x90) as proof of (P0 b)
% Found x100:(P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x100:(P ((breln1invset A) (((breln1compset A) R) S))))=> x100) as proof of (P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x100:(P ((breln1invset A) (((breln1compset A) R) S))))=> x100) as proof of (P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found x90:(P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x90:(P ((breln1invset A) (((breln1compset A) R) S))))=> x90) as proof of (P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x90:(P ((breln1invset A) (((breln1compset A) R) S))))=> x90) as proof of (P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x100:(P b)
% Found (fun (x100:(P b))=> x100) as proof of (P b)
% Found (fun (x100:(P b))=> x100) as proof of (P0 b)
% Found x9:(P ((breln1invset A) (((breln1compset A) R) S)))
% Instantiate: b:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x100 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x10 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found x1000:=(x100 x8):((breln1 A0) ((breln1invset A0) S))
% Found (x100 x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found ((x10 S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found x1000:=(x100 x7):((breln1 A0) ((breln1invset A0) R))
% Found (x100 x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x10 R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x4000 (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((x400 x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> (((x40 ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x100 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x10 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found x1000:=(x100 x8):((breln1 A0) ((breln1invset A0) S))
% Found (x100 x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found ((x10 S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found x1000:=(x100 x7):((breln1 A0) ((breln1invset A0) R))
% Found (x100 x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x10 R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x4000 (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((x400 x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> (((x40 ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x11:((in Xy) A0)
% Instantiate: A0:=A:fofType
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x9:(P ((breln1invset A) (((breln1compset A) R) S)))
% Instantiate: A0:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found x9 as proof of (P0 A0)
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x9:(P0 b)
% Instantiate: b:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found (fun (x9:(P0 b))=> x9) as proof of (P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b))=> x9) as proof of ((P0 b)->(P0 ((breln1invset A) (((breln1compset A) R) S))))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b))=> x9) as proof of (P b)
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: b:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x9:(P ((breln1invset A) (((breln1compset A) R) S)))
% Instantiate: a:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found x9 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x90:(P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x90:(P ((breln1invset A) (((breln1compset A) R) S))))=> x90) as proof of (P ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x90:(P ((breln1invset A) (((breln1compset A) R) S))))=> x90) as proof of (P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: A0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 A0)
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: A0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x9:(P2 b)
% Instantiate: b:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found (fun (x9:(P2 b))=> x9) as proof of (P2 ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (P2:(fofType->Prop)) (x9:(P2 b))=> x9) as proof of ((P2 b)->(P2 ((breln1invset A) (((breln1compset A) R) S))))
% Found (fun (P2:(fofType->Prop)) (x9:(P2 b))=> x9) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x9:(P2 b)
% Instantiate: b:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found (fun (x9:(P2 b))=> x9) as proof of (P2 ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (P2:(fofType->Prop)) (x9:(P2 b))=> x9) as proof of ((P2 b)->(P2 ((breln1invset A) (((breln1compset A) R) S))))
% Found (fun (P2:(fofType->Prop)) (x9:(P2 b))=> x9) as proof of (P1 b)
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x100 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x10 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found x1000:=(x100 x8):((breln1 A0) ((breln1invset A0) S))
% Found (x100 x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found ((x10 S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found x1000:=(x100 x7):((breln1 A0) ((breln1invset A0) R))
% Found (x100 x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x10 R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x4000 (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((x400 x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> (((x40 ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x100 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x10 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found x1000:=(x100 x8):((breln1 A0) ((breln1invset A0) S))
% Found (x100 x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found ((x10 S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found x1000:=(x100 x7):((breln1 A0) ((breln1invset A0) R))
% Found (x100 x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x10 R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x4000 (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((x400 x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> (((x40 ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x11:((in Xy) A0)
% Instantiate: A0:=A:fofType
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x9:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: b:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found x9:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: b:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x100:(P b)
% Found (fun (x100:(P b))=> x100) as proof of (P b)
% Found (fun (x100:(P b))=> x100) as proof of (P0 b)
% Found x100:(P b)
% Found (fun (x100:(P b))=> x100) as proof of (P b)
% Found (fun (x100:(P b))=> x100) as proof of (P0 b)
% Found x90:(P b)
% Found (fun (x90:(P b))=> x90) as proof of (P b)
% Found (fun (x90:(P b))=> x90) as proof of (P0 b)
% Found x90:(P b)
% Found (fun (x90:(P b))=> x90) as proof of (P b)
% Found (fun (x90:(P b))=> x90) as proof of (P0 b)
% Found x9:(P b)
% Found x9 as proof of (P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x9:(P b)
% Instantiate: b0:=b:fofType
% Found x9 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x9:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: A0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P2 A0)
% Found x9:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: A0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P2 A0)
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: b:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x9:(P b)
% Instantiate: A0:=b:fofType
% Found x9 as proof of (P0 A0)
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: a:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 a)
% Found x110:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x110:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x110) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x110:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x110) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b1)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b1)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b1)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x100:(P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P2 b)
% Found x100:(P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P2 b)
% Found x90:(P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P2 b)
% Found x90:(P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P2 b)
% Found x100:(P0 b)
% Found (fun (x100:(P0 b))=> x100) as proof of (P0 b)
% Found (fun (x100:(P0 b))=> x100) as proof of (P1 b)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found x9:(P0 b0)
% Instantiate: b0:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found (fun (x9:(P0 b0))=> x9) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b0))=> x9) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b0))=> x9) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found x9:(P0 b0)
% Instantiate: b0:=((breln1invset A) (((breln1compset A) R) S)):fofType
% Found (fun (x9:(P0 b0))=> x9) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b0))=> x9) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b0))=> x9) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x7:((breln1 A) R)
% Instantiate: A1:=A:fofType;A0:=R:fofType
% Found x7 as proof of ((breln1 A1) A0)
% Found x7:((breln1 A) R)
% Instantiate: A1:=A:fofType;A0:=R:fofType
% Found x7 as proof of ((breln1 A1) A0)
% Found x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P b0)
% Found (fun (x100:(P b0))=> x100) as proof of (P b0)
% Found (fun (x100:(P b0))=> x100) as proof of (P0 b0)
% Found x90:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found x90:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: b0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: b0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x90:(P b0)
% Found (fun (x90:(P b0))=> x90) as proof of (P b0)
% Found (fun (x90:(P b0))=> x90) as proof of (P0 b0)
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x9 as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x11:((in Xy) A0)
% Instantiate: Xz:=Xy:fofType;A0:=A:fofType
% Found x11 as proof of ((in Xz) A)
% Found x10:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Instantiate: A0:=A:fofType
% Found x11 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found x110:(P1 ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x110:(P1 ((breln1invset A) (((breln1compset A) R) S))))=> x110) as proof of (P1 ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x110:(P1 ((breln1invset A) (((breln1compset A) R) S))))=> x110) as proof of (P2 ((breln1invset A) (((breln1compset A) R) S)))
% Found x110:(P1 b)
% Found (fun (x110:(P1 b))=> x110) as proof of (P1 b)
% Found (fun (x110:(P1 b))=> x110) as proof of (P2 b)
% Found x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found x9:(P0 ((breln1invset A) (((breln1compset A) R) S)))
% Found (fun (x9:(P0 ((breln1invset A) (((breln1compset A) R) S))))=> x9) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x9:(P0 ((breln1invset A) (((breln1compset A) R) S))))=> x9) as proof of ((P0 ((breln1invset A) (((breln1compset A) R) S)))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 ((breln1invset A) (((breln1compset A) R) S))))=> x9) as proof of (P ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) R) S))
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: A0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b0)
% Found x9:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Instantiate: A0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found x9 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b1)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b1)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b1)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((breln1invset A) R))
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x100 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x10 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found x1000:=(x100 x8):((breln1 A0) ((breln1invset A0) S))
% Found (x100 x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found ((x10 S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found x1000:=(x100 x7):((breln1 A0) ((breln1invset A0) R))
% Found (x100 x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x10 R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x4000 (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((x400 x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> (((x40 ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x11:((in Xy) A0)
% Instantiate: A0:=A:fofType
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x100 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x10 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found x1000:=(x100 x8):((breln1 A0) ((breln1invset A0) S))
% Found (x100 x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found ((x10 S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found x1000:=(x100 x7):((breln1 A0) ((breln1invset A0) R))
% Found (x100 x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x10 R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x4000 (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((x400 x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> (((x40 ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x100 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x10 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found x1000:=(x100 x8):((breln1 A0) ((breln1invset A0) S))
% Found (x100 x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found ((x10 S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found x1000:=(x100 x7):((breln1 A0) ((breln1invset A0) R))
% Found (x100 x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x10 R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x4000 (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((x400 x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> (((x40 ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x11:((in Xy) A0)
% Instantiate: A0:=A:fofType
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x100 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x10 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found x1000:=(x100 x8):((breln1 A0) ((breln1invset A0) S))
% Found (x100 x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found ((x10 S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found (((x1 A0) S) x8) as proof of ((breln1 A0) ((breln1invset A) S))
% Found x1000:=(x100 x7):((breln1 A0) ((breln1invset A0) R))
% Found (x100 x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x10 R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found (((x1 A0) R) x7) as proof of ((breln1 A0) ((breln1invset A) R))
% Found ((x4000 (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((x400 x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> (((x40 ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (((fun (x10:((breln1 A0) ((breln1invset A) S)))=> ((((x4 A0) ((breln1invset A) S)) x10) ((breln1invset A) R))) (((x1 A0) S) x8)) (((x1 A0) R) x7)) as proof of ((breln1 A0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b)
% Found x90:(P0 b)
% Found (fun (x90:(P0 b))=> x90) as proof of (P0 b)
% Found (fun (x90:(P0 b))=> x90) as proof of (P1 b)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x90:(P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P2 b)
% Found x90:(P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P2 b)
% Found x90:(P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P2 b)
% Found x90:(P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P1 b)
% Found (fun (x90:(P1 b))=> x90) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x100:(P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P2 b)
% Found x100:(P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P2 b)
% Found x9:(P b)
% Instantiate: b0:=b:fofType
% Found x9 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P2 b)
% Found x100:(P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P1 b)
% Found (fun (x100:(P1 b))=> x100) as proof of (P2 b)
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x100:(P1 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x100) as proof of (P2 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x1300:=(x130 x8):((breln1 A) ((breln1invset A) S))
% Found (x130 x8) as proof of ((breln1 A) ((breln1invset A) S))
% Found ((x13 S) x8) as proof of ((breln1 A) ((breln1invset A) S))
% Found (((x1 A) S) x8) as proof of ((breln1 A) ((breln1invset A) S))
% Found (((x1 A) S) x8) as proof of ((breln1 A) ((breln1invset A) S))
% Found x1300:=(x130 x7):((breln1 A) ((breln1invset A) R))
% Found (x130 x7) as proof of ((breln1 A) ((breln1invset A) R))
% Found ((x13 R) x7) as proof of ((breln1 A) ((breln1invset A) R))
% Found (((x1 A) R) x7) as proof of ((breln1 A) ((breln1invset A) R))
% Found (((x1 A) R) x7) as proof of ((breln1 A) ((breln1invset A) R))
% Found x1300:=(x130 x7):((breln1 A) ((breln1invset A) R))
% Found (x130 x7) as proof of ((breln1 A) ((breln1invset A) R))
% Found ((x13 R) x7) as proof of ((breln1 A) ((breln1invset A) R))
% Found (((x1 A) R) x7) as proof of ((breln1 A) ((breln1invset A) R))
% Found (((x1 A) R) x7) as proof of ((breln1 A) ((breln1invset A) R))
% Found x1300:=(x130 x8):((breln1 A) ((breln1invset A) S))
% Found (x130 x8) as proof of ((breln1 A) ((breln1invset A) S))
% Found ((x13 S) x8) as proof of ((breln1 A) ((breln1invset A) S))
% Found (((x1 A) S) x8) as proof of ((breln1 A) ((breln1invset A) S))
% Found (((x1 A) S) x8) as proof of ((breln1 A) ((breln1invset A) S))
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x9:(P0 b0)
% Instantiate: b0:=(((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)):fofType
% Found (fun (x9:(P0 b0))=> x9) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b0))=> x9) as proof of ((P0 b0)->(P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b0))=> x9) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))):(((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (eq_ref0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) as proof of (((eq fofType) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))) b0)
% Found x9:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x9:(P0 b))=> x9) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b))=> x9) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x9:(P0 b))=> x9) as proof of (P b0)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found x400000:=(x40000 x8):((breln1 A) (((breln1compset A) R) S))
% Found (x40000 x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found (((((x4 A) R) x7) S) x8) as proof of ((breln1 A) (((breln1compset A) R) S))
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x10:((in Xx) A0)
% Found x10 as proof of ((in Xx) A)
% Found x11:((in Xy) A0)
% Found x11 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found eq_ref00:=(eq_ref0 ((breln1invset A) (((breln1compset A) R) S))):(((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) ((breln1invset A) (((breln1compset A) R) S)))
% Found (eq_ref0 ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found ((eq_ref fofType) ((breln1invset A) (((breln1compset A) R) S))) as proof of (((eq fofType) ((breln1invset A) (((breln1compset A) R) S))) b)
% Found x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found (fun (x90:(P (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R))))=> x90) as proof of (P0 (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x130 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x13 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found x400000:=(x40000 x8):((breln1 A0) (((breln1compset A0) R) S))
% Found (x40000 x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((x4000 S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((x400 x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found ((((x40 R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (((((x4 A0) R) x7) S) x8) as proof of ((breln1 A0) (((breln1compset A) R) S))
% Found (x130 (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found ((x13 (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found (((x1 A0) (((breln1compset A) R) S)) (((((x4 A0) R) x7) S) x8)) as proof of ((breln1 A0) ((breln1invset A) (((breln1compset A) R) S)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((breln1invset A) S)) ((breln1invset A) R)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofT
% EOF
%------------------------------------------------------------------------------