%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU791^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n101.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 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU791^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n101.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 11:29:16 CDT 2014
% % CPUTime  : 300.10 
% 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 0x17ceea8>, <kernel.DependentProduct object at 0x17ce8c0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x13f2638>, <kernel.DependentProduct object at 0x17ce8c0>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x17ceab8>, <kernel.Sort object at 0x12bc998>) 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 0x17ce320>, <kernel.DependentProduct object at 0x17cecf8>) of role type named binunion_type
% Using role type
% Declaring binunion:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x17ceb90>, <kernel.DependentProduct object at 0x17ceea8>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x17ceab8>, <kernel.DependentProduct object at 0x17ce320>) of role type named breln1_type
% Using role type
% Declaring breln1:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x17ceb48>, <kernel.Sort object at 0x12bc998>) 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 0x17ce128>, <kernel.DependentProduct object at 0x17ceea8>) of role type named breln1compset_type
% Using role type
% Declaring breln1compset:(fofType->(fofType->(fofType->fofType)))
% FOF formula (<kernel.Constant object at 0x17ceb48>, <kernel.Sort object at 0x12bc998>) 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 0x17ceb48>, <kernel.Sort object at 0x12bc998>) 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 0x12b6b00>, <kernel.Sort object at 0x12bc998>) 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 (<kernel.Constant object at 0x17ceb48>, <kernel.Sort object at 0x12bc998>) of role type named breln1unionprop_type
% Using role type
% Declaring breln1unionprop:Prop
% FOF formula (((eq Prop) breln1unionprop) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((breln1 A) ((binunion R) S))))))) of role definition named breln1unionprop
% A new definition: (((eq Prop) breln1unionprop) (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((breln1 A) ((binunion R) S)))))))
% Defined: breln1unionprop:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((breln1 A) ((binunion R) S))))))
% FOF formula (<kernel.Constant object at 0x17ce128>, <kernel.Sort object at 0x12bc998>) of role type named breln1unionIL_type
% Using role type
% Declaring breln1unionIL:Prop
% FOF formula (((eq Prop) breln1unionIL) (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)) ((binunion R) S)))))))))))) of role definition named breln1unionIL
% A new definition: (((eq Prop) breln1unionIL) (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)) ((binunion R) S))))))))))))
% Defined: breln1unionIL:=(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)) ((binunion R) S)))))))))))
% FOF formula (<kernel.Constant object at 0x182abd8>, <kernel.Sort object at 0x12bc998>) of role type named breln1unionIR_type
% Using role type
% Declaring breln1unionIR:Prop
% FOF formula (((eq Prop) breln1unionIR) (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)) S)->((in ((kpair Xx) Xy)) ((binunion R) S)))))))))))) of role definition named breln1unionIR
% A new definition: (((eq Prop) breln1unionIR) (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)) S)->((in ((kpair Xx) Xy)) ((binunion R) S))))))))))))
% Defined: breln1unionIR:=(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)) S)->((in ((kpair Xx) Xy)) ((binunion R) S)))))))))))
% FOF formula (<kernel.Constant object at 0x182ab90>, <kernel.Sort object at 0x12bc998>) of role type named breln1unionE_type
% Using role type
% Declaring breln1unionE:Prop
% FOF formula (((eq Prop) breln1unionE) (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)) ((binunion R) S))->((or ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xx) Xy)) S)))))))))))) of role definition named breln1unionE
% A new definition: (((eq Prop) breln1unionE) (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)) ((binunion R) S))->((or ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xx) Xy)) S))))))))))))
% Defined: breln1unionE:=(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)) ((binunion R) S))->((or ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xx) Xy)) S)))))))))))
% FOF formula (setextsub->(subbreln1->(breln1compprop->(breln1compI->(breln1compE->(breln1unionprop->(breln1unionIL->(breln1unionIR->(breln1unionE->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (T:fofType), (((breln1 A) T)->(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))))))))))))))))) of role conjecture named woz2A
% Conjecture to prove = (setextsub->(subbreln1->(breln1compprop->(breln1compI->(breln1compE->(breln1unionprop->(breln1unionIL->(breln1unionIR->(breln1unionE->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (T:fofType), (((breln1 A) T)->(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))))))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(setextsub->(subbreln1->(breln1compprop->(breln1compI->(breln1compE->(breln1unionprop->(breln1unionIL->(breln1unionIR->(breln1unionE->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (T:fofType), (((breln1 A) T)->(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))))))))))))))))']
% 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 binunion:(fofType->(fofType->fofType)).
% 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 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.
% Definition breln1unionprop:=(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->((breln1 A) ((binunion R) S)))))):Prop.
% Definition breln1unionIL:=(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)) ((binunion R) S))))))))))):Prop.
% Definition breln1unionIR:=(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)) S)->((in ((kpair Xx) Xy)) ((binunion R) S))))))))))):Prop.
% Definition breln1unionE:=(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)) ((binunion R) S))->((or ((in ((kpair Xx) Xy)) R)) ((in ((kpair Xx) Xy)) S))))))))))):Prop.
% Trying to prove (setextsub->(subbreln1->(breln1compprop->(breln1compI->(breln1compE->(breln1unionprop->(breln1unionIL->(breln1unionIR->(breln1unionE->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (T:fofType), (((breln1 A) T)->(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))))))))))))))))
% Found x120:(P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x120:(P (((breln1compset A) ((binunion R) S)) T)))=> x120) as proof of (P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x120:(P (((breln1compset A) ((binunion R) S)) T)))=> x120) as proof of (P0 (((breln1compset A) ((binunion R) S)) T))
% Found x110:(P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x110:(P (((breln1compset A) ((binunion R) S)) T)))=> x110) as proof of (P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x110:(P (((breln1compset A) ((binunion R) S)) T)))=> x110) as proof of (P0 (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x11:(P (((breln1compset A) ((binunion R) S)) T))
% Instantiate: b:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found x11 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x11:(P (((breln1compset A) ((binunion R) S)) T))
% Instantiate: A0:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found x11 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x11:(P0 b)
% Instantiate: b:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found (fun (x11:(P0 b))=> x11) as proof of (P0 (((breln1compset A) ((binunion R) S)) T))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b))=> x11) as proof of ((P0 b)->(P0 (((breln1compset A) ((binunion R) S)) T)))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b))=> x11) as proof of (P b)
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: b:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x110:(P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x110:(P (((breln1compset A) ((binunion R) S)) T)))=> x110) as proof of (P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x110:(P (((breln1compset A) ((binunion R) S)) T)))=> x110) as proof of (P0 (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: A0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 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) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x120:(P b)
% Found (fun (x120:(P b))=> x120) as proof of (P b)
% Found (fun (x120:(P b))=> x120) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x110:(P b)
% Found (fun (x110:(P b))=> x110) as proof of (P b)
% Found (fun (x110:(P b))=> x110) as proof of (P0 b)
% Found x120:(P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x120:(P (((breln1compset A) ((binunion R) S)) T)))=> x120) as proof of (P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x120:(P (((breln1compset A) ((binunion R) S)) T)))=> x120) as proof of (P0 (((breln1compset A) ((binunion R) S)) T))
% Found x110:(P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x110:(P (((breln1compset A) ((binunion R) S)) T)))=> x110) as proof of (P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x110:(P (((breln1compset A) ((binunion R) S)) T)))=> x110) as proof of (P0 (((breln1compset A) ((binunion R) S)) T))
% Found x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) 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 x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% 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 x120:(P b)
% Found (fun (x120:(P b))=> x120) as proof of (P b)
% Found (fun (x120:(P b))=> x120) as proof of (P0 b)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x11:(P (((breln1compset A) ((binunion R) S)) T))
% Instantiate: b:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found x11 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x11:(P (((breln1compset A) ((binunion R) S)) T))
% Instantiate: A0:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found x11 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x11:(P0 b)
% Instantiate: b:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found (fun (x11:(P0 b))=> x11) as proof of (P0 (((breln1compset A) ((binunion R) S)) T))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b))=> x11) as proof of ((P0 b)->(P0 (((breln1compset A) ((binunion R) S)) T)))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b))=> x11) as proof of (P b)
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: b:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found x11:(P (((breln1compset A) ((binunion R) S)) T))
% Instantiate: a:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found x11 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x110:(P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x110:(P (((breln1compset A) ((binunion R) S)) T)))=> x110) as proof of (P (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x110:(P (((breln1compset A) ((binunion R) S)) T)))=> x110) as proof of (P0 (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% 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 x400000:=(x40000 x9):((breln1 A0) ((binunion R) S))
% Found (x40000 x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((x4000 S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((x400 x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((((x40 R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((((x4 A0) R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((((x4 A0) R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((x1200 (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((x120 x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> (((x12 ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found x120000:=(x12000 x10):((breln1 A0) (((breln1compset A0) R) T))
% Found (x12000 x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((x1200 T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((x120 x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((((x12 R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found x120000:=(x12000 x10):((breln1 A0) (((breln1compset A0) S) T))
% Found (x12000 x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x1200 T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((x120 x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((((x12 S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x4000 (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((x400 x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> (((x40 (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((((x4 A0) (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((((x4 A0) (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x400000:=(x40000 x9):((breln1 A0) ((binunion R) S))
% Found (x40000 x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((x4000 S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((x400 x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((((x40 R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((((x4 A0) R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((((x4 A0) R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((x1200 (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((x120 x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> (((x12 ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found x120000:=(x12000 x10):((breln1 A0) (((breln1compset A0) R) T))
% Found (x12000 x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((x1200 T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((x120 x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((((x12 R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found x120000:=(x12000 x10):((breln1 A0) (((breln1compset A0) S) T))
% Found (x12000 x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x1200 T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((x120 x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((((x12 S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x4000 (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((x400 x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> (((x40 (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((((x4 A0) (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((((x4 A0) (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: A0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P0 A0)
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: A0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P0 A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x11:(P2 b)
% Instantiate: b:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found (fun (x11:(P2 b))=> x11) as proof of (P2 (((breln1compset A) ((binunion R) S)) T))
% Found (fun (P2:(fofType->Prop)) (x11:(P2 b))=> x11) as proof of ((P2 b)->(P2 (((breln1compset A) ((binunion R) S)) T)))
% Found (fun (P2:(fofType->Prop)) (x11:(P2 b))=> x11) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x11:(P2 b)
% Instantiate: b:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found (fun (x11:(P2 b))=> x11) as proof of (P2 (((breln1compset A) ((binunion R) S)) T))
% Found (fun (P2:(fofType->Prop)) (x11:(P2 b))=> x11) as proof of ((P2 b)->(P2 (((breln1compset A) ((binunion R) S)) T)))
% Found (fun (P2:(fofType->Prop)) (x11:(P2 b))=> x11) as proof of (P1 b)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x11:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: b:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found x11:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: b:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P b)
% Found (fun (x120:(P b))=> x120) as proof of (P b)
% Found (fun (x120:(P b))=> x120) as proof of (P0 b)
% Found x120:(P b)
% Found (fun (x120:(P b))=> x120) as proof of (P b)
% Found (fun (x120:(P b))=> x120) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found x11:(P b)
% Found x11 as proof of (P0 (((breln1compset A) ((binunion R) S)) T))
% Found x110:(P b)
% Found (fun (x110:(P b))=> x110) as proof of (P b)
% Found (fun (x110:(P b))=> x110) as proof of (P0 b)
% Found x110:(P b)
% Found (fun (x110:(P b))=> x110) as proof of (P b)
% Found (fun (x110:(P b))=> x110) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x11:(P b)
% Instantiate: b0:=b:fofType
% Found x11 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: b:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found x11:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: A0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P2 A0)
% Found x11:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: A0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P2 A0)
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x11:(P b)
% Instantiate: A0:=b:fofType
% Found x11 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b1)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b1)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b1)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: a:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P0 a)
% Found x130:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x130:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x130) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x130:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x130) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% 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 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 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A) T)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A) T)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 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) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found x120:(P1 b)
% Found (fun (x120:(P1 b))=> x120) as proof of (P1 b)
% Found (fun (x120:(P1 b))=> x120) as proof of (P2 b)
% Found x120:(P1 b)
% Found (fun (x120:(P1 b))=> x120) as proof of (P1 b)
% Found (fun (x120:(P1 b))=> x120) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x400000:=(x40000 x9):((breln1 A0) ((binunion R) S))
% Found (x40000 x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((x4000 S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((x400 x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((((x40 R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((((x4 A0) R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((((x4 A0) R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((x1200 (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((x120 x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> (((x12 ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found x120000:=(x12000 x10):((breln1 A0) (((breln1compset A0) R) T))
% Found (x12000 x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((x1200 T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((x120 x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((((x12 R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found x120000:=(x12000 x10):((breln1 A0) (((breln1compset A0) S) T))
% Found (x12000 x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x1200 T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((x120 x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((((x12 S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x4000 (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((x400 x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> (((x40 (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((((x4 A0) (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((((x4 A0) (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x400000:=(x40000 x9):((breln1 A0) ((binunion R) S))
% Found (x40000 x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((x4000 S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((x400 x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((((x40 R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((((x4 A0) R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found (((((x4 A0) R) x8) S) x9) as proof of ((breln1 A0) ((binunion R) S))
% Found ((x1200 (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((x120 x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> (((x12 ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found (((fun (x13:((breln1 A0) ((binunion R) S)))=> ((((x1 A0) ((binunion R) S)) x13) T)) (((((x4 A0) R) x8) S) x9)) x10) as proof of ((breln1 A0) (((breln1compset A) ((binunion R) S)) T))
% Found x120000:=(x12000 x10):((breln1 A0) (((breln1compset A0) R) T))
% Found (x12000 x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((x1200 T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((x120 x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((((x12 R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found x120000:=(x12000 x10):((breln1 A0) (((breln1compset A0) S) T))
% Found (x12000 x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x1200 T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((x120 x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((((x12 S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x4000 (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((x400 x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> (((x40 (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((((x4 A0) (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (((fun (x12:((breln1 A0) (((breln1compset A) R) T)))=> ((((x4 A0) (((breln1compset A) R) T)) x12) (((breln1compset A) S) T))) (((((x1 A0) R) x8) T) x10)) (((((x1 A0) S) x9) T) x10)) as proof of ((breln1 A0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% 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 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 x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A0)
% Found x120:(P0 b)
% Found (fun (x120:(P0 b))=> x120) as proof of (P0 b)
% Found (fun (x120:(P0 b))=> x120) as proof of (P1 b)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found x11:(P0 b0)
% Instantiate: b0:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found (fun (x11:(P0 b0))=> x11) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b0))=> x11) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b0))=> x11) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found x11:(P0 b0)
% Instantiate: b0:=(((breln1compset A) ((binunion R) S)) T):fofType
% Found (fun (x11:(P0 b0))=> x11) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b0))=> x11) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b0))=> x11) as proof of (P b0)
% Found x8:((breln1 A) R)
% Instantiate: A1:=A:fofType;A0:=R:fofType
% Found x8 as proof of ((breln1 A1) A0)
% Found x8:((breln1 A) R)
% Instantiate: A1:=A:fofType;A0:=R:fofType
% Found x8 as proof of ((breln1 A1) A0)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x120:(P b0)
% Found (fun (x120:(P b0))=> x120) as proof of (P b0)
% Found (fun (x120:(P b0))=> x120) as proof of (P0 b0)
% Found x110:(P b)
% Found (fun (x110:(P b))=> x110) as proof of (P b)
% Found (fun (x110:(P b))=> x110) as proof of (P0 b)
% Found x110:(P b)
% Found (fun (x110:(P b))=> x110) as proof of (P b)
% Found (fun (x110:(P b))=> x110) as proof of (P0 b)
% Found x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) 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 x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) 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 x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: b0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 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 x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: b0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 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 x110:(P b0)
% Found (fun (x110:(P b0))=> x110) as proof of (P b0)
% Found (fun (x110:(P b0))=> x110) as proof of (P0 b0)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A0) T)
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x11 as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P b)
% Found (fun (x120:(P b))=> x120) as proof of (P b)
% Found (fun (x120:(P b))=> x120) as proof of (P0 b)
% Found x120:(P b)
% Found (fun (x120:(P b))=> x120) as proof of (P b)
% Found (fun (x120:(P b))=> x120) as proof of (P0 b)
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found x11:(P0 (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x11:(P0 (((breln1compset A) ((binunion R) S)) T)))=> x11) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x11:(P0 (((breln1compset A) ((binunion R) S)) T)))=> x11) as proof of ((P0 (((breln1compset A) ((binunion R) S)) T))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 (((breln1compset A) ((binunion R) S)) T)))=> x11) as proof of (P (((breln1compset A) ((binunion R) S)) T))
% Found x130:(P1 (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x130:(P1 (((breln1compset A) ((binunion R) S)) T)))=> x130) as proof of (P1 (((breln1compset A) ((binunion R) S)) T))
% Found (fun (x130:(P1 (((breln1compset A) ((binunion R) S)) T)))=> x130) as proof of (P2 (((breln1compset A) ((binunion R) S)) T))
% Found x130:(P1 b)
% Found (fun (x130:(P1 b))=> x130) as proof of (P1 b)
% Found (fun (x130:(P1 b))=> x130) as proof of (P2 b)
% Found x12:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Instantiate: Xz:=Xx:fofType;A0:=A:fofType
% Found x12 as proof of ((in Xz) A)
% Found x13:((in Xy) A0)
% Instantiate: A0:=A:fofType
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Instantiate: A0:=A:fofType
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Instantiate: Xz:=Xx:fofType;A0:=A:fofType
% Found x12 as proof of ((in Xz) A)
% Found x12:((in Xx) A0)
% Instantiate: Xz:=Xx:fofType;A0:=A:fofType
% Found x12 as proof of ((in Xz) A)
% Found x12:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Instantiate: A0:=A:fofType
% Found x13 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: A0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 as proof of (P0 A0)
% Found x11:(P ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Instantiate: A0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found x11 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 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b1)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b1)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b1)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% 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) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((breln1compset A) ((binunion R) S)) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (((breln1compset A) S) T))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b)
% Found x110:(P0 b)
% Found (fun (x110:(P0 b))=> x110) as proof of (P0 b)
% Found (fun (x110:(P0 b))=> x110) as proof of (P1 b)
% 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 x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x110:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x110) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) 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 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) 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 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) 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 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) 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 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) 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 x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A) T)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x10:((breln1 A) T)
% Found x10 as proof of ((breln1 A) T)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x150000:=(x15000 x10):((breln1 A0) (((breln1compset A0) R) T))
% Found (x15000 x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((x1500 T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((x150 x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((((x15 R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found x150000:=(x15000 x10):((breln1 A0) (((breln1compset A0) S) T))
% Found (x15000 x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x1500 T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((x150 x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((((x15 S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found x150000:=(x15000 x10):((breln1 A0) (((breln1compset A0) S) T))
% Found (x15000 x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x1500 T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((x150 x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((((x15 S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found x150000:=(x15000 x10):((breln1 A0) (((breln1compset A0) R) T))
% Found (x15000 x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((x1500 T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((x150 x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((((x15 R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found x150000:=(x15000 x10):((breln1 A0) (((breln1compset A0) S) T))
% Found (x15000 x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x1500 T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((x150 x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((((x15 S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found x150000:=(x15000 x10):((breln1 A0) (((breln1compset A0) R) T))
% Found (x15000 x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((x1500 T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((x150 x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((((x15 R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found x150000:=(x15000 x10):((breln1 A0) (((breln1compset A0) S) T))
% Found (x15000 x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((x1500 T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((x150 x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found ((((x15 S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found (((((x1 A0) S) x9) T) x10) as proof of ((breln1 A0) (((breln1compset A) S) T))
% Found x150000:=(x15000 x10):((breln1 A0) (((breln1compset A0) R) T))
% Found (x15000 x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((x1500 T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((x150 x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found ((((x15 R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found (((((x1 A0) R) x8) T) x10) as proof of ((breln1 A0) (((breln1compset A) R) T))
% Found x11:(P b)
% Instantiate: b0:=b:fofType
% Found x11 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 b)
% Found (fun (x120:(P1 b))=> x120) as proof of (P1 b)
% Found (fun (x120:(P1 b))=> x120) as proof of (P2 b)
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (x120:(P1 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))=> x120) as proof of (P2 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% 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 x11:(P0 b0)
% Instantiate: b0:=((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)):fofType
% Found (fun (x11:(P0 b0))=> x11) as proof of (P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b0))=> x11) as proof of ((P0 b0)->(P0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b0))=> x11) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))):(((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T)))
% Found (eq_ref0 ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found ((eq_ref fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) as proof of (((eq fofType) ((binunion (((breln1compset A) R) T)) (((breln1compset A) S) T))) b0)
% Found x11:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x11:(P0 b))=> x11) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b))=> x11) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x11:(P0 b))=> x11) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found eq_ref00:=(eq_ref0 (((breln1compset A) ((binunion R) S)) T)):(((eq fofType) (((breln1compset A) ((binunion R) S)) T)) (((breln1compset A) ((binunion R) S)) T))
% Found (eq_ref0 (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found ((eq_ref fofType) (((breln1compset A) ((binunion R) S)) T)) as proof of (((eq fofType) (((breln1compset A) ((binunion R) S)) T)) b)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A)
% Found x12:((in Xx) A0)
% Found x12 as proof of ((in Xx) A)
% Found x13:((in Xy) A0)
% Found x13 as proof of ((in Xy) A
% EOF
%------------------------------------------------------------------------------