%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : MSC025^2 : TPTP v6.1.0. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n108.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 13:26:43 EDT 2014

% Result   : Timeout 300.02s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : MSC025^2 : TPTP v6.1.0. Released v5.5.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n108.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 07:39:26 CDT 2014
% % CPUTime  : 300.02 
% 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 0x135e998>, <kernel.Constant object at 0x135e3b0>) of role type named one
% Using role type
% Declaring one:fofType
% FOF formula (<kernel.Constant object at 0x173b878>, <kernel.Single object at 0x135e560>) of role type named two
% Using role type
% Declaring two:fofType
% FOF formula (forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))) of role axiom named binarity_exhaust
% A new axiom: (forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% FOF formula (not (((eq fofType) one) two)) of role axiom named binarity_distinc
% A new axiom: (not (((eq fofType) one) two))
% FOF formula (<kernel.Constant object at 0x135eea8>, <kernel.DependentProduct object at 0x135e950>) of role type named b1_ty
% Using role type
% Declaring b1:(Prop->fofType)
% FOF formula (forall (X:Prop), ((and (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two)))) of role axiom named b1
% A new axiom: (forall (X:Prop), ((and (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))))
% FOF formula (<kernel.Constant object at 0x135eef0>, <kernel.DependentProduct object at 0x135e7e8>) of role type named b2_ty
% Using role type
% Declaring b2:(Prop->fofType)
% FOF formula (forall (X:Prop), ((and (X->(((eq fofType) (b2 X)) two))) ((X->False)->(((eq fofType) (b2 X)) one)))) of role axiom named b2
% A new axiom: (forall (X:Prop), ((and (X->(((eq fofType) (b2 X)) two))) ((X->False)->(((eq fofType) (b2 X)) one))))
% FOF formula (forall (F:(Prop->fofType)), ((forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))->((or (((eq (Prop->fofType)) F) b1)) (((eq (Prop->fofType)) F) b2)))) of role conjecture named goal
% Conjecture to prove = (forall (F:(Prop->fofType)), ((forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))->((or (((eq (Prop->fofType)) F) b1)) (((eq (Prop->fofType)) F) b2)))):Prop
% We need to prove ['(forall (F:(Prop->fofType)), ((forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))->((or (((eq (Prop->fofType)) F) b1)) (((eq (Prop->fofType)) F) b2))))']
% Parameter fofType:Type.
% Parameter one:fofType.
% Parameter two:fofType.
% Axiom binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))).
% Axiom binarity_distinc:(not (((eq fofType) one) two)).
% Parameter b1:(Prop->fofType).
% Axiom b1_TPTP_next:(forall (X:Prop), ((and (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two)))).
% Parameter b2:(Prop->fofType).
% Axiom b2_TPTP_next:(forall (X:Prop), ((and (X->(((eq fofType) (b2 X)) two))) ((X->False)->(((eq fofType) (b2 X)) one)))).
% Trying to prove (forall (F:(Prop->fofType)), ((forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))->((or (((eq (Prop->fofType)) F) b1)) (((eq (Prop->fofType)) F) b2))))
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found eta_expansion_dep000:=(eta_expansion_dep00 F):(((eq (Prop->fofType)) F) (fun (x:Prop)=> (F x)))
% Found (eta_expansion_dep00 F) as proof of (((eq (Prop->fofType)) F) b)
% Found ((eta_expansion_dep0 (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found eta_expansion_dep000:=(eta_expansion_dep00 F):(((eq (Prop->fofType)) F) (fun (x:Prop)=> (F x)))
% Found (eta_expansion_dep00 F) as proof of (((eq (Prop->fofType)) F) b)
% Found ((eta_expansion_dep0 (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found eta_expansion_dep000:=(eta_expansion_dep00 F):(((eq (Prop->fofType)) F) (fun (x:Prop)=> (F x)))
% Found (eta_expansion_dep00 F) as proof of (((eq (Prop->fofType)) F) b)
% Found ((eta_expansion_dep0 (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found eta_expansion_dep000:=(eta_expansion_dep00 F):(((eq (Prop->fofType)) F) (fun (x:Prop)=> (F x)))
% Found (eta_expansion_dep00 F) as proof of (((eq (Prop->fofType)) F) b)
% Found ((eta_expansion_dep0 (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) F) as proof of (((eq (Prop->fofType)) F) b)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P b1)->(P b1))
% Found (eq_ref00 P) as proof of (P0 b1)
% Found ((eq_ref0 b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found eq_ref000:=(eq_ref00 P):((P b2)->(P b2))
% Found (eq_ref00 P) as proof of (P0 b2)
% Found ((eq_ref0 b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found eq_ref000:=(eq_ref00 P):((P b1)->(P b1))
% Found (eq_ref00 P) as proof of (P0 b1)
% Found ((eq_ref0 b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found eq_ref000:=(eq_ref00 P):((P b2)->(P b2))
% Found (eq_ref00 P) as proof of (P0 b2)
% Found ((eq_ref0 b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: X:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of X
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: X:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of X
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found eq_ref000:=(eq_ref00 P):((P F)->(P F))
% Found (eq_ref00 P) as proof of (P0 F)
% Found ((eq_ref0 F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found (((eq_ref (Prop->fofType)) F) P) as proof of (P0 F)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: X:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of X
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: X:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of X
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found eta_expansion000:=(eta_expansion00 F):(((eq (Prop->fofType)) F) (fun (x:Prop)=> (F x)))
% Found (eta_expansion00 F) as proof of (((eq (Prop->fofType)) F) b)
% Found ((eta_expansion0 fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found eta_expansion000:=(eta_expansion00 F):(((eq (Prop->fofType)) F) (fun (x:Prop)=> (F x)))
% Found (eta_expansion00 F) as proof of (((eq (Prop->fofType)) F) b)
% Found ((eta_expansion0 fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found eq_ref000:=(eq_ref00 P):((P b1)->(P b1))
% Found (eq_ref00 P) as proof of (P0 b1)
% Found ((eq_ref0 b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found eq_ref000:=(eq_ref00 P):((P b2)->(P b2))
% Found (eq_ref00 P) as proof of (P0 b2)
% Found ((eq_ref0 b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found eq_ref000:=(eq_ref00 P):((P b2)->(P b2))
% Found (eq_ref00 P) as proof of (P0 b2)
% Found ((eq_ref0 b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found eq_ref000:=(eq_ref00 P):((P b1)->(P b1))
% Found (eq_ref00 P) as proof of (P0 b1)
% Found ((eq_ref0 b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: X:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of X
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: X:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of X
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b1):(((eq (Prop->fofType)) b1) (fun (x:Prop)=> (b1 x)))
% Found (eta_expansion_dep00 b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found ((eta_expansion_dep0 (fun (x1:Prop)=> fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b2):(((eq (Prop->fofType)) b2) (fun (x:Prop)=> (b2 x)))
% Found (eta_expansion_dep00 b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found ((eta_expansion_dep0 (fun (x1:Prop)=> fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b2)
% Found eta_expansion000:=(eta_expansion00 F):(((eq (Prop->fofType)) F) (fun (x:Prop)=> (F x)))
% Found (eta_expansion00 F) as proof of (((eq (Prop->fofType)) F) b)
% Found ((eta_expansion0 fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) b1)
% Found eta_expansion000:=(eta_expansion00 F):(((eq (Prop->fofType)) F) (fun (x:Prop)=> (F x)))
% Found (eta_expansion00 F) as proof of (((eq (Prop->fofType)) F) b)
% Found ((eta_expansion0 fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found (((eta_expansion Prop) fofType) F) as proof of (((eq (Prop->fofType)) F) b)
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: X:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% Instantiate: X:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop
% Found eta_expansion as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b1):(((eq (Prop->fofType)) b1) (fun (x:Prop)=> (b1 x)))
% Found (eta_expansion_dep00 b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found ((eta_expansion_dep0 (fun (x1:Prop)=> fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b2):(((eq (Prop->fofType)) b2) (fun (x:Prop)=> (b2 x)))
% Found (eta_expansion_dep00 b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found ((eta_expansion_dep0 (fun (x1:Prop)=> fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found eq_ref000:=(eq_ref00 P):((P b1)->(P b1))
% Found (eq_ref00 P) as proof of (P0 b1)
% Found ((eq_ref0 b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found eq_ref000:=(eq_ref00 P):((P b1)->(P b1))
% Found (eq_ref00 P) as proof of (P0 b1)
% Found ((eq_ref0 b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found eq_ref000:=(eq_ref00 P):((P b2)->(P b2))
% Found (eq_ref00 P) as proof of (P0 b2)
% Found ((eq_ref0 b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found eq_ref000:=(eq_ref00 P):((P b2)->(P b2))
% Found (eq_ref00 P) as proof of (P0 b2)
% Found ((eq_ref0 b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found eq_ref00:=(eq_ref0 (((eq (Prop->fofType)) F) b2)):(((eq Prop) (((eq (Prop->fofType)) F) b2)) (((eq (Prop->fofType)) F) b2))
% Found (eq_ref0 (((eq (Prop->fofType)) F) b2)) as proof of (((eq Prop) (((eq (Prop->fofType)) F) b2)) b)
% Found ((eq_ref Prop) (((eq (Prop->fofType)) F) b2)) as proof of (((eq Prop) (((eq (Prop->fofType)) F) b2)) b)
% Found ((eq_ref Prop) (((eq (Prop->fofType)) F) b2)) as proof of (((eq Prop) (((eq (Prop->fofType)) F) b2)) b)
% Found ((eq_ref Prop) (((eq (Prop->fofType)) F) b2)) as proof of (((eq Prop) (((eq (Prop->fofType)) F) b2)) b)
% Found classic0:=(classic (((eq (Prop->fofType)) F) b1)):((or (((eq (Prop->fofType)) F) b1)) (not (((eq (Prop->fofType)) F) b1)))
% Found (classic (((eq (Prop->fofType)) F) b1)) as proof of (P b)
% Found (classic (((eq (Prop->fofType)) F) b1)) as proof of (P b)
% Found (classic (((eq (Prop->fofType)) F) b1)) as proof of (P b)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found x2:(P F)
% Instantiate: X:=(P F):Prop
% Found x2 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found x2:(P F)
% Instantiate: X:=(P F):Prop
% Found x2 as proof of X
% Found x2:(P F)
% Instantiate: X:=(P F):Prop
% Found x2 as proof of X
% Found x2:(P F)
% Instantiate: X:=(P F):Prop
% Found x2 as proof of X
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found eq_ref00:=(eq_ref0 b2):(((eq (Prop->fofType)) b2) b2)
% Found (eq_ref0 b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found ((eq_ref (Prop->fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found ((eq_ref (Prop->fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found ((eq_ref (Prop->fofType)) b2) as proof of (((eq (Prop->fofType)) b2) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found ((eq_ref (Prop->fofType)) b) as proof of (((eq (Prop->fofType)) b) F)
% Found eq_ref00:=(eq_ref0 b1):(((eq (Prop->fofType)) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found ((eq_ref (Prop->fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found ((eq_ref (Prop->fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found ((eq_ref (Prop->fofType)) b1) as proof of (((eq (Prop->fofType)) b1) b)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found eq_ref000:=(eq_ref00 P):((P b1)->(P b1))
% Found (eq_ref00 P) as proof of (P0 b1)
% Found ((eq_ref0 b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found eq_ref000:=(eq_ref00 P):((P b2)->(P b2))
% Found (eq_ref00 P) as proof of (P0 b2)
% Found ((eq_ref0 b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found eq_ref000:=(eq_ref00 P):((P b2)->(P b2))
% Found (eq_ref00 P) as proof of (P0 b2)
% Found ((eq_ref0 b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found (((eq_ref (Prop->fofType)) b2) P) as proof of (P0 b2)
% Found eq_ref000:=(eq_ref00 P):((P b1)->(P b1))
% Found (eq_ref00 P) as proof of (P0 b1)
% Found ((eq_ref0 b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found (((eq_ref (Prop->fofType)) b1) P) as proof of (P0 b1)
% Found eq_ref000:=(eq_ref00 P):((P (b2 x0))->(P (b2 x0)))
% Found (eq_ref00 P) as proof of (P0 (b2 x0))
% Found ((eq_ref0 (b2 x0)) P) as proof of (P0 (b2 x0))
% Found (((eq_ref fofType) (b2 x0)) P) as proof of (P0 (b2 x0))
% Found (((eq_ref fofType) (b2 x0)) P) as proof of (P0 (b2 x0))
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found eq_ref000:=(eq_ref00 P):((P (b1 x0))->(P (b1 x0)))
% Found (eq_ref00 P) as proof of (P0 (b1 x0))
% Found ((eq_ref0 (b1 x0)) P) as proof of (P0 (b1 x0))
% Found (((eq_ref fofType) (b1 x0)) P) as proof of (P0 (b1 x0))
% Found (((eq_ref fofType) (b1 x0)) P) as proof of (P0 (b1 x0))
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found eq_ref000:=(eq_ref00 P):((P (b2 x0))->(P (b2 x0)))
% Found (eq_ref00 P) as proof of (P0 (b2 x0))
% Found ((eq_ref0 (b2 x0)) P) as proof of (P0 (b2 x0))
% Found (((eq_ref fofType) (b2 x0)) P) as proof of (P0 (b2 x0))
% Found (((eq_ref fofType) (b2 x0)) P) as proof of (P0 (b2 x0))
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found eq_ref000:=(eq_ref00 P):((P (b1 x0))->(P (b1 x0)))
% Found (eq_ref00 P) as proof of (P0 (b1 x0))
% Found ((eq_ref0 (b1 x0)) P) as proof of (P0 (b1 x0))
% Found (((eq_ref fofType) (b1 x0)) P) as proof of (P0 (b1 x0))
% Found (((eq_ref fofType) (b1 x0)) P) as proof of (P0 (b1 x0))
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found eq_ref000:=(eq_ref00 P):((P (F x0))->(P (F x0)))
% Found (eq_ref00 P) as proof of (P0 (F x0))
% Found ((eq_ref0 (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found (((eq_ref fofType) (F x0)) P) as proof of (P0 (F x0))
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found x2:(P F)
% Instantiate: X:=(P F):Prop
% Found x2 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found x2:(P F)
% Instantiate: X:=(P F):Prop
% Found x2 as proof of X
% Found x2:(P F)
% Instantiate: X:=(P F):Prop
% Found x2 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found x2:(P F)
% Instantiate: X:=(P F):Prop
% Found x2 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found eq_ref00:=(eq_ref0 (((eq (Prop->fofType)) F) b2)):(((eq Prop) (((eq (Prop->fofType)) F) b2)) (((eq (Prop->fofType)) F) b2))
% Found (eq_ref0 (((eq (Prop->fofType)) F) b2)) as proof of (((eq Prop) (((eq (Prop->fofType)) F) b2)) b)
% Found ((eq_ref Prop) (((eq (Prop->fofType)) F) b2)) as proof of (((eq Prop) (((eq (Prop->fofType)) F) b2)) b)
% Found ((eq_ref Prop) (((eq (Prop->fofType)) F) b2)) as proof of (((eq Prop) (((eq (Prop->fofType)) F) b2)) b)
% Found ((eq_ref Prop) (((eq (Prop->fofType)) F) b2)) as proof of (((eq Prop) (((eq (Prop->fofType)) F) b2)) b)
% Found classic0:=(classic (((eq (Prop->fofType)) F) b1)):((or (((eq (Prop->fofType)) F) b1)) (not (((eq (Prop->fofType)) F) b1)))
% Found (classic (((eq (Prop->fofType)) F) b1)) as proof of (P b)
% Found (classic (((eq (Prop->fofType)) F) b1)) as proof of (P b)
% Found (classic (((eq (Prop->fofType)) F) b1)) as proof of (P b)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found b1_TPTP_next__proj1:=(fun (X:Prop)=> (((proj1 (X->(((eq fofType) (b1 X)) one))) ((X->False)->(((eq fofType) (b1 X)) two))) (b1_TPTP_next X))):(forall (X:Prop), (X->(((eq fofType) (b1 X)) one)))
% Instantiate: X:=(forall (X:Prop), (X->(((eq fofType) (b1 X)) one))):Prop
% Found b1_TPTP_next__proj1 as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found binarity_distinc:(not (((eq fofType) one) two))
% Instantiate: X:=(((eq fofType) one) two):Prop
% Found binarity_distinc as proof of (X->False)
% Found binarity_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% Instantiate: X:=(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))):Prop
% Found binarity_exhaust as proof of X
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b1 x0))
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found eq_ref00:=(eq_ref0 (F x0)):(((eq fofType) (F x0)) (F x0))
% Found (eq_ref0 (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found ((eq_ref fofType) (F x0)) as proof of (((eq fofType) (F x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (b2 x0))
% Found eq_ref00:=(eq_ref0 b):(((eq (Prop->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (Prop->fofType)) b) F)
% Fo
% EOF
%------------------------------------------------------------------------------