%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : CSR146^3 : TPTP v6.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n115.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 13:21:06 EDT 2014

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

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : CSR146^3 : TPTP v6.1.0. Released v4.1.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n115.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 10:09:26 CDT 2014
% % CPUTime  : 300.09 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x246e998>, <kernel.Type object at 0x246e908>) of role type named numbers
% Using role type
% Declaring num:Type
% FOF formula (<kernel.Constant object at 0x1f58638>, <kernel.DependentProduct object at 0x246e908>) of role type named holdsDuring_THFTYPE_IiooI
% Using role type
% Declaring holdsDuring_THFTYPE_IiooI:(fofType->(Prop->Prop))
% FOF formula (<kernel.Constant object at 0x246e9e0>, <kernel.DependentProduct object at 0x246e998>) of role type named husband_THFTYPE_IiioI
% Using role type
% Declaring husband_THFTYPE_IiioI:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x246eb00>, <kernel.Single object at 0x246ea28>) of role type named lChris_THFTYPE_i
% Using role type
% Declaring lChris_THFTYPE_i:fofType
% FOF formula (<kernel.Constant object at 0x246e950>, <kernel.Single object at 0x246ecf8>) of role type named lCorina_THFTYPE_i
% Using role type
% Declaring lCorina_THFTYPE_i:fofType
% FOF formula (<kernel.Constant object at 0x246e9e0>, <kernel.DependentProduct object at 0x246e5f0>) of role type named lYearFn_THFTYPE_IiiI
% Using role type
% Declaring lYearFn_THFTYPE_IiiI:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x246e680>, <kernel.Single object at 0x246ecf8>) of role type named n2009_THFTYPE_i
% Using role type
% Declaring n2009_THFTYPE_i:fofType
% FOF formula (<kernel.Constant object at 0x246e950>, <kernel.DependentProduct object at 0x246e9e0>) of role type named wife_THFTYPE_IiioI
% Using role type
% Declaring wife_THFTYPE_IiioI:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x246e9e0>, <kernel.DependentProduct object at 0x246e680>) of role type named inverse_THFTYPE_IIiioIIiioIoI
% Using role type
% Declaring inverse_THFTYPE_IIiioIIiioIoI:((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))
% FOF formula ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI) of role axiom named ax
% A new axiom: ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% FOF formula (forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1))))) of role axiom named ax_001
% A new axiom: (forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% FOF formula (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True)) of role axiom named ax_002
% A new axiom: (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% FOF formula ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X)))) of role axiom named ax_003
% A new axiom: ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% FOF formula ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i)) of role axiom named ax_004
% A new axiom: ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% FOF formula ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) of role conjecture named con
% Conjecture to prove = ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))):Prop
% Parameter num_DUMMY:num.
% We need to prove ['((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))']
% Parameter num:Type.
% Parameter fofType:Type.
% Parameter holdsDuring_THFTYPE_IiooI:(fofType->(Prop->Prop)).
% Parameter husband_THFTYPE_IiioI:(fofType->(fofType->Prop)).
% Parameter lChris_THFTYPE_i:fofType.
% Parameter lCorina_THFTYPE_i:fofType.
% Parameter lYearFn_THFTYPE_IiiI:(fofType->fofType).
% Parameter n2009_THFTYPE_i:fofType.
% Parameter wife_THFTYPE_IiioI:(fofType->(fofType->Prop)).
% Parameter inverse_THFTYPE_IIiioIIiioIoI:((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop)).
% Axiom ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI).
% Axiom ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1))))).
% Axiom ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True)).
% Axiom ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X)))).
% Axiom ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i)).
% Trying to prove ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Instantiate: x:=(fun (x1:fofType) (x00:fofType)=> ((wife_THFTYPE_IiioI x00) x1)):(fofType->(fofType->Prop))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Instantiate: x1:=(fun (x3:fofType) (x20:fofType)=> ((wife_THFTYPE_IiioI x20) x3)):(fofType->(fofType->Prop))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x1 lChris_THFTYPE_i) lCorina_THFTYPE_i))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Instantiate: x:=(fun (x3:fofType) (x20:fofType)=> ((wife_THFTYPE_IiioI x20) x3)):(fofType->(fofType->Prop))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))
% Found eq_ref00:=(eq_ref0 (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))):(((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found (eq_ref0 (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) b)
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) b)
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) b)
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) b)
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))))
% Found (fun (x:(fofType->(fofType->Prop)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))))
% Found (fun (x:(fofType->(fofType->Prop)))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->(fofType->Prop))), (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))))
% Found (fun (x:(fofType->(fofType->Prop)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))))
% Found (fun (x:(fofType->(fofType->Prop)))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->(fofType->Prop))), (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))))))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found eq_ref00:=(eq_ref0 (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))):(((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found (eq_ref0 (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) b)
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) b)
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) b)
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))) b)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x1 lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x1 lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x1 lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))))
% Found (fun (x1:(fofType->(fofType->Prop)))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x1 lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))))
% Found (fun (x1:(fofType->(fofType->Prop)))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->(fofType->Prop))), (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x1 lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x1 lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x1 lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))))
% Found (fun (x1:(fofType->(fofType->Prop)))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x1 lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))))
% Found (fun (x1:(fofType->(fofType->Prop)))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->(fofType->Prop))), (((eq Prop) (f x)) ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((x lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))))))
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))), (((eq (forall (x50:A), (B x50))) f) (fun (x50:A)=> (f x50))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x50:A), (((eq B) (f x50)) (g x50)))->(((eq (A->B)) f) g)))
% Found x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x2 as proof of (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found I:True
% Found I as proof of True
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x50:A), ((ex B) (fun (y:B)=> ((R x50) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), ((R x50) (f x50)))))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x50:A), ((F x50)->P))->(((ex A) F)->P)))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found x0:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found x0 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x50:A) (y:B), (((eq C) ((f x50) y)) ((g x50) y)))->(((eq (A->(B->C))) f) g)))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), (((ex B) (fun (y:B)=> ((R x50) y)))->((R x50) (f x50))))))))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x50:A)=> (f x50))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))) (g:(forall (x50:A), (B x50))), ((forall (x50:A), (((eq (B x50)) (f x50)) (g x50)))->(((eq (forall (x50:A), (B x50))) f) g)))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x50:A)=> (P x50)))->(P (co P))))))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))) (g:(forall (x50:A), (B x50))), ((forall (x50:A), (((eq (B x50)) (f x50)) (g x50)))->(((eq (forall (x50:A), (B x50))) f) g)))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x50:A), ((F x50)->P))->(((ex A) F)->P)))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x50:A), ((ex B) (fun (y:B)=> ((R x50) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), ((R x50) (f x50)))))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x50:A), (((eq B) (f x50)) (g x50)))->(((eq (A->B)) f) g)))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found I:True
% Found I as proof of True
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x50:A)=> (f x50))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x50:A)=> (P x50)))->(P (co P))))))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x2 as proof of (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))), (((eq (forall (x50:A), (B x50))) f) (fun (x50:A)=> (f x50))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x50:A) (y:B), (((eq C) ((f x50) y)) ((g x50) y)))->(((eq (A->(B->C))) f) g)))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), (((ex B) (fun (y:B)=> ((R x50) y)))->((R x50) (f x50))))))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found x0:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found x0 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found I:True
% Found I as proof of True
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found I:True
% Found I as proof of True
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found eta_expansion000:=(eta_expansion00 (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))):(((eq (fofType->(fofType->Prop))) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) (fun (x:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (eta_expansion00 (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) as proof of (((eq (fofType->(fofType->Prop))) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) b)
% Found ((eta_expansion0 (fofType->Prop)) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) as proof of (((eq (fofType->(fofType->Prop))) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) b)
% Found (((eta_expansion fofType) (fofType->Prop)) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) as proof of (((eq (fofType->(fofType->Prop))) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) b)
% Found (((eta_expansion fofType) (fofType->Prop)) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) as proof of (((eq (fofType->(fofType->Prop))) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) b)
% Found (((eta_expansion fofType) (fofType->Prop)) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) as proof of (((eq (fofType->(fofType->Prop))) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))) b)
% Found eq_ref00:=(eq_ref0 (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))):(((eq (fofType->(fofType->Prop))) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2))))
% Found (eq_ref0 (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))) as proof of (((eq (fofType->(fofType->Prop))) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))) b)
% Found ((eq_ref (fofType->(fofType->Prop))) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))) as proof of (((eq (fofType->(fofType->Prop))) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))) b)
% Found ((eq_ref (fofType->(fofType->Prop))) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))) as proof of (((eq (fofType->(fofType->Prop))) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))) b)
% Found ((eq_ref (fofType->(fofType->Prop))) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))) as proof of (((eq (fofType->(fofType->Prop))) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2)))) b)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found I:True
% Found I as proof of True
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x50:A) (y:B), (((eq C) ((f x50) y)) ((g x50) y)))->(((eq (A->(B->C))) f) g)))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x50:A)=> (f x50))))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))) (g:(forall (x50:A), (B x50))), ((forall (x50:A), (((eq (B x50)) (f x50)) (g x50)))->(((eq (forall (x50:A), (B x50))) f) g)))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x50:A)=> (P x50)))->(P (co P))))))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x50:A), (((eq B) (f x50)) (g x50)))->(((eq (A->B)) f) g)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found x0:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x0 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x50:A), ((ex B) (fun (y:B)=> ((R x50) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), ((R x50) (f x50)))))))
% Found x2:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found x2 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), (((ex B) (fun (y:B)=> ((R x50) y)))->((R x50) (f x50))))))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))), (((eq (forall (x50:A), (B x50))) f) (fun (x50:A)=> (f x50))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found I:True
% Found I as proof of True
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x50:A), ((F x50)->P))->(((ex A) F)->P)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found I:True
% Found I as proof of True
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), (((ex B) (fun (y:B)=> ((R x50) y)))->((R x50) (f x50))))))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x50:A), (((eq B) (f x50)) (g x50)))->(((eq (A->B)) f) g)))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found x0:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x0 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x2:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found x2 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x50:A) (y:B), (((eq C) ((f x50) y)) ((g x50) y)))->(((eq (A->(B->C))) f) g)))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x50:A)=> (f x50))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x50:A), ((F x50)->P))->(((ex A) F)->P)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x50:A), ((ex B) (fun (y:B)=> ((R x50) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), ((R x50) (f x50)))))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))), (((eq (forall (x50:A), (B x50))) f) (fun (x50:A)=> (f x50))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))) (g:(forall (x50:A), (B x50))), ((forall (x50:A), (((eq (B x50)) (f x50)) (g x50)))->(((eq (forall (x50:A), (B x50))) f) g)))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x50:A)=> (P x50)))->(P (co P))))))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found I:True
% Found I as proof of True
% Found eta_expansion_dep000:=(eta_expansion_dep00 (f x)):(((eq (fofType->Prop)) (f x)) (fun (x0:fofType)=> ((f x) x0)))
% Found (eta_expansion_dep00 (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found (fun (x:fofType)=> (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (f x))) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found (fun (x:fofType)=> (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (f x))) as proof of (forall (x:fofType), (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)))))
% Found eta_expansion000:=(eta_expansion00 (f x)):(((eq (fofType->Prop)) (f x)) (fun (x0:fofType)=> ((f x) x0)))
% Found (eta_expansion00 (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found ((eta_expansion0 Prop) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (((eta_expansion fofType) Prop) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (((eta_expansion fofType) Prop) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (fun (x:fofType)=> (((eta_expansion fofType) Prop) (f x))) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (fun (x:fofType)=> (((eta_expansion fofType) Prop) (f x))) as proof of (forall (x:fofType), (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (f x)):(((eq (fofType->Prop)) (f x)) (fun (x0:fofType)=> ((f x) x0)))
% Found (eta_expansion_dep00 (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (fun (x:fofType)=> (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (f x))) as proof of (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (fun (x:fofType)=> (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (f x))) as proof of (forall (x:fofType), (((eq (fofType->Prop)) (f x)) (fun (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))))
% Found eta_expansion000:=(eta_expansion00 (f x)):(((eq (fofType->Prop)) (f x)) (fun (x0:fofType)=> ((f x) x0)))
% Found (eta_expansion00 (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found ((eta_expansion0 Prop) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found (((eta_expansion fofType) Prop) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found (((eta_expansion fofType) Prop) (f x)) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found (fun (x:fofType)=> (((eta_expansion fofType) Prop) (f x))) as proof of (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found (fun (x:fofType)=> (((eta_expansion fofType) Prop) (f x))) as proof of (forall (x:fofType), (((eq (fofType->Prop)) (f x)) (fun (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)))))
% Found eq_ref00:=(eq_ref0 ((f x) y)):(((eq Prop) ((f x) y)) ((f x) y))
% Found (eq_ref0 ((f x) y)) as proof of (((eq Prop) ((f x) y)) ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI y) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))
% Found ((eq_ref Prop) ((f x) y)) as proof of (((eq Prop) ((f x) y)) ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI y) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))
% Found ((eq_ref Prop) ((f x) y)) as proof of (((eq Prop) ((f x) y)) ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI y) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))
% Found (fun (y:fofType)=> ((eq_ref Prop) ((f x) y))) as proof of (((eq Prop) ((f x) y)) ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI y) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True)))))))
% Found (fun (x:fofType) (y:fofType)=> ((eq_ref Prop) ((f x) y))) as proof of (forall (y:fofType), (((eq Prop) ((f x) y)) ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI y) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found (fun (x:fofType) (y:fofType)=> ((eq_ref Prop) ((f x) y))) as proof of (forall (x:fofType) (y:fofType), (((eq Prop) ((f x) y)) ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI y) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found eq_ref00:=(eq_ref0 ((f x) y)):(((eq Prop) ((f x) y)) ((f x) y))
% Found (eq_ref0 ((f x) y)) as proof of (((eq Prop) ((f x) y)) (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)))
% Found ((eq_ref Prop) ((f x) y)) as proof of (((eq Prop) ((f x) y)) (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)))
% Found ((eq_ref Prop) ((f x) y)) as proof of (((eq Prop) ((f x) y)) (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)))
% Found (fun (y:fofType)=> ((eq_ref Prop) ((f x) y))) as proof of (((eq Prop) ((f x) y)) (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)))
% Found (fun (x:fofType) (y:fofType)=> ((eq_ref Prop) ((f x) y))) as proof of (forall (y:fofType), (((eq Prop) ((f x) y)) (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found (fun (x:fofType) (y:fofType)=> ((eq_ref Prop) ((f x) y))) as proof of (forall (x:fofType) (y:fofType), (((eq Prop) ((f x) y)) (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Instantiate: REL2:=wife_THFTYPE_IiioI:(fofType->(fofType->Prop))
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) REL2)
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Instantiate: REL2:=wife_THFTYPE_IiioI:(fofType->(fofType->Prop))
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) REL2)
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Instantiate: REL2:=wife_THFTYPE_IiioI:(fofType->(fofType->Prop))
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) REL2)
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Instantiate: REL2:=wife_THFTYPE_IiioI:(fofType->(fofType->Prop))
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) REL2)
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Instantiate: REL2:=wife_THFTYPE_IiioI:(fofType->(fofType->Prop))
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) REL2)
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Instantiate: REL2:=wife_THFTYPE_IiioI:(fofType->(fofType->Prop))
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) REL2)
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Instantiate: REL2:=wife_THFTYPE_IiioI:(fofType->(fofType->Prop))
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) REL2)
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Instantiate: REL2:=wife_THFTYPE_IiioI:(fofType->(fofType->Prop))
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) REL2)
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->(fofType->Prop))->Prop)) a) (fun (x:(fofType->(fofType->Prop)))=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->(fofType->Prop)))=> Prop)) a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->(fofType->Prop))) (fun (x1:(fofType->(fofType->Prop)))=> Prop)) a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->(fofType->Prop))) (fun (x1:(fofType->(fofType->Prop)))=> Prop)) a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->(fofType->Prop))) (fun (x1:(fofType->(fofType->Prop)))=> Prop)) a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->(fofType->Prop))->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->(fofType->Prop))->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found eq_ref00:=(eq_ref0 (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))):(((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))))
% Found (eq_ref0 (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found ((eq_ref Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found ((eq_ref Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found ((eq_ref Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->(fofType->Prop))->Prop)) a) (fun (x:(fofType->(fofType->Prop)))=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found (((eta_expansion (fofType->(fofType->Prop))) Prop) a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found (((eta_expansion (fofType->(fofType->Prop))) Prop) a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found (((eta_expansion (fofType->(fofType->Prop))) Prop) a) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->(fofType->Prop))->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->(fofType->Prop))->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found ((eq_ref ((fofType->(fofType->Prop))->Prop)) b) as proof of (((eq ((fofType->(fofType->Prop))->Prop)) b) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))
% Found eq_ref00:=(eq_ref0 (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))):(((eq Prop) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))))
% Found (eq_ref0 (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found ((eq_ref Prop) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found ((eq_ref Prop) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found ((eq_ref Prop) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found eq_ref00:=(eq_ref0 (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))):(((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))))
% Found (eq_ref0 (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found ((eq_ref Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found ((eq_ref Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found ((eq_ref Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) as proof of (((eq Prop) (not (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True)))) b)
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))) (g:(forall (x50:A), (B x50))), ((forall (x50:A), (((eq (B x50)) (f x50)) (g x50)))->(((eq (forall (x50:A), (B x50))) f) g)))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x50:A) (y:B), (((eq C) ((f x50) y)) ((g x50) y)))->(((eq (A->(B->C))) f) g)))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), (((ex B) (fun (y:B)=> ((R x50) y)))->((R x50) (f x50))))))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x50:A), ((ex B) (fun (y:B)=> ((R x50) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), ((R x50) (f x50)))))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x50:A)=> (f x50))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found I:True
% Found I as proof of True
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x50:A), ((F x50)->P))->(((ex A) F)->P)))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x50:A)=> (P x50)))->(P (co P))))))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x50:A), (((eq B) (f x50)) (g x50)))->(((eq (A->B)) f) g)))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))), (((eq (forall (x50:A), (B x50))) f) (fun (x50:A)=> (f x50))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x2 as proof of (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x0:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found x0 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x50:A), ((F x50)->P))->(((ex A) F)->P)))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x50:A)=> (P x50)))->(P (co P))))))))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))), (((eq (forall (x50:A), (B x50))) f) (fun (x50:A)=> (f x50))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x50:A), ((ex B) (fun (y:B)=> ((R x50) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), ((R x50) (f x50)))))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x50:A) (y:B), (((eq C) ((f x50) y)) ((g x50) y)))->(((eq (A->(B->C))) f) g)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x2 as proof of (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x0:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found x0 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x50:A)=> (f x50))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x50:A), (((eq B) (f x50)) (g x50)))->(((eq (A->B)) f) g)))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found I:True
% Found I as proof of True
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), (((ex B) (fun (y:B)=> ((R x50) y)))->((R x50) (f x50))))))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))) (g:(forall (x50:A), (B x50))), ((forall (x50:A), (((eq (B x50)) (f x50)) (g x50)))->(((eq (forall (x50:A), (B x50))) f) g)))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found I:True
% Found I as proof of True
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found I:True
% Found I as proof of True
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found I:True
% Found I as proof of True
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found lChris_THFTYPE_i:fofType
% Found lChris_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), (((ex B) (fun (y:B)=> ((R x50) y)))->((R x50) (f x50))))))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x50:A) (y:B), (((eq C) ((f x50) y)) ((g x50) y)))->(((eq (A->(B->C))) f) g)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))), (((eq (forall (x50:A), (B x50))) f) (fun (x50:A)=> (f x50))))
% Found x2:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found x2 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x50:A), (((eq B) (f x50)) (g x50)))->(((eq (A->B)) f) g)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found x0:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x0 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found I:True
% Found I as proof of True
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))) (g:(forall (x50:A), (B x50))), ((forall (x50:A), (((eq (B x50)) (f x50)) (g x50)))->(((eq (forall (x50:A), (B x50))) f) g)))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x50:A)=> (f x50))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x50:A), ((F x50)->P))->(((ex A) F)->P)))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x50:A)=> (P x50)))->(P (co P))))))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x50:A), ((ex B) (fun (y:B)=> ((R x50) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), ((R x50) (f x50)))))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found I:True
% Found I as proof of True
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL2:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), (((ex B) (fun (y:B)=> ((R x50) y)))->((R x50) (f x50))))))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found x0:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x0 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x50:A)=> (f x50))))
% Found ax_001__proj10:=(ax_001__proj1 husband_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) husband_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((husband_THFTYPE_IiioI INST2) INST1)))))
% Found x2:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found x2 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x50:A) (y:B), (((eq C) ((f x50) y)) ((g x50) y)))->(((eq (A->(B->C))) f) g)))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x50:A)=> (P x50)))->(P (co P))))))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))) (g:(forall (x50:A), (B x50))), ((forall (x50:A), (((eq (B x50)) (f x50)) (g x50)))->(((eq (forall (x50:A), (B x50))) f) g)))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))), (((eq (forall (x50:A), (B x50))) f) (fun (x50:A)=> (f x50))))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x50:A), (((eq B) (f x50)) (g x50)))->(((eq (A->B)) f) g)))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x50:A), ((F x50)->P))->(((ex A) F)->P)))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x50:A), ((ex B) (fun (y:B)=> ((R x50) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), ((R x50) (f x50)))))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found I:True
% Found I as proof of True
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x6:A), ((ex B) (fun (y:B)=> ((R x6) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x6:A), ((R x6) (f x6)))))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x6:A) (y:B), (((eq C) ((f x6) y)) ((g x6) y)))->(((eq (A->(B->C))) f) g)))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x2 as proof of (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x6:A)=> (f x6))))
% Found x0:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found x0 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x6:A), (B x6))), (((eq (forall (x6:A), (B x6))) f) (fun (x6:A)=> (f x6))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x6:A), (((eq B) (f x6)) (g x6)))->(((eq (A->B)) f) g)))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found ax_001__proj10:=(ax_001__proj1 REL2):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((REL2 INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((REL2 INST2) INST1)))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x6:A)=> (P x6)))->(P (co P))))))))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x6:A), (((ex B) (fun (y:B)=> ((R x6) y)))->((R x6) (f x6))))))))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x6:A), (B x6))) (g:(forall (x6:A), (B x6))), ((forall (x6:A), (((eq (B x6)) (f x6)) (g x6)))->(((eq (forall (x6:A), (B x6))) f) g)))
% Found I:True
% Found I as proof of True
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x6:A), ((F x6)->P))->(((ex A) F)->P)))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x6:A), (B x6))), (((eq (forall (x6:A), (B x6))) f) (fun (x6:A)=> (f x6))))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x6:A), (((ex B) (fun (y:B)=> ((R x6) y)))->((R x6) (f x6))))))))
% Found I:True
% Found I as proof of True
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x6:A) (y:B), (((eq C) ((f x6) y)) ((g x6) y)))->(((eq (A->(B->C))) f) g)))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x6:A)=> (f x6))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x6:A), ((ex B) (fun (y:B)=> ((R x6) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x6:A), ((R x6) (f x6)))))))
% Found x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x2 as proof of (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x6:A), ((F x6)->P))->(((ex A) F)->P)))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x6:A), (B x6))) (g:(forall (x6:A), (B x6))), ((forall (x6:A), (((eq (B x6)) (f x6)) (g x6)))->(((eq (forall (x6:A), (B x6))) f) g)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax_001__proj10:=(ax_001__proj1 wife_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((wife_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) wife_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((wife_THFTYPE_IiioI INST2) INST1)))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x6:A), (((eq B) (f x6)) (g x6)))->(((eq (A->B)) f) g)))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found x0:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found x0 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x6:A)=> (P x6)))->(P (co P))))))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->(fofType->Prop))) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->(fofType->Prop))) b) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found ((eq_ref (fofType->(fofType->Prop))) b) as proof of (((eq (fofType->(fofType->Prop))) b) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found ((eq_ref (fofType->(fofType->Prop))) b) as proof of (((eq (fofType->(fofType->Prop))) b) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found ((eq_ref (fofType->(fofType->Prop))) b) as proof of (((eq (fofType->(fofType->Prop))) b) (fun (x3:fofType) (x20:fofType)=> ((ex (fofType->(fofType->Prop))) (fun (R:(fofType->(fofType->Prop)))=> ((and ((holdsDuring_THFTYPE_IiooI x20) ((R lChris_THFTYPE_i) lCorina_THFTYPE_i))) (not (((eq (fofType->(fofType->Prop))) R) (fun (X:fofType) (Y:fofType)=> True))))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->(fofType->Prop))) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> (fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> (fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> (fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> (fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->(fofType->Prop))) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found ((eq_ref (fofType->(fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found ((eq_ref (fofType->(fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found ((eq_ref (fofType->(fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->(fofType->Prop))) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->(fofType->Prop))) b) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2))))
% Found ((eq_ref (fofType->(fofType->Prop))) b) as proof of (((eq (fofType->(fofType->Prop))) b) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2))))
% Found ((eq_ref (fofType->(fofType->Prop))) b) as proof of (((eq (fofType->(fofType->Prop))) b) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2))))
% Found ((eq_ref (fofType->(fofType->Prop))) b) as proof of (((eq (fofType->(fofType->Prop))) b) (fun (x2:fofType) (x10:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x2))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->(fofType->Prop))) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found ((eq_ref (fofType->(fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found ((eq_ref (fofType->(fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found ((eq_ref (fofType->(fofType->Prop))) a) as proof of (((eq (fofType->(fofType->Prop))) a) b)
% Found x0:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found x0 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x2 as proof of (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x6:A)=> (f x6))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x6:A), ((F x6)->P))->(((ex A) F)->P)))
% Found I:True
% Found I as proof of True
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x6:A) (y:B), (((eq C) ((f x6) y)) ((g x6) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x6:A), (B x6))) (g:(forall (x6:A), (B x6))), ((forall (x6:A), (((eq (B x6)) (f x6)) (g x6)))->(((eq (forall (x6:A), (B x6))) f) g)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x6:A), (B x6))), (((eq (forall (x6:A), (B x6))) f) (fun (x6:A)=> (f x6))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x6:A)=> (P x6)))->(P (co P))))))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x6:A), ((ex B) (fun (y:B)=> ((R x6) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x6:A), ((R x6) (f x6)))))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found ax_001__proj10:=(ax_001__proj1 REL2):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((REL2 INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((REL2 INST2) INST1)))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x6:A), (((ex B) (fun (y:B)=> ((R x6) y)))->((R x6) (f x6))))))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x6:A), (((eq B) (f x6)) (g x6)))->(((eq (A->B)) f) g)))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x6:A), ((F x6)->P))->(((ex A) F)->P)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x6:A), (((ex B) (fun (y:B)=> ((R x6) y)))->((R x6) (f x6))))))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x6:A), (B x6))) (g:(forall (x6:A), (B x6))), ((forall (x6:A), (((eq (B x6)) (f x6)) (g x6)))->(((eq (forall (x6:A), (B x6))) f) g)))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x6:A)=> (P x6)))->(P (co P))))))))
% Found x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found x2 as proof of (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x6:A), ((ex B) (fun (y:B)=> ((R x6) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x6:A), ((R x6) (f x6)))))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found I:True
% Found I as proof of True
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x6:A), (B x6))), (((eq (forall (x6:A), (B x6))) f) (fun (x6:A)=> (f x6))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x6:A), (((eq B) (f x6)) (g x6)))->(((eq (A->B)) f) g)))
% Found x0:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found x0 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x6:A) (y:B), (((eq C) ((f x6) y)) ((g x6) y)))->(((eq (A->(B->C))) f) g)))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found ax_001__proj10:=(ax_001__proj1 wife_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((wife_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) wife_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((wife_THFTYPE_IiioI INST2) INST1)))))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x6:A)=> (f x6))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found ax_001__proj10:=(ax_001__proj1 REL2):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((REL2 INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((REL2 INST2) INST1)))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found I:True
% Found I as proof of True
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Instantiate: REL2:=wife_THFTYPE_IiioI:(fofType->(fofType->Prop));x1:=husband_THFTYPE_IiioI:(fofType->(fofType->Prop))
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI x1) REL2)
% Found (x20 ax) as proof of ((inverse_THFTYPE_IIiioIIiioIoI (fun (x5:fofType) (x40:fofType)=> True)) REL2)
% Found ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax) as proof of ((inverse_THFTYPE_IIiioIIiioIoI (fun (x5:fofType) (x40:fofType)=> True)) REL2)
% Found ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax) as proof of ((inverse_THFTYPE_IIiioIIiioIoI (fun (x5:fofType) (x40:fofType)=> True)) REL2)
% Found ((ax_001__proj10000 ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax)) I) as proof of ((REL2 x) lChris_THFTYPE_i)
% Found (((ax_001__proj1000 (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax)) I) as proof of ((REL2 x) lChris_THFTYPE_i)
% Found ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> (((ax_001__proj100 REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax)) I) as proof of ((REL2 x) lChris_THFTYPE_i)
% Found ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> (((ax_001__proj10 REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax)) I) as proof of ((REL2 x) lChris_THFTYPE_i)
% Found ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj1 REL2) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax)) I) as proof of ((REL2 x) lChris_THFTYPE_i)
% Found ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj1 REL2) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax)) I) as proof of ((REL2 x) lChris_THFTYPE_i)
% Found ((ax_001__proj20000 ax) ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj1 REL2) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax)) I)) as proof of ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)
% Found (((ax_001__proj2000 husband_THFTYPE_IiioI) ax) ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj1 REL2) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) REL2))) ax)) I)) as proof of ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)
% Found ((((ax_001__proj200 wife_THFTYPE_IiioI) husband_THFTYPE_IiioI) ax) ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((ax_001__proj1 wife_THFTYPE_IiioI) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) wife_THFTYPE_IiioI))) ax)) I)) as proof of ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)
% Found (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj20 REL2) REL1) x3) x)) wife_THFTYPE_IiioI) husband_THFTYPE_IiioI) ax) ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((ax_001__proj1 wife_THFTYPE_IiioI) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) wife_THFTYPE_IiioI))) ax)) I)) as proof of ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)
% Found (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj2 REL2) REL1) x3) lChris_THFTYPE_i)) REL2) REL1) x3) x)) wife_THFTYPE_IiioI) husband_THFTYPE_IiioI) ax) ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((ax_001__proj1 wife_THFTYPE_IiioI) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) wife_THFTYPE_IiioI))) ax)) I)) as proof of ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)
% Found (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj2 REL2) REL1) x3) lChris_THFTYPE_i)) REL2) REL1) x3) x)) wife_THFTYPE_IiioI) husband_THFTYPE_IiioI) ax) ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((ax_001__proj1 wife_THFTYPE_IiioI) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) wife_THFTYPE_IiioI))) ax)) I)) as proof of ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x)
% Found (x0 (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj2 REL2) REL1) x3) lChris_THFTYPE_i)) REL2) REL1) x3) x)) wife_THFTYPE_IiioI) husband_THFTYPE_IiioI) ax) ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((ax_001__proj1 wife_THFTYPE_IiioI) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) wife_THFTYPE_IiioI))) ax)) I))) as proof of False
% Found (fun (x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))=> (x0 (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj2 REL2) REL1) x3) lChris_THFTYPE_i)) REL2) REL1) x3) x)) wife_THFTYPE_IiioI) husband_THFTYPE_IiioI) ax) ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((ax_001__proj1 wife_THFTYPE_IiioI) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) wife_THFTYPE_IiioI))) ax)) I)))) as proof of False
% Found (fun (x2:(((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))=> (x0 (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> (((((fun (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2))=> ((((ax_001__proj2 REL2) REL1) x3) lChris_THFTYPE_i)) REL2) REL1) x3) x)) wife_THFTYPE_IiioI) husband_THFTYPE_IiioI) ax) ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((fun (REL1:(fofType->(fofType->Prop))) (x3:((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI))=> ((((ax_001__proj1 wife_THFTYPE_IiioI) REL1) x3) lChris_THFTYPE_i)) REL1) x3) x)) (fun (x5:fofType) (x40:fofType)=> True)) ((x2 (fun (x4:(fofType->(fofType->Prop)))=> ((inverse_THFTYPE_IIiioIIiioIoI x4) wife_THFTYPE_IiioI))) ax)) I)))) as proof of (not (((eq (fofType->(fofType->Prop))) x1) (fun (X:fofType) (Y:fofType)=> True)))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found I:True
% Found I as proof of True
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found ax_001__proj10:=(ax_001__proj1 wife_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((wife_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) wife_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((wife_THFTYPE_IiioI INST2) INST1)))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found lCorina_THFTYPE_i:fofType
% Found lCorina_THFTYPE_i as proof of fofType
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found I:True
% Found I as proof of True
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found ax_001__proj10:=(ax_001__proj1 REL2):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((REL2 INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((REL2 INST2) INST1)))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax_001__proj10:=(ax_001__proj1 REL2):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((REL2 INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((REL2 INST2) INST1)))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found I:True
% Found I as proof of True
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found n2009_THFTYPE_i:fofType
% Found n2009_THFTYPE_i as proof of fofType
% Found n2009_THFTYPE_i:fofType
% Found n2009_THFTYPE_i as proof of fofType
% Found n2009_THFTYPE_i:fofType
% Found n2009_THFTYPE_i as proof of fofType
% Found n2009_THFTYPE_i:fofType
% Found n2009_THFTYPE_i as proof of fofType
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x40:A)=> (f x40))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))) (g:(forall (x40:A), (B x40))), ((forall (x40:A), (((eq (B x40)) (f x40)) (g x40)))->(((eq (forall (x40:A), (B x40))) f) g)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x40:A), (((eq B) (f x40)) (g x40)))->(((eq (A->B)) f) g)))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found x1:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found x1 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x0))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x40:A)=> (P x40)))->(P (co P))))))))
% Found ax_001__proj10:=(ax_001__proj1 wife_THFTYPE_IiioI):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) wife_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((wife_THFTYPE_IiioI INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) wife_THFTYPE_IiioI)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((wife_THFTYPE_IiioI INST2) INST1)))))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x40:A), (B x40))), (((eq (forall (x40:A), (B x40))) f) (fun (x40:A)=> (f x40))))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found I:True
% Found I as proof of True
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x40:A), ((F x40)->P))->(((ex A) F)->P)))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x20:A), ((P x20)->((ex A) P)))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found ax_001__proj10:=(ax_001__proj1 REL2):(forall (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL1 INST1) INST2)->((REL2 INST2) INST1)))))
% Found ax_001__proj10 as proof of (forall (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL2)->(forall (INST1:fofType) (INST2:fofType), (((REL10 INST1) INST2)->((REL2 INST2) INST1)))))
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x50:A) (y:B), (((eq C) ((f x50) y)) ((g x50) y)))->(((eq (A->(B->C))) f) g)))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% Found eta_expansion_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))), (((eq (forall (x50:A), (B x50))) f) (fun (x50:A)=> (f x50))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Found x2:(not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found x2 as proof of (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) x1))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), (((ex B) (fun (y:B)=> ((R x50) y)))->((R x50) (f x50))))))))
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x50:A), (B x50))) (g:(forall (x50:A), (B x50))), ((forall (x50:A), (((eq (B x50)) (f x50)) (g x50)))->(((eq (forall (x50:A), (B x50))) f) g)))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% 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))))
% Found eta_expansion as proof of (forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x50:A)=> (f x50))))
% Found eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_ref as proof of (forall (T:Type) (a:T), (((eq T) a) a))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found eq_sym as proof of (forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x50:A), ((ex B) (fun (y:B)=> ((R x50) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x50:A), ((R x50) (f x50)))))))
% Found eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_trans as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found eq_substitution as proof of (forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Found ax_001:(forall (REL2:(fofType->(fofType->Prop))) (REL1:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL1) REL2)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL1 INST1) INST2)) ((REL2 INST2) INST1)))))
% Found ax_001 as proof of (forall (REL20:(fofType->(fofType->Prop))) (REL10:(fofType->(fofType->Prop))), (((inverse_THFTYPE_IIiioIIiioIoI REL10) REL20)->(forall (INST1:fofType) (INST2:fofType), ((iff ((REL10 INST1) INST2)) ((REL20 INST2) INST1)))))
% Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found I:True
% Found I as proof of True
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% Found functional_extensionality as proof of (forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x50:A), (((eq B) (f x50)) (g x50)))->(((eq (A->B)) f) g)))
% Found ax_004:((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found ax_004 as proof of ((holdsDuring_THFTYPE_IiooI (lYearFn_THFTYPE_IiiI n2009_THFTYPE_i)) ((wife_THFTYPE_IiioI lCorina_THFTYPE_i) lChris_THFTYPE_i))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Found x0:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x0 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% Found ex_intro as proof of (forall (A:Type) (P:(A->Prop)) (x30:A), ((P x30)->((ex A) P)))
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Found choice_operator as proof of (forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x50:A)=> (P x50)))->(P (co P))))))))
% Found ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% Found ex_ind as proof of (forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x50:A), ((F x50)->P))->(((ex A) F)->P)))
% Found ax:((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found ax as proof of ((inverse_THFTYPE_IIiioIIiioIoI husband_THFTYPE_IiioI) wife_THFTYPE_IiioI)
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Found functional_extensionality_double as proof of (forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x40:A) (y:B), (((eq C) ((f x40) y)) ((g x40) y)))->(((eq (A->(B->C))) f) g)))
% Found ax_002:(forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found ax_002 as proof of (forall (Z:fofType), ((holdsDuring_THFTYPE_IiooI Z) True))
% Found eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found eq_stepl as proof of (forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% Found x00:(((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found x00 as proof of (((eq (fofType->(fofType->Prop))) x) (fun (X:fofType) (Y:fofType)=> True))
% Found choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% Found choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x40:A), ((ex B) (fun (y:B)=> ((R x40) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), ((R x40) (f x40)))))))
% Found ax_003:((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found ax_003 as proof of ((ex fofType) (fun (X:fofType)=> (not ((husband_THFTYPE_IiioI lChris_THFTYPE_i) X))))
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Found classical_choice as proof of (forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x40:A), (((ex B) (fun (y:B)=> ((R x40) y)))->((R x40) (f x40))))))))
% Found cho
% EOF
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