TSTP Solution File: SYO250^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO250^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:00 EDT 2022
% Result : Timeout 300.03s 300.23s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO250^5 : TPTP v7.5.0. Released v4.0.0.
% 0.12/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 11 21:51:33 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.47/0.63 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.47/0.63 FOF formula ((ex fofType) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) of role conjecture named cSIXFRIENDS
% 0.47/0.63 Conjecture to prove = ((ex fofType) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))):Prop
% 0.47/0.63 Parameter fofType_DUMMY:fofType.
% 0.47/0.63 We need to prove ['((ex fofType) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh)))))))))))))))))))))))))))))))']
% 0.47/0.64 Parameter fofType:Type.
% 0.47/0.64 Trying to prove ((ex fofType) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh)))))))))))))))))))))))))))))))
% 19.33/19.52 Found eta_expansion000:=(eta_expansion00 (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))):(((eq (fofType->Prop)) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) (fun (x:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh)))))))))))))))))))))))))))))))
% 19.33/19.54 Found (eta_expansion00 (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) b)
% 19.33/19.56 Found ((eta_expansion0 Prop) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) b)
% 19.33/19.57 Found (((eta_expansion fofType) Prop) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) b)
% 19.33/19.59 Found (((eta_expansion fofType) Prop) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) b)
% 19.43/19.61 Found (((eta_expansion fofType) Prop) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))))) b)
% 121.23/121.47 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 121.23/121.47 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh)))))))))))))))))))))))))))))))
% 121.30/121.49 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh)))))))))))))))))))))))))))))))
% 121.30/121.51 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh)))))))))))))))))))))))))))))))
% 121.30/121.53 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> ((ex fofType) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) Xa) Xaa))) (not (((eq fofType) Xa) Xb)))) (not (((eq fofType) Xa) Xbb)))) (not (((eq fofType) Xa) Xc)))) (not (((eq fofType) Xa) Xcc)))) (not (((eq fofType) Xa) Xd)))) (not (((eq fofType) Xa) Xdd)))) (not (((eq fofType) Xa) Xe)))) (not (((eq fofType) Xa) Xee)))) (not (((eq fofType) Xa) Xh)))) (not (((eq fofType) Xa) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xa)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P Xa)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P Xa)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P Xa)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh)))))))))))))))))))))))))))))))
% 148.82/149.00 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 148.82/149.00 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 148.82/149.00 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 148.82/149.00 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 148.82/149.00 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 148.82/149.00 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 148.82/149.00 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 148.82/149.00 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% 148.82/149.00 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 148.82/149.00 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 148.82/149.00 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 148.82/149.00 Found eta_expansion000:=(eta_expansion00 (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))):(((eq (fofType->Prop)) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) (fun (x0:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) x0))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) x0) Xb)))) (not (((eq fofType) x0) Xbb)))) (not (((eq fofType) x0) Xc)))) (not (((eq fofType) x0) Xcc)))) (not (((eq fofType) x0) Xd)))) (not (((eq fofType) x0) Xdd)))) (not (((eq fofType) x0) Xe)))) (not (((eq fofType) x0) Xee)))) (not (((eq fofType) x0) Xh)))) (not (((eq fofType) x0) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P x0))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P x0))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P x0))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P x0)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh)))))))))))))))))))))))))))))
% 148.85/149.02 Found (eta_expansion00 (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) b)
% 148.85/149.04 Found ((eta_expansion0 Prop) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) b)
% 148.85/149.06 Found (((eta_expansion fofType) Prop) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) b)
% 148.85/149.08 Found (((eta_expansion fofType) Prop) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) b)
% 148.85/149.10 Found (((eta_expansion fofType) Prop) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xb)) (P Xcc)))->(not (((eq fofType) (P Xd)) (P Xee)))))) (((and ((and ((and (((eq fofType) (P Xc)) (P Xcc))) (((eq fofType) (P Xcc)) (P Xd)))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P x)) (P Xbb))))->(not (((eq fofType) (P Xe)) (P Xhh)))))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xd)) (P Xdd)))) (not (((eq fofType) (P Xb)) (P Xcc))))->(((eq fofType) (P Xe)) (P Xhh))))) (((and ((and (((eq fofType) (P Xe)) (P Xee))) (((eq fofType) (P Xh)) (P Xhh)))) (((eq fofType) (P Xc)) (P Xdd)))->(not (((eq fofType) (P x)) (P Xbb)))))) (((and ((and ((and (((eq fofType) (P Xb)) (P Xbb))) (((eq fofType) (P Xbb)) (P Xc)))) (((eq fofType) (P Xc)) (P Xcc)))) (not (((eq fofType) (P Xe)) (P Xhh))))->(((eq fofType) (P Xd)) (P Xee))))->((or ((or ((or ((or ((or (not (((eq fofType) (P x)) (P Xaa)))) (not (((eq fofType) (P Xb)) (P Xbb))))) (not (((eq fofType) (P Xc)) (P Xcc))))) (not (((eq fofType) (P Xd)) (P Xdd))))) (not (((eq fofType) (P Xe)) (P Xee))))) (not (((eq fofType) (P Xh)) (P Xhh))))))))))))))))))))))))))))) as proof of (((eq (fofType->Prop)) (fun (Xaa:fofType)=> ((ex fofType) (fun (Xb:fofType)=> ((ex fofType) (fun (Xbb:fofType)=> ((ex fofType) (fun (Xc:fofType)=> ((ex fofType) (fun (Xcc:fofType)=> ((ex fofType) (fun (Xd:fofType)=> ((ex fofType) (fun (Xdd:fofType)=> ((ex fofType) (fun (Xe:fofType)=> ((ex fofType) (fun (Xee:fofType)=> ((ex fofType) (fun (Xh:fofType)=> ((ex fofType) (fun (Xhh:fofType)=> (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (not (((eq fofType) x) Xaa))) (not (((eq fofType) x) Xb)))) (not (((eq fofType) x) Xbb)))) (not (((eq fofType) x) Xc)))) (not (((eq fofType) x) Xcc)))) (not (((eq fofType) x) Xd)))) (not (((eq fofType) x) Xdd)))) (not (((eq fofType) x) Xe)))) (not (((eq fofType) x) Xee)))) (not (((eq fofType) x) Xh)))) (not (((eq fofType) x) Xhh)))) (not (((eq fofType) Xaa) Xb)))) (not (((eq fofType) Xaa) Xbb)))) (not (((eq fofType) Xaa) Xc)))) (not (((eq fofType) Xaa) Xcc)))) (not (((eq fofType) Xaa) Xd)))) (not (((eq fofType) Xaa) Xdd)))) (not (((eq fofType) Xaa) Xe)))) (not (((eq fofType) Xaa) Xee)))) (not (((eq fofType) Xaa) Xh)))) (not (((eq fofType) Xaa) Xhh)))) (not (((eq fofType) Xb) Xbb)))) (not (((eq fofType) Xb) Xc)))) (not (((eq fofType) Xb) Xcc)))) (not (((eq fofType) Xb) Xd)))) (not (((eq fofType) Xb) Xdd)))) (not (((eq fofType) Xb) Xe)))) (not (((eq fofType) Xb) Xee)))) (not (((eq fofType) Xb) Xh)))) (not (((eq fofType) Xb) Xhh)))) (not (((eq fofType) Xc) Xcc)))) (not (((eq fofType) Xc) Xd)))) (not (((eq fofType) Xc) Xdd)))) (not (((eq fofType) Xc) Xe)))) (not (((eq fofType) Xc) Xee)))) (not (((eq fofType) Xc) Xh)))) (not (((eq fofType) Xc) Xhh)))) (not (((eq fofType) Xcc) Xd)))) (not (((eq fofType) Xcc) Xdd)))) (not (((eq fofType) Xcc) Xe)))) (not (((eq fofType) Xcc) Xee)))) (not (((eq fofType) Xcc) Xh)))) (not (((eq fofType) Xcc) Xhh)))) (not (((eq fofType) Xd) Xdd)))) (not (((eq fofType) Xd) Xe)))) (not (((eq fofType) Xd) Xee)))) (not (((eq fofType) Xd) Xh)))) (not (((eq fofType) Xd) Xhh)))) (not (((eq fofType) Xdd) Xe)))) (not (((eq fofType) Xdd) Xee)))) (not (((eq fofType) Xdd) Xh)))) (not (((eq fofType) Xdd) Xhh)))) (not (((eq fofType) Xe) Xee)))) (not (((eq fofType) Xe) Xh)))) (not (((eq fofType) Xe) Xhh)))) (not (((eq fofType) Xee) Xh)))) (not (((eq fofType) Xee) Xhh)))) (not (((eq fofType) Xh) Xhh)))->(forall (P:(fofType->fofType)), (((and ((and ((and ((and ((and (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xb)) (P Xbb)))) (((eq fofType) (P Xe)) (P Xhh)))->(((eq fofType) (P Xc)) (P Xdd)))) (((and ((and (((eq fofType) (P x)) (P Xaa))) (((eq fofType) (P Xh)) (
%------------------------------------------------------------------------------