%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : NUM802^5 : TPTP v7.0.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n129.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32218.625MB % OS : Linux 3.10.0-693.2.2.el7.x86_64 % CPULimit : 300s % DateTime : Mon Jan 8 13:11:48 EST 2018 % Result : Timeout 291.55s % Output : None % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : NUM802^5 : TPTP v7.0.0. Released v4.0.0. % 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.03/0.23 % Computer : n129.star.cs.uiowa.edu % 0.03/0.23 % Model : x86_64 x86_64 % 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % 0.03/0.23 % Memory : 32218.625MB % 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 % 0.03/0.23 % CPULimit : 300 % 0.03/0.23 % DateTime : Fri Jan 5 14:22:04 CST 2018 % 0.03/0.23 % CPUTime : % 0.03/0.24 Python 2.7.13 % 1.51/1.75 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 1.51/1.75 FOF formula (<kernel.Constant object at 0x2b6a638e2d88>, <kernel.Constant object at 0x2b6a638e23b0>) of role type named c_2 % 1.51/1.75 Using role type % 1.51/1.75 Declaring c_2:fofType % 1.51/1.75 FOF formula (<kernel.Constant object at 0x2b6a63948cb0>, <kernel.DependentProduct object at 0x2b6a638e2ef0>) of role type named absval % 1.51/1.75 Using role type % 1.51/1.75 Declaring absval:(fofType->fofType) % 1.51/1.75 FOF formula (<kernel.Constant object at 0x2b6a638e23f8>, <kernel.Single object at 0x2b6a638e27a0>) of role type named c0 % 1.51/1.75 Using role type % 1.51/1.75 Declaring c0:fofType % 1.51/1.75 FOF formula (<kernel.Constant object at 0x2b6a638e2d88>, <kernel.DependentProduct object at 0x2b6a638e23b0>) of role type named c_less_ % 1.51/1.75 Using role type % 1.51/1.75 Declaring c_less_:(fofType->(fofType->Prop)) % 1.51/1.75 FOF formula (((c_less_ c_2) c0)->((forall (Xu:fofType) (Xv:fofType), (((c_less_ Xu) c0)->(not (((eq fofType) Xu) (absval Xv)))))->((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))))) of role conjecture named cBLEDSOE_FENG_8 % 1.51/1.75 Conjecture to prove = (((c_less_ c_2) c0)->((forall (Xu:fofType) (Xv:fofType), (((c_less_ Xu) c0)->(not (((eq fofType) Xu) (absval Xv)))))->((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))))):Prop % 1.51/1.75 We need to prove ['(((c_less_ c_2) c0)->((forall (Xu:fofType) (Xv:fofType), (((c_less_ Xu) c0)->(not (((eq fofType) Xu) (absval Xv)))))->((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2))))))'] % 1.51/1.75 Parameter fofType:Type. % 1.51/1.75 Parameter c_2:fofType. % 1.51/1.75 Parameter absval:(fofType->fofType). % 1.51/1.75 Parameter c0:fofType. % 1.51/1.75 Parameter c_less_:(fofType->(fofType->Prop)). % 1.51/1.75 Trying to prove (((c_less_ c_2) c0)->((forall (Xu:fofType) (Xv:fofType), (((c_less_ Xu) c0)->(not (((eq fofType) Xu) (absval Xv)))))->((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))))) % 1.51/1.75 Found c0:fofType % 1.51/1.75 Found c0 as proof of fofType % 1.51/1.75 Found (x00 c0) as proof of False % 1.51/1.75 Found (x00 c0) as proof of False % 1.51/1.75 Found (fun (x00:(x1 (absval Xy)))=> (x00 c0)) as proof of False % 1.51/1.75 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c0)) as proof of ((x1 (absval Xy))->False) % 1.51/1.75 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c0)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 1.51/1.75 Found c0:fofType % 1.51/1.75 Found c0 as proof of fofType % 1.51/1.75 Found (x2 c0) as proof of False % 1.51/1.75 Found (x2 c0) as proof of False % 1.51/1.75 Found (fun (x2:(x1 (absval Xy)))=> (x2 c0)) as proof of False % 1.51/1.75 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c0)) as proof of (not (x1 (absval Xy))) % 1.51/1.75 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c0)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 1.51/1.75 Found eq_ref00:=(eq_ref0 (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))):(((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) % 1.51/1.75 Found (eq_ref0 (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) b) % 1.51/1.75 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) b) % 1.51/1.75 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) b) % 1.51/1.75 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) b) % 5.61/5.82 Found eta_expansion000:=(eta_expansion00 (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))):(((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) (fun (x:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (x (absval Xy))))) (x c_2)))) % 5.61/5.82 Found (eta_expansion00 (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) b) % 5.61/5.82 Found ((eta_expansion0 Prop) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) b) % 5.61/5.82 Found (((eta_expansion (fofType->Prop)) Prop) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) b) % 5.61/5.82 Found (((eta_expansion (fofType->Prop)) Prop) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) b) % 5.61/5.82 Found (((eta_expansion (fofType->Prop)) Prop) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) b) % 5.61/5.82 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 5.61/5.82 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) (x1 c_2))) % 5.61/5.82 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) (x1 c_2))) % 5.61/5.82 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) (x1 c_2))) % 5.61/5.82 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) (x1 c_2))) % 5.61/5.82 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (forall (Xy:fofType), (not (x (absval Xy))))) (x c_2)))) % 5.61/5.82 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 5.61/5.82 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) (x1 c_2))) % 5.61/5.82 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) (x1 c_2))) % 5.61/5.82 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) (x1 c_2))) % 5.61/5.82 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) (x1 c_2))) % 5.61/5.82 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (forall (Xy:fofType), (not (x (absval Xy))))) (x c_2)))) % 5.61/5.82 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b) % 5.61/5.82 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) % 5.61/5.82 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) % 5.61/5.82 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) % 5.61/5.82 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) % 5.61/5.82 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 6.67/6.87 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 6.67/6.87 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found eq_ref00:=(eq_ref0 (x1 c_2)):(((eq Prop) (x1 c_2)) (x1 c_2)) % 6.67/6.87 Found (eq_ref0 (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b) % 6.67/6.87 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b) % 6.67/6.87 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b) % 6.67/6.87 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b) % 6.67/6.87 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 6.67/6.87 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 6.67/6.87 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x))) % 6.67/6.87 Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 6.67/6.87 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 6.67/6.87 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 6.67/6.87 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 6.67/6.87 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 6.67/6.87 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b) % 6.67/6.87 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 6.67/6.87 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 6.67/6.87 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 6.67/6.87 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 6.67/6.87 Found eq_ref00:=(eq_ref0 (x1 c_2)):(((eq Prop) (x1 c_2)) (x1 c_2)) % 10.67/10.86 Found (eq_ref0 (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b) % 10.67/10.86 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b) % 10.67/10.86 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b) % 10.67/10.86 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b) % 10.67/10.86 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 10.67/10.86 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 10.67/10.86 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 10.67/10.86 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 10.67/10.86 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 10.67/10.86 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 10.67/10.86 Found (eq_ref0 a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 10.67/10.86 Found (eq_ref0 a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 10.67/10.86 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 10.67/10.86 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 10.67/10.86 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 10.67/10.86 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 10.67/10.86 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 10.67/10.86 Found (eq_ref0 a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 10.67/10.86 Found (eq_ref0 a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) c_2) % 10.67/10.86 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 10.67/10.86 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 10.67/10.86 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 10.67/10.86 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 10.67/10.86 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 10.67/10.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 10.67/10.86 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 10.67/10.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 10.67/10.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 10.67/10.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 10.67/10.86 Found ((eq_trans0000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 10.67/10.86 Found (((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 10.67/10.86 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 10.67/10.86 Found (((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 10.67/10.86 Found ((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 14.55/14.74 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 14.55/14.74 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 14.55/14.74 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 14.55/14.74 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 14.55/14.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 14.55/14.74 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found ((eq_trans0000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found (((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found (((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found ((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 14.55/14.74 Found eq_ref000:=(eq_ref00 P0):((P0 (f x1))->(P0 (f x1))) % 14.55/14.74 Found (eq_ref00 P0) as proof of (P1 (f x1)) % 14.55/14.74 Found ((eq_ref0 (f x1)) P0) as proof of (P1 (f x1)) % 14.55/14.74 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 14.55/14.74 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 14.55/14.74 Found eq_ref000:=(eq_ref00 P0):((P0 (f x1))->(P0 (f x1))) % 14.55/14.74 Found (eq_ref00 P0) as proof of (P1 (f x1)) % 14.55/14.74 Found ((eq_ref0 (f x1)) P0) as proof of (P1 (f x1)) % 14.55/14.74 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 14.55/14.74 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 14.55/14.74 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 14.55/14.74 Found (eq_ref00 P) as proof of (P0 c_2) % 14.55/14.74 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 14.55/14.74 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 14.55/14.74 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 14.55/14.74 Found c_2:fofType % 14.55/14.74 Found c_2 as proof of fofType % 14.55/14.74 Found (x00 c_2) as proof of False % 14.55/14.74 Found (x00 c_2) as proof of False % 14.55/14.74 Found (fun (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of False % 14.55/14.74 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of ((x1 (absval Xy))->False) % 14.55/14.74 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 14.55/14.74 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 14.55/14.74 Found (eq_ref00 P) as proof of (P0 c_2) % 14.55/14.74 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 14.55/14.74 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 14.55/14.74 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 14.55/14.74 Found c_2:fofType % 14.55/14.74 Found c_2 as proof of fofType % 14.55/14.74 Found c_2:fofType % 14.55/14.74 Found c_2 as proof of fofType % 14.55/14.74 Found ((x00 c_2) c_2) as proof of False % 16.17/16.38 Found ((x00 c_2) c_2) as proof of False % 16.17/16.38 Found (fun (x00:(x1 (absval Xy)))=> ((x00 c_2) c_2)) as proof of False % 16.17/16.38 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) c_2)) as proof of ((x1 (absval Xy))->False) % 16.17/16.38 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 16.17/16.38 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 16.17/16.38 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 16.17/16.38 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 16.17/16.38 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 16.17/16.38 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 16.17/16.38 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 16.17/16.38 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 16.17/16.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 16.17/16.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 16.17/16.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 16.17/16.38 Found c_2:fofType % 16.17/16.38 Found c_2 as proof of fofType % 16.17/16.38 Found (x2 c_2) as proof of False % 16.17/16.38 Found (x2 c_2) as proof of False % 16.17/16.38 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 16.17/16.38 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (not (x1 (absval Xy))) % 16.17/16.38 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 16.17/16.38 Found c_2:fofType % 16.17/16.38 Found c_2 as proof of fofType % 16.17/16.38 Found c_2:fofType % 16.17/16.38 Found c_2 as proof of fofType % 16.17/16.38 Found ((x2 c_2) c_2) as proof of False % 16.17/16.38 Found ((x2 c_2) c_2) as proof of False % 16.17/16.38 Found (fun (x2:(x1 (absval Xy)))=> ((x2 c_2) c_2)) as proof of False % 16.17/16.38 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) c_2)) as proof of (not (x1 (absval Xy))) % 16.17/16.38 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 16.17/16.38 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 16.17/16.38 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 16.17/16.38 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 16.17/16.38 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 16.17/16.38 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 16.17/16.38 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 16.17/16.38 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 16.17/16.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 16.17/16.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 16.17/16.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 16.17/16.38 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 16.17/16.38 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 16.17/16.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 16.17/16.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 16.17/16.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 16.17/16.38 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 16.17/16.38 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 16.17/16.38 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 16.17/16.38 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 16.17/16.38 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 16.17/16.38 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 16.17/16.38 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 16.17/16.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 16.17/16.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 16.17/16.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 16.17/16.38 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 22.42/22.61 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 22.42/22.61 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 22.42/22.61 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 22.42/22.61 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 22.42/22.61 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 22.42/22.61 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 22.42/22.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 22.42/22.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 22.42/22.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 22.42/22.61 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 22.42/22.61 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 22.42/22.61 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 22.42/22.61 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 22.42/22.61 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 22.42/22.61 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 22.42/22.61 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 22.42/22.61 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 22.42/22.61 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 22.42/22.61 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 22.42/22.61 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 22.42/22.61 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 22.42/22.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 22.42/22.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 22.42/22.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 22.42/22.61 Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))) % 22.42/22.61 Instantiate: b:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop % 22.42/22.61 Found eta_expansion as proof of b % 22.42/22.61 Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))) % 22.42/22.61 Instantiate: b:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop % 22.42/22.61 Found eta_expansion as proof of b % 22.42/22.61 Found x00:(x1 (absval Xy)) % 22.42/22.61 Instantiate: b:=False:Prop % 22.42/22.61 Found (fun (x00:(x1 (absval Xy)))=> x00) as proof of False % 22.42/22.61 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> x00) as proof of ((x1 (absval Xy))->False) % 22.42/22.61 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> x00) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 22.42/22.61 Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))) % 22.42/22.61 Instantiate: b:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop % 22.42/22.61 Found eta_expansion as proof of b % 22.42/22.61 Found eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))) % 22.42/22.61 Instantiate: b:=(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x)))):Prop % 22.42/22.61 Found eta_expansion as proof of b % 22.42/22.61 Found x2:(x1 (absval Xy)) % 22.42/22.61 Instantiate: b:=False:Prop % 22.42/22.61 Found (fun (x2:(x1 (absval Xy)))=> x2) as proof of False % 22.42/22.61 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> x2) as proof of (not (x1 (absval Xy))) % 22.42/22.61 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> x2) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 22.42/22.61 Found c_2:fofType % 22.42/22.61 Found c_2 as proof of fofType % 22.42/22.61 Found (x00 c_2) as proof of False % 24.20/24.43 Found (x00 c_2) as proof of False % 24.20/24.43 Found (fun (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of False % 24.20/24.43 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of ((x1 (absval Xy))->False) % 24.20/24.43 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 24.20/24.43 Found ((conj00 (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2))) eta_expansion) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) b) % 24.20/24.43 Found (((conj0 b) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2))) eta_expansion) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) b) % 24.20/24.43 Found ((((conj (forall (Xy:fofType), ((x1 (absval Xy))->False))) b) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2))) eta_expansion) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) b) % 24.20/24.43 Found ((((conj (forall (Xy:fofType), ((x1 (absval Xy))->False))) b) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2))) eta_expansion) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) b) % 24.20/24.43 Found ((((conj (forall (Xy:fofType), ((x1 (absval Xy))->False))) b) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2))) eta_expansion) as proof of (P b) % 24.20/24.43 Found c_2:fofType % 24.20/24.43 Found c_2 as proof of fofType % 24.20/24.43 Found (x2 c_2) as proof of False % 24.20/24.43 Found (x2 c_2) as proof of False % 24.20/24.43 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 24.20/24.43 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (not (x1 (absval Xy))) % 24.20/24.43 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 24.20/24.43 Found ((conj00 (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2))) eta_expansion) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) b) % 24.20/24.43 Found (((conj0 b) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2))) eta_expansion) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) b) % 24.20/24.43 Found ((((conj (forall (Xy:fofType), (not (x1 (absval Xy))))) b) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2))) eta_expansion) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) b) % 24.20/24.43 Found ((((conj (forall (Xy:fofType), (not (x1 (absval Xy))))) b) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2))) eta_expansion) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) b) % 24.20/24.43 Found ((((conj (forall (Xy:fofType), (not (x1 (absval Xy))))) b) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2))) eta_expansion) as proof of (P b) % 24.20/24.43 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 24.20/24.43 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 24.20/24.43 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 24.20/24.43 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 24.20/24.43 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 24.20/24.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 24.20/24.43 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 24.20/24.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 24.20/24.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 24.20/24.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 24.20/24.43 Found ((eq_trans0000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.20/24.43 Found (((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.20/24.43 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found (((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found ((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found ((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 24.95/25.18 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 24.95/25.18 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 24.95/25.18 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 24.95/25.18 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 24.95/25.18 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 24.95/25.18 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 24.95/25.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 24.95/25.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 24.95/25.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 24.95/25.18 Found ((eq_trans0000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found (((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found (((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found ((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found ((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 24.95/25.18 Found eq_ref000:=(eq_ref00 P0):((P0 (f x1))->(P0 (f x1))) % 34.55/34.81 Found (eq_ref00 P0) as proof of (P1 (f x1)) % 34.55/34.81 Found ((eq_ref0 (f x1)) P0) as proof of (P1 (f x1)) % 34.55/34.81 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 34.55/34.81 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 34.55/34.81 Found eq_ref000:=(eq_ref00 P0):((P0 (f x1))->(P0 (f x1))) % 34.55/34.81 Found (eq_ref00 P0) as proof of (P1 (f x1)) % 34.55/34.81 Found ((eq_ref0 (f x1)) P0) as proof of (P1 (f x1)) % 34.55/34.81 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 34.55/34.81 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 34.55/34.81 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 34.55/34.81 Found (eq_ref00 P) as proof of (P0 c_2) % 34.55/34.81 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 34.55/34.81 Found (eq_ref00 P) as proof of (P0 c_2) % 34.55/34.81 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found c_2:fofType % 34.55/34.81 Found c_2 as proof of fofType % 34.55/34.81 Found (x00 c_2) as proof of False % 34.55/34.81 Found (x00 c_2) as proof of False % 34.55/34.81 Found (fun (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of False % 34.55/34.81 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of ((x1 (absval Xy))->False) % 34.55/34.81 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 34.55/34.81 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 34.55/34.81 Found (eq_ref00 P) as proof of (P0 c_2) % 34.55/34.81 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 34.55/34.81 Found (eq_ref00 P) as proof of (P0 c_2) % 34.55/34.81 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 34.55/34.81 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 34.55/34.81 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 34.55/34.81 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 34.55/34.81 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 34.55/34.81 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 34.55/34.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 34.55/34.81 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 34.55/34.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 34.55/34.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 34.55/34.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 34.55/34.81 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 34.55/34.81 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 34.55/34.81 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 34.55/34.81 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 34.55/34.81 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 34.55/34.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 34.55/34.81 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 34.55/34.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 34.55/34.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 34.55/34.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 34.55/34.81 Found c_2:fofType % 34.55/34.81 Found c_2 as proof of fofType % 34.55/34.81 Found c_2:fofType % 34.55/34.81 Found c_2 as proof of fofType % 34.55/34.81 Found ((x00 c_2) c_2) as proof of False % 34.55/34.81 Found ((x00 c_2) c_2) as proof of False % 34.55/34.81 Found (fun (x00:(x1 (absval Xy)))=> ((x00 c_2) c_2)) as proof of False % 34.55/34.81 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) c_2)) as proof of ((x1 (absval Xy))->False) % 34.55/34.81 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 34.55/34.81 Found c_2:fofType % 34.55/34.81 Found c_2 as proof of fofType % 34.55/34.81 Found (x2 c_2) as proof of False % 34.55/34.81 Found (x2 c_2) as proof of False % 34.55/34.81 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 34.55/34.81 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (not (x1 (absval Xy))) % 34.55/34.81 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 34.55/34.81 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 34.55/34.81 Found (eq_ref0 a) as proof of (((eq Prop) a) b) % 34.55/34.81 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 36.57/36.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 36.57/36.85 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 36.57/36.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 36.57/36.85 Found (eq_ref0 b) as proof of (((eq Prop) b) (x1 c_2)) % 36.57/36.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x1 c_2)) % 36.57/36.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x1 c_2)) % 36.57/36.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x1 c_2)) % 36.57/36.85 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 36.57/36.85 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 36.57/36.85 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 36.57/36.85 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 36.57/36.85 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 36.57/36.85 Found (eta_expansion_dep00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 36.57/36.85 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 36.57/36.85 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 36.57/36.85 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 36.57/36.85 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 36.57/36.85 Found eq_ref00:=(eq_ref0 f):(((eq ((fofType->Prop)->Prop)) f) f) % 36.57/36.85 Found (eq_ref0 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 36.57/36.85 Found ((eq_ref ((fofType->Prop)->Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 36.57/36.85 Found ((eq_ref ((fofType->Prop)->Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 36.57/36.85 Found ((eq_ref ((fofType->Prop)->Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 36.57/36.85 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 36.57/36.85 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 36.57/36.85 Found c_2:fofType % 36.57/36.85 Found c_2 as proof of fofType % 36.57/36.85 Found c_2:fofType % 36.57/36.85 Found c_2 as proof of fofType % 36.57/36.85 Found ((x2 c_2) c_2) as proof of False % 36.57/36.85 Found ((x2 c_2) c_2) as proof of False % 36.57/36.85 Found (fun (x2:(x1 (absval Xy)))=> ((x2 c_2) c_2)) as proof of False % 36.57/36.85 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) c_2)) as proof of (not (x1 (absval Xy))) % 36.57/36.85 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 36.57/36.85 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 36.57/36.85 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 36.57/36.85 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 36.57/36.85 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 36.57/36.85 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 36.57/36.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 38.17/38.39 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 38.17/38.39 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 38.17/38.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 38.17/38.39 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 38.17/38.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 38.17/38.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 38.17/38.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 38.17/38.39 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 38.17/38.39 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 38.17/38.39 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 38.17/38.39 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 38.17/38.39 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 38.17/38.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 38.17/38.39 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 38.17/38.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 38.17/38.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 38.17/38.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 38.17/38.39 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 38.17/38.39 Found (eta_expansion00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 38.17/38.39 Found (eta_expansion00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 38.17/38.39 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 38.17/38.39 Found (eq_ref0 a) as proof of (((eq Prop) a) b) % 38.17/38.39 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 38.17/38.39 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 38.17/38.39 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 38.17/38.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 38.17/38.39 Found (eq_ref0 b) as proof of (((eq Prop) b) (x1 c_2)) % 38.17/38.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x1 c_2)) % 38.17/38.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x1 c_2)) % 38.17/38.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x1 c_2)) % 38.17/38.39 Found c_2:fofType % 38.17/38.39 Found c_2 as proof of fofType % 38.17/38.39 Found (x00 c_2) as proof of False % 38.17/38.39 Found (x00 c_2) as proof of False % 38.17/38.39 Found (fun (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of False % 38.17/38.39 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of ((x1 (absval Xy))->False) % 38.17/38.39 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 38.17/38.39 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 38.17/38.39 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 38.17/38.39 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 38.17/38.39 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 38.17/38.39 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 38.17/38.39 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 38.17/38.39 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 38.17/38.39 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 38.17/38.39 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 38.17/38.39 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 38.17/38.39 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 38.17/38.39 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 39.60/39.81 Found c_2:fofType % 39.60/39.81 Found c_2 as proof of fofType % 39.60/39.81 Found (x2 c_2) as proof of False % 39.60/39.81 Found (x2 c_2) as proof of False % 39.60/39.81 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 39.60/39.81 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (not (x1 (absval Xy))) % 39.60/39.81 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 39.60/39.81 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 39.60/39.81 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 39.60/39.81 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 39.60/39.81 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 39.60/39.81 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 39.60/39.81 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 39.60/39.81 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 39.60/39.81 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 39.60/39.81 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 39.60/39.81 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 39.60/39.81 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 39.60/39.81 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 39.60/39.81 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 39.60/39.81 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 39.60/39.81 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 39.60/39.81 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 39.60/39.81 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 39.60/39.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 39.60/39.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 39.60/39.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 39.60/39.81 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 39.60/39.81 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 39.60/39.81 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 39.60/39.81 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 39.60/39.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 39.60/39.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 39.60/39.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 43.47/43.67 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 43.47/43.67 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 43.47/43.67 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 43.47/43.67 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 43.47/43.67 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 43.47/43.67 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 43.47/43.68 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 43.47/43.68 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 43.47/43.68 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 43.47/43.68 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 43.47/43.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 43.47/43.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 43.47/43.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 43.47/43.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 43.47/43.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 43.47/43.68 Found c_2:fofType % 43.47/43.68 Found c_2 as proof of fofType % 43.47/43.68 Found c_2:fofType % 43.47/43.68 Found c_2 as proof of fofType % 43.47/43.68 Found ((x00 c_2) c_2) as proof of False % 43.47/43.68 Found ((x00 c_2) c_2) as proof of False % 43.47/43.68 Found (fun (x00:(x1 (absval Xy)))=> ((x00 c_2) c_2)) as proof of False % 43.47/43.68 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) c_2)) as proof of ((x1 (absval Xy))->False) % 43.47/43.68 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 43.47/43.68 Found c_2:fofType % 43.47/43.68 Found c_2 as proof of fofType % 43.47/43.68 Found c_2:fofType % 43.47/43.68 Found c_2 as proof of fofType % 43.47/43.68 Found ((x2 c_2) c_2) as proof of False % 43.47/43.68 Found ((x2 c_2) c_2) as proof of False % 43.47/43.68 Found (fun (x2:(x1 (absval Xy)))=> ((x2 c_2) c_2)) as proof of False % 43.47/43.68 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) c_2)) as proof of (not (x1 (absval Xy))) % 43.47/43.68 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 43.47/43.68 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x))) % 43.47/43.68 Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 43.47/43.68 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 43.47/43.68 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 43.47/43.68 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 43.47/43.68 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 43.47/43.68 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x))) % 43.47/43.68 Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 43.47/43.68 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 46.09/46.35 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 46.09/46.35 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 46.09/46.35 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 46.09/46.35 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 46.09/46.35 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 46.09/46.35 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 46.09/46.35 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 46.09/46.35 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 46.09/46.35 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 46.09/46.35 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 46.09/46.35 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 46.09/46.35 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 46.09/46.35 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 46.09/46.35 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 46.09/46.35 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 46.09/46.35 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 46.09/46.35 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 46.09/46.35 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 46.09/46.35 Found (eta_expansion_dep00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 46.09/46.35 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 46.09/46.35 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 46.09/46.35 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 46.09/46.35 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 46.09/46.35 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 46.09/46.35 Found (eta_expansion00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 46.09/46.35 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 46.09/46.35 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 48.15/48.35 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 48.15/48.35 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 48.15/48.35 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 48.15/48.35 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.35 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.35 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.35 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.35 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 48.15/48.35 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 48.15/48.35 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.35 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.35 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 48.15/48.36 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 48.15/48.36 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 48.15/48.36 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 48.15/48.36 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 48.15/48.36 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 48.15/48.36 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 48.15/48.36 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 48.15/48.36 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 48.15/48.36 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 48.15/48.36 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 48.15/48.36 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 48.15/48.36 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 48.15/48.36 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 48.15/48.36 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 48.15/48.36 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 48.15/48.36 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 48.15/48.36 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 48.15/48.36 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 48.15/48.36 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 48.15/48.36 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 48.15/48.36 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 50.27/50.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 50.27/50.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 50.27/50.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 50.27/50.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 50.27/50.49 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 50.27/50.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 50.27/50.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 50.27/50.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 50.27/50.49 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 50.27/50.49 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 50.27/50.49 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 50.27/50.49 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 50.27/50.49 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 50.27/50.49 Found x2:(P0 (f x1)) % 50.27/50.49 Instantiate: b:=(f x1):Prop % 50.27/50.49 Found x2 as proof of (P1 b) % 50.27/50.49 Found x2:(P0 (f x1)) % 50.27/50.49 Instantiate: b:=(f x1):Prop % 50.27/50.49 Found x2 as proof of (P1 b) % 50.27/50.49 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 50.27/50.49 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 50.27/50.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 50.27/50.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 50.27/50.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 50.27/50.49 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 50.27/50.49 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 50.27/50.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 50.27/50.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 50.27/50.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 50.27/50.49 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 50.27/50.49 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 50.27/50.49 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 50.27/50.49 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 50.27/50.49 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 50.27/50.49 Found (eq_sym010 ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 50.27/50.49 Found ((eq_sym01 b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 50.27/50.49 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 50.27/50.49 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 50.27/50.49 Found ((eq_trans0000 ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 50.27/50.49 Found (((eq_trans000 (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 50.27/50.49 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 50.31/50.50 Found (((((eq_trans0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 50.31/50.50 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 50.31/50.50 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 50.31/50.50 Found (eq_sym000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 50.31/50.50 Found ((eq_sym00 (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 50.31/50.50 Found (((eq_sym0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 50.31/50.50 Found ((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 50.31/50.50 Found ((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 50.35/50.55 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 50.35/50.55 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 50.35/50.55 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 50.35/50.55 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 50.35/50.55 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 50.35/50.55 Found (eq_sym010 ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 50.35/50.55 Found ((eq_sym01 b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 50.35/50.55 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 50.35/50.55 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 50.35/50.55 Found ((eq_trans0000 ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 50.35/50.55 Found (((eq_trans000 (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 50.35/50.55 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 50.35/50.55 Found (((((eq_trans0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 50.35/50.55 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 50.35/50.55 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 50.35/50.55 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 50.35/50.55 Found (eq_sym000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.45/52.71 Found ((eq_sym00 (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.45/52.71 Found (((eq_sym0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.45/52.71 Found ((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.45/52.71 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 52.45/52.71 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 52.45/52.71 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 52.45/52.71 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 52.45/52.71 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 52.45/52.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 52.45/52.71 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.45/52.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.45/52.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.45/52.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.45/52.71 Found ((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.45/52.71 Found ((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.45/52.71 Found (((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_trans0000 x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.45/52.71 Found (((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.45/52.71 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.71/52.93 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.71/52.93 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.71/52.93 Found (fun (P0:(Prop->Prop))=> (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.71/52.93 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 52.71/52.93 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 52.71/52.93 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 52.71/52.93 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 52.71/52.93 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 52.71/52.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 52.71/52.93 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.71/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.71/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.71/52.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 52.71/52.93 Found ((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.71/52.93 Found ((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.71/52.93 Found (((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_trans0000 x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.71/52.93 Found (((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 52.71/52.93 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.13/53.34 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.13/53.34 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.13/53.34 Found (fun (P0:(Prop->Prop))=> (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.13/53.34 Found eq_ref000:=(eq_ref00 P0):((P0 (f x1))->(P0 (f x1))) % 53.13/53.34 Found (eq_ref00 P0) as proof of (P1 (f x1)) % 53.13/53.34 Found ((eq_ref0 (f x1)) P0) as proof of (P1 (f x1)) % 53.13/53.34 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 53.13/53.34 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 53.13/53.34 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 53.13/53.34 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 53.13/53.34 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 53.13/53.34 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 53.13/53.34 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 53.13/53.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 53.13/53.34 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 53.13/53.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 53.13/53.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 53.13/53.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 53.13/53.34 Found (((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.13/53.34 Found (((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.13/53.34 Found ((((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_trans0000 x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.49 Found ((((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.49 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.49 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.49 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.49 Found (fun (P0:(Prop->Prop))=> ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.49 Found eq_ref000:=(eq_ref00 P0):((P0 (f x1))->(P0 (f x1))) % 53.27/53.49 Found (eq_ref00 P0) as proof of (P1 (f x1)) % 53.27/53.49 Found ((eq_ref0 (f x1)) P0) as proof of (P1 (f x1)) % 53.27/53.49 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 53.27/53.49 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 53.27/53.49 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 53.27/53.49 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 53.27/53.49 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 53.27/53.49 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 53.27/53.49 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 53.27/53.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 53.27/53.49 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 53.27/53.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 53.27/53.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 53.27/53.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 53.27/53.50 Found (((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.50 Found (((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.50 Found ((((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_trans0000 x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.50 Found ((((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.50 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.50 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.50 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 53.27/53.50 Found (fun (P0:(Prop->Prop))=> ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 58.49/58.74 Found x2:(P c_2) % 58.49/58.74 Instantiate: b:=c_2:fofType % 58.49/58.74 Found x2 as proof of (P0 b) % 58.49/58.74 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 58.49/58.74 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 58.49/58.74 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 58.49/58.74 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 58.49/58.74 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 58.49/58.74 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 58.49/58.74 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 58.49/58.74 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 58.49/58.74 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 58.49/58.74 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 58.49/58.74 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 58.49/58.74 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 58.49/58.74 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 58.49/58.74 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 58.49/58.74 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 58.49/58.74 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 58.49/58.74 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 58.49/58.74 Found x2:(P c_2) % 58.49/58.74 Instantiate: b:=c_2:fofType % 58.49/58.74 Found x2 as proof of (P0 b) % 58.49/58.74 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 58.49/58.74 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 58.49/58.74 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 58.49/58.74 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 58.49/58.74 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 58.49/58.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 58.49/58.74 Found (eq_ref0 b) as proof of (P0 b) % 58.49/58.74 Found ((eq_ref Prop) b) as proof of (P0 b) % 58.49/58.74 Found ((eq_ref Prop) b) as proof of (P0 b) % 58.49/58.74 Found ((eq_ref Prop) b) as proof of (P0 b) % 58.49/58.74 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 58.49/58.74 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 58.49/58.74 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 58.49/58.74 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 58.49/58.74 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 58.49/58.74 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 58.49/58.74 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 58.49/58.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 58.49/58.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 58.49/58.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 58.49/58.74 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 58.49/58.74 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 58.49/58.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 58.49/58.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 58.49/58.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 58.49/58.74 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 58.49/58.74 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 60.23/60.47 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 60.23/60.47 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 60.23/60.47 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 60.23/60.47 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 60.23/60.47 Found (eq_ref00 P) as proof of (P0 c_2) % 60.23/60.47 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 60.23/60.47 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 60.23/60.47 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 60.23/60.47 Found x2:(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 60.23/60.47 Instantiate: b:=((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)):Prop % 60.23/60.47 Found x2 as proof of (P1 b) % 60.23/60.47 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 60.23/60.47 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 60.23/60.47 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 60.23/60.47 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 60.23/60.47 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 60.23/60.47 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 60.23/60.47 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 60.23/60.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 60.23/60.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 60.23/60.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 60.23/60.47 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 60.23/60.47 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 60.23/60.47 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 60.23/60.47 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 60.23/60.47 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 60.23/60.47 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 60.23/60.47 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 60.23/60.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 60.23/60.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 60.23/60.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 60.23/60.47 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 60.23/60.47 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 60.23/60.47 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 60.23/60.47 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 60.23/60.47 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 60.23/60.47 Found ((eq_sym0100 ((eq_ref Prop) (f x1))) x2) as proof of (P0 (f x1)) % 60.23/60.47 Found ((eq_sym0100 ((eq_ref Prop) (f x1))) x2) as proof of (P0 (f x1)) % 60.23/60.47 Found (((fun (x3:(((eq Prop) (f x1)) b))=> ((eq_sym010 x3) P0)) ((eq_ref Prop) (f x1))) x2) as proof of (P0 (f x1)) % 60.23/60.47 Found (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_sym01 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P0)) ((eq_ref Prop) (f x1))) x2) as proof of (P0 (f x1)) % 60.23/60.47 Found (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P0)) ((eq_ref Prop) (f x1))) x2) as proof of (P0 (f x1)) % 60.23/60.47 Found (fun (x2:(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P0)) ((eq_ref Prop) (f x1))) x2)) as proof of (P0 (f x1)) % 62.68/62.93 Found (fun (P0:(Prop->Prop)) (x2:(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P0)) ((eq_ref Prop) (f x1))) x2)) as proof of ((P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P0 (f x1))) % 62.68/62.93 Found (fun (P0:(Prop->Prop)) (x2:(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P0)) ((eq_ref Prop) (f x1))) x2)) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 62.68/62.93 Found (eq_sym000 (fun (P0:(Prop->Prop)) (x2:(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P0)) ((eq_ref Prop) (f x1))) x2))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 62.68/62.93 Found ((eq_sym00 (f x1)) (fun (P0:(Prop->Prop)) (x2:(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P0)) ((eq_ref Prop) (f x1))) x2))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 62.68/62.93 Found (((eq_sym0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) (fun (P0:(Prop->Prop)) (x2:(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P0)) ((eq_ref Prop) (f x1))) x2))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 62.68/62.93 Found ((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) (fun (P0:(Prop->Prop)) (x2:(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P0)) ((eq_ref Prop) (f x1))) x2))) as proof of (((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 62.68/62.93 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 62.68/62.93 Found (eq_ref0 b) as proof of (P b) % 62.68/62.93 Found ((eq_ref fofType) b) as proof of (P b) % 62.68/62.93 Found ((eq_ref fofType) b) as proof of (P b) % 62.68/62.93 Found ((eq_ref fofType) b) as proof of (P b) % 62.68/62.93 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 62.68/62.93 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 62.68/62.93 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 62.68/62.93 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 62.68/62.93 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 62.68/62.93 Found x2:(P (absval Xv)) % 62.68/62.93 Instantiate: b:=(absval Xv):fofType % 62.68/62.93 Found x2 as proof of (P0 b) % 62.68/62.93 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 62.68/62.93 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 62.68/62.93 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 62.68/62.93 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 62.68/62.93 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 62.68/62.93 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 62.68/62.93 Found (eq_ref00 P) as proof of (P0 c_2) % 62.68/62.93 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 62.68/62.93 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 62.68/62.93 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 62.68/62.93 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 68.22/68.42 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 68.22/68.42 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 68.22/68.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 68.22/68.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 68.22/68.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 68.22/68.42 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 68.22/68.42 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 68.22/68.42 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 68.22/68.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 68.22/68.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 68.22/68.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 68.22/68.42 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 68.22/68.42 Found (eq_ref0 b) as proof of (P b) % 68.22/68.42 Found ((eq_ref fofType) b) as proof of (P b) % 68.22/68.42 Found ((eq_ref fofType) b) as proof of (P b) % 68.22/68.42 Found ((eq_ref fofType) b) as proof of (P b) % 68.22/68.42 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 68.22/68.42 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 68.22/68.42 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 68.22/68.42 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 68.22/68.42 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 68.22/68.42 Found x2:(P (absval Xv)) % 68.22/68.42 Instantiate: b:=(absval Xv):fofType % 68.22/68.42 Found x2 as proof of (P0 b) % 68.22/68.42 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 68.22/68.42 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 68.22/68.42 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 68.22/68.42 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 68.22/68.42 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 68.22/68.42 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 68.22/68.42 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 68.22/68.42 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 68.22/68.42 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 68.22/68.42 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 68.22/68.42 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 68.22/68.42 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 68.22/68.42 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 68.22/68.42 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 68.22/68.42 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 68.22/68.42 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 68.22/68.42 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 68.22/68.42 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 68.22/68.42 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 68.22/68.42 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 68.22/68.42 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 68.22/68.42 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 68.22/68.42 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 68.22/68.42 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 69.36/69.57 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 69.36/69.57 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 69.36/69.57 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 69.36/69.57 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 69.36/69.57 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 69.36/69.57 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 69.36/69.57 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 69.36/69.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 69.36/69.57 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 75.12/75.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 75.12/75.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 75.12/75.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 75.12/75.34 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 75.12/75.34 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 75.12/75.34 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 75.12/75.34 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 75.12/75.34 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 75.12/75.34 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 75.12/75.34 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 75.12/75.34 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 75.12/75.34 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 75.12/75.34 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 75.12/75.34 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 75.12/75.34 Found (eq_ref00 P) as proof of (P0 b) % 75.12/75.34 Found ((eq_ref0 b) P) as proof of (P0 b) % 75.12/75.34 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 75.12/75.34 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 75.12/75.34 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 75.12/75.34 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 75.12/75.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 75.12/75.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 75.12/75.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 75.12/75.34 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 75.12/75.34 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 75.12/75.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 75.12/75.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 75.12/75.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 75.12/75.34 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 75.12/75.34 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 75.12/75.34 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 75.12/75.34 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 75.12/75.34 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 75.12/75.34 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 75.12/75.34 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 75.12/75.34 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 75.12/75.34 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 75.12/75.34 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 75.12/75.34 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 75.12/75.34 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 75.12/75.34 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 75.12/75.34 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 75.12/75.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 80.98/81.24 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 80.98/81.24 Found (eq_ref00 P) as proof of (P0 b) % 80.98/81.24 Found ((eq_ref0 b) P) as proof of (P0 b) % 80.98/81.24 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 80.98/81.24 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 80.98/81.24 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 80.98/81.24 Found (eq_ref00 P) as proof of (P0 c_2) % 80.98/81.24 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 80.98/81.24 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 80.98/81.24 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 80.98/81.24 Found c_2:fofType % 80.98/81.24 Found c_2 as proof of fofType % 80.98/81.24 Found (x2 c_2) as proof of False % 80.98/81.24 Found (x2 c_2) as proof of False % 80.98/81.24 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 80.98/81.24 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of ((x1 (absval Xy))->False) % 80.98/81.24 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 80.98/81.24 Found c_2:fofType % 80.98/81.24 Found c_2 as proof of fofType % 80.98/81.24 Found (x2 c_2) as proof of False % 80.98/81.24 Found (x2 c_2) as proof of False % 80.98/81.24 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 80.98/81.24 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (not (x1 (absval Xy))) % 80.98/81.24 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 80.98/81.24 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 80.98/81.24 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 80.98/81.24 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 80.98/81.24 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 80.98/81.24 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 80.98/81.24 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 80.98/81.24 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 80.98/81.24 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 80.98/81.24 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 80.98/81.24 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 80.98/81.24 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 80.98/81.24 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 80.98/81.24 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 80.98/81.24 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 88.94/89.19 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 88.94/89.19 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 88.94/89.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 88.94/89.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 88.94/89.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 88.94/89.19 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 88.94/89.19 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 88.94/89.19 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 88.94/89.19 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 88.94/89.19 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 88.94/89.19 Found c_2:fofType % 88.94/89.19 Found c_2 as proof of fofType % 88.94/89.19 Found (x2 c_2) as proof of False % 88.94/89.19 Found (x2 c_2) as proof of False % 88.94/89.19 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 88.94/89.19 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (not (x1 (absval Xy))) % 88.94/89.19 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 88.94/89.19 Found c_2:fofType % 88.94/89.19 Found c_2 as proof of fofType % 88.94/89.19 Found (x2 c_2) as proof of False % 88.94/89.19 Found (x2 c_2) as proof of False % 88.94/89.19 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 88.94/89.19 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (not (x1 (absval Xy))) % 88.94/89.19 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 88.94/89.19 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 88.94/89.19 Found (eq_ref00 P) as proof of (P0 c_2) % 88.94/89.19 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 88.94/89.19 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 88.94/89.19 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 88.94/89.19 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 88.94/89.19 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 88.94/89.19 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 88.94/89.19 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 88.94/89.19 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 88.94/89.19 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 88.94/89.19 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 88.94/89.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 88.94/89.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 88.94/89.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 88.94/89.19 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 88.94/89.19 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 88.94/89.19 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 88.94/89.19 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 88.94/89.19 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 88.94/89.19 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 88.94/89.19 Found (eq_ref0 b0) as proof of (((eq fofType) b0) c_2) % 88.94/89.19 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 88.94/89.19 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 88.94/89.19 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 88.94/89.19 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 88.94/89.19 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 88.94/89.19 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 88.94/89.19 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 88.94/89.19 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 88.94/89.19 Found (eq_sym010 ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 88.94/89.19 Found ((eq_sym01 b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 88.94/89.19 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 88.94/89.19 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 88.94/89.19 Found ((eq_trans0000 ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 88.94/89.19 Found (((eq_trans000 (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 88.94/89.20 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 88.94/89.20 Found (((((eq_trans0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 88.94/89.20 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 88.94/89.20 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 88.94/89.20 Found (eq_sym0000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 88.94/89.20 Found (eq_sym0000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 88.94/89.20 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((eq_sym000 x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 88.94/89.20 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((eq_sym00 (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 88.94/89.20 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((((eq_sym0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 89.16/89.37 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 89.16/89.37 Found (fun (P0:(Prop->Prop))=> ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 89.16/89.37 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 89.16/89.37 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 89.16/89.37 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 89.16/89.37 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 89.16/89.37 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 89.16/89.37 Found (eq_sym010 ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 89.16/89.37 Found ((eq_sym01 b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 89.16/89.37 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 89.16/89.37 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 89.16/89.37 Found ((eq_trans0000 ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 89.16/89.37 Found (((eq_trans000 (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 89.16/89.37 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 89.16/89.37 Found (((((eq_trans0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 89.16/89.37 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 89.16/89.38 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 89.16/89.38 Found (eq_sym0000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 89.16/89.38 Found (eq_sym0000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 89.16/89.38 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((eq_sym000 x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 89.16/89.38 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((eq_sym00 (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 89.16/89.38 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((((eq_sym0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 89.16/89.38 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 91.32/91.52 Found (fun (P0:(Prop->Prop))=> ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 91.32/91.52 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 91.32/91.52 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 91.32/91.52 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 91.32/91.52 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 91.32/91.52 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 91.32/91.52 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 91.32/91.52 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 91.32/91.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 91.32/91.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 91.32/91.52 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 91.32/91.52 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 91.32/91.52 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 91.32/91.52 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 91.32/91.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 91.32/91.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 91.32/91.52 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 91.32/91.52 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 91.32/91.52 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 91.32/91.52 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 91.32/91.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 91.32/91.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 91.32/91.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 91.32/91.52 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 91.32/91.52 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 91.32/91.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 91.32/91.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 91.32/91.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 91.32/91.52 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 91.32/91.52 Found (eta_expansion_dep00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 91.32/91.52 Found (eta_expansion00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 91.32/91.52 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 91.32/91.52 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 95.38/95.59 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 95.38/95.59 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 95.38/95.59 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 95.38/95.59 Found (eta_expansion00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 95.38/95.59 Found (eta_expansion00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 95.38/95.59 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 95.38/95.59 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 95.38/95.59 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 95.38/95.59 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 95.38/95.59 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 95.38/95.59 Found (eq_ref00 P) as proof of (P0 b) % 95.38/95.59 Found ((eq_ref0 b) P) as proof of (P0 b) % 95.38/95.59 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 95.38/95.59 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 95.38/95.59 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 95.38/95.59 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 95.38/95.59 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 95.38/95.59 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1)) % 95.38/95.59 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (b x))) % 101.47/101.68 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 101.47/101.68 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 101.47/101.68 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 101.47/101.68 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 101.47/101.68 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 101.47/101.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 101.47/101.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 101.47/101.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 101.47/101.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 101.47/101.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 101.47/101.68 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 101.47/101.68 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 101.47/101.68 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 101.47/101.68 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 101.47/101.68 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 101.47/101.68 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 101.47/101.68 Found ex_intro0:=(ex_intro (fofType->Prop)):(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P))) % 101.47/101.68 Instantiate: a:=(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P))):Prop % 101.47/101.68 Found ex_intro0 as proof of a % 101.47/101.68 Found ex_intro0:=(ex_intro (fofType->Prop)):(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P))) % 101.47/101.68 Instantiate: a:=(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P))):Prop % 101.47/101.68 Found ex_intro0 as proof of a % 101.47/101.68 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 101.47/101.68 Found (eq_ref0 b0) as proof of (((eq fofType) b0) c_2) % 101.47/101.68 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 101.47/101.68 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 101.47/101.68 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 101.47/101.68 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 101.47/101.68 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x))) % 101.47/101.68 Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 101.47/101.68 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 101.47/101.68 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 101.47/101.68 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 101.47/101.68 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 101.47/101.68 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 101.47/101.68 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 101.47/101.68 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 106.03/106.31 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 106.03/106.31 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 106.03/106.31 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 106.03/106.31 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 106.03/106.31 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 106.03/106.31 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 106.03/106.31 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 106.03/106.31 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 106.03/106.31 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 106.03/106.31 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 106.03/106.31 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 106.03/106.31 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 106.03/106.31 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 106.03/106.31 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x))) % 106.03/106.31 Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 106.03/106.31 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 106.03/106.31 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 106.03/106.31 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 106.03/106.31 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0) % 106.03/106.31 Found c_2:fofType % 106.03/106.31 Found c_2 as proof of fofType % 106.03/106.31 Found False:Prop % 106.03/106.31 Found False as proof of Prop % 106.03/106.31 Found ((x00 c_2) False) as proof of False % 106.03/106.31 Found ((x00 c_2) False) as proof of False % 106.03/106.31 Found (fun (x00:(x1 (absval Xy)))=> ((x00 c_2) False)) as proof of False % 106.03/106.31 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False)) as proof of ((x1 (absval Xy))->False) % 106.03/106.31 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 106.03/106.31 Found ((conj00 (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) % 106.03/106.31 Found (((conj0 a) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) % 106.03/106.31 Found ((((conj (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) % 107.98/108.22 Found ((((conj (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) % 107.98/108.22 Found ((((conj (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of (P a) % 107.98/108.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 107.98/108.22 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 107.98/108.22 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 107.98/108.22 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 107.98/108.22 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 107.98/108.22 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 107.98/108.22 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 107.98/108.22 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 107.98/108.22 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 107.98/108.22 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 107.98/108.22 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 107.98/108.22 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 107.98/108.22 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 107.98/108.22 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 107.98/108.22 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 107.98/108.22 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 107.98/108.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 107.98/108.22 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 107.98/108.22 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 107.98/108.22 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 107.98/108.22 Found False:Prop % 107.98/108.22 Found False as proof of Prop % 107.98/108.22 Found c_2:fofType % 107.98/108.22 Found c_2 as proof of fofType % 107.98/108.22 Found ((x2 c_2) False) as proof of False % 107.98/108.22 Found ((x2 c_2) False) as proof of False % 107.98/108.22 Found (fun (x2:(x1 (absval Xy)))=> ((x2 c_2) False)) as proof of False % 107.98/108.22 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False)) as proof of (not (x1 (absval Xy))) % 107.98/108.22 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 107.98/108.22 Found ((conj00 (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) a) % 107.98/108.22 Found (((conj0 a) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) a) % 110.33/110.54 Found ((((conj (forall (Xy:fofType), (not (x1 (absval Xy))))) a) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) a) % 110.33/110.54 Found ((((conj (forall (Xy:fofType), (not (x1 (absval Xy))))) a) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) a) % 110.33/110.54 Found ((((conj (forall (Xy:fofType), (not (x1 (absval Xy))))) a) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of (P a) % 110.33/110.54 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 110.33/110.54 Found (eta_expansion00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->Prop)->Prop)) f) (fun (x:(fofType->Prop))=> (f x))) % 110.33/110.54 Found (eta_expansion00 f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found (((eta_expansion (fofType->Prop)) Prop) f) as proof of (((eq ((fofType->Prop)->Prop)) f) b) % 110.33/110.54 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 110.33/110.54 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 110.33/110.54 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 110.33/110.54 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 110.33/110.54 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 110.33/110.54 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 110.33/110.54 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 110.33/110.54 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 110.33/110.54 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 110.33/110.54 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 110.33/110.54 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 110.33/110.54 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 110.33/110.54 Found x2:(P0 (f x1)) % 110.33/110.54 Instantiate: b:=(f x1):Prop % 110.33/110.54 Found x2 as proof of (P1 b) % 110.33/110.54 Found x2:(P0 (f x1)) % 110.33/110.54 Instantiate: b:=(f x1):Prop % 110.33/110.54 Found x2 as proof of (P1 b) % 110.33/110.54 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 110.33/110.54 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 110.33/110.54 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 110.33/110.54 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 110.33/110.54 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 110.33/110.54 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 112.12/112.37 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 112.12/112.37 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 112.12/112.37 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 112.12/112.37 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 112.12/112.37 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 112.12/112.37 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 112.12/112.37 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 112.12/112.37 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 112.12/112.37 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 112.12/112.37 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 112.12/112.37 Found (eq_ref0 b) as proof of (((eq fofType) b) b0) % 112.12/112.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 112.12/112.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 112.12/112.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 112.12/112.37 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 112.12/112.37 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 112.12/112.37 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 112.12/112.37 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 112.12/112.37 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 112.12/112.37 Found (eq_sym010 ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 112.12/112.37 Found ((eq_sym01 b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 112.12/112.37 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 112.12/112.37 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 112.12/112.37 Found ((eq_trans0000 ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 112.12/112.37 Found (((eq_trans000 (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 112.12/112.37 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 112.12/112.37 Found (((((eq_trans0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 112.12/112.37 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 112.12/112.37 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 114.74/115.01 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 114.74/115.01 Found (eq_sym000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 114.74/115.01 Found ((eq_sym00 (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 114.74/115.01 Found (((eq_sym0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 114.74/115.01 Found ((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 114.74/115.01 Found ((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 114.74/115.01 Found c_2:fofType % 114.74/115.01 Found c_2 as proof of fofType % 114.74/115.01 Found (x00 c_2) as proof of False % 114.74/115.01 Found (x00 c_2) as proof of False % 114.74/115.01 Found (fun (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of False % 114.74/115.01 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of ((x1 (absval Xy))->False) % 114.74/115.01 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> (x00 c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 114.74/115.01 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 114.74/115.01 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 115.17/115.43 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 115.17/115.43 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 115.17/115.43 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 115.17/115.43 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 115.17/115.43 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 115.17/115.43 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 115.17/115.43 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 115.17/115.43 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 115.17/115.43 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 115.17/115.43 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 115.17/115.43 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 115.17/115.43 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 115.17/115.43 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 115.17/115.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 115.17/115.43 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 115.17/115.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 115.17/115.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 115.17/115.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 115.17/115.43 Found ((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.17/115.43 Found ((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.17/115.43 Found (((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_trans0000 x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.17/115.43 Found (((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.17/115.43 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.17/115.43 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.17/115.43 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.33/115.54 Found (fun (P0:(Prop->Prop))=> (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.33/115.54 Found (fun (P0:(Prop->Prop))=> (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 115.33/115.54 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 115.33/115.54 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 115.33/115.54 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 115.33/115.54 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 115.33/115.54 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 115.33/115.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 115.33/115.54 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 115.33/115.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 115.33/115.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 115.33/115.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 115.33/115.54 Found ((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.33/115.54 Found ((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.33/115.54 Found (((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_trans0000 x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.33/115.54 Found (((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.33/115.54 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 115.33/115.54 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.33 Found (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.33 Found (fun (P0:(Prop->Prop))=> (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.33 Found (fun (P0:(Prop->Prop))=> (((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) P0)) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 116.09/116.33 Found c_2:fofType % 116.09/116.33 Found c_2 as proof of fofType % 116.09/116.33 Found (x2 c_2) as proof of False % 116.09/116.33 Found (x2 c_2) as proof of False % 116.09/116.33 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 116.09/116.33 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (not (x1 (absval Xy))) % 116.09/116.33 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 116.09/116.33 Found eq_ref000:=(eq_ref00 P0):((P0 (f x1))->(P0 (f x1))) % 116.09/116.33 Found (eq_ref00 P0) as proof of (P1 (f x1)) % 116.09/116.33 Found ((eq_ref0 (f x1)) P0) as proof of (P1 (f x1)) % 116.09/116.33 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 116.09/116.33 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 116.09/116.33 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 116.09/116.33 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 116.09/116.33 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 116.09/116.33 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 116.09/116.33 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 116.09/116.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 116.09/116.33 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 116.09/116.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 116.09/116.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 116.09/116.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 116.09/116.33 Found (((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.34 Found (((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.34 Found ((((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_trans0000 x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.34 Found ((((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.34 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.34 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.34 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.34 Found (fun (P0:(Prop->Prop))=> ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.09/116.34 Found (fun (P0:(Prop->Prop))=> ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 116.22/116.50 Found eq_ref000:=(eq_ref00 P0):((P0 (f x1))->(P0 (f x1))) % 116.22/116.50 Found (eq_ref00 P0) as proof of (P1 (f x1)) % 116.22/116.50 Found ((eq_ref0 (f x1)) P0) as proof of (P1 (f x1)) % 116.22/116.50 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 116.22/116.50 Found (((eq_ref Prop) (f x1)) P0) as proof of (P1 (f x1)) % 116.22/116.50 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 116.22/116.50 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 116.22/116.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 116.22/116.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 116.22/116.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 116.22/116.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 116.22/116.50 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 116.22/116.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 116.22/116.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 116.22/116.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 116.22/116.50 Found (((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.22/116.50 Found (((eq_trans00000 ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.22/116.50 Found ((((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_trans0000 x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.22/116.50 Found ((((fun (x2:(((eq Prop) (f x1)) b)) (x3:(((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_trans000 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.22/116.50 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 116.22/116.50 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((((eq_trans0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 118.93/119.13 Found ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 118.93/119.13 Found (fun (P0:(Prop->Prop))=> ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 118.93/119.13 Found (fun (P0:(Prop->Prop))=> ((((fun (x2:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (x3:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((((eq_trans Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x2) x3) (fun (x5:Prop)=> ((P0 (f x1))->(P0 x5))))) ((eq_ref Prop) (f x1))) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_ref Prop) (f x1)) P0))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 118.93/119.13 Found x2:(P c_2) % 118.93/119.13 Instantiate: b:=c_2:fofType % 118.93/119.13 Found x2 as proof of (P0 b) % 118.93/119.13 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 118.93/119.13 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 118.93/119.13 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 118.93/119.13 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 118.93/119.13 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 118.93/119.13 Found x2:(P c_2) % 118.93/119.13 Instantiate: b:=c_2:fofType % 118.93/119.13 Found x2 as proof of (P0 b) % 118.93/119.13 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 118.93/119.13 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 118.93/119.13 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 118.93/119.13 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 118.93/119.13 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 118.93/119.13 Found c_2:fofType % 118.93/119.13 Found c_2 as proof of fofType % 118.93/119.13 Found False:Prop % 118.93/119.13 Found False as proof of Prop % 118.93/119.13 Found ((x00 c_2) False) as proof of False % 118.93/119.13 Found ((x00 c_2) False) as proof of False % 118.93/119.13 Found (fun (x00:(x1 (absval Xy)))=> ((x00 c_2) False)) as proof of False % 118.93/119.13 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False)) as proof of ((x1 (absval Xy))->False) % 118.93/119.13 Found (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 118.93/119.13 Found False:Prop % 118.93/119.13 Found False as proof of Prop % 118.93/119.13 Found c_2:fofType % 118.93/119.13 Found c_2 as proof of fofType % 118.93/119.13 Found ((x2 c_2) False) as proof of False % 118.93/119.13 Found ((x2 c_2) False) as proof of False % 118.93/119.13 Found (fun (x2:(x1 (absval Xy)))=> ((x2 c_2) False)) as proof of False % 118.93/119.13 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False)) as proof of (not (x1 (absval Xy))) % 118.93/119.13 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 126.29/126.52 Found x2:(P c_2) % 126.29/126.52 Instantiate: b:=c_2:fofType % 126.29/126.52 Found x2 as proof of (P0 b) % 126.29/126.52 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 126.29/126.52 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 126.29/126.52 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 126.29/126.52 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 126.29/126.52 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 126.29/126.52 Found x2:(P c_2) % 126.29/126.52 Instantiate: b:=c_2:fofType % 126.29/126.52 Found x2 as proof of (P0 b) % 126.29/126.52 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 126.29/126.52 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 126.29/126.52 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 126.29/126.52 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 126.29/126.52 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 126.29/126.52 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 126.29/126.52 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 126.29/126.52 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 126.29/126.52 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 126.29/126.52 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 126.29/126.52 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 126.29/126.52 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1)) % 126.29/126.52 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 126.29/126.52 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 126.29/126.52 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1)) % 126.29/126.52 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1)) % 126.29/126.52 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x))) % 126.29/126.52 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 126.29/126.52 Found (eq_ref00 P) as proof of (P0 c_2) % 126.29/126.52 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 126.29/126.52 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 126.29/126.52 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 126.29/126.52 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 126.29/126.52 Found (eq_ref00 P) as proof of (P0 c_2) % 126.29/126.52 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 126.29/126.52 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 126.29/126.52 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 126.29/126.52 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 126.29/126.52 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 126.29/126.52 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 126.29/126.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 126.29/126.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 126.29/126.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 126.29/126.52 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 126.29/126.52 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 126.29/126.52 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 126.29/126.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 126.29/126.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 126.29/126.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 126.29/126.52 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 126.29/126.52 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 126.29/126.52 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 131.46/131.67 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 131.46/131.67 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 131.46/131.67 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 131.46/131.67 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 131.46/131.67 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 131.46/131.67 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 131.46/131.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 131.46/131.67 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 131.46/131.67 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 131.46/131.67 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 131.46/131.67 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 131.46/131.67 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 131.46/131.67 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 131.46/131.67 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 131.46/131.67 Found (eq_ref0 a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (x1 c_2)) % 131.46/131.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 131.46/131.67 Found (eq_ref0 b) as proof of (P b) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (P b) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (P b) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (P b) % 131.46/131.67 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 131.46/131.67 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 131.46/131.67 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 131.46/131.67 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 131.46/131.67 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 131.46/131.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 131.46/131.67 Found (eq_ref0 b) as proof of (P b) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (P b) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (P b) % 131.46/131.67 Found ((eq_ref fofType) b) as proof of (P b) % 131.46/131.67 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 131.46/131.67 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 131.46/131.67 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 131.46/131.67 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 131.46/131.67 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 131.46/131.67 Found x2:(P (absval Xv)) % 131.46/131.67 Instantiate: b:=(absval Xv):fofType % 131.46/131.67 Found x2 as proof of (P0 b) % 131.46/131.67 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 131.46/131.67 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 131.46/131.67 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 131.46/131.67 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found x2:(P (absval Xv)) % 135.58/135.83 Instantiate: b:=(absval Xv):fofType % 135.58/135.83 Found x2 as proof of (P0 b) % 135.58/135.83 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 135.58/135.83 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 135.58/135.83 Found (eq_ref00 P) as proof of (P0 c_2) % 135.58/135.83 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 135.58/135.83 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 135.58/135.83 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 135.58/135.83 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 135.58/135.83 Found (eq_ref00 P) as proof of (P0 c_2) % 135.58/135.83 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 135.58/135.83 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 135.58/135.83 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 135.58/135.83 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 135.58/135.83 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 135.58/135.83 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 135.58/135.83 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 135.58/135.83 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 135.58/135.83 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 135.58/135.83 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 135.58/135.83 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 135.58/135.83 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 135.58/135.83 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 135.58/135.83 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 135.58/135.83 Found (eq_ref0 b) as proof of (P b) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (P b) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (P b) % 135.58/135.83 Found ((eq_ref fofType) b) as proof of (P b) % 135.58/135.83 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 135.58/135.83 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 135.58/135.83 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 135.58/135.83 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 135.58/135.83 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 135.58/135.83 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 147.88/148.12 Found (eq_ref0 b) as proof of (P b) % 147.88/148.12 Found ((eq_ref fofType) b) as proof of (P b) % 147.88/148.12 Found ((eq_ref fofType) b) as proof of (P b) % 147.88/148.12 Found ((eq_ref fofType) b) as proof of (P b) % 147.88/148.12 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 147.88/148.12 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 147.88/148.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 147.88/148.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 147.88/148.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 147.88/148.12 Found x2:(P (absval Xv)) % 147.88/148.12 Instantiate: b:=(absval Xv):fofType % 147.88/148.12 Found x2 as proof of (P0 b) % 147.88/148.12 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 147.88/148.12 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 147.88/148.12 Found x2:(P (absval Xv)) % 147.88/148.12 Instantiate: b:=(absval Xv):fofType % 147.88/148.12 Found x2 as proof of (P0 b) % 147.88/148.12 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 147.88/148.12 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 147.88/148.12 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 147.88/148.12 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 147.88/148.12 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 147.88/148.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 147.88/148.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 147.88/148.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 147.88/148.12 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 147.88/148.12 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 147.88/148.12 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 147.88/148.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 147.88/148.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 147.88/148.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 147.88/148.12 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 147.88/148.12 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 147.88/148.12 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 147.88/148.12 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 147.88/148.12 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 147.88/148.12 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 147.88/148.12 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 147.88/148.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 149.22/149.46 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 149.22/149.46 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 149.22/149.46 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 149.22/149.46 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 149.22/149.46 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 149.22/149.46 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 149.22/149.46 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 149.22/149.46 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 149.22/149.46 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 149.22/149.46 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 149.22/149.46 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 149.22/149.46 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 149.22/149.46 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 149.22/149.46 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 149.22/149.46 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 149.22/149.46 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 149.22/149.46 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 149.22/149.46 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 149.22/149.46 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 149.22/149.46 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 149.22/149.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 149.22/149.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 149.22/149.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 149.22/149.46 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 149.22/149.46 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 149.22/149.46 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 149.22/149.46 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 149.22/149.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 149.22/149.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 149.22/149.46 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 149.22/149.46 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 150.35/150.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 150.35/150.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 150.35/150.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 150.35/150.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 150.35/150.56 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 150.35/150.56 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 150.35/150.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 150.35/150.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 150.35/150.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 150.35/150.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 150.35/150.56 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 150.35/150.56 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 150.35/150.56 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 150.35/150.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 150.35/150.56 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 158.23/158.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 158.23/158.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 158.23/158.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 158.23/158.46 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 158.23/158.46 Found (eq_ref00 P) as proof of (P0 b) % 158.23/158.46 Found ((eq_ref0 b) P) as proof of (P0 b) % 158.23/158.46 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 158.23/158.46 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 158.23/158.46 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 158.23/158.46 Found (eq_ref00 P) as proof of (P0 b) % 158.23/158.46 Found ((eq_ref0 b) P) as proof of (P0 b) % 158.23/158.46 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 158.23/158.46 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 158.23/158.46 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 158.23/158.46 Found (eq_ref00 P) as proof of (P0 b) % 158.23/158.46 Found ((eq_ref0 b) P) as proof of (P0 b) % 158.23/158.46 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 158.23/158.46 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 158.23/158.46 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 158.23/158.46 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 158.23/158.46 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 158.23/158.46 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 158.23/158.46 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 158.23/158.46 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 158.23/158.46 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 158.23/158.46 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 158.23/158.46 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 158.23/158.46 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 158.23/158.46 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 158.23/158.46 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 158.23/158.46 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 158.23/158.46 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 158.23/158.46 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 158.23/158.46 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 158.23/158.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 158.23/158.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 158.23/158.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 158.23/158.46 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 158.23/158.46 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 158.23/158.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 158.23/158.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 158.23/158.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 158.23/158.46 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 158.23/158.46 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 158.23/158.46 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 160.93/161.17 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 160.93/161.17 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 160.93/161.17 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 160.93/161.17 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 160.93/161.17 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 160.93/161.17 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 160.93/161.17 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 160.93/161.17 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 160.93/161.17 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 160.93/161.17 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 160.93/161.17 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 160.93/161.17 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 160.93/161.17 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 160.93/161.17 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 169.62/169.87 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 169.62/169.87 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 169.62/169.87 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 169.62/169.87 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 169.62/169.87 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 169.62/169.87 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 169.62/169.87 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 169.62/169.87 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 169.62/169.87 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 169.62/169.87 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 169.62/169.87 Found (eq_ref00 P) as proof of (P0 b) % 169.62/169.87 Found ((eq_ref0 b) P) as proof of (P0 b) % 169.62/169.87 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 169.62/169.87 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 169.62/169.87 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 169.62/169.87 Found (eq_ref00 P) as proof of (P0 b) % 169.62/169.87 Found ((eq_ref0 b) P) as proof of (P0 b) % 169.62/169.87 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 169.62/169.87 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 169.62/169.87 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 169.62/169.87 Found (eq_ref00 P) as proof of (P0 b) % 169.62/169.87 Found ((eq_ref0 b) P) as proof of (P0 b) % 169.62/169.87 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 169.62/169.87 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 169.62/169.87 Found x2:(P (absval Xv)) % 169.62/169.87 Instantiate: b:=(absval Xv):fofType % 169.62/169.87 Found x2 as proof of (P0 b) % 169.62/169.87 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 169.62/169.87 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 169.62/169.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 169.62/169.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 169.62/169.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 169.62/169.87 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 169.62/169.87 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 169.62/169.87 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 172.93/173.22 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 172.93/173.22 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 172.93/173.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 172.93/173.22 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 172.93/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 172.93/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 172.93/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 172.93/173.22 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 172.93/173.22 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 172.93/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 172.93/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 172.93/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 172.93/173.22 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 172.93/173.22 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 172.93/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 172.93/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 172.93/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 172.93/173.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 172.93/173.22 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 172.93/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 172.93/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 173.02/173.22 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 173.02/173.22 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 173.02/173.22 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 173.02/173.22 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 173.02/173.22 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 173.02/173.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 173.02/173.22 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 173.02/173.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 174.51/174.75 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 174.51/174.75 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 174.51/174.75 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 174.51/174.75 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 174.51/174.75 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 174.51/174.75 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 174.51/174.75 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 174.51/174.75 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 174.51/174.75 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 174.51/174.75 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 174.51/174.75 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 174.51/174.75 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 174.51/174.75 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 174.51/174.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 189.87/190.12 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 189.87/190.12 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 189.87/190.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 189.87/190.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 189.87/190.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 189.87/190.12 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 189.87/190.12 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 189.87/190.12 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 189.87/190.12 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 189.87/190.12 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 189.87/190.12 Found x2:(P (absval Xv)) % 189.87/190.12 Instantiate: b:=(absval Xv):fofType % 189.87/190.12 Found x2 as proof of (P0 b) % 189.87/190.12 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 189.87/190.12 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 189.87/190.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 189.87/190.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 189.87/190.12 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 189.87/190.12 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 189.87/190.12 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 189.87/190.12 Found (eq_ref0 b0) as proof of (((eq fofType) b0) c_2) % 189.87/190.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 189.87/190.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 189.87/190.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 189.87/190.12 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 189.87/190.12 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 189.87/190.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 189.87/190.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 189.87/190.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 189.87/190.12 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 189.87/190.12 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 189.87/190.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 189.87/190.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 189.87/190.12 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 189.87/190.12 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 189.87/190.12 Found (eq_ref0 b0) as proof of (((eq fofType) b0) c_2) % 189.87/190.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 189.87/190.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 189.87/190.12 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 189.87/190.12 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 189.87/190.12 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 189.87/190.12 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 189.87/190.12 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 193.93/194.15 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 193.93/194.15 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 193.93/194.15 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 193.93/194.15 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 193.93/194.15 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 193.93/194.15 Found (eq_ref00 P) as proof of (P0 b) % 193.93/194.15 Found ((eq_ref0 b) P) as proof of (P0 b) % 193.93/194.15 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 193.93/194.15 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 193.93/194.15 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 193.93/194.15 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 193.93/194.15 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 193.93/194.15 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 193.93/194.15 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 193.93/194.15 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 193.93/194.15 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 193.93/194.15 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 193.93/194.15 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 193.93/194.15 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 193.93/194.15 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 193.93/194.15 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 193.93/194.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 193.93/194.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 193.93/194.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 193.93/194.15 Found (eq_sym010 ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 193.93/194.15 Found ((eq_sym01 b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 193.93/194.15 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 193.93/194.15 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 193.93/194.15 Found ((eq_trans0000 ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 193.93/194.15 Found (((eq_trans000 (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 193.93/194.15 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 193.93/194.15 Found (((((eq_trans0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 193.93/194.15 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 193.93/194.15 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 193.93/194.16 Found (eq_sym0000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 193.93/194.16 Found (eq_sym0000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 193.93/194.16 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((eq_sym000 x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 193.93/194.16 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((eq_sym00 (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 193.93/194.16 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((((eq_sym0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 193.93/194.16 Found ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 193.93/194.16 Found (fun (P0:(Prop->Prop))=> ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 194.07/194.33 Found (fun (P0:(Prop->Prop))=> ((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) P0)) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))))) as proof of (forall (P:(Prop->Prop)), ((P (f x1))->(P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))) % 194.07/194.33 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 194.07/194.33 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 194.07/194.33 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 194.07/194.33 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 194.07/194.33 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 194.07/194.33 Found (eq_sym010 ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 194.07/194.33 Found ((eq_sym01 b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 194.07/194.33 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 194.07/194.33 Found (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1))) as proof of (((eq Prop) b) (f x1)) % 194.07/194.33 Found ((eq_trans0000 ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 194.07/194.33 Found (((eq_trans000 (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) b) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 194.07/194.33 Found ((((eq_trans00 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 194.07/194.33 Found (((((eq_trans0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 194.07/194.33 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 194.07/194.33 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (forall (P:(Prop->Prop)), ((P ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P (f x1)))) % 194.07/194.33 Found ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1)))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 194.07/194.35 Found ((eq_sym0000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 194.07/194.35 Found ((eq_sym0000 ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 194.07/194.35 Found (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((eq_sym000 x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 194.07/194.35 Found (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((eq_sym00 (f x1)) x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 194.07/194.35 Found (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((((eq_sym0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) (((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 194.07/194.35 Found (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 194.07/194.35 Found (fun (P0:(Prop->Prop))=> (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) ((((((eq_trans Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) ((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((eq_ref Prop) (f x1))))) (((eq_ref Prop) (f x1)) P0))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 197.06/197.30 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 197.06/197.30 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 197.06/197.30 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 197.06/197.30 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 197.06/197.30 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 197.06/197.30 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 197.06/197.30 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 197.06/197.30 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 197.06/197.30 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 197.06/197.30 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 197.06/197.30 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 197.06/197.30 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 197.06/197.30 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 197.06/197.30 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 197.06/197.30 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 197.06/197.30 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 197.06/197.30 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 197.06/197.30 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 197.06/197.30 Found (eq_ref0 b0) as proof of (((eq fofType) b0) c_2) % 197.06/197.30 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 197.06/197.30 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 197.06/197.30 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 197.06/197.30 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 197.06/197.30 Found (eq_ref0 b0) as proof of (((eq fofType) b0) c_2) % 197.06/197.30 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 197.06/197.30 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 197.06/197.30 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 197.06/197.30 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 197.06/197.30 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 197.06/197.30 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 197.06/197.30 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 197.06/197.30 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 197.06/197.30 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 197.06/197.30 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 197.06/197.30 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 197.06/197.30 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 197.06/197.30 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 197.06/197.30 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 197.06/197.30 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 197.06/197.30 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 197.06/197.30 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 197.06/197.30 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 197.06/197.30 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->Prop)) b0) b0) % 199.31/199.62 Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 199.31/199.62 Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 199.31/199.62 Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 199.31/199.62 Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 199.31/199.62 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 199.31/199.62 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 199.31/199.62 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 199.31/199.62 Found ex_intro0:=(ex_intro (fofType->Prop)):(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P))) % 199.31/199.62 Instantiate: b:=(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P))):Prop % 199.31/199.62 Found ex_intro0 as proof of b % 199.31/199.62 Found ex_intro0 as proof of a % 199.31/199.62 Found ((conj00 (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) % 199.31/199.62 Found (((conj0 a) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) % 199.31/199.62 Found ((((conj (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) % 199.31/199.62 Found ((((conj (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) % 199.31/199.62 Found ((((conj (forall (Xy:fofType), ((x1 (absval Xy))->False))) a) (fun (Xy:fofType) (x00:(x1 (absval Xy)))=> ((x00 c_2) False))) ex_intro0) as proof of (P a) % 199.31/199.62 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 199.31/199.62 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 199.31/199.62 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 199.31/199.62 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 199.31/199.62 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 199.31/199.62 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 199.31/199.62 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 203.22/203.46 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 203.22/203.46 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 203.22/203.46 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 203.22/203.46 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 203.22/203.46 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 203.22/203.46 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 203.22/203.46 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 203.22/203.46 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 203.22/203.46 Found (eq_ref0 b0) as proof of (((eq fofType) b0) c_2) % 203.22/203.46 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 203.22/203.46 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 203.22/203.46 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 203.22/203.46 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 203.22/203.46 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 203.22/203.46 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 203.22/203.46 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 203.22/203.46 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 203.22/203.46 Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->Prop)) b0) b0) % 203.22/203.46 Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 203.22/203.46 Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 203.22/203.46 Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 203.22/203.46 Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 203.22/203.46 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 203.22/203.46 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 203.22/203.46 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 203.22/203.46 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 203.22/203.46 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 203.22/203.46 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 203.22/203.46 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 203.22/203.46 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 203.22/203.46 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 203.22/203.46 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 203.22/203.46 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 203.22/203.46 Found ex_intro0:=(ex_intro (fofType->Prop)):(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P))) % 203.22/203.46 Instantiate: b:=(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P))):Prop % 203.22/203.46 Found ex_intro0 as proof of b % 203.22/203.46 Found ex_intro0 as proof of a % 203.22/203.46 Found ((conj00 (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) a) % 203.22/203.46 Found (((conj0 a) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) a) % 203.22/203.46 Found ((((conj (forall (Xy:fofType), (not (x1 (absval Xy))))) a) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) a) % 203.22/203.46 Found ((((conj (forall (Xy:fofType), (not (x1 (absval Xy))))) a) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of ((and (forall (Xy:fofType), (not (x1 (absval Xy))))) a) % 203.22/203.46 Found ((((conj (forall (Xy:fofType), (not (x1 (absval Xy))))) a) (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> ((x2 c_2) False))) ex_intro0) as proof of (P a) % 208.01/208.25 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 208.01/208.25 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 208.01/208.25 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 208.01/208.25 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 208.01/208.25 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 208.01/208.25 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 208.01/208.25 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 208.01/208.25 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 208.01/208.25 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 208.01/208.25 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 208.01/208.25 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 208.01/208.25 Found (eq_ref00 P) as proof of (P0 b) % 208.01/208.25 Found ((eq_ref0 b) P) as proof of (P0 b) % 208.01/208.25 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 208.01/208.25 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 208.01/208.25 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 208.01/208.25 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 208.01/208.25 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 208.01/208.25 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 208.01/208.25 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 208.01/208.25 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 208.01/208.25 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 208.01/208.25 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 208.01/208.25 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 208.01/208.25 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 208.01/208.25 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 208.01/208.25 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 208.01/208.25 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 208.01/208.25 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 208.01/208.25 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 208.01/208.25 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 208.01/208.25 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 208.01/208.25 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 208.01/208.25 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 208.01/208.25 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 208.01/208.25 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x))) % 208.01/208.25 Found (eta_expansion_dep00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 211.47/211.75 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 211.47/211.75 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 211.47/211.75 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 211.47/211.75 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 211.47/211.75 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 211.47/211.75 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 211.47/211.75 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 211.47/211.75 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 211.47/211.75 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 211.47/211.75 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 211.47/211.75 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 211.47/211.75 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (a x1)) % 211.47/211.75 Found (fun (x1:(fofType->Prop))=> ((eq_ref Prop) (f x1))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (a x))) % 211.47/211.75 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x))) % 211.47/211.75 Found (eta_expansion_dep00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b) % 211.47/211.75 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 211.47/211.75 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 211.47/211.75 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 211.47/211.75 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 211.47/211.75 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 215.30/215.53 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 215.30/215.53 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 215.30/215.53 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 215.30/215.53 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 215.30/215.53 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 215.30/215.53 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b0) % 215.30/215.53 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 215.30/215.53 Found (eq_ref0 b0) as proof of (((eq fofType) b0) c_2) % 215.30/215.53 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 215.30/215.53 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 215.30/215.53 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) c_2) % 215.30/215.53 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 215.30/215.53 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 215.30/215.53 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 215.30/215.53 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 215.30/215.53 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 215.30/215.53 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x))) % 215.30/215.53 Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 215.30/215.53 Found (eta_expansion00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 215.30/215.53 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 215.30/215.53 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 215.30/215.53 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 215.30/215.53 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 215.30/215.53 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x))) % 215.30/215.53 Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 215.30/215.53 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 215.30/215.53 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 215.30/215.53 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 215.30/215.53 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 215.30/215.53 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x))) % 215.30/215.53 Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 215.30/215.53 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 217.02/217.27 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 217.02/217.27 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a) % 217.02/217.27 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.27 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.27 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.27 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.27 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b) % 217.02/217.27 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 217.02/217.27 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 217.02/217.27 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 217.02/217.27 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 217.02/217.27 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 217.02/217.28 Found (eta_expansion00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 217.02/217.28 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 217.02/217.28 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 217.02/217.28 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 217.02/217.28 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 217.02/217.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 217.02/217.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 217.02/217.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 217.02/217.28 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 217.02/217.28 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 217.02/217.28 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 217.02/217.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 217.02/217.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 217.02/217.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 217.02/217.28 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 217.02/217.28 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 217.02/217.28 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 217.02/217.28 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 232.55/232.80 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 232.55/232.80 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 232.55/232.80 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 232.55/232.80 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 232.55/232.80 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 232.55/232.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 232.55/232.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 232.55/232.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 232.55/232.80 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 232.55/232.80 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 232.55/232.80 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 232.55/232.80 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 232.55/232.80 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 232.55/232.80 Found eq_ref000:=(eq_ref00 P):((P (absval Xv))->(P (absval Xv))) % 232.55/232.80 Found (eq_ref00 P) as proof of (P0 (absval Xv)) % 232.55/232.80 Found ((eq_ref0 (absval Xv)) P) as proof of (P0 (absval Xv)) % 232.55/232.80 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 232.55/232.80 Found (((eq_ref fofType) (absval Xv)) P) as proof of (P0 (absval Xv)) % 232.55/232.80 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 232.55/232.80 Found (eq_ref0 b) as proof of (((eq fofType) b) c_2) % 232.55/232.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 232.55/232.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 232.55/232.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c_2) % 232.55/232.80 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 232.55/232.80 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 232.55/232.80 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 232.55/232.80 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 232.55/232.80 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 232.55/232.80 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 232.55/232.80 Found (eq_ref00 P) as proof of (P0 b) % 232.55/232.80 Found ((eq_ref0 b) P) as proof of (P0 b) % 232.55/232.80 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 232.55/232.80 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 232.55/232.80 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 232.55/232.80 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 232.55/232.80 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 232.55/232.80 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 232.55/232.80 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 232.55/232.80 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 232.55/232.80 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 232.55/232.80 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 232.55/232.80 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 232.55/232.80 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 232.55/232.80 Found eq_ref00:=(eq_ref0 (x1 a)):(((eq Prop) (x1 a)) (x1 a)) % 232.55/232.80 Found (eq_ref0 (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 232.55/232.80 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 232.55/232.80 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 232.55/232.80 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 232.55/232.80 Found eq_ref00:=(eq_ref0 (x1 a)):(((eq Prop) (x1 a)) (x1 a)) % 232.55/232.80 Found (eq_ref0 (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 232.55/232.80 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 232.55/232.80 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 232.55/232.80 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 232.55/232.80 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 232.55/232.80 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 232.55/232.80 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 232.55/232.80 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 232.55/232.80 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 232.55/232.80 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 232.55/232.80 Found (eq_ref0 b) as proof of (((eq fofType) b) b0) % 232.55/232.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 232.55/232.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 232.55/232.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 232.55/232.80 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 232.55/232.80 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 238.39/238.69 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 238.39/238.69 Found (eq_ref0 b) as proof of (((eq fofType) b) b0) % 238.39/238.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 238.39/238.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 238.39/238.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 238.39/238.69 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 238.39/238.69 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 238.39/238.69 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 238.39/238.69 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 238.39/238.69 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 238.39/238.69 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 238.39/238.69 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 238.39/238.69 Found eq_ref00:=(eq_ref0 (x1 a)):(((eq Prop) (x1 a)) (x1 a)) % 238.39/238.69 Found (eq_ref0 (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found eq_ref00:=(eq_ref0 (x1 a)):(((eq Prop) (x1 a)) (x1 a)) % 238.39/238.69 Found (eq_ref0 (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found eq_ref00:=(eq_ref0 (x1 a)):(((eq Prop) (x1 a)) (x1 a)) % 238.39/238.69 Found (eq_ref0 (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found eq_ref00:=(eq_ref0 (x1 a)):(((eq Prop) (x1 a)) (x1 a)) % 238.39/238.69 Found (eq_ref0 (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found eq_ref00:=(eq_ref0 (x1 a)):(((eq Prop) (x1 a)) (x1 a)) % 238.39/238.69 Found (eq_ref0 (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found eq_ref00:=(eq_ref0 (x1 a)):(((eq Prop) (x1 a)) (x1 a)) % 238.39/238.69 Found (eq_ref0 (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found ((eq_ref Prop) (x1 a)) as proof of (((eq Prop) (x1 a)) b) % 238.39/238.69 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 238.39/238.69 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 238.39/238.69 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 238.39/238.69 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 238.39/238.69 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b0) % 238.39/238.69 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 238.39/238.69 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 238.39/238.69 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 238.39/238.69 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 238.39/238.69 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 238.39/238.69 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 238.39/238.69 Found (eq_ref0 b) as proof of (((eq fofType) b) b0) % 240.03/240.28 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 240.03/240.28 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 240.03/240.28 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 240.03/240.28 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 240.03/240.28 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 240.03/240.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 240.03/240.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 240.03/240.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 240.03/240.28 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 240.03/240.28 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 240.03/240.28 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 240.03/240.28 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 240.03/240.28 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 240.03/240.28 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 240.03/240.28 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 240.03/240.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 240.03/240.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 240.03/240.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 240.03/240.28 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 240.03/240.28 Found (eq_ref0 b) as proof of (((eq fofType) b) b0) % 240.03/240.28 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 240.03/240.28 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 240.03/240.28 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 240.03/240.28 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b) % 240.03/240.28 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 240.03/240.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 240.03/240.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 240.03/240.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 240.03/240.28 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 240.03/240.28 Found (eta_expansion00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 240.03/240.28 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b) % 240.03/240.28 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 240.03/240.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 240.03/240.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 240.03/240.28 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) f) % 240.03/240.28 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 240.03/240.28 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 240.03/240.28 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 244.26/244.58 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x))) % 244.26/244.58 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 244.26/244.58 Found ((eta_expansion_dep0 (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 244.26/244.58 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 244.26/244.58 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 244.26/244.58 Found (((eta_expansion_dep (fofType->Prop)) (fun (x2:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b) % 244.26/244.58 Found x2:(P0 (f x1)) % 244.26/244.58 Instantiate: a:=(f x1):Prop % 244.26/244.58 Found x2 as proof of (P1 a) % 244.26/244.58 Found x2:(P c_2) % 244.26/244.58 Instantiate: b:=c_2:fofType % 244.26/244.58 Found x2 as proof of (P0 b) % 244.26/244.58 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 244.26/244.58 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 244.26/244.58 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 244.26/244.58 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 244.26/244.58 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 244.26/244.58 Found x2:(P0 (f x1)) % 244.26/244.58 Instantiate: a:=(f x1):Prop % 244.26/244.58 Found x2 as proof of (P1 a) % 244.26/244.58 Found c_2:fofType % 244.26/244.58 Found c_2 as proof of fofType % 244.26/244.58 Found (x2 c_2) as proof of False % 244.26/244.58 Found (x2 c_2) as proof of False % 244.26/244.58 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 244.26/244.58 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of ((x1 (absval Xy))->False) % 244.26/244.58 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), ((x1 (absval Xy))->False)) % 244.26/244.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 244.26/244.58 Found (eq_ref0 a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 244.26/244.58 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 244.26/244.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 244.26/244.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 244.26/244.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 244.26/244.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 244.26/244.58 Found (eq_ref0 a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 244.26/244.58 Found (eq_ref0 a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 244.26/244.58 Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 244.26/244.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 244.26/244.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 244.26/244.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 244.26/244.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a) % 244.26/244.58 Found (eq_ref0 a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b) % 244.26/244.58 Found c_2:fofType % 244.26/244.58 Found c_2 as proof of fofType % 244.26/244.58 Found (x2 c_2) as proof of False % 244.26/244.58 Found (x2 c_2) as proof of False % 244.26/244.58 Found (fun (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of False % 244.26/244.58 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (not (x1 (absval Xy))) % 254.28/254.59 Found (fun (Xy:fofType) (x2:(x1 (absval Xy)))=> (x2 c_2)) as proof of (forall (Xy:fofType), (not (x1 (absval Xy)))) % 254.28/254.59 Found x2:(P c_2) % 254.28/254.59 Instantiate: b:=c_2:fofType % 254.28/254.59 Found x2 as proof of (P0 b) % 254.28/254.59 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 254.28/254.59 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 254.28/254.59 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 254.28/254.59 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 254.28/254.59 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 254.28/254.59 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 254.28/254.59 Found (eq_ref0 b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 254.28/254.59 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 254.28/254.59 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 254.28/254.59 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 254.28/254.59 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 254.28/254.59 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 254.28/254.59 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 254.28/254.59 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 254.28/254.59 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 254.28/254.59 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 254.28/254.59 Found (eq_ref0 b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 254.28/254.59 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 254.28/254.59 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 254.28/254.59 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 254.28/254.59 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 254.28/254.59 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 254.28/254.59 Found (eq_ref0 b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 254.28/254.59 Found (eq_ref0 b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0) % 254.28/254.59 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 254.28/254.59 Found (eq_ref00 P) as proof of (P0 c_2) % 254.28/254.59 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 254.28/254.59 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 254.28/254.59 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 254.28/254.59 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 254.28/254.59 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 254.28/254.59 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 254.28/254.59 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 254.28/254.59 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 254.28/254.59 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 254.28/254.59 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 254.28/254.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 262.37/262.63 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 262.37/262.63 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 262.37/262.63 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 262.37/262.63 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 262.37/262.63 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 262.37/262.63 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 262.37/262.63 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 262.37/262.63 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 262.37/262.63 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 262.37/262.63 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 262.37/262.63 Found eta_expansion000:=(eta_expansion00 (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))):(((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) (fun (x:(fofType->Prop))=> ((and (forall (Xy:fofType), ((x (absval Xy))->False))) (x c_2)))) % 262.37/262.63 Found (eta_expansion00 (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) b0) % 262.37/262.63 Found ((eta_expansion0 Prop) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) b0) % 262.37/262.63 Found (((eta_expansion (fofType->Prop)) Prop) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) b0) % 262.37/262.63 Found (((eta_expansion (fofType->Prop)) Prop) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) b0) % 262.37/262.63 Found (((eta_expansion (fofType->Prop)) Prop) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), ((A (absval Xy))->False))) (A c_2)))) b0) % 262.37/262.63 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 262.37/262.63 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 262.37/262.63 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 262.37/262.63 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 262.37/262.63 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 262.37/262.63 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 262.37/262.63 Found (eq_ref0 b) as proof of (P b) % 262.37/262.63 Found ((eq_ref fofType) b) as proof of (P b) % 262.37/262.63 Found ((eq_ref fofType) b) as proof of (P b) % 262.37/262.63 Found ((eq_ref fofType) b) as proof of (P b) % 262.37/262.63 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 262.37/262.63 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 262.37/262.63 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 262.37/262.63 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 262.37/262.63 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 262.37/262.63 Found x2:(P c_2) % 262.37/262.63 Instantiate: a:=c_2:fofType % 262.37/262.63 Found x2 as proof of (P0 a) % 262.37/262.63 Found x2:(P (absval Xv)) % 262.37/262.63 Instantiate: b:=(absval Xv):fofType % 262.37/262.63 Found x2 as proof of (P0 b) % 262.37/262.63 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 262.37/262.63 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 262.37/262.63 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 262.37/262.63 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 262.37/262.63 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 262.37/262.63 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 262.37/262.63 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 262.37/262.63 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 262.37/262.63 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 262.37/262.63 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 262.37/262.63 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 264.55/264.87 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 264.55/264.87 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 264.55/264.87 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 264.55/264.87 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 264.55/264.87 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 264.55/264.87 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 264.55/264.87 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 264.55/264.87 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 264.55/264.87 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 264.55/264.87 Found eq_ref00:=(eq_ref0 (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))):(((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) % 264.55/264.87 Found (eq_ref0 (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) b0) % 264.55/264.87 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) b0) % 264.55/264.87 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) b0) % 264.55/264.87 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xy:fofType), (not (A (absval Xy))))) (A c_2)))) b0) % 264.55/264.87 Found eq_ref000:=(eq_ref00 P):((P c_2)->(P c_2)) % 264.55/264.87 Found (eq_ref00 P) as proof of (P0 c_2) % 264.55/264.87 Found ((eq_ref0 c_2) P) as proof of (P0 c_2) % 264.55/264.87 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 264.55/264.87 Found (((eq_ref fofType) c_2) P) as proof of (P0 c_2) % 264.55/264.87 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0) % 264.55/264.87 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a) % 264.55/264.87 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 264.55/264.87 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 264.55/264.87 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 264.55/264.87 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0) % 264.55/264.87 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a) % 264.55/264.87 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 264.55/264.87 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 264.55/264.87 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 264.55/264.87 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 264.55/264.87 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 264.55/264.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 264.55/264.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 264.55/264.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 264.55/264.87 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 264.55/264.87 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 264.55/264.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 264.55/264.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 264.55/264.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 264.55/264.87 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 264.55/264.87 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b) % 264.55/264.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 264.55/264.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 264.55/264.87 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b) % 264.55/264.87 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 264.55/264.87 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 264.55/264.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 264.55/264.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 264.55/264.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 264.55/264.87 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 264.55/264.87 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 264.55/264.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 264.55/264.87 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 271.45/271.75 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 271.45/271.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 271.45/271.75 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 271.45/271.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 271.45/271.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 271.45/271.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 271.45/271.75 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 271.45/271.75 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 271.45/271.75 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 271.45/271.75 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 271.45/271.75 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 271.45/271.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 271.45/271.75 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 271.45/271.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 271.45/271.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 271.45/271.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 271.45/271.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 271.45/271.75 Found (eq_ref0 b) as proof of (P b) % 271.45/271.75 Found ((eq_ref fofType) b) as proof of (P b) % 271.45/271.75 Found ((eq_ref fofType) b) as proof of (P b) % 271.45/271.75 Found ((eq_ref fofType) b) as proof of (P b) % 271.45/271.75 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 271.45/271.75 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 271.45/271.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 271.45/271.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 271.45/271.75 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 271.45/271.75 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0) % 271.45/271.75 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0) % 271.45/271.75 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 271.45/271.75 Found (eq_ref0 b) as proof of (P2 b) % 271.45/271.75 Found ((eq_ref Prop) b) as proof of (P2 b) % 271.45/271.75 Found ((eq_ref Prop) b) as proof of (P2 b) % 271.45/271.75 Found ((eq_ref Prop) b) as proof of (P2 b) % 271.45/271.75 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 271.45/271.75 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 271.45/271.75 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 271.45/271.75 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 271.45/271.75 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 271.45/271.75 Found x2:(P c_2) % 271.45/271.75 Instantiate: a:=c_2:fofType % 271.45/271.75 Found x2 as proof of (P0 a) % 271.45/271.75 Found eq_ref00:=(eq_ref0 (x1 c_2)):(((eq Prop) (x1 c_2)) (x1 c_2)) % 271.45/271.75 Found (eq_ref0 (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b0) % 271.45/271.75 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b0) % 271.45/271.75 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b0) % 271.45/271.75 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b0) % 271.45/271.75 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0) % 271.45/271.75 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 271.45/271.75 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0) % 278.45/278.77 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 278.45/278.77 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 278.45/278.77 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 278.45/278.77 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 278.45/278.77 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 278.45/278.77 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 278.45/278.77 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 278.45/278.77 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 278.45/278.77 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 278.45/278.77 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 278.45/278.77 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 278.45/278.77 Found (eq_ref0 b) as proof of (((eq fofType) b) (absval Xv)) % 278.45/278.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 278.45/278.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 278.45/278.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (absval Xv)) % 278.45/278.77 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 278.45/278.77 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 278.45/278.77 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 278.45/278.77 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 278.45/278.77 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 278.45/278.77 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 278.45/278.77 Found (eq_ref0 a) as proof of (((eq fofType) a) b) % 278.45/278.77 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 278.45/278.77 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 278.45/278.77 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b) % 278.45/278.77 Found x2:(P (absval Xv)) % 278.45/278.77 Instantiate: b:=(absval Xv):fofType % 278.45/278.77 Found x2 as proof of (P0 b) % 278.45/278.77 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 278.45/278.77 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 278.45/278.77 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 278.45/278.77 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 278.45/278.77 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 278.45/278.77 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0) % 278.45/278.77 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0) % 278.45/278.77 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a) % 278.45/278.77 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 278.45/278.77 Found (eq_ref0 b) as proof of (P1 b) % 278.45/278.77 Found ((eq_ref fofType) b) as proof of (P1 b) % 278.45/278.77 Found ((eq_ref fofType) b) as proof of (P1 b) % 278.45/278.77 Found ((eq_ref fofType) b) as proof of (P1 b) % 278.45/278.77 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 278.45/278.77 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 278.45/278.77 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 278.45/278.77 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 278.45/278.77 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 278.45/278.77 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 278.45/278.77 Found (eq_ref0 b) as proof of (P1 b) % 278.45/278.77 Found ((eq_ref fofType) b) as proof of (P1 b) % 278.45/278.77 Found ((eq_ref fofType) b) as proof of (P1 b) % 278.45/278.77 Found ((eq_ref fofType) b) as proof of (P1 b) % 278.45/278.77 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 278.45/278.77 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 278.45/278.77 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 278.45/278.77 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 278.45/278.77 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 278.45/278.77 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 278.45/278.77 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 291.55/291.85 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 291.55/291.85 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 291.55/291.85 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 291.55/291.85 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 291.55/291.85 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 291.55/291.85 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 291.55/291.85 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 291.55/291.85 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 291.55/291.85 Found eq_ref00:=(eq_ref0 (x1 c_2)):(((eq Prop) (x1 c_2)) (x1 c_2)) % 291.55/291.85 Found (eq_ref0 (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b0) % 291.55/291.85 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b0) % 291.55/291.85 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b0) % 291.55/291.85 Found ((eq_ref Prop) (x1 c_2)) as proof of (((eq Prop) (x1 c_2)) b0) % 291.55/291.85 Found x2:(P1 (absval Xv)) % 291.55/291.85 Instantiate: b:=(absval Xv):fofType % 291.55/291.85 Found x2 as proof of (P2 b) % 291.55/291.85 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 291.55/291.85 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 291.55/291.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 291.55/291.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 291.55/291.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 291.55/291.85 Found x2:(P1 (absval Xv)) % 291.55/291.85 Instantiate: b:=(absval Xv):fofType % 291.55/291.85 Found x2 as proof of (P2 b) % 291.55/291.85 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 291.55/291.85 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b) % 291.55/291.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 291.55/291.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 291.55/291.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b) % 291.55/291.85 Found eq_ref00:=(eq_ref0 c_2):(((eq fofType) c_2) c_2) % 291.55/291.85 Found (eq_ref0 c_2) as proof of (((eq fofType) c_2) b0) % 291.55/291.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 291.55/291.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 291.55/291.85 Found ((eq_ref fofType) c_2) as proof of (((eq fofType) c_2) b0) % 291.55/291.85 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0) % 291.55/291.85 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (absval Xv)) % 291.55/291.85 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 291.55/291.85 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 291.55/291.85 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (absval Xv)) % 291.55/291.85 Found x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 291.55/291.85 Instantiate: b:=((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)):Prop % 291.55/291.85 Found x2 as proof of (P3 b) % 291.55/291.85 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 291.55/291.85 Found (eq_ref00 P) as proof of (P0 b) % 291.55/291.85 Found ((eq_ref0 b) P) as proof of (P0 b) % 291.55/291.85 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 291.55/291.85 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 291.55/291.85 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 291.55/291.85 Found (eq_ref00 P) as proof of (P0 b) % 291.55/291.85 Found ((eq_ref0 b) P) as proof of (P0 b) % 291.55/291.85 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 291.55/291.85 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 291.55/291.85 Found eq_ref000:=(eq_ref00 P):((P b)->(P b)) % 291.55/291.85 Found (eq_ref00 P) as proof of (P0 b) % 291.55/291.85 Found ((eq_ref0 b) P) as proof of (P0 b) % 291.55/291.85 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 291.55/291.85 Found (((eq_ref fofType) b) P) as proof of (P0 b) % 291.55/291.85 Found eq_ref000:=(eq_ref00 P1):((P1 (absval Xv))->(P1 (absval Xv))) % 291.55/291.85 Found (eq_ref00 P1) as proof of (P2 (absval Xv)) % 291.55/291.85 Found ((eq_ref0 (absval Xv)) P1) as proof of (P2 (absval Xv)) % 291.55/291.85 Found (((eq_ref fofType) (absval Xv)) P1) as proof of (P2 (absval Xv)) % 291.55/291.85 Found (((eq_ref fofType) (absval Xv)) P1) as proof of (P2 (absval Xv)) % 291.55/291.85 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1)) % 291.55/291.85 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b) % 291.55/291.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 291.55/291.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 291.55/291.85 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b) % 291.55/291.85 Found ((eq_sym0100 ((eq_ref Prop) (f x1))) x2) as proof of (P2 (f x1)) % 291.55/291.85 Found ((eq_sym0100 ((eq_ref Prop) (f x1))) x2) as proof of (P2 (f x1)) % 291.55/291.85 Found (((fun (x3:(((eq Prop) (f x1)) b))=> ((eq_sym010 x3) P2)) ((eq_ref Prop) (f x1))) x2) as proof of (P2 (f x1)) % 291.55/291.85 Found (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((eq_sym01 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2) as proof of (P2 (f x1)) % 291.55/291.87 Found (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2) as proof of (P2 (f x1)) % 291.55/291.87 Found (fun (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2)) as proof of (P2 (f x1)) % 291.55/291.87 Found (fun (P2:(Prop->Prop)) (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2)) as proof of ((P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P2 (f x1))) % 291.55/291.87 Found (fun (P2:(Prop->Prop)) (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2)) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) % 291.55/291.87 Found ((eq_sym0000 (fun (P2:(Prop->Prop)) (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 291.55/291.87 Found ((eq_sym0000 (fun (P2:(Prop->Prop)) (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 291.55/291.87 Found (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((eq_sym000 x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) (fun (P2:(Prop->Prop)) (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 291.55/291.88 Found (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((eq_sym00 (f x1)) x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) (fun (P2:(Prop->Prop)) (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 291.55/291.88 Found (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> ((((eq_sym0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) (fun (P2:(Prop->Prop)) (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> ((((eq_sym0 (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 294.35/294.65 Found (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) (fun (P2:(Prop->Prop)) (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2))) (((eq_ref Prop) (f x1)) P0)) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 294.35/294.65 Found (fun (P0:(Prop->Prop))=> (((fun (x2:(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)))=> (((((eq_sym Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) (f x1)) x2) (fun (x4:Prop)=> ((P0 (f x1))->(P0 x4))))) (fun (P2:(Prop->Prop)) (x2:(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((fun (x3:(((eq Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))))=> (((((eq_sym Prop) (f x1)) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) x3) P2)) ((eq_ref Prop) (f x1))) x2))) (((eq_ref Prop) (f x1)) P0))) as proof of ((P0 (f x1))->(P0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 294.35/294.65 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 294.35/294.65 Found (eq_ref0 b) as proof of (P1 b) % 294.35/294.65 Found ((eq_ref fofType) b) as proof of (P1 b) % 294.35/294.65 Found ((eq_ref fofType) b) as proof of (P1 b) % 294.35/294.65 Found ((eq_ref fofType) b) as proof of (P1 b) % 294.35/294.65 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 294.35/294.65 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 294.35/294.65 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 294.35/294.65 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 294.35/294.65 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 294.35/294.65 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 294.35/294.65 Found (eq_ref0 b) as proof of (P1 b) % 294.35/294.65 Found ((eq_ref fofType) b) as proof of (P1 b) % 294.35/294.65 Found ((eq_ref fofType) b) as proof of (P1 b) % 294.35/294.65 Found ((eq_ref fofType) b) as proof of (P1 b) % 294.35/294.65 Found eq_ref00:=(eq_ref0 (absval Xv)):(((eq fofType) (absval Xv)) (absval Xv)) % 294.35/294.65 Found (eq_ref0 (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 294.35/294.65 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 294.35/294.65 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 294.35/294.65 Found ((eq_ref fofType) (absval Xv)) as proof of (((eq fofType) (absval Xv)) b) % 294.35/294.65 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 294.35/294.65 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 294.35/294.65 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 294.35/294.65 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 294.35/294.65 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 294.35/294.65 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a) % 294.35/294.65 Found (eq_ref0 a) as proof of (((eq fofType) a) Xv) % 294.35/294.65 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 294.35/294.65 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 294.35/294.65 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xv) % 294.35/294.65 Found eq_ref000:=(eq_ref00 P2):((P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 294.35/294.65 Found (eq_ref00 P2) as proof of (P3 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 294.35/294.65 Found ((eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) P2) as proof of (P3 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 296.14/296.49 Found (((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) P2) as proof of (P3 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 296.14/296.49 Found (((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) P2) as proof of (P3 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 296.14/296.49 Found eq_ref000:=(eq_ref00 P2):((P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))->(P2 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2)))) % 296.14/296.49 Found (eq_ref00 P2) as proof of (P3 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 296.14/296.49 Found ((eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) P2) as proof of (P3 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 296.14/296.49 Found (((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) P2) as proof of (P3 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 296.14/296.49 Found (((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) P2) as proof of (P3 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 296.14/296.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 296.14/296.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 296.14/296.49 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 296.14/296.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 296.14/296.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 296.14/296.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 296.14/296.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 296.14/296.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) % 296.14/296.49 Found (eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 296.14/296.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 296.14/296.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 296.14/296.49 Found ((eq_ref Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) as proof of (((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) b) % 296.14/296.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b) % 296.14/296.49 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x1)) % 296.14/296.49 Found eq_ref00:=(eq_ref0 ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))):(((eq Prop) ((and (forall (Xy:fofType), ((x1 (absval Xy))->False))) (x1 c_2))) ((and (forall ( %------------------------------------------------------------------------------