0.10/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.11	% Command    : do_cvc5 %s %d
0.10/0.32	% Computer : n017.cluster.edu
0.10/0.32	% Model    : x86_64 x86_64
0.10/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.32	% Memory   : 8042.1875MB
0.10/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.32	% CPULimit   : 960
0.10/0.32	% WCLimit    : 120
0.10/0.32	% DateTime   : Tue Aug  9 05:48:15 EDT 2022
0.10/0.32	% CPUTime    : 
0.18/0.45	%----Proving TH0
0.63/0.80	------- cvc5-thf casc j11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p...
0.63/0.80	--- Run --ho-elim --full-saturate-quant at 10...
0.63/0.80	% SZS status Theorem for theBenchmark
0.63/0.80	% SZS output start Proof for theBenchmark
0.63/0.80	(let ((_let_1 (not induction2_gthm))) (let ((_let_2 (= hoasinduction_no_psi_cond_lthm (=> hoasinduction_lem0 (=> induction2 (=> axvarid (=> hoasinduction_lem3v2a hoasinduction_no_psi_cond))))))) (let ((_let_3 (= hoasinduction_no_psi_cond (forall ((P (-> subst term subst Bool))) (=> (forall ((A term) (B term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (=> (@ (@ _let_1 B) id) (@ (@ _let_1 (@ (@ (@ (@ hoasap id) A) id) B)) id))))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (@ (@ _let_1 (@ (@ F id) A)) id)))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (forall ((A term)) (@ (@ (@ P id) A) id)))))))) (let ((_let_4 (= hoasinduction_lthm_3 (=> hoasinduction_lem0 (=> induction2 (=> axvarid (=> hoasinduction_lem3v2a hoasinduction))))))) (let ((_let_5 (=> hoasinduction_lem1 (=> hoasinduction_lem2 (=> hoasinduction_lem3 hoasinduction))))) (let ((_let_6 (= hoasinduction_lthm (=> induction2 _let_5)))) (let ((_let_7 (= hoasinduction_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar _let_5))))))))))))))))))))))))))))))))))))) (let ((_let_8 (= hoasinduction (forall ((P (-> subst term subst Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P M) A) (@ (@ comp K) N)) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N) (@ (@ (@ P M) A) (@ (@ comp K) N)))) (=> (forall ((A term)) (=> (@ (@ (@ hoasvar id) A) id) (@ (@ (@ P id) A) id))) (=> (forall ((A term) (B term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (=> (@ (@ _let_1 B) id) (@ (@ _let_1 (@ (@ (@ (@ hoasap id) A) id) B)) id))))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (@ (@ _let_1 (@ (@ F id) A)) id)))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (forall ((A term)) (@ (@ (@ P id) A) id))))))))))) (let ((_let_9 (= hoasinduction_lem3b_lthm hoasinduction_lem3b))) (let ((_let_10 (= hoasinduction_lem3b_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar (=> hoasinduction_lem1 (=> hoasinduction_lem2 hoasinduction_lem3b))))))))))))))))))))))))))))))))))))))) (let ((_let_11 (= hoasinduction_lem3b (forall ((B term)) (exists ((F (-> subst term term))) (= (@ (@ sub B) (@ (@ push one) sh)) (@ (@ F sh) one))))))) (let ((_let_12 (= hoasinduction_lem3a_lthm (=> axvarid (=> axvarshift (=> hoasinduction_lem3aa hoasinduction_lem3a)))))) (let ((_let_13 (= hoasinduction_lem3a_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar (=> hoasinduction_lem1 (=> hoasinduction_lem2 hoasinduction_lem3a))))))))))))))))))))))))))))))))))))))) (let ((_let_14 (= hoasinduction_lem3a (forall ((P (-> subst term subst Bool))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (@ (@ _let_1 (@ (@ F id) A)) id)))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (forall ((A term)) (=> (forall ((B term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 B) id) (@ (@ _let_1 (@ (@ sub A) (@ (@ push B) id))) id)))) (@ (@ (@ P id) (@ lam A)) id)))))))) (let ((_let_15 (= hoasinduction_lem3_lthm (=> axvarid (=> axvarshift (=> hoasinduction_lem3aa hoasinduction_lem3)))))) (let ((_let_16 (= hoasinduction_lem3_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar (=> hoasinduction_lem1 (=> hoasinduction_lem2 hoasinduction_lem3))))))))))))))))))))))))))))))))))))))) (let ((_let_17 (= hoasinduction_lem3 (forall ((P (-> subst term subst Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P M) A) (@ (@ comp K) N)) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N) (@ (@ (@ P M) A) (@ (@ comp K) N)))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (@ (@ _let_1 (@ (@ F id) A)) id)))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (forall ((A term)) (=> (forall ((B term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 B) id) (@ (@ _let_1 (@ (@ sub A) (@ (@ push B) id))) id)))) (@ (@ (@ P id) (@ lam A)) id)))))))))) (let ((_let_18 (= hoasinduction_lem3aaa (forall ((P (-> subst term subst Bool))) (=> (forall ((F (-> subst term term))) (=> (exists ((C term)) (forall ((M subst) (A term) (N subst)) (let ((_let_1 (@ (@ sub A) N))) (let ((_let_2 (@ (@ comp M) N))) (let ((_let_3 (@ sub C))) (and (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ sub (@ _let_3 (@ (@ push A) M))) N)) (= (@ _let_3 (@ (@ push _let_1) _let_2)) (@ (@ F _let_2) _let_1)))))))) (=> (forall ((A term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (@ (@ _let_1 (@ (@ F id) A)) id)))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (forall ((A term)) (=> (forall ((B term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 B) id) (@ (@ _let_1 (@ (@ sub A) (@ (@ push B) id))) id)))) (@ (@ (@ P id) (@ lam (@ (@ sub A) (@ (@ push one) sh)))) id)))))))) (let ((_let_19 (= hoasinduction_lem3aa_lthm (=> axclos (=> axmap hoasinduction_lem3aa))))) (let ((_let_20 (= hoasinduction_lem3aa (forall ((P (-> subst term subst Bool))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (@ (@ _let_1 (@ (@ F id) A)) id)))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (forall ((A term)) (=> (forall ((B term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 B) id) (@ (@ _let_1 (@ (@ sub A) (@ (@ push B) id))) id)))) (@ (@ (@ P id) (@ lam (@ (@ sub A) (@ (@ push one) sh)))) id)))))))) (let ((_let_21 (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem2)))))))))))))))))))))))))))))))))))) (let ((_let_22 (= hoasinduction_lem2_lthm _let_21))) (let ((_let_23 (= hoasinduction_lem2_gthm _let_21))) (let ((_let_24 (= hoasinduction_lem2 (forall ((P (-> subst term subst Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P M) A) (@ (@ comp K) N)) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N) (@ (@ (@ P M) A) (@ (@ comp K) N)))) (=> (forall ((A term) (B term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (=> (@ (@ _let_1 B) id) (@ (@ _let_1 (@ (@ (@ (@ hoasap id) A) id) B)) id))))) (forall ((A term) (B term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (=> (@ (@ _let_1 B) id) (@ (@ _let_1 (@ (@ ap A) B)) id)))))))))))) (let ((_let_25 (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem1)))))))))))))))))))))))))))))))))))) (let ((_let_26 (= hoasinduction_lem1_lthm _let_25))) (let ((_let_27 (= hoasinduction_lem1_gthm _let_25))) (let ((_let_28 (= hoasinduction_lem1 (forall ((P (-> subst term subst Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P M) A) (@ (@ comp K) N)) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N) (@ (@ (@ P M) A) (@ (@ comp K) N)))) (=> (forall ((A term)) (=> (@ (@ (@ hoasvar id) A) id) (@ (@ (@ P id) A) id))) (forall ((A term)) (=> (@ var A) (@ (@ (@ P id) A) id)))))))))) (let ((_let_29 (= hoasinduction_lem3v2a_lthm (=> hoasinduction_lem3v2_f (=> axvarid (=> axvarshift (=> axclos (=> axmap hoasinduction_lem3v2a)))))))) (let ((_let_30 (= hoasinduction_lem3v2a (forall ((P (-> subst term subst Bool)) (Q (-> term Bool))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (@ (@ _let_1 (@ (@ F id) A)) id)))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (=> (@ (@ hoasinduction_p_and_p_prime P) Q) (forall ((A term)) (=> (forall ((B term)) (=> (@ Q B) (@ Q (@ (@ sub A) (@ (@ push B) id))))) (@ Q (@ lam A)))))))))) (let ((_let_31 (= hoasinduction_lem3v2_lthm (=> axvarid (=> axvarshift (=> axclos (=> axmap hoasinduction_lem3v2))))))) (let ((_let_32 (= hoasinduction_lem3v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem3v2))))))))))))))))))))))))))))))))))))) (let ((_let_33 (= hoasinduction_lem3v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P M) A) (@ (@ comp K) N)) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N) (@ (@ (@ P M) A) (@ (@ comp K) N)))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (@ (@ _let_1 (@ (@ F id) A)) id)))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (=> (@ (@ hoasinduction_p_and_p_prime P) Q) (forall ((A term)) (=> (forall ((B term)) (=> (@ Q B) (@ Q (@ (@ sub A) (@ (@ push B) id))))) (@ Q (@ lam A)))))))))))) (let ((_let_34 (= hoasinduction_lem3v2_f_lthm hoasinduction_lem3v2_f))) (let ((_let_35 (= hoasinduction_lem3v2_f (forall ((B term)) (exists ((F (-> subst term term))) (forall ((A term) (M subst)) (= (@ (@ F M) A) (@ (@ sub B) (@ (@ push A) M))))))))) (let ((_let_36 (= hoasinduction_lem2v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem2v2))))))))))))))))))))))))))))))))))))) (let ((_let_37 (= hoasinduction_lem2v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P M) A) (@ (@ comp K) N)) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N) (@ (@ (@ P M) A) (@ (@ comp K) N)))) (=> (forall ((A term) (B term)) (let ((_let_1 (@ P id))) (=> (@ (@ _let_1 A) id) (=> (@ (@ _let_1 B) id) (@ (@ _let_1 (@ (@ (@ (@ hoasap id) A) id) B)) id))))) (=> (@ (@ hoasinduction_p_and_p_prime P) Q) (forall ((A term) (B term)) (=> (@ Q A) (=> (@ Q B) (@ Q (@ (@ ap A) B))))))))))))) (let ((_let_38 (= hoasinduction_lem1v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem1v2))))))))))))))))))))))))))))))))))))) (let ((_let_39 (= hoasinduction_lem1v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P M) A) (@ (@ comp K) N)) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N) (@ (@ (@ P M) A) (@ (@ comp K) N)))) (=> (forall ((A term)) (=> (@ (@ (@ hoasvar id) A) id) (@ (@ (@ P id) A) id))) (=> (@ (@ hoasinduction_p_and_p_prime P) Q) (forall ((A term)) (=> (@ var A) (@ Q A))))))))))) (let ((_let_40 (= hoasinduction_lem0_lthm hoasinduction_lem0))) (let ((_let_41 (= hoasinduction_lem0 (forall ((P (-> subst term subst Bool))) (exists ((Q (-> term Bool))) (@ (@ hoasinduction_p_and_p_prime P) Q)))))) (let ((_let_42 (= hoasinduction_p_and_p_prime (lambda ((P (-> subst term subst Bool)) (Q (-> term Bool))) (forall ((X term)) (= (@ Q X) (@ (@ (@ P id) X) id))))))) (let ((_let_43 (= hoasapnotvar_lthm (=> axvarid (=> apnotvar hoasapnotvar))))) (let ((_let_44 (= hoasapnotvar_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar hoasapnotvar)))))))))))))))))))))))))))))))))))) (let ((_let_45 (= hoasapnotvar (forall ((A term) (B term)) (not (@ (@ (@ hoasvar id) (@ (@ (@ (@ hoasap id) A) id) B)) id)))))) (let ((_let_46 (= hoaslamnotvar_lthm (=> axvarid (=> lamnotvar hoaslamnotvar))))) (let ((_let_47 (= hoaslamnotvar_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap hoaslamnotvar))))))))))))))))))))))))))))))))))) (let ((_let_48 (= hoaslamnotvar (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (not (@ (@ (@ hoasvar id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id))))))) (let ((_let_49 (= hoaslamnotap_lthm (=> lamnotap hoaslamnotap)))) (let ((_let_50 (= hoaslamnotap_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj hoaslamnotap)))))))))))))))))))))))))))))))))) (let ((_let_51 (= hoaslamnotap (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (forall ((A term) (B term)) (not (= (@ (@ hoaslam id) (lambda ((M subst) (C term)) (@ (@ F M) C))) (@ (@ (@ (@ hoasap id) A) id) B))))))))) (let ((_let_52 (= hoaslaminj_lthm (=> axvarcons (=> axshiftcons (=> laminj hoaslaminj)))))) (let ((_let_53 (= hoaslaminj_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 hoaslaminj))))))))))))))))))))))))))))))))) (let ((_let_54 (= hoaslaminj (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N)))) (forall ((G (-> subst term term))) (let ((_let_1 (@ hoaslam id))) (=> (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ G M) A)) N) (@ (@ G (@ (@ comp M) N)) (@ (@ sub A) N)))) (=> (= (@ _let_1 (lambda ((M subst) (A term)) (@ (@ F M) A))) (@ _let_1 (lambda ((M subst) (A term)) (@ (@ G M) A)))) (forall ((M subst) (A term)) (= (@ (@ F M) A) (@ (@ G M) A)))))))))))) (let ((_let_55 (= hoasapinj2_lthm (=> apinj2 hoasapinj2)))) (let ((_let_56 (= hoasapinj2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 hoasapinj2)))))))))))))))))))))))))))))))) (let ((_let_57 (= hoasapinj2 (forall ((A term) (B term) (C term) (D term)) (let ((_let_1 (@ hoasap id))) (=> (= (@ (@ (@ _let_1 A) id) C) (@ (@ (@ _let_1 B) id) D)) (= C D))))))) (let ((_let_58 (= hoasapinj1_lthm (=> axvarid (=> apinj1 hoasapinj1))))) (let ((_let_59 (= hoasapinj1_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset hoasapinj1))))))))))))))))))))))))))))))) (let ((_let_60 (= hoasapinj1 (forall ((A term) (B term) (C term) (D term)) (let ((_let_1 (@ hoasap id))) (=> (= (@ (@ (@ _let_1 A) id) C) (@ (@ (@ _let_1 B) id) D)) (= A B))))))) (let ((_let_61 (= hoasvar (lambda ((M subst) (A term) (N subst)) (@ var (@ (@ sub A) N)))))) (let ((_let_62 (= hoaslam (lambda ((M subst) (F (-> subst term term))) (@ lam (@ (@ F sh) one)))))) (let ((_let_63 (= hoasap (lambda ((M subst) (A term) (N subst) (B term)) (@ (@ ap (@ (@ sub A) N)) B))))) (let ((_let_64 (= termmset_lthm (=> axvarid (=> axclos termmset))))) (let ((_let_65 (= termmset_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid termmset)))))))))))))))))))))))))))))) (let ((_let_66 (= termmset (and (forall ((A term) (M subst) (N subst)) (let ((_let_1 (@ sub A))) (= (@ (@ sub (@ _let_1 M)) N) (@ _let_1 (@ (@ comp M) N))))) (forall ((A term)) (= (@ (@ sub A) id) A)))))) (let ((_let_67 (= substmonoid_lthm (=> axidl (=> axassoc (=> axidr substmonoid)))))) (let ((_let_68 (= substmonoid_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 substmonoid))))))))))))))))))))))))))))) (let ((_let_69 (= substmonoid (and (forall ((M subst) (N subst) (K subst)) (let ((_let_1 (@ comp M))) (= (@ (@ comp (@ _let_1 N)) K) (@ _let_1 (@ (@ comp N) K))))) (forall ((M subst)) (= (@ (@ comp id) M) M)) (forall ((M subst)) (= (@ (@ comp M) id) M)))))) (let ((_let_70 (=> induction2lem induction2))) (let ((_let_71 (= induction2_lthm (=> axvarid _let_70)))) (let ((_let_72 (= induction2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop _let_70))))))))))))))))))))))))))) (let ((_let_73 (= induction2 (forall ((P (-> term Bool))) (=> (forall ((A term)) (=> (@ var A) (@ P A))) (=> (forall ((A term) (B term)) (=> (@ P A) (=> (@ P B) (@ P (@ (@ ap A) B))))) (=> (forall ((A term)) (=> (forall ((B term)) (=> (@ P B) (@ P (@ (@ sub A) (@ (@ push B) id))))) (@ P (@ lam A)))) (forall ((A term)) (@ P A))))))))) (let ((_let_74 (=> induction (=> pushprop induction2lem)))) (let ((_let_75 (= induction2lem_lthm (=> axapp (=> axvarcons (=> axabs (=> axclos (=> axshiftcons (=> axassoc (=> axmap (=> axidr _let_74))))))))))) (let ((_let_76 (= induction2lem_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar _let_74))))))))))))))))))))))))) (let ((_let_77 (= induction2lem (forall ((P (-> term Bool))) (=> (forall ((A term) (B term)) (=> (@ P A) (=> (@ P B) (@ P (@ (@ ap A) B))))) (=> (forall ((A term)) (=> (forall ((B term)) (=> (@ P B) (@ P (@ (@ sub A) (@ (@ push B) id))))) (@ P (@ lam A)))) (forall ((A term) (M subst)) (=> (forall ((B term)) (=> (@ var B) (@ P (@ (@ sub B) M)))) (@ P (@ (@ sub A) M)))))))))) (let ((_let_78 (=> ulamvar1 (=> axvarcons (=> axclos (=> axshiftcons (=> ulamvarind pushprop))))))) (let ((_let_79 (= pushprop_lthm (=> pushprop_lem0 _let_78)))) (let ((_let_80 (= pushprop_lthm_orig _let_78))) (let ((_let_81 (= pushprop_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop)))))))))))))))))))))))))) (let ((_let_82 (= pushprop (forall ((P (-> term Bool)) (A term) (M subst)) (=> (forall ((B term)) (=> (@ var B) (@ P (@ (@ sub B) M)))) (=> (@ P A) (forall ((B term)) (=> (@ var B) (@ P (@ (@ sub B) (@ (@ push A) M))))))))))) (let ((_let_83 (= pushprop_lem3v2_lthm pushprop_lem3v2))) (let ((_let_84 (= pushprop_lem3v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst)) (=> (@ (@ (@ (@ pushprop_p_and_p_prime A) M) P) Q) (=> (forall ((B term)) (=> (@ var B) (@ Q B))) (forall ((B term)) (=> (@ var B) (@ P (@ (@ sub B) (@ (@ push A) M))))))))))) (let ((_let_85 (= pushprop_lem2v2_lthm (=> axclos (=> axshiftcons pushprop_lem2v2))))) (let ((_let_86 (= pushprop_lem2v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop_lem2v2)))))))))))))))))))))))))) (let ((_let_87 (= pushprop_lem2v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst)) (=> (@ (@ (@ (@ pushprop_p_and_p_prime A) M) P) Q) (=> (forall ((B term)) (=> (@ var B) (@ P (@ (@ sub B) M)))) (forall ((C term)) (=> (@ var C) (=> (@ Q C) (@ Q (@ (@ sub C) sh))))))))))) (let ((_let_88 (= pushprop_lem1v2_lthm (=> axvarcons pushprop_lem1v2)))) (let ((_let_89 (= pushprop_lem1v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop_lem1v2)))))))))))))))))))))))))) (let ((_let_90 (= pushprop_lem1v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst)) (=> (@ P A) (=> (@ (@ (@ (@ pushprop_p_and_p_prime A) M) P) Q) (@ Q one))))))) (let ((_let_91 (= pushprop_lem1_lthm (=> axvarcons (=> axclos (=> axshiftcons (=> ulamvarind pushprop_lem1))))))) (let ((_let_92 (= pushprop_lem1_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop_lem1)))))))))))))))))))))))))) (let ((_let_93 (= pushprop_lem1 (forall ((P (-> term Bool)) (K (-> term Bool)) (A term) (M subst) (B term)) (=> (@ P A) (@ K (@ (@ sub A) (@ (@ push B) M)))))))) (let ((_let_94 (= pushprop_lem0_lthm pushprop_lem0))) (let ((_let_95 (= pushprop_lem0_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop_lem0)))))))))))))))))))))))))) (let ((_let_96 (= pushprop_lem0 (forall ((P (-> term Bool)) (A term) (M subst)) (exists ((Q (-> term Bool))) (@ (@ (@ (@ pushprop_p_and_p_prime A) M) P) Q)))))) (let ((_let_97 (= pushprop_p_and_p_prime (lambda ((A term) (M subst) (P (-> term Bool)) (Q (-> term Bool))) (forall ((X term)) (= (@ Q X) (@ P (@ (@ sub X) (@ (@ push A) M))))))))) (let ((_let_98 (= induction (forall ((P (-> term Bool))) (=> (forall ((A term)) (=> (@ var A) (@ P A))) (=> (forall ((A term) (B term)) (=> (@ P A) (=> (@ P B) (@ P (@ (@ ap A) B))))) (=> (forall ((A term)) (=> (@ P A) (@ P (@ lam A)))) (forall ((A term)) (@ P A))))))))) (let ((_let_99 (forall ((A term)) (not (@ var (@ lam A)))))) (let ((_let_100 (= lamnotvar _let_99))) (let ((_let_101 (forall ((A term) (B term)) (not (@ var (@ (@ ap A) B)))))) (let ((_let_102 (= apnotvar _let_101))) (let ((_let_103 (forall ((A term) (B term) (C term)) (not (= (@ lam A) (@ (@ ap B) C)))))) (let ((_let_104 (= lamnotap _let_103))) (let ((_let_105 (= shinj (forall ((A term) (B term)) (=> (= (@ (@ sub A) sh) (@ (@ sub B) sh)) (= A B)))))) (let ((_let_106 (= laminj (forall ((A term) (B term)) (=> (= (@ lam A) (@ lam B)) (= A B)))))) (let ((_let_107 (= apinj2 (forall ((A term) (B term) (C term) (D term)) (=> (= (@ (@ ap A) C) (@ (@ ap B) D)) (= C D)))))) (let ((_let_108 (= apinj1 (forall ((A term) (B term) (C term) (D term)) (=> (= (@ (@ ap A) C) (@ (@ ap B) D)) (= A B)))))) (let ((_let_109 (= ulamvarind (forall ((P (-> term Bool))) (=> (@ P one) (=> (forall ((A term)) (=> (@ var A) (=> (@ P A) (@ P (@ (@ sub A) sh))))) (forall ((A term)) (=> (@ var A) (@ P A))))))))) (let ((_let_110 (= ulamvarsh (forall ((A term)) (=> (@ var A) (@ var (@ (@ sub A) sh))))))) (let ((_let_111 (@ var one))) (let ((_let_112 (= ulamvar1 _let_111))) (let ((_let_113 (= axscons (forall ((M subst)) (= (@ (@ push (@ (@ sub one) M)) (@ (@ comp sh) M)) M))))) (let ((_let_114 (= axvarshift (= (@ (@ push one) sh) id)))) (let ((_let_115 (= axidr (forall ((M subst)) (= (@ (@ comp M) id) M))))) (let ((_let_116 (forall ((A term) (M subst) (N subst)) (= (@ (@ comp (@ (@ push A) M)) N) (@ (@ push (@ (@ sub A) N)) (@ (@ comp M) N)))))) (let ((_let_117 (= axmap _let_116))) (let ((_let_118 (forall ((M subst) (N subst) (K subst)) (let ((_let_1 (@ comp M))) (= (@ (@ comp (@ _let_1 N)) K) (@ _let_1 (@ (@ comp N) K))))))) (let ((_let_119 (= axassoc _let_118))) (let ((_let_120 (= axshiftcons (forall ((A term) (M subst)) (= (@ (@ comp sh) (@ (@ push A) M)) M))))) (let ((_let_121 (= axidl (forall ((M subst)) (= (@ (@ comp id) M) M))))) (let ((_let_122 (forall ((A term) (M subst) (N subst)) (let ((_let_1 (@ sub A))) (= (@ (@ sub (@ _let_1 M)) N) (@ _let_1 (@ (@ comp M) N))))))) (let ((_let_123 (= axclos _let_122))) (let ((_let_124 (forall ((A term) (M subst)) (= (@ (@ sub (@ lam A)) M) (@ lam (@ (@ sub A) (@ (@ push one) (@ (@ comp M) sh)))))))) (let ((_let_125 (= axabs _let_124))) (let ((_let_126 (= axvarid (forall ((A term)) (= (@ (@ sub A) id) A))))) (let ((_let_127 (= axvarcons (forall ((A term) (M subst)) (= (@ (@ sub one) (@ (@ push A) M)) A))))) (let ((_let_128 (forall ((A term) (B term) (M subst)) (= (@ (@ sub (@ (@ ap A) B)) M) (@ (@ ap (@ (@ sub A) M)) (@ (@ sub B) M)))))) (let ((_let_129 (= axapp _let_128))) (let ((_let_130 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_131 (ho_11 (ho_10 k_9 skv_30) _let_130))) (let ((_let_132 (ho_7 skv_19 _let_131))) (let ((_let_133 (= skv_30 _let_131))) (let ((_let_134 (ho_7 skv_19 skv_30))) (let ((_let_135 (ho_7 k_8 skv_30))) (let ((_let_136 (not _let_135))) (let ((_let_137 (or _let_136 _let_132))) (let ((_let_138 (not _let_132))) (let ((_let_139 (forall ((B term)) (or (not (ho_7 k_8 B)) (ho_7 skv_19 (ho_11 (ho_10 k_9 B) (ho_3 (ho_2 k_1 one) sh))))))) (let ((_let_140 (not _let_137))) (let ((_let_141 (ho_3 (ho_2 k_1 skv_26) _let_130))) (let ((_let_142 (ho_7 skv_19 (ho_11 (ho_10 k_9 skv_29) _let_141)))) (let ((_let_143 (ho_7 k_8 skv_29))) (let ((_let_144 (not _let_143))) (let ((_let_145 (ho_7 skv_19 skv_26))) (let ((_let_146 (not _let_145))) (let ((_let_147 (not _let_139))) (let ((_let_148 (or _let_147 _let_146 _let_144 _let_142))) (let ((_let_149 (forall ((BOUND_VARIABLE_9149 |u_(-> term Bool)|) (A term) (M subst) (BOUND_VARIABLE_3268 term)) (or (not (forall ((B term)) (or (not 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BOUND_VARIABLE_9167 (ho_16 k_17 A))))) (ho_7 BOUND_VARIABLE_9167 BOUND_VARIABLE_3158))))) (let ((_let_153 (forall ((A term)) (= A (ho_11 (ho_10 k_9 A) (ho_3 (ho_2 k_1 one) sh)))))) (let ((_let_154 (ASSUME :args (_let_129)))) (let ((_let_155 (EQ_RESOLVE (ASSUME :args (_let_127)) (MACRO_SR_EQ_INTRO :args (_let_127 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_156 (EQ_RESOLVE (ASSUME :args (_let_126)) (MACRO_SR_EQ_INTRO :args (_let_126 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_157 (ASSUME :args (_let_125)))) (let ((_let_158 (ASSUME :args (_let_123)))) (let ((_let_159 (EQ_RESOLVE (ASSUME :args (_let_121)) (MACRO_SR_EQ_INTRO :args (_let_121 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_160 (EQ_RESOLVE (ASSUME :args (_let_120)) (MACRO_SR_EQ_INTRO :args (_let_120 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_161 (ASSUME :args (_let_119)))) (let ((_let_162 (ASSUME :args (_let_117)))) (let ((_let_163 (EQ_RESOLVE (ASSUME :args (_let_115)) (MACRO_SR_EQ_INTRO :args (_let_115 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_164 (EQ_RESOLVE (ASSUME :args (_let_114)) (MACRO_SR_EQ_INTRO :args (_let_114 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_165 (EQ_RESOLVE (ASSUME :args (_let_113)) (MACRO_SR_EQ_INTRO :args (_let_113 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_166 (ASSUME :args (_let_112)))) (let ((_let_167 (EQ_RESOLVE (ASSUME :args (_let_110)) (MACRO_SR_EQ_INTRO :args (_let_110 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_168 (EQ_RESOLVE (ASSUME :args (_let_109)) (MACRO_SR_EQ_INTRO :args (_let_109 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_169 (EQ_RESOLVE (ASSUME :args (_let_108)) (MACRO_SR_EQ_INTRO :args (_let_108 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_170 (EQ_RESOLVE (ASSUME :args (_let_107)) (MACRO_SR_EQ_INTRO :args (_let_107 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_171 (EQ_RESOLVE (ASSUME :args (_let_106)) (MACRO_SR_EQ_INTRO :args (_let_106 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_172 (EQ_RESOLVE (ASSUME :args (_let_105)) (MACRO_SR_EQ_INTRO :args (_let_105 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_173 (ASSUME :args (_let_104)))) (let ((_let_174 (ASSUME :args (_let_102)))) (let ((_let_175 (ASSUME :args (_let_100)))) (let ((_let_176 (EQ_RESOLVE (ASSUME :args (_let_98)) (MACRO_SR_EQ_INTRO :args (_let_98 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_177 (ASSUME :args (_let_97)))) (let ((_let_178 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_96)) (MACRO_SR_EQ_INTRO :args (_let_96 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= pushprop_lem0 (forall ((P (-> term Bool)) (A term) (M subst)) (not (forall ((Q (-> term Bool))) (not (@ (@ (@ (@ pushprop_p_and_p_prime A) M) P) Q)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_179 (EQ_RESOLVE (ASSUME :args (_let_95)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_95 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_180 (EQ_RESOLVE (SYMM (ASSUME :args (_let_94))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= pushprop_lem0 pushprop_lem0_lthm) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_181 (EQ_RESOLVE (ASSUME :args (_let_93)) (MACRO_SR_EQ_INTRO :args (_let_93 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_182 (EQ_RESOLVE (ASSUME :args (_let_92)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_92 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_183 (EQ_RESOLVE (ASSUME :args (_let_91)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_91 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_184 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_90)) (MACRO_SR_EQ_INTRO :args (_let_90 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= pushprop_lem1v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst)) (or (not (@ P A)) (not (@ (@ (@ (@ pushprop_p_and_p_prime A) M) P) Q)) (@ Q one)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_185 (EQ_RESOLVE (ASSUME :args (_let_89)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_89 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_186 (EQ_RESOLVE (ASSUME :args (_let_88)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_88 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_187 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_87)) (MACRO_SR_EQ_INTRO :args (_let_87 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= pushprop_lem2v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst) (BOUND_VARIABLE_3208 term)) (or (not (@ (@ (@ (@ pushprop_p_and_p_prime A) M) P) Q)) (not (forall ((B term)) (or (not (@ var B)) (@ P (@ (@ sub B) M))))) (not (@ var BOUND_VARIABLE_3208)) (not (@ Q BOUND_VARIABLE_3208)) (@ Q (@ (@ sub BOUND_VARIABLE_3208) sh))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_188 (EQ_RESOLVE (ASSUME :args (_let_86)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_86 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_189 (EQ_RESOLVE (ASSUME :args (_let_85)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_85 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_190 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_84)) (MACRO_SR_EQ_INTRO :args (_let_84 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= pushprop_lem3v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst) (BOUND_VARIABLE_3239 term)) (or (not (@ (@ (@ (@ pushprop_p_and_p_prime A) M) P) Q)) (not (forall ((B term)) (or (not (@ var B)) (@ Q B)))) (not (@ var BOUND_VARIABLE_3239)) (@ P (@ (@ sub BOUND_VARIABLE_3239) (@ (@ push A) M)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_191 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_192 (EQ_RESOLVE (ASSUME :args (_let_82)) (MACRO_SR_EQ_INTRO :args (_let_82 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_193 (EQ_RESOLVE (ASSUME :args (_let_81)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_81 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_194 (EQ_RESOLVE (ASSUME :args (_let_80)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_80 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_195 (EQ_RESOLVE (ASSUME :args (_let_79)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_79 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_196 (EQ_RESOLVE (ASSUME :args (_let_77)) (MACRO_SR_EQ_INTRO :args (_let_77 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_197 (EQ_RESOLVE (ASSUME :args (_let_76)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_76 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_198 (EQ_RESOLVE (ASSUME :args (_let_75)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_75 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_199 (EQ_RESOLVE (ASSUME :args (_let_73)) (MACRO_SR_EQ_INTRO :args (_let_73 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_200 (ASSUME :args (_let_72)))) (let ((_let_201 (EQ_RESOLVE _let_200 (MACRO_SR_EQ_INTRO (AND_INTRO _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_72 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_202 (EQ_RESOLVE (ASSUME :args (_let_71)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_71 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_203 (EQ_RESOLVE (ASSUME :args (_let_69)) (MACRO_SR_EQ_INTRO :args (_let_69 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_204 (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_68 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_205 (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_67 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_206 (EQ_RESOLVE (ASSUME :args (_let_66)) (MACRO_SR_EQ_INTRO :args (_let_66 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_207 (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_65 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_208 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_209 (ASSUME :args (_let_63)))) (let ((_let_210 (ASSUME :args (_let_62)))) (let ((_let_211 (ASSUME :args (_let_61)))) (let ((_let_212 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_60)) (MACRO_SR_EQ_INTRO :args (_let_60 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasapinj1 (forall ((A term) (B term) (C term) (D term)) (let ((_let_1 (@ hoasap id))) (or (not (= (@ (@ (@ _let_1 A) id) C) (@ (@ (@ _let_1 B) id) D))) (= A B))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_213 (EQ_RESOLVE (ASSUME :args (_let_59)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_59 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_214 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_215 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO :args (_let_57 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasapinj2 (forall ((A term) (B term) (C term) (D term)) (let ((_let_1 (@ hoasap id))) (or (not (= (@ (@ (@ _let_1 A) id) C) (@ (@ (@ _let_1 B) id) D))) (= C D))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_216 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_217 (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_55 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_218 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_54)) (MACRO_SR_EQ_INTRO :args (_let_54 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoaslaminj (forall ((F (-> subst term term)) (BOUND_VARIABLE_3431 subst) (BOUND_VARIABLE_3429 term) (BOUND_VARIABLE_3427 (-> subst term term))) (let ((_let_1 (@ hoaslam id))) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ BOUND_VARIABLE_3427 M) A)) N) (@ (@ BOUND_VARIABLE_3427 (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (= (@ _let_1 (lambda ((M subst) (A term)) (@ (@ F M) A))) (@ _let_1 (lambda ((M subst) (A term)) (@ (@ BOUND_VARIABLE_3427 M) A))))) (= (@ (@ F BOUND_VARIABLE_3431) BOUND_VARIABLE_3429) (@ (@ BOUND_VARIABLE_3427 BOUND_VARIABLE_3431) BOUND_VARIABLE_3429)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_219 (EQ_RESOLVE (ASSUME :args (_let_53)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_53 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_220 (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_52 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_221 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO :args (_let_51 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoaslamnotap (forall ((F (-> subst term term)) (BOUND_VARIABLE_3469 term) (BOUND_VARIABLE_3467 term)) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (= (@ (@ hoaslam id) (lambda ((M subst) (C term)) (@ (@ F M) C))) (@ (@ (@ (@ hoasap id) BOUND_VARIABLE_3467) id) BOUND_VARIABLE_3469)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_222 (EQ_RESOLVE (ASSUME :args (_let_50)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_50 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_223 (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_49 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_224 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO :args (_let_48 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoaslamnotvar (forall ((F (-> subst term term))) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (@ (@ (@ hoasvar id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_225 (EQ_RESOLVE (ASSUME :args (_let_47)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_47 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_226 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_227 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_228 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_229 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_230 (ASSUME :args (_let_42)))) (let ((_let_231 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem0 (forall ((P (-> subst term subst Bool))) (not (forall ((Q (-> term Bool))) (not (@ (@ hoasinduction_p_and_p_prime P) Q)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_232 (EQ_RESOLVE (SYMM (ASSUME :args (_let_40))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem0 hoasinduction_lem0_lthm) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_233 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem1v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_3524 term)) (or (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P M) A) (@ (@ comp K) N))) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)))) (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ comp K) N))))) (not (forall ((A term)) (or (not (@ (@ (@ hoasvar id) A) id)) (@ (@ (@ P id) A) id)))) (not (@ (@ hoasinduction_p_and_p_prime P) Q)) (not (@ var BOUND_VARIABLE_3524)) (@ Q BOUND_VARIABLE_3524)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_234 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_235 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem2v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_3569 term) (BOUND_VARIABLE_3567 term)) (or (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P M) A) (@ (@ comp K) N))) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)))) (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ comp K) N))))) (not (forall ((A term) (B term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (not (@ (@ _let_1 B) id)) (@ (@ _let_1 (@ (@ (@ (@ hoasap id) A) id) B)) id))))) (not (@ (@ hoasinduction_p_and_p_prime P) Q)) (not (@ Q BOUND_VARIABLE_3567)) (not (@ Q BOUND_VARIABLE_3569)) (@ Q (@ (@ ap BOUND_VARIABLE_3567) BOUND_VARIABLE_3569))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_236 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_237 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_238 (EQ_RESOLVE (SYMM (ASSUME :args (_let_34))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem3v2_f hoasinduction_lem3v2_f_lthm) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_239 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem3v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_3635 term)) (or (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P M) A) (@ (@ comp K) N))) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)))) (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ comp K) N))))) (not (forall ((F (-> subst term term))) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (forall ((A term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (@ (@ _let_1 (@ (@ F id) A)) id))))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (not (@ (@ hoasinduction_p_and_p_prime P) Q)) (not (forall ((B term)) (or (not (@ Q B)) (@ Q (@ (@ sub BOUND_VARIABLE_3635) (@ (@ push B) id)))))) (@ Q (@ lam BOUND_VARIABLE_3635))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_240 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_241 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_242 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem3v2a (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_3682 term)) (or (not (forall ((F (-> subst term term))) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (forall ((A term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (@ (@ _let_1 (@ (@ F id) A)) id))))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (not (@ (@ hoasinduction_p_and_p_prime P) Q)) (not (forall ((B term)) (or (not (@ Q B)) (@ Q (@ (@ sub BOUND_VARIABLE_3682) (@ (@ push B) id)))))) (@ Q (@ lam BOUND_VARIABLE_3682))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_243 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_244 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem1 (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3723 term)) (or (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P M) A) (@ (@ comp K) N))) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)))) (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ comp K) N))))) (not (forall ((A term)) (or (not (@ (@ (@ hoasvar id) A) id)) (@ (@ (@ P id) A) id)))) (not (@ var BOUND_VARIABLE_3723)) (@ (@ (@ P id) BOUND_VARIABLE_3723) id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_245 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_246 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_247 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem2 (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3766 term) (BOUND_VARIABLE_3764 term)) (let ((_let_1 (@ P id))) (or (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P M) A) (@ (@ comp K) N))) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)))) (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ comp K) N))))) (not (forall ((A term) (B term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (not (@ (@ _let_1 B) id)) (@ (@ _let_1 (@ (@ (@ (@ hoasap id) A) id) B)) id))))) (not (@ (@ _let_1 BOUND_VARIABLE_3764) id)) (not (@ (@ _let_1 BOUND_VARIABLE_3766) id)) (@ (@ _let_1 (@ (@ ap BOUND_VARIABLE_3764) BOUND_VARIABLE_3766)) id))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_248 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_249 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_250 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem3aa (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3812 term)) (or (not (forall ((F (-> subst term term))) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (forall ((A term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (@ (@ _let_1 (@ (@ F id) A)) id))))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (not (forall ((B term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 B) id)) (@ (@ _let_1 (@ (@ sub BOUND_VARIABLE_3812) (@ (@ push B) id))) id))))) (@ (@ (@ P id) (@ lam (@ (@ sub BOUND_VARIABLE_3812) (@ (@ push one) sh)))) id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_251 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_252 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem3aaa (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3927 term)) (or (not (forall ((F (-> subst term term)) (BOUND_VARIABLE_3891 term)) (or (not (forall ((A term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (@ (@ _let_1 (@ (@ F id) A)) id))))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id) (not (forall ((BOUND_VARIABLE_3833 subst) (BOUND_VARIABLE_3835 term) (BOUND_VARIABLE_3837 subst)) (= (@ (@ sub (@ (@ F BOUND_VARIABLE_3833) BOUND_VARIABLE_3835)) BOUND_VARIABLE_3837) (@ (@ sub (@ (@ sub BOUND_VARIABLE_3891) (@ (@ push BOUND_VARIABLE_3835) BOUND_VARIABLE_3833))) BOUND_VARIABLE_3837)))) (not (forall ((BOUND_VARIABLE_3851 subst) (BOUND_VARIABLE_3853 term) (BOUND_VARIABLE_3855 subst)) (let ((_let_1 (@ (@ comp BOUND_VARIABLE_3851) BOUND_VARIABLE_3855))) (let ((_let_2 (@ (@ sub BOUND_VARIABLE_3853) BOUND_VARIABLE_3855))) (= (@ (@ F _let_1) _let_2) (@ (@ sub BOUND_VARIABLE_3891) (@ (@ push _let_2) _let_1)))))))))) (not (forall ((B term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 B) id)) (@ (@ _let_1 (@ (@ sub BOUND_VARIABLE_3927) (@ (@ push B) id))) id))))) (@ (@ (@ P id) (@ lam (@ (@ sub BOUND_VARIABLE_3927) (@ (@ push one) sh)))) id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_253 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem3 (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3986 term)) (or (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P M) A) (@ (@ comp K) N))) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)))) (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ comp K) N))))) (not (forall ((F (-> subst term term))) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (forall ((A term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (@ (@ _let_1 (@ (@ F id) A)) id))))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (not (forall ((B term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 B) id)) (@ (@ _let_1 (@ (@ sub BOUND_VARIABLE_3986) (@ (@ push B) id))) id))))) (@ (@ (@ P id) (@ lam BOUND_VARIABLE_3986)) id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_254 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_255 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_256 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_lem3a (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_4032 term)) (or (not (forall ((F (-> subst term term))) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (forall ((A term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (@ (@ _let_1 (@ (@ F id) A)) id))))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (not (forall ((B term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 B) id)) (@ (@ _let_1 (@ (@ sub BOUND_VARIABLE_4032) (@ (@ push B) id))) id))))) (@ (@ (@ P id) (@ lam BOUND_VARIABLE_4032)) id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_257 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_258 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_259 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_260 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_261 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_262 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_4102 term)) (or (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P M) A) (@ (@ comp K) N))) (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)))) (not (forall ((M subst) (A term) (N subst) (K subst)) (or (not (@ (@ (@ P (@ (@ comp M) K)) (@ (@ sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ comp K) N))))) (not (forall ((A term)) (or (not (@ (@ (@ hoasvar id) A) id)) (@ (@ (@ P id) A) id)))) (not (forall ((A term) (B term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (not (@ (@ _let_1 B) id)) (@ (@ _let_1 (@ (@ (@ (@ hoasap id) A) id) B)) id))))) (not (forall ((F (-> subst term term))) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (forall ((A term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (@ (@ _let_1 (@ (@ F id) A)) id))))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (@ (@ (@ P id) BOUND_VARIABLE_4102) id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_263 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_264 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_265 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_266 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args ((= hoasinduction_no_psi_cond (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_4137 term)) (or (not (forall ((A term) (B term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (not (@ (@ _let_1 B) id)) (@ (@ _let_1 (@ (@ (@ (@ hoasap id) A) id) B)) id))))) (not (forall ((F (-> subst term term))) (or (not (forall ((M subst) (A term) (N subst)) (= (@ (@ sub (@ (@ F M) A)) N) (@ (@ F (@ (@ comp M) N)) (@ (@ sub A) N))))) (not (forall ((A term)) (let ((_let_1 (@ P id))) (or (not (@ (@ _let_1 A) id)) (@ (@ _let_1 (@ (@ F id) A)) id))))) (@ (@ (@ P id) (@ (@ hoaslam id) (lambda ((M subst) (A term)) (@ (@ F M) A)))) id)))) (@ (@ (@ P id) BOUND_VARIABLE_4137) id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_267 (ASSUME :args (_let_1)))) (let ((_let_268 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE _let_267 (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (NOT_IMPLIES_ELIM1 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (RESOLUTION (EQUIV_ELIM2 _let_200) _let_267 :args (true induction2_gthm))))))))))))) _let_164) (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154) :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> _let_128 (=> (forall ((A term) (M subst)) (= A (@ (@ sub one) (@ (@ push A) M)))) (=> (forall ((A term)) (= A (@ (@ sub A) (@ (@ push one) sh)))) (=> _let_124 (=> _let_122 (=> (forall ((M subst)) (= M (@ (@ comp (@ (@ push one) sh)) M))) (=> (forall ((A term) (M subst)) (= M (@ (@ comp sh) (@ (@ push A) M)))) (=> _let_118 (=> _let_116 (=> (forall ((M subst)) (= M (@ (@ comp M) (@ (@ push one) sh)))) (=> (forall ((M subst)) (= M (@ (@ push (@ (@ sub one) M)) (@ (@ comp sh) M)))) (=> _let_111 (=> (forall ((A term)) (or (not (@ var A)) (@ var (@ (@ sub A) sh)))) (=> (forall ((P (-> term Bool)) (BOUND_VARIABLE_3103 term)) (or (not (@ P one)) (not (forall ((A term)) (or (not (@ var A)) (not (@ P A)) (@ P (@ (@ sub A) sh))))) (not (@ var BOUND_VARIABLE_3103)) (@ P BOUND_VARIABLE_3103))) (=> (forall ((A term) (B term) (C term) (D term)) (or (not (= (@ (@ ap A) C) (@ (@ ap B) D))) (= A B))) (=> (forall ((A term) (B term) (C term) (D term)) (or (not (= (@ (@ ap A) C) (@ (@ ap B) D))) (= C D))) (=> (forall ((A term) (B term)) (or (not (= (@ lam A) (@ lam B))) (= A B))) (=> (forall ((A term) (B term)) (or (not (= (@ (@ sub A) sh) (@ (@ sub B) sh))) (= A B))) (=> _let_103 (=> _let_101 (=> _let_99 (=> (forall ((P (-> term Bool)) (BOUND_VARIABLE_3158 term)) (or (not (forall ((A term)) (or (not (@ var A)) (@ P A)))) (not (forall ((A term) (B term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ ap A) B))))) (not (forall ((A term)) (or (not (@ P A)) (@ P (@ lam A))))) (@ P BOUND_VARIABLE_3158))) (=> (forall ((P (-> term Bool)) (A term) (M subst) (BOUND_VARIABLE_3268 term)) (or (not (forall ((B term)) (or (not (@ var B)) (@ P (@ (@ sub B) M))))) (not (@ P A)) (not (@ var BOUND_VARIABLE_3268)) (@ P (@ (@ sub BOUND_VARIABLE_3268) (@ (@ push A) M))))) (=> (forall ((P (-> term Bool)) (BOUND_VARIABLE_3314 subst) (BOUND_VARIABLE_3312 term)) (or (not (forall ((A term) (B term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ ap A) B))))) (not (forall ((A term)) (or (not (forall ((B term)) (or (not (@ P B)) (@ P (@ (@ sub A) (@ (@ push B) (@ (@ push one) sh))))))) (@ P (@ lam A))))) (not (forall ((B term)) (or (not (@ var B)) (@ P (@ (@ sub B) BOUND_VARIABLE_3314))))) (@ P (@ (@ sub BOUND_VARIABLE_3312) BOUND_VARIABLE_3314)))) (forall ((P (-> term Bool)) (BOUND_VARIABLE_3359 term)) (or (not (forall ((A term)) (or (not (@ var A)) (@ P A)))) (not (forall ((A term) (B term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ ap A) B))))) (not (forall ((A term)) (or (not (forall ((B term)) (or (not (@ P B)) (@ P (@ (@ sub A) 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true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
0.63/0.81	% SZS output end Proof for theBenchmark
0.63/0.81	EOF