0.00/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.11	% Command    : do_cvc5 %s %d
0.10/0.31	% Computer   : n018.cluster.edu
0.10/0.31	% Model      : x86_64 x86_64
0.10/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory     : 8042.1875MB
0.10/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 1200
0.10/0.31	% WCLimit    : 120
0.10/0.31	% DateTime   : Tue Jul 13 12:37:23 EDT 2021
0.10/0.31	% CPUTime    : 
0.15/0.43	%----THF division
0.15/0.44	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.15/0.44	--- Run --ho-elim --full-saturate-quant at 10...
0.15/0.56	% SZS status Theorem for theBenchmark
0.45/0.70	% SZS output start Proof for theBenchmark
0.45/0.70	(proof
0.45/0.70	(let ((_let_1 (not hoasinduction_lem3a_lthm))) (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 (= lamnotvar (forall ((A term)) (not (var (lam A))))))) (let ((_let_100 (= apnotvar (forall ((A term) (B term)) (not (var ((ap A) B))))))) (let ((_let_101 (= lamnotap (forall ((A term) (B term) (C term)) (not (= (lam A) ((ap B) C))))))) (let ((_let_102 (= shinj (forall ((A term) (B term)) (=> (= ((sub A) sh) ((sub B) sh)) (= A B)))))) (let ((_let_103 (= laminj (forall ((A term) (B term)) (=> (= (lam A) (lam B)) (= A B)))))) (let ((_let_104 (= apinj2 (forall ((A term) (B term) (C term) (D term)) (=> (= ((ap A) C) ((ap B) D)) (= C D)))))) (let ((_let_105 (= apinj1 (forall ((A term) (B term) (C term) (D term)) (=> (= ((ap A) C) ((ap B) D)) (= A B)))))) (let ((_let_106 (= 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_107 (= ulamvarsh (forall ((A term)) (=> (var A) (var ((sub A) sh))))))) (let ((_let_108 (= ulamvar1 (var one)))) (let ((_let_109 (= axscons (forall ((M subst)) (= ((push ((sub one) M)) ((comp sh) M)) M))))) (let ((_let_110 (= axvarshift (= ((push one) sh) id)))) (let ((_let_111 (= axidr (forall ((M subst)) (= ((comp M) id) M))))) (let ((_let_112 (= axmap (forall ((A term) (M subst) (N subst)) (= ((comp ((push A) M)) N) ((push ((sub A) N)) ((comp M) N))))))) (let ((_let_113 (= axassoc (forall ((M subst) (N subst) (K subst)) (let ((_let_1 (comp M))) (= ((comp (_let_1 N)) K) (_let_1 ((comp N) K)))))))) (let ((_let_114 (= axshiftcons (forall ((A term) (M subst)) (= ((comp sh) ((push A) M)) M))))) (let ((_let_115 (= axidl (forall ((M subst)) (= ((comp id) M) M))))) (let ((_let_116 (= axclos (forall ((A term) (M subst) (N subst)) (let ((_let_1 (sub A))) (= ((sub (_let_1 M)) N) (_let_1 ((comp M) N)))))))) (let ((_let_117 (= axabs (forall ((A term) (M subst)) (= ((sub (lam A)) M) (lam ((sub A) ((push one) ((comp M) sh))))))))) (let ((_let_118 (= axvarid (forall ((A term)) (= ((sub A) id) A))))) (let ((_let_119 (= axvarcons (forall ((A term) (M subst)) (= ((sub one) ((push A) M)) A))))) (let ((_let_120 (= axapp (forall ((A term) (B term) (M subst)) (= ((sub ((ap A) B)) M) ((ap ((sub A) M)) ((sub B) M))))))) (let ((_let_121 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_122 (ho_4 skv_19 _let_121))) (let ((_let_123 (ho_6 (ho_5 _let_122 (ho_16 k_17 skv_20)) _let_121))) (let ((_let_124 (ho_11 (ho_10 k_9 skv_20) _let_121))) (let ((_let_125 (= skv_20 _let_124))) (let ((_let_126 (ho_6 (ho_5 _let_122 (ho_16 k_17 _let_124)) _let_121))) (let ((_let_127 (forall ((B term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_2 (ho_4 skv_19 _let_1))) (or (not (ho_6 (ho_5 _let_2 B) _let_1)) (ho_6 (ho_5 _let_2 (ho_11 (ho_10 k_9 skv_20) (ho_3 (ho_2 k_1 B) _let_1))) _let_1))))))) (let ((_let_128 (not _let_127))) (let ((_let_129 (forall ((BOUND_VARIABLE_8560 |u_(-> subst term term)|)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (or (not (forall ((M subst) (A term) (N subst)) (= (ho_16 (ho_18 BOUND_VARIABLE_8560 (ho_3 (ho_13 k_12 M) N)) (ho_11 (ho_10 k_9 A) N)) (ho_11 (ho_10 k_9 (ho_16 (ho_18 BOUND_VARIABLE_8560 M) A)) N)))) (not (forall ((A term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_2 (ho_4 skv_19 _let_1))) (or (not (ho_6 (ho_5 _let_2 A) _let_1)) (ho_6 (ho_5 _let_2 (ho_16 (ho_18 BOUND_VARIABLE_8560 _let_1) A)) _let_1)))))) (ho_6 (ho_5 (ho_4 skv_19 _let_1) (ho_16 k_17 (ho_16 (ho_18 BOUND_VARIABLE_8560 sh) one))) _let_1)))))) (let ((_let_130 (not _let_129))) (let ((_let_131 (or _let_130 _let_128 _let_123))) (let ((_let_132 (not _let_123))) (let ((_let_133 (forall ((BOUND_VARIABLE_8544 |u_(-> subst term subst Bool)|) (BOUND_VARIABLE_4016 term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (or (not (forall ((BOUND_VARIABLE_8560 |u_(-> subst term term)|)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (or (not (forall ((M subst) (A term) (N subst)) (= (ho_16 (ho_18 BOUND_VARIABLE_8560 (ho_3 (ho_13 k_12 M) N)) (ho_11 (ho_10 k_9 A) N)) (ho_11 (ho_10 k_9 (ho_16 (ho_18 BOUND_VARIABLE_8560 M) A)) N)))) (not (forall ((A term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_2 (ho_4 BOUND_VARIABLE_8544 _let_1))) (or (not (ho_6 (ho_5 _let_2 A) _let_1)) (ho_6 (ho_5 _let_2 (ho_16 (ho_18 BOUND_VARIABLE_8560 _let_1) A)) _let_1)))))) (ho_6 (ho_5 (ho_4 BOUND_VARIABLE_8544 _let_1) (ho_16 k_17 (ho_16 (ho_18 BOUND_VARIABLE_8560 sh) one))) _let_1))))) (not (forall ((B term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_2 (ho_4 BOUND_VARIABLE_8544 _let_1))) (or (not (ho_6 (ho_5 _let_2 B) _let_1)) (ho_6 (ho_5 _let_2 (ho_11 (ho_10 k_9 BOUND_VARIABLE_4016) (ho_3 (ho_2 k_1 B) _let_1))) _let_1)))))) (ho_6 (ho_5 (ho_4 BOUND_VARIABLE_8544 _let_1) (ho_16 k_17 BOUND_VARIABLE_4016)) _let_1)))))) (let ((_let_134 (not _let_131))) (let ((_let_135 (forall ((BOUND_VARIABLE_8599 |u_(-> subst term subst Bool)|) (BOUND_VARIABLE_3796 term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (or (not (forall ((BOUND_VARIABLE_8614 |u_(-> subst term term)|)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (or (not (forall ((M subst) (A term) (N subst)) (= (ho_16 (ho_18 BOUND_VARIABLE_8614 (ho_3 (ho_13 k_12 M) N)) (ho_11 (ho_10 k_9 A) N)) (ho_11 (ho_10 k_9 (ho_16 (ho_18 BOUND_VARIABLE_8614 M) A)) N)))) (not (forall ((A term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_2 (ho_4 BOUND_VARIABLE_8599 _let_1))) (or (not (ho_6 (ho_5 _let_2 A) _let_1)) (ho_6 (ho_5 _let_2 (ho_16 (ho_18 BOUND_VARIABLE_8614 _let_1) A)) _let_1)))))) (ho_6 (ho_5 (ho_4 BOUND_VARIABLE_8599 _let_1) (ho_16 k_17 (ho_16 (ho_18 BOUND_VARIABLE_8614 sh) one))) _let_1))))) (not (forall ((B term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_2 (ho_4 BOUND_VARIABLE_8599 _let_1))) (or (not (ho_6 (ho_5 _let_2 B) _let_1)) (ho_6 (ho_5 _let_2 (ho_11 (ho_10 k_9 BOUND_VARIABLE_3796) (ho_3 (ho_2 k_1 B) _let_1))) _let_1)))))) (ho_6 (ho_5 (ho_4 BOUND_VARIABLE_8599 _let_1) (ho_16 k_17 (ho_11 (ho_10 k_9 BOUND_VARIABLE_3796) _let_1))) _let_1)))))) (let ((_let_136 (forall ((A term)) (= A (ho_11 (ho_10 k_9 A) (ho_3 (ho_2 k_1 one) sh)))))) (let ((_let_137 (ASSUME |:args| (_let_120)))) (let ((_let_138 (EQ_RESOLVE (ASSUME |:args| (_let_119)) (MACRO_SR_EQ_INTRO |:args| (_let_119 7 12))))) (let ((_let_139 (EQ_RESOLVE (ASSUME |:args| (_let_118)) (MACRO_SR_EQ_INTRO |:args| (_let_118 7 12))))) (let ((_let_140 (ASSUME |:args| (_let_117)))) (let ((_let_141 (ASSUME |:args| (_let_116)))) (let ((_let_142 (EQ_RESOLVE (ASSUME |:args| (_let_115)) (MACRO_SR_EQ_INTRO |:args| (_let_115 7 12))))) (let ((_let_143 (EQ_RESOLVE (ASSUME |:args| (_let_114)) (MACRO_SR_EQ_INTRO |:args| (_let_114 7 12))))) (let ((_let_144 (ASSUME |:args| (_let_113)))) (let ((_let_145 (ASSUME |:args| (_let_112)))) (let ((_let_146 (EQ_RESOLVE (ASSUME |:args| (_let_111)) (MACRO_SR_EQ_INTRO |:args| (_let_111 7 12))))) (let ((_let_147 (EQ_RESOLVE (ASSUME |:args| (_let_110)) (MACRO_SR_EQ_INTRO |:args| (_let_110 7 12))))) (let ((_let_148 (EQ_RESOLVE (ASSUME |:args| (_let_109)) (MACRO_SR_EQ_INTRO |:args| (_let_109 7 12))))) (let ((_let_149 (ASSUME |:args| (_let_108)))) (let ((_let_150 (EQ_RESOLVE (ASSUME |:args| (_let_107)) (MACRO_SR_EQ_INTRO |:args| (_let_107 7 12))))) (let ((_let_151 (EQ_RESOLVE (ASSUME |:args| (_let_106)) (MACRO_SR_EQ_INTRO |:args| (_let_106 7 12))))) (let ((_let_152 (EQ_RESOLVE (ASSUME |:args| (_let_105)) (MACRO_SR_EQ_INTRO |:args| (_let_105 7 12))))) (let ((_let_153 (EQ_RESOLVE (ASSUME |:args| (_let_104)) (MACRO_SR_EQ_INTRO |:args| (_let_104 7 12))))) (let ((_let_154 (EQ_RESOLVE (ASSUME |:args| (_let_103)) (MACRO_SR_EQ_INTRO |:args| (_let_103 7 12))))) (let ((_let_155 (EQ_RESOLVE (ASSUME |:args| (_let_102)) (MACRO_SR_EQ_INTRO |:args| (_let_102 7 12))))) (let ((_let_156 (ASSUME |:args| (_let_101)))) (let ((_let_157 (ASSUME |:args| (_let_100)))) (let ((_let_158 (ASSUME |:args| (_let_99)))) (let ((_let_159 (EQ_RESOLVE (ASSUME |:args| (_let_98)) (MACRO_SR_EQ_INTRO |:args| (_let_98 7 12))))) (let ((_let_160 (ASSUME |:args| (_let_97)))) (let ((_let_161 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_96)) (MACRO_SR_EQ_INTRO |:args| (_let_96 7 12))) (MACRO_SR_EQ_INTRO _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |: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)))))) 7 12))))) (let ((_let_162 (EQ_RESOLVE (ASSUME |:args| (_let_95)) (MACRO_SR_EQ_INTRO _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_95 7 12))))) (let ((_let_163 (EQ_RESOLVE (ASSUME |:args| (_let_94)) (MACRO_SR_EQ_INTRO _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_94 7 12))))) (let ((_let_164 (EQ_RESOLVE (ASSUME |:args| (_let_93)) (MACRO_SR_EQ_INTRO |:args| (_let_93 7 12))))) (let ((_let_165 (EQ_RESOLVE (ASSUME |:args| (_let_92)) (MACRO_SR_EQ_INTRO _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_92 7 12))))) (let ((_let_166 (EQ_RESOLVE (ASSUME |:args| (_let_91)) (MACRO_SR_EQ_INTRO _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_91 7 12))))) (let ((_let_167 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_90)) (MACRO_SR_EQ_INTRO |:args| (_let_90 7 12))) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |: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)))) 7 12))))) (let ((_let_168 (EQ_RESOLVE (ASSUME |:args| (_let_89)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_89 7 12))))) (let ((_let_169 (EQ_RESOLVE (ASSUME |:args| (_let_88)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_88 7 12))))) (let ((_let_170 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_87)) (MACRO_SR_EQ_INTRO |:args| (_let_87 7 12))) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= pushprop_lem2v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst) (BOUND_VARIABLE_3196 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_3196)) (not (Q BOUND_VARIABLE_3196)) (Q ((sub BOUND_VARIABLE_3196) sh))))) 7 12))))) (let ((_let_171 (EQ_RESOLVE (ASSUME |:args| (_let_86)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_86 7 12))))) (let ((_let_172 (EQ_RESOLVE (ASSUME |:args| (_let_85)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_85 7 12))))) (let ((_let_173 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_84)) (MACRO_SR_EQ_INTRO |:args| (_let_84 7 12))) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= pushprop_lem3v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst) (BOUND_VARIABLE_3227 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_3227)) (P ((sub BOUND_VARIABLE_3227) ((push A) M)))))) 7 12))))) (let ((_let_174 (EQ_RESOLVE (ASSUME |:args| (_let_83)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_83 7 12))))) (let ((_let_175 (EQ_RESOLVE (ASSUME |:args| (_let_82)) (MACRO_SR_EQ_INTRO |:args| (_let_82 7 12))))) (let ((_let_176 (EQ_RESOLVE (ASSUME |:args| (_let_81)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_81 7 12))))) (let ((_let_177 (EQ_RESOLVE (ASSUME |:args| (_let_80)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_80 7 12))))) (let ((_let_178 (EQ_RESOLVE (ASSUME |:args| (_let_79)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_79 7 12))))) (let ((_let_179 (EQ_RESOLVE (ASSUME |:args| (_let_77)) (MACRO_SR_EQ_INTRO |:args| (_let_77 7 12))))) (let ((_let_180 (EQ_RESOLVE (ASSUME |:args| (_let_76)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_76 7 12))))) (let ((_let_181 (EQ_RESOLVE (ASSUME |:args| (_let_75)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_75 7 12))))) (let ((_let_182 (EQ_RESOLVE (ASSUME |:args| (_let_73)) (MACRO_SR_EQ_INTRO |:args| (_let_73 7 12))))) (let ((_let_183 (EQ_RESOLVE (ASSUME |:args| (_let_72)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_72 7 12))))) (let ((_let_184 (EQ_RESOLVE (ASSUME |:args| (_let_71)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_71 7 12))))) (let ((_let_185 (EQ_RESOLVE (ASSUME |:args| (_let_69)) (MACRO_SR_EQ_INTRO |:args| (_let_69 7 12))))) (let ((_let_186 (EQ_RESOLVE (ASSUME |:args| (_let_68)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_68 7 12))))) (let ((_let_187 (EQ_RESOLVE (ASSUME |:args| (_let_67)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_67 7 12))))) (let ((_let_188 (EQ_RESOLVE (ASSUME |:args| (_let_66)) (MACRO_SR_EQ_INTRO |:args| (_let_66 7 12))))) (let ((_let_189 (EQ_RESOLVE (ASSUME |:args| (_let_65)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_65 7 12))))) (let ((_let_190 (EQ_RESOLVE (ASSUME |:args| (_let_64)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_64 7 12))))) (let ((_let_191 (ASSUME |:args| (_let_63)))) (let ((_let_192 (ASSUME |:args| (_let_62)))) (let ((_let_193 (ASSUME |:args| (_let_61)))) (let ((_let_194 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_60)) (MACRO_SR_EQ_INTRO |:args| (_let_60 7 12))) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |: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))))) 7 12))))) (let ((_let_195 (EQ_RESOLVE (ASSUME |:args| (_let_59)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_59 7 12))))) (let ((_let_196 (EQ_RESOLVE (ASSUME |:args| (_let_58)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_58 7 12))))) (let ((_let_197 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_57)) (MACRO_SR_EQ_INTRO |:args| (_let_57 7 12))) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |: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))))) 7 12))))) (let ((_let_198 (EQ_RESOLVE (ASSUME |:args| (_let_56)) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_56 7 12))))) (let ((_let_199 (EQ_RESOLVE (ASSUME |:args| (_let_55)) (MACRO_SR_EQ_INTRO _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_55 7 12))))) (let ((_let_200 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_54)) (MACRO_SR_EQ_INTRO |:args| (_let_54 7 12))) (MACRO_SR_EQ_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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoaslaminj (forall ((F (-> subst term term)) (BOUND_VARIABLE_3419 subst) (BOUND_VARIABLE_3417 term) (BOUND_VARIABLE_3415 (-> 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_3415 M) A)) N) ((BOUND_VARIABLE_3415 ((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_3415 M) A))))) (= ((F BOUND_VARIABLE_3419) BOUND_VARIABLE_3417) ((BOUND_VARIABLE_3415 BOUND_VARIABLE_3419) BOUND_VARIABLE_3417)))))) 7 12))))) (let ((_let_201 (EQ_RESOLVE (ASSUME |:args| (_let_53)) (MACRO_SR_EQ_INTRO _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_53 7 12))))) (let ((_let_202 (EQ_RESOLVE (ASSUME |:args| (_let_52)) (MACRO_SR_EQ_INTRO _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_52 7 12))))) (let ((_let_203 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_51)) (MACRO_SR_EQ_INTRO |:args| (_let_51 7 12))) (MACRO_SR_EQ_INTRO _let_202 _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoaslamnotap (forall ((F (-> subst term term)) (BOUND_VARIABLE_3457 term) (BOUND_VARIABLE_3455 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_3455) id) BOUND_VARIABLE_3457)))))) 7 12))))) (let ((_let_204 (EQ_RESOLVE (ASSUME |:args| (_let_50)) (MACRO_SR_EQ_INTRO _let_203 _let_202 _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_50 7 12))))) (let ((_let_205 (EQ_RESOLVE (ASSUME |:args| (_let_49)) (MACRO_SR_EQ_INTRO _let_204 _let_203 _let_202 _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_49 7 12))))) (let ((_let_206 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_48)) (MACRO_SR_EQ_INTRO |:args| (_let_48 7 12))) (MACRO_SR_EQ_INTRO _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |: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))))) 7 12))))) (let ((_let_207 (EQ_RESOLVE (ASSUME |:args| (_let_47)) (MACRO_SR_EQ_INTRO _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_47 7 12))))) (let ((_let_208 (EQ_RESOLVE (ASSUME |:args| (_let_46)) (MACRO_SR_EQ_INTRO _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_46 7 12))))) (let ((_let_209 (EQ_RESOLVE (ASSUME |:args| (_let_45)) (MACRO_SR_EQ_INTRO _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_45 7 12))))) (let ((_let_210 (EQ_RESOLVE (ASSUME |:args| (_let_44)) (MACRO_SR_EQ_INTRO _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_44 7 12))))) (let ((_let_211 (EQ_RESOLVE (ASSUME |:args| (_let_43)) (MACRO_SR_EQ_INTRO _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_43 7 12))))) (let ((_let_212 (ASSUME |:args| (_let_42)))) (let ((_let_213 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_41)) (MACRO_SR_EQ_INTRO |:args| (_let_41 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem0 (forall ((P (-> subst term subst Bool))) (not (forall ((Q (-> term Bool))) (not ((hoasinduction_p_and_p_prime P) Q)))))) 7 12))))) (let ((_let_214 (EQ_RESOLVE (ASSUME |:args| (_let_40)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_40 7 12))))) (let ((_let_215 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_39)) (MACRO_SR_EQ_INTRO |:args| (_let_39 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem1v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_3510 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_3510)) (Q BOUND_VARIABLE_3510)))) 7 12))))) (let ((_let_216 (EQ_RESOLVE (ASSUME |:args| (_let_38)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_38 7 12))))) (let ((_let_217 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_37)) (MACRO_SR_EQ_INTRO |:args| (_let_37 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem2v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_3555 term) (BOUND_VARIABLE_3553 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_3553)) (not (Q BOUND_VARIABLE_3555)) (Q ((ap BOUND_VARIABLE_3553) BOUND_VARIABLE_3555))))) 7 12))))) (let ((_let_218 (EQ_RESOLVE (ASSUME |:args| (_let_36)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_36 7 12))))) (let ((_let_219 (EQ_RESOLVE (ASSUME |:args| (_let_35)) (MACRO_SR_EQ_INTRO |:args| (_let_35 7 12))))) (let ((_let_220 (EQ_RESOLVE (ASSUME |:args| (_let_34)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_34 7 12))))) (let ((_let_221 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_33)) (MACRO_SR_EQ_INTRO |:args| (_let_33 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem3v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_3619 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_3619) ((push B) id)))))) (Q (lam BOUND_VARIABLE_3619))))) 7 12))))) (let ((_let_222 (EQ_RESOLVE (ASSUME |:args| (_let_32)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_32 7 12))))) (let ((_let_223 (EQ_RESOLVE (ASSUME |:args| (_let_31)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_31 7 12))))) (let ((_let_224 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_30)) (MACRO_SR_EQ_INTRO |:args| (_let_30 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem3v2a (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_3666 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_3666) ((push B) id)))))) (Q (lam BOUND_VARIABLE_3666))))) 7 12))))) (let ((_let_225 (EQ_RESOLVE (ASSUME |:args| (_let_29)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_29 7 12))))) (let ((_let_226 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_28)) (MACRO_SR_EQ_INTRO |:args| (_let_28 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem1 (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3707 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_3707)) (((P id) BOUND_VARIABLE_3707) id)))) 7 12))))) (let ((_let_227 (EQ_RESOLVE (ASSUME |:args| (_let_27)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_27 7 12))))) (let ((_let_228 (EQ_RESOLVE (ASSUME |:args| (_let_26)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_26 7 12))))) (let ((_let_229 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_24)) (MACRO_SR_EQ_INTRO |:args| (_let_24 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem2 (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3750 term) (BOUND_VARIABLE_3748 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_3748) id)) (not ((_let_1 BOUND_VARIABLE_3750) id)) ((_let_1 ((ap BOUND_VARIABLE_3748) BOUND_VARIABLE_3750)) id))))) 7 12))))) (let ((_let_230 (EQ_RESOLVE (ASSUME |:args| (_let_23)) (MACRO_SR_EQ_INTRO _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_23 7 12))))) (let ((_let_231 (EQ_RESOLVE (ASSUME |:args| (_let_22)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_22 7 12))))) (let ((_let_232 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_20)) (MACRO_SR_EQ_INTRO |:args| (_let_20 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem3aa (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3796 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_3796) ((push B) id))) id))))) (((P id) (lam ((sub BOUND_VARIABLE_3796) ((push one) sh)))) id)))) 7 12))))) (let ((_let_233 (EQ_RESOLVE (ASSUME |:args| (_let_19)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_19 7 12))))) (let ((_let_234 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_18)) (MACRO_SR_EQ_INTRO |:args| (_let_18 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem3aaa (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3911 term)) (or (not (forall ((F (-> subst term term)) (BOUND_VARIABLE_3875 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_3817 subst) (BOUND_VARIABLE_3819 term) (BOUND_VARIABLE_3821 subst)) (= ((sub ((F BOUND_VARIABLE_3817) BOUND_VARIABLE_3819)) BOUND_VARIABLE_3821) ((sub ((sub BOUND_VARIABLE_3875) ((push BOUND_VARIABLE_3819) BOUND_VARIABLE_3817))) BOUND_VARIABLE_3821)))) (not (forall ((BOUND_VARIABLE_3835 subst) (BOUND_VARIABLE_3837 term) (BOUND_VARIABLE_3839 subst)) (let ((_let_1 ((comp BOUND_VARIABLE_3835) BOUND_VARIABLE_3839))) (let ((_let_2 ((sub BOUND_VARIABLE_3837) BOUND_VARIABLE_3839))) (= ((F _let_1) _let_2) ((sub BOUND_VARIABLE_3875) ((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_3911) ((push B) id))) id))))) (((P id) (lam ((sub BOUND_VARIABLE_3911) ((push one) sh)))) id)))) 7 12))))) (let ((_let_235 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_17)) (MACRO_SR_EQ_INTRO |:args| (_let_17 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem3 (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3970 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_3970) ((push B) id))) id))))) (((P id) (lam BOUND_VARIABLE_3970)) id)))) 7 12))))) (let ((_let_236 (EQ_RESOLVE (ASSUME |:args| (_let_16)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_16 7 12))))) (let ((_let_237 (EQ_RESOLVE (ASSUME |:args| (_let_15)) (MACRO_SR_EQ_INTRO _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_15 7 12))))) (let ((_let_238 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_14)) (MACRO_SR_EQ_INTRO |:args| (_let_14 7 12))) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_lem3a (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_4016 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_4016) ((push B) id))) id))))) (((P id) (lam BOUND_VARIABLE_4016)) id)))) 7 12))))) (let ((_let_239 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_13 7 12))))) (let ((_let_240 (ASSUME |:args| (_let_12)))) (let ((_let_241 (EQ_RESOLVE _let_240 (MACRO_SR_EQ_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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_12 7 12))))) (let ((_let_242 (EQ_RESOLVE (ASSUME |:args| (_let_11)) (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12))))) (let ((_let_243 (EQ_RESOLVE (ASSUME |:args| (_let_10)) (MACRO_SR_EQ_INTRO _let_242 _let_241 _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_10 7 12))))) (let ((_let_244 (EQ_RESOLVE (ASSUME |:args| (_let_9)) (MACRO_SR_EQ_INTRO _let_243 _let_242 _let_241 _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_9 7 12))))) (let ((_let_245 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_8)) (MACRO_SR_EQ_INTRO |:args| (_let_8 7 12))) (MACRO_SR_EQ_INTRO _let_244 _let_243 _let_242 _let_241 _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_4086 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_4086) id)))) 7 12))))) (let ((_let_246 (EQ_RESOLVE (ASSUME |:args| (_let_7)) (MACRO_SR_EQ_INTRO _let_245 _let_244 _let_243 _let_242 _let_241 _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_7 7 12))))) (let ((_let_247 (EQ_RESOLVE (ASSUME |:args| (_let_6)) (MACRO_SR_EQ_INTRO _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_6 7 12))))) (let ((_let_248 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (MACRO_SR_EQ_INTRO _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_4 7 12))))) (let ((_let_249 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_3)) (MACRO_SR_EQ_INTRO |:args| (_let_3 7 12))) (MACRO_SR_EQ_INTRO _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| ((= hoasinduction_no_psi_cond (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_4121 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_4121) id)))) 7 12))))) (let ((_let_250 (ASSUME |:args| (_let_1)))) (let ((_let_251 (EQ_RESOLVE _let_250 (TRANS (MACRO_SR_EQ_INTRO (EQ_RESOLVE (NOT_IMPLIES_ELIM1 (NOT_IMPLIES_ELIM2 (RESOLUTION (EQUIV_ELIM2 _let_240) _let_250 |:args| (true hoasinduction_lem3a_lthm)))) _let_147) (EQ_RESOLVE (ASSUME |:args| (_let_2)) (MACRO_SR_EQ_INTRO _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_2 7 12))) _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _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_200 _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 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 |:args| (_let_1 7 12)) (PREPROCESS |:args| ((= (not (=> (forall ((A term)) (= A ((sub A) ((push one) sh)))) (=> (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_3796 term)) (let ((_let_1 ((push one) sh))) (or (not (forall ((F (-> subst term term))) (let ((_let_1 ((push one) sh))) (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 ((push one) sh))) (let ((_let_2 (P _let_1))) (or (not ((_let_2 A) _let_1)) ((_let_2 ((F _let_1) A)) _let_1)))))) (((P _let_1) (lam ((F sh) one))) _let_1))))) (not (forall ((B term)) (let ((_let_1 ((push one) sh))) (let ((_let_2 (P _let_1))) (or (not ((_let_2 B) _let_1)) ((_let_2 ((sub BOUND_VARIABLE_3796) ((push B) _let_1))) _let_1)))))) (((P _let_1) (lam ((sub BOUND_VARIABLE_3796) _let_1))) _let_1)))) (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_4016 term)) (let ((_let_1 ((push one) sh))) (or (not (forall ((F (-> subst term term))) (let ((_let_1 ((push one) sh))) (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 ((push one) sh))) (let ((_let_2 (P _let_1))) (or (not ((_let_2 A) _let_1)) ((_let_2 ((F _let_1) A)) _let_1)))))) (((P _let_1) (lam ((F sh) one))) _let_1))))) (not (forall ((B term)) (let ((_let_1 ((push one) sh))) (let ((_let_2 (P _let_1))) (or (not ((_let_2 B) _let_1)) ((_let_2 ((sub BOUND_VARIABLE_4016) ((push B) _let_1))) _let_1)))))) (((P _let_1) (lam BOUND_VARIABLE_4016)) _let_1))))))) (not (=> _let_136 (=> _let_135 _let_133)))))))))) (let ((_let_252 (NOT_IMPLIES_ELIM2 _let_251))) (let ((_let_253 (20))) (let ((_let_254 (not _let_133))) (let ((_let_255 (_let_254))) (let ((_let_256 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_255)) |:args| _let_255)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_254) _let_133))) (REFL |:args| (_let_134)) |:args| _let_253)) (NOT_IMPLIES_ELIM2 _let_252) |:args| (_let_134 true _let_133)))) (let ((_let_257 (_let_136))) (let ((_let_258 (forall ((B term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_2 (ho_4 skv_19 _let_1))) (or (not (ho_6 (ho_5 _let_2 B) _let_1)) (ho_6 (ho_5 _let_2 (ho_11 (ho_10 k_9 skv_20) (ho_3 (ho_2 k_1 B) _let_1))) _let_1))))))) (let ((_let_259 (not _let_258))) (let ((_let_260 (forall ((BOUND_VARIABLE_8614 |u_(-> subst term term)|)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (or (not (forall ((M subst) (A term) (N subst)) (= (ho_16 (ho_18 BOUND_VARIABLE_8614 (ho_3 (ho_13 k_12 M) N)) (ho_11 (ho_10 k_9 A) N)) (ho_11 (ho_10 k_9 (ho_16 (ho_18 BOUND_VARIABLE_8614 M) A)) N)))) (not (forall ((A term)) (let ((_let_1 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_2 (ho_4 skv_19 _let_1))) (or (not (ho_6 (ho_5 _let_2 A) _let_1)) (ho_6 (ho_5 _let_2 (ho_16 (ho_18 BOUND_VARIABLE_8614 _let_1) A)) _let_1)))))) (ho_6 (ho_5 (ho_4 skv_19 _let_1) (ho_16 k_17 (ho_16 (ho_18 BOUND_VARIABLE_8614 sh) one))) _let_1)))))) (let ((_let_261 (not _let_260))) (let ((_let_262 (or _let_261 _let_259 _let_126))) (let ((_let_263 (_let_135))) (let ((_let_264 (REFL |:args| (_let_131)))) (let ((_let_265 (not _let_126))) (let ((_let_266 (not _let_125))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME |:args| (_let_132)))) (CONG (CONG (REFL |:args| (_let_122)) (CONG (REFL |:args| (k_17)) (SYMM (SYMM (ASSUME |:args| (_let_125)))) |:args| (23 ho_16)) |:args| (23 ho_5)) (REFL |:args| (_let_121)) |:args| (23 ho_6)) (TRUE_INTRO (ASSUME |:args| (_let_126))))) |:args| (_let_126 _let_125 _let_132))) (CONG (REFL |:args| (_let_265)) (REFL |:args| (_let_266)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_132) _let_123))) |:args| _let_253)) |:args| ((or _let_123 _let_266 _let_265))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_262)) |:args| ((or _let_261 _let_259 _let_126 (not _let_262)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM2 (THEORY_LEMMA |:args| ((= _let_260 _let_129) 12))) |:args| ((or _let_130 _let_260))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_131 0)) (CONG _let_264 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_130) _let_129))) |:args| _let_253)) |:args| ((or _let_129 _let_131))) _let_256 |:args| (_let_129 true _let_131)) |:args| (_let_260 false _let_129)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM2 (THEORY_LEMMA |:args| ((= _let_258 _let_127) 12))) |:args| ((or _let_128 _let_258))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_131 1)) (CONG _let_264 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_128) _let_127))) |:args| _let_253)) |:args| ((or _let_127 _let_131))) _let_256 |:args| (_let_127 true _let_131)) |:args| (_let_258 false _let_127)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_263) |:args| (skv_19 skv_20)) |:args| _let_263)) (NOT_IMPLIES_ELIM1 _let_252) |:args| (_let_262 false _let_135)) |:args| (_let_126 false _let_260 false _let_258 false _let_262)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_257) |:args| (skv_20)) |:args| _let_257)) (NOT_IMPLIES_ELIM1 _let_251) |:args| (_let_125 false _let_136)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_131 2)) _let_256 |:args| (_let_132 true _let_131)) |:args| (false false _let_126 false _let_125 true _let_123)) |:args| (_let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_77 _let_76 _let_75 _let_73 _let_72 _let_71 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_24 _let_23 _let_22 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_4 _let_3 _let_2 _let_1 (not false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
0.45/0.70	)
0.45/0.70	% SZS output end Proof for theBenchmark
0.45/0.70	EOF