0.03/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.11 % Command : do_cvc5 %s %d 0.10/0.31 % Computer : n002.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 12:46:48 EDT 2021 0.10/0.31 % CPUTime : 0.15/0.43 %----THF division 0.15/0.43 ------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120... 0.15/0.43 --- Run --ho-elim --full-saturate-quant at 10... 0.43/0.64 % SZS status Theorem for theBenchmark 0.55/0.78 % SZS output start Proof for theBenchmark 0.55/0.78 (proof 0.55/0.78 (let ((_let_1 (not induction2_gthm))) (let ((_let_2 (= hoasinduction_no_psi_cond_lthm (=> hoasinduction_lem0 (=> induction2 (=> axvarid (=> hoasinduction_lem3v2a hoasinduction_no_psi_cond))))))) (let ((_let_3 (= hoasinduction_no_psi_cond (forall ((P (-> subst term subst Bool))) (=> (forall ((A term) (B term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) (=> ((_let_1 B) id) ((_let_1 ((((hoasap id) A) id) B)) id))))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) ((_let_1 ((F id) A)) id)))) (((P id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id)))) (forall ((A term)) (((P id) A) id)))))))) (let ((_let_4 (= hoasinduction_lthm_3 (=> hoasinduction_lem0 (=> induction2 (=> axvarid (=> hoasinduction_lem3v2a hoasinduction))))))) (let ((_let_5 (=> hoasinduction_lem1 (=> hoasinduction_lem2 (=> hoasinduction_lem3 hoasinduction))))) (let ((_let_6 (= hoasinduction_lthm (=> induction2 _let_5)))) (let ((_let_7 (= hoasinduction_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar _let_5))))))))))))))))))))))))))))))))))))) (let ((_let_8 (= hoasinduction (forall ((P (-> subst term subst Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P M) A) ((comp K) N)) (((P ((comp M) K)) ((sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P ((comp M) K)) ((sub A) K)) N) (((P M) A) ((comp K) N)))) (=> (forall ((A term)) (=> (((hoasvar id) A) id) (((P id) A) id))) (=> (forall ((A term) (B term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) (=> ((_let_1 B) id) ((_let_1 ((((hoasap id) A) id) B)) id))))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) ((_let_1 ((F id) A)) id)))) (((P id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id)))) (forall ((A term)) (((P id) A) id))))))))))) (let ((_let_9 (= hoasinduction_lem3b_lthm hoasinduction_lem3b))) (let ((_let_10 (= hoasinduction_lem3b_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar (=> hoasinduction_lem1 (=> hoasinduction_lem2 hoasinduction_lem3b))))))))))))))))))))))))))))))))))))))) (let ((_let_11 (= hoasinduction_lem3b (forall ((B term)) (exists ((F (-> subst term term))) (= ((sub B) ((push one) sh)) ((F sh) one))))))) (let ((_let_12 (= hoasinduction_lem3a_lthm (=> axvarid (=> axvarshift (=> hoasinduction_lem3aa hoasinduction_lem3a)))))) (let ((_let_13 (= hoasinduction_lem3a_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar (=> hoasinduction_lem1 (=> hoasinduction_lem2 hoasinduction_lem3a))))))))))))))))))))))))))))))))))))))) (let ((_let_14 (= hoasinduction_lem3a (forall ((P (-> subst term subst Bool))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) ((_let_1 ((F id) A)) id)))) (((P id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id)))) (forall ((A term)) (=> (forall ((B term)) (let ((_let_1 (P id))) (=> ((_let_1 B) id) ((_let_1 ((sub A) ((push B) id))) id)))) (((P id) (lam A)) id)))))))) (let ((_let_15 (= hoasinduction_lem3_lthm (=> axvarid (=> axvarshift (=> hoasinduction_lem3aa hoasinduction_lem3)))))) (let ((_let_16 (= hoasinduction_lem3_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar (=> hoasinduction_lem1 (=> hoasinduction_lem2 hoasinduction_lem3))))))))))))))))))))))))))))))))))))))) (let ((_let_17 (= hoasinduction_lem3 (forall ((P (-> subst term subst Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P M) A) ((comp K) N)) (((P ((comp M) K)) ((sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P ((comp M) K)) ((sub A) K)) N) (((P M) A) ((comp K) N)))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) ((_let_1 ((F id) A)) id)))) (((P id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id)))) (forall ((A term)) (=> (forall ((B term)) (let ((_let_1 (P id))) (=> ((_let_1 B) id) ((_let_1 ((sub A) ((push B) id))) id)))) (((P id) (lam A)) id)))))))))) (let ((_let_18 (= hoasinduction_lem3aaa (forall ((P (-> subst term subst Bool))) (=> (forall ((F (-> subst term term))) (=> (exists ((C term)) (forall ((M subst) (A term) (N subst)) (let ((_let_1 ((sub A) N))) (let ((_let_2 ((comp M) N))) (let ((_let_3 (sub C))) (and (= ((sub ((F M) A)) N) ((sub (_let_3 ((push A) M))) N)) (= (_let_3 ((push _let_1) _let_2)) ((F _let_2) _let_1)))))))) (=> (forall ((A term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) ((_let_1 ((F id) A)) id)))) (((P id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id)))) (forall ((A term)) (=> (forall ((B term)) (let ((_let_1 (P id))) (=> ((_let_1 B) id) ((_let_1 ((sub A) ((push B) id))) id)))) (((P id) (lam ((sub A) ((push one) sh)))) id)))))))) (let ((_let_19 (= hoasinduction_lem3aa_lthm (=> axclos (=> axmap hoasinduction_lem3aa))))) (let ((_let_20 (= hoasinduction_lem3aa (forall ((P (-> subst term subst Bool))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) ((_let_1 ((F id) A)) id)))) (((P id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id)))) (forall ((A term)) (=> (forall ((B term)) (let ((_let_1 (P id))) (=> ((_let_1 B) id) ((_let_1 ((sub A) ((push B) id))) id)))) (((P id) (lam ((sub A) ((push one) sh)))) id)))))))) (let ((_let_21 (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem2)))))))))))))))))))))))))))))))))))) (let ((_let_22 (= hoasinduction_lem2_lthm _let_21))) (let ((_let_23 (= hoasinduction_lem2_gthm _let_21))) (let ((_let_24 (= hoasinduction_lem2 (forall ((P (-> subst term subst Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P M) A) ((comp K) N)) (((P ((comp M) K)) ((sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P ((comp M) K)) ((sub A) K)) N) (((P M) A) ((comp K) N)))) (=> (forall ((A term) (B term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) (=> ((_let_1 B) id) ((_let_1 ((((hoasap id) A) id) B)) id))))) (forall ((A term) (B term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) (=> ((_let_1 B) id) ((_let_1 ((ap A) B)) id)))))))))))) (let ((_let_25 (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem1)))))))))))))))))))))))))))))))))))) (let ((_let_26 (= hoasinduction_lem1_lthm _let_25))) (let ((_let_27 (= hoasinduction_lem1_gthm _let_25))) (let ((_let_28 (= hoasinduction_lem1 (forall ((P (-> subst term subst Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P M) A) ((comp K) N)) (((P ((comp M) K)) ((sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P ((comp M) K)) ((sub A) K)) N) (((P M) A) ((comp K) N)))) (=> (forall ((A term)) (=> (((hoasvar id) A) id) (((P id) A) id))) (forall ((A term)) (=> (var A) (((P id) A) id)))))))))) (let ((_let_29 (= hoasinduction_lem3v2a_lthm (=> hoasinduction_lem3v2_f (=> axvarid (=> axvarshift (=> axclos (=> axmap hoasinduction_lem3v2a)))))))) (let ((_let_30 (= hoasinduction_lem3v2a (forall ((P (-> subst term subst Bool)) (Q (-> term Bool))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) ((_let_1 ((F id) A)) id)))) (((P id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id)))) (=> ((hoasinduction_p_and_p_prime P) Q) (forall ((A term)) (=> (forall ((B term)) (=> (Q B) (Q ((sub A) ((push B) id))))) (Q (lam A)))))))))) (let ((_let_31 (= hoasinduction_lem3v2_lthm (=> axvarid (=> axvarshift (=> axclos (=> axmap hoasinduction_lem3v2))))))) (let ((_let_32 (= hoasinduction_lem3v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem3v2))))))))))))))))))))))))))))))))))))) (let ((_let_33 (= hoasinduction_lem3v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P M) A) ((comp K) N)) (((P ((comp M) K)) ((sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P ((comp M) K)) ((sub A) K)) N) (((P M) A) ((comp K) N)))) (=> (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (=> (forall ((A term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) ((_let_1 ((F id) A)) id)))) (((P id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id)))) (=> ((hoasinduction_p_and_p_prime P) Q) (forall ((A term)) (=> (forall ((B term)) (=> (Q B) (Q ((sub A) ((push B) id))))) (Q (lam A)))))))))))) (let ((_let_34 (= hoasinduction_lem3v2_f_lthm hoasinduction_lem3v2_f))) (let ((_let_35 (= hoasinduction_lem3v2_f (forall ((B term)) (exists ((F (-> subst term term))) (forall ((A term) (M subst)) (= ((F M) A) ((sub B) ((push A) M))))))))) (let ((_let_36 (= hoasinduction_lem2v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem2v2))))))))))))))))))))))))))))))))))))) (let ((_let_37 (= hoasinduction_lem2v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P M) A) ((comp K) N)) (((P ((comp M) K)) ((sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P ((comp M) K)) ((sub A) K)) N) (((P M) A) ((comp K) N)))) (=> (forall ((A term) (B term)) (let ((_let_1 (P id))) (=> ((_let_1 A) id) (=> ((_let_1 B) id) ((_let_1 ((((hoasap id) A) id) B)) id))))) (=> ((hoasinduction_p_and_p_prime P) Q) (forall ((A term) (B term)) (=> (Q A) (=> (Q B) (Q ((ap A) B))))))))))))) (let ((_let_38 (= hoasinduction_lem1v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar (=> hoasapnotvar hoasinduction_lem1v2))))))))))))))))))))))))))))))))))))) (let ((_let_39 (= hoasinduction_lem1v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P M) A) ((comp K) N)) (((P ((comp M) K)) ((sub A) K)) N))) (=> (forall ((M subst) (A term) (N subst) (K subst)) (=> (((P ((comp M) K)) ((sub A) K)) N) (((P M) A) ((comp K) N)))) (=> (forall ((A term)) (=> (((hoasvar id) A) id) (((P id) A) id))) (=> ((hoasinduction_p_and_p_prime P) Q) (forall ((A term)) (=> (var A) (Q A))))))))))) (let ((_let_40 (= hoasinduction_lem0_lthm hoasinduction_lem0))) (let ((_let_41 (= hoasinduction_lem0 (forall ((P (-> subst term subst Bool))) (exists ((Q (-> term Bool))) ((hoasinduction_p_and_p_prime P) Q)))))) (let ((_let_42 (= hoasinduction_p_and_p_prime (lambda ((P (-> subst term subst Bool)) (Q (-> term Bool))) (forall ((X term)) (= (Q X) (((P id) X) id))))))) (let ((_let_43 (= hoasapnotvar_lthm (=> axvarid (=> apnotvar hoasapnotvar))))) (let ((_let_44 (= hoasapnotvar_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap (=> hoaslamnotvar hoasapnotvar)))))))))))))))))))))))))))))))))))) (let ((_let_45 (= hoasapnotvar (forall ((A term) (B term)) (not (((hoasvar id) ((((hoasap id) A) id) B)) id)))))) (let ((_let_46 (= hoaslamnotvar_lthm (=> axvarid (=> lamnotvar hoaslamnotvar))))) (let ((_let_47 (= hoaslamnotvar_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj (=> hoaslamnotap hoaslamnotvar))))))))))))))))))))))))))))))))))) (let ((_let_48 (= hoaslamnotvar (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (not (((hoasvar id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id))))))) (let ((_let_49 (= hoaslamnotap_lthm (=> lamnotap hoaslamnotap)))) (let ((_let_50 (= hoaslamnotap_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 (=> hoaslaminj hoaslamnotap)))))))))))))))))))))))))))))))))) (let ((_let_51 (= hoaslamnotap (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (forall ((A term) (B term)) (not (= ((hoaslam id) (lambda ((M subst) (C term)) ((F M) C))) ((((hoasap id) A) id) B))))))))) (let ((_let_52 (= hoaslaminj_lthm (=> axvarcons (=> axshiftcons (=> laminj hoaslaminj)))))) (let ((_let_53 (= hoaslaminj_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 (=> hoasapinj2 hoaslaminj))))))))))))))))))))))))))))))))) (let ((_let_54 (= hoaslaminj (forall ((F (-> subst term term))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N)))) (forall ((G (-> subst term term))) (let ((_let_1 (hoaslam id))) (=> (forall ((M subst) (A term) (N subst)) (= ((sub ((G M) A)) N) ((G ((comp M) N)) ((sub A) N)))) (=> (= (_let_1 (lambda ((M subst) (A term)) ((F M) A))) (_let_1 (lambda ((M subst) (A term)) ((G M) A)))) (forall ((M subst) (A term)) (= ((F M) A) ((G M) A)))))))))))) (let ((_let_55 (= hoasapinj2_lthm (=> apinj2 hoasapinj2)))) (let ((_let_56 (= hoasapinj2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset (=> hoasapinj1 hoasapinj2)))))))))))))))))))))))))))))))) (let ((_let_57 (= hoasapinj2 (forall ((A term) (B term) (C term) (D term)) (let ((_let_1 (hoasap id))) (=> (= (((_let_1 A) id) C) (((_let_1 B) id) D)) (= C D))))))) (let ((_let_58 (= hoasapinj1_lthm (=> axvarid (=> apinj1 hoasapinj1))))) (let ((_let_59 (= hoasapinj1_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid (=> termmset hoasapinj1))))))))))))))))))))))))))))))) (let ((_let_60 (= hoasapinj1 (forall ((A term) (B term) (C term) (D term)) (let ((_let_1 (hoasap id))) (=> (= (((_let_1 A) id) C) (((_let_1 B) id) D)) (= A B))))))) (let ((_let_61 (= hoasvar (lambda ((M subst) (A term) (N subst)) (var ((sub A) N)))))) (let ((_let_62 (= hoaslam (lambda ((M subst) (F (-> subst term term))) (lam ((F sh) one)))))) (let ((_let_63 (= hoasap (lambda ((M subst) (A term) (N subst) (B term)) ((ap ((sub A) N)) B))))) (let ((_let_64 (= termmset_lthm (=> axvarid (=> axclos termmset))))) (let ((_let_65 (= termmset_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 (=> substmonoid termmset)))))))))))))))))))))))))))))) (let ((_let_66 (= termmset (and (forall ((A term) (M subst) (N subst)) (let ((_let_1 (sub A))) (= ((sub (_let_1 M)) N) (_let_1 ((comp M) N))))) (forall ((A term)) (= ((sub A) id) A)))))) (let ((_let_67 (= substmonoid_lthm (=> axidl (=> axassoc (=> axidr substmonoid)))))) (let ((_let_68 (= substmonoid_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop (=> induction2lem (=> induction2 substmonoid))))))))))))))))))))))))))))) (let ((_let_69 (= substmonoid (and (forall ((M subst) (N subst) (K subst)) (let ((_let_1 (comp M))) (= ((comp (_let_1 N)) K) (_let_1 ((comp N) K))))) (forall ((M subst)) (= ((comp id) M) M)) (forall ((M subst)) (= ((comp M) id) M)))))) (let ((_let_70 (=> induction2lem induction2))) (let ((_let_71 (= induction2_lthm (=> axvarid _let_70)))) (let ((_let_72 (= induction2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction (=> pushprop _let_70))))))))))))))))))))))))))) (let ((_let_73 (= induction2 (forall ((P (-> term Bool))) (=> (forall ((A term)) (=> (var A) (P A))) (=> (forall ((A term) (B term)) (=> (P A) (=> (P B) (P ((ap A) B))))) (=> (forall ((A term)) (=> (forall ((B term)) (=> (P B) (P ((sub A) ((push B) id))))) (P (lam A)))) (forall ((A term)) (P A))))))))) (let ((_let_74 (=> induction (=> pushprop induction2lem)))) (let ((_let_75 (= induction2lem_lthm (=> axapp (=> axvarcons (=> axabs (=> axclos (=> axshiftcons (=> axassoc (=> axmap (=> axidr _let_74))))))))))) (let ((_let_76 (= induction2lem_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar _let_74))))))))))))))))))))))))) (let ((_let_77 (= induction2lem (forall ((P (-> term Bool))) (=> (forall ((A term) (B term)) (=> (P A) (=> (P B) (P ((ap A) B))))) (=> (forall ((A term)) (=> (forall ((B term)) (=> (P B) (P ((sub A) ((push B) id))))) (P (lam A)))) (forall ((A term) (M subst)) (=> (forall ((B term)) (=> (var B) (P ((sub B) M)))) (P ((sub A) M)))))))))) (let ((_let_78 (=> ulamvar1 (=> axvarcons (=> axclos (=> axshiftcons (=> ulamvarind pushprop))))))) (let ((_let_79 (= pushprop_lthm (=> pushprop_lem0 _let_78)))) (let ((_let_80 (= pushprop_lthm_orig _let_78))) (let ((_let_81 (= pushprop_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop)))))))))))))))))))))))))) (let ((_let_82 (= pushprop (forall ((P (-> term Bool)) (A term) (M subst)) (=> (forall ((B term)) (=> (var B) (P ((sub B) M)))) (=> (P A) (forall ((B term)) (=> (var B) (P ((sub B) ((push A) M))))))))))) (let ((_let_83 (= pushprop_lem3v2_lthm pushprop_lem3v2))) (let ((_let_84 (= pushprop_lem3v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst)) (=> ((((pushprop_p_and_p_prime A) M) P) Q) (=> (forall ((B term)) (=> (var B) (Q B))) (forall ((B term)) (=> (var B) (P ((sub B) ((push A) M))))))))))) (let ((_let_85 (= pushprop_lem2v2_lthm (=> axclos (=> axshiftcons pushprop_lem2v2))))) (let ((_let_86 (= pushprop_lem2v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop_lem2v2)))))))))))))))))))))))))) (let ((_let_87 (= pushprop_lem2v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst)) (=> ((((pushprop_p_and_p_prime A) M) P) Q) (=> (forall ((B term)) (=> (var B) (P ((sub B) M)))) (forall ((C term)) (=> (var C) (=> (Q C) (Q ((sub C) sh))))))))))) (let ((_let_88 (= pushprop_lem1v2_lthm (=> axvarcons pushprop_lem1v2)))) (let ((_let_89 (= pushprop_lem1v2_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop_lem1v2)))))))))))))))))))))))))) (let ((_let_90 (= pushprop_lem1v2 (forall ((P (-> term Bool)) (Q (-> term Bool)) (A term) (M subst)) (=> (P A) (=> ((((pushprop_p_and_p_prime A) M) P) Q) (Q one))))))) (let ((_let_91 (= pushprop_lem1_lthm (=> axvarcons (=> axclos (=> axshiftcons (=> ulamvarind pushprop_lem1))))))) (let ((_let_92 (= pushprop_lem1_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop_lem1)))))))))))))))))))))))))) (let ((_let_93 (= pushprop_lem1 (forall ((P (-> term Bool)) (K (-> term Bool)) (A term) (M subst) (B term)) (=> (P A) (K ((sub A) ((push B) M)))))))) (let ((_let_94 (= pushprop_lem0_lthm pushprop_lem0))) (let ((_let_95 (= pushprop_lem0_gthm (=> axapp (=> axvarcons (=> axvarid (=> axabs (=> axclos (=> axidl (=> axshiftcons (=> axassoc (=> axmap (=> axidr (=> axvarshift (=> axscons (=> ulamvar1 (=> ulamvarsh (=> ulamvarind (=> apinj1 (=> apinj2 (=> laminj (=> shinj (=> lamnotap (=> apnotvar (=> lamnotvar (=> induction pushprop_lem0)))))))))))))))))))))))))) (let ((_let_96 (= pushprop_lem0 (forall ((P (-> term Bool)) (A term) (M subst)) (exists ((Q (-> term Bool))) ((((pushprop_p_and_p_prime A) M) P) Q)))))) (let ((_let_97 (= pushprop_p_and_p_prime (lambda ((A term) (M subst) (P (-> term Bool)) (Q (-> term Bool))) (forall ((X term)) (= (Q X) (P ((sub X) ((push A) M))))))))) (let ((_let_98 (= induction (forall ((P (-> term Bool))) (=> (forall ((A term)) (=> (var A) (P A))) (=> (forall ((A term) (B term)) (=> (P A) (=> (P B) (P ((ap A) B))))) (=> (forall ((A term)) (=> (P A) (P (lam A)))) (forall ((A term)) (P A))))))))) (let ((_let_99 (forall ((A term)) (not (var (lam A)))))) (let ((_let_100 (= lamnotvar _let_99))) (let ((_let_101 (forall ((A term) (B term)) (not (var ((ap A) B)))))) (let ((_let_102 (= apnotvar _let_101))) (let ((_let_103 (forall ((A term) (B term) (C term)) (not (= (lam A) ((ap B) C)))))) (let ((_let_104 (= lamnotap _let_103))) (let ((_let_105 (= shinj (forall ((A term) (B term)) (=> (= ((sub A) sh) ((sub B) sh)) (= A B)))))) (let ((_let_106 (= laminj (forall ((A term) (B term)) (=> (= (lam A) (lam B)) (= A B)))))) (let ((_let_107 (= apinj2 (forall ((A term) (B term) (C term) (D term)) (=> (= ((ap A) C) ((ap B) D)) (= C D)))))) (let ((_let_108 (= apinj1 (forall ((A term) (B term) (C term) (D term)) (=> (= ((ap A) C) ((ap B) D)) (= A B)))))) (let ((_let_109 (= ulamvarind (forall ((P (-> term Bool))) (=> (P one) (=> (forall ((A term)) (=> (var A) (=> (P A) (P ((sub A) sh))))) (forall ((A term)) (=> (var A) (P A))))))))) (let ((_let_110 (= ulamvarsh (forall ((A term)) (=> (var A) (var ((sub A) sh))))))) (let ((_let_111 (var one))) (let ((_let_112 (= ulamvar1 _let_111))) (let ((_let_113 (= axscons (forall ((M subst)) (= ((push ((sub one) M)) ((comp sh) M)) M))))) (let ((_let_114 (= axvarshift (= ((push one) sh) id)))) (let ((_let_115 (= axidr (forall ((M subst)) (= ((comp M) id) M))))) (let ((_let_116 (forall ((A term) (M subst) (N subst)) (= ((comp ((push A) M)) N) ((push ((sub A) N)) ((comp M) N)))))) (let ((_let_117 (= axmap _let_116))) (let ((_let_118 (forall ((M subst) (N subst) (K subst)) (let ((_let_1 (comp M))) (= ((comp (_let_1 N)) K) (_let_1 ((comp N) K))))))) (let ((_let_119 (= axassoc _let_118))) (let ((_let_120 (= axshiftcons (forall ((A term) (M subst)) (= ((comp sh) ((push A) M)) M))))) (let ((_let_121 (= axidl (forall ((M subst)) (= ((comp id) M) M))))) (let ((_let_122 (forall ((A term) (M subst) (N subst)) (let ((_let_1 (sub A))) (= ((sub (_let_1 M)) N) (_let_1 ((comp M) N))))))) (let ((_let_123 (= axclos _let_122))) (let ((_let_124 (forall ((A term) (M subst)) (= ((sub (lam A)) M) (lam ((sub A) ((push one) ((comp M) sh)))))))) (let ((_let_125 (= axabs _let_124))) (let ((_let_126 (= axvarid (forall ((A term)) (= ((sub A) id) A))))) (let ((_let_127 (= axvarcons (forall ((A term) (M subst)) (= ((sub one) ((push A) M)) A))))) (let ((_let_128 (forall ((A term) (B term) (M subst)) (= ((sub ((ap A) B)) M) ((ap ((sub A) M)) ((sub B) M)))))) (let ((_let_129 (= axapp _let_128))) (let ((_let_130 (ho_3 (ho_2 k_1 one) sh))) (let ((_let_131 (ho_11 (ho_10 k_9 skv_30) _let_130))) (let ((_let_132 (ho_7 skv_19 _let_131))) (let ((_let_133 (= skv_30 _let_131))) (let ((_let_134 (ho_7 skv_19 skv_30))) (let ((_let_135 (ho_7 k_8 skv_30))) (let ((_let_136 (not _let_135))) (let ((_let_137 (or _let_136 _let_132))) (let ((_let_138 (not _let_132))) (let ((_let_139 (forall ((B term)) (or (not (ho_7 k_8 B)) (ho_7 skv_19 (ho_11 (ho_10 k_9 B) (ho_3 (ho_2 k_1 one) sh))))))) (let ((_let_140 (not _let_137))) (let ((_let_141 (ho_3 (ho_2 k_1 skv_26) _let_130))) (let ((_let_142 (ho_7 skv_19 (ho_11 (ho_10 k_9 skv_29) _let_141)))) (let ((_let_143 (ho_7 k_8 skv_29))) (let ((_let_144 (not _let_143))) (let ((_let_145 (ho_7 skv_19 skv_26))) (let ((_let_146 (not _let_145))) (let ((_let_147 (not _let_139))) (let ((_let_148 (or _let_147 _let_146 _let_144 _let_142))) (let ((_let_149 (forall ((BOUND_VARIABLE_8970 |u_(-> term Bool)|) (A term) (M subst) (BOUND_VARIABLE_3256 term)) (or (not (forall ((B term)) (or (not (ho_7 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(B term)) (or (not (ho_7 BOUND_VARIABLE_8927 A)) (not (ho_7 BOUND_VARIABLE_8927 B)) (ho_7 BOUND_VARIABLE_8927 (ho_16 (ho_15 k_14 A) B))))) (not (forall ((A term)) (or (not (forall ((B term)) (or (not (ho_7 BOUND_VARIABLE_8927 B)) (ho_7 BOUND_VARIABLE_8927 (ho_11 (ho_10 k_9 A) (ho_3 (ho_2 k_1 B) (ho_3 (ho_2 k_1 one) sh))))))) (ho_7 BOUND_VARIABLE_8927 (ho_16 k_17 A))))) (not (forall ((B term)) (or (not (ho_7 k_8 B)) (ho_7 BOUND_VARIABLE_8927 (ho_11 (ho_10 k_9 B) BOUND_VARIABLE_3302))))) (ho_7 BOUND_VARIABLE_8927 (ho_11 (ho_10 k_9 BOUND_VARIABLE_3300) BOUND_VARIABLE_3302)))))) (let ((_let_152 (forall ((BOUND_VARIABLE_8988 |u_(-> term Bool)|) (BOUND_VARIABLE_3148 term)) (or (not (forall ((A term)) (or (not (ho_7 k_8 A)) (ho_7 BOUND_VARIABLE_8988 A)))) (not (forall ((A term) (B term)) (or (not (ho_7 BOUND_VARIABLE_8988 A)) (not (ho_7 BOUND_VARIABLE_8988 B)) (ho_7 BOUND_VARIABLE_8988 (ho_16 (ho_15 k_14 A) B))))) (not (forall ((A term)) (or (not (ho_7 BOUND_VARIABLE_8988 A)) (ho_7 BOUND_VARIABLE_8988 (ho_16 k_17 A))))) (ho_7 BOUND_VARIABLE_8988 BOUND_VARIABLE_3148))))) (let ((_let_153 (forall ((A term)) (= A (ho_11 (ho_10 k_9 A) (ho_3 (ho_2 k_1 one) sh)))))) (let ((_let_154 (ASSUME |:args| (_let_129)))) (let ((_let_155 (EQ_RESOLVE (ASSUME |:args| (_let_127)) (MACRO_SR_EQ_INTRO |:args| (_let_127 7 12))))) (let ((_let_156 (EQ_RESOLVE (ASSUME |:args| (_let_126)) (MACRO_SR_EQ_INTRO |:args| (_let_126 7 12))))) (let ((_let_157 (ASSUME |:args| (_let_125)))) (let ((_let_158 (ASSUME |:args| (_let_123)))) (let ((_let_159 (EQ_RESOLVE (ASSUME |:args| (_let_121)) (MACRO_SR_EQ_INTRO |:args| (_let_121 7 12))))) (let ((_let_160 (EQ_RESOLVE (ASSUME |:args| (_let_120)) (MACRO_SR_EQ_INTRO |:args| (_let_120 7 12))))) (let ((_let_161 (ASSUME |:args| (_let_119)))) (let ((_let_162 (ASSUME |:args| (_let_117)))) (let ((_let_163 (EQ_RESOLVE (ASSUME |:args| (_let_115)) (MACRO_SR_EQ_INTRO |:args| (_let_115 7 12))))) (let ((_let_164 (EQ_RESOLVE (ASSUME |:args| (_let_114)) (MACRO_SR_EQ_INTRO |:args| (_let_114 7 12))))) (let ((_let_165 (EQ_RESOLVE (ASSUME |:args| (_let_113)) (MACRO_SR_EQ_INTRO |:args| (_let_113 7 12))))) (let ((_let_166 (ASSUME |:args| (_let_112)))) (let ((_let_167 (EQ_RESOLVE (ASSUME |:args| (_let_110)) (MACRO_SR_EQ_INTRO |:args| (_let_110 7 12))))) (let ((_let_168 (EQ_RESOLVE (ASSUME |:args| (_let_109)) (MACRO_SR_EQ_INTRO |:args| (_let_109 7 12))))) (let ((_let_169 (EQ_RESOLVE (ASSUME |:args| (_let_108)) (MACRO_SR_EQ_INTRO |:args| (_let_108 7 12))))) (let ((_let_170 (EQ_RESOLVE (ASSUME |:args| (_let_107)) (MACRO_SR_EQ_INTRO |:args| (_let_107 7 12))))) (let ((_let_171 (EQ_RESOLVE (ASSUME |:args| (_let_106)) (MACRO_SR_EQ_INTRO |:args| (_let_106 7 12))))) (let ((_let_172 (EQ_RESOLVE (ASSUME |:args| (_let_105)) (MACRO_SR_EQ_INTRO |:args| (_let_105 7 12))))) (let ((_let_173 (ASSUME |:args| (_let_104)))) (let ((_let_174 (ASSUME |:args| (_let_102)))) (let ((_let_175 (ASSUME |:args| (_let_100)))) (let ((_let_176 (EQ_RESOLVE (ASSUME |:args| (_let_98)) (MACRO_SR_EQ_INTRO |:args| (_let_98 7 12))))) (let ((_let_177 (ASSUME |:args| (_let_97)))) (let ((_let_178 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_96)) (MACRO_SR_EQ_INTRO |:args| (_let_96 7 12))) (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 |: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_179 (EQ_RESOLVE (ASSUME |:args| (_let_95)) (MACRO_SR_EQ_INTRO _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_95 7 12))))) (let ((_let_180 (EQ_RESOLVE (ASSUME |:args| (_let_94)) (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 |:args| (_let_94 7 12))))) (let ((_let_181 (EQ_RESOLVE (ASSUME |:args| (_let_93)) (MACRO_SR_EQ_INTRO |:args| (_let_93 7 12))))) (let ((_let_182 (EQ_RESOLVE (ASSUME |:args| (_let_92)) (MACRO_SR_EQ_INTRO _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_92 7 12))))) (let ((_let_183 (EQ_RESOLVE (ASSUME |:args| (_let_91)) (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 |:args| (_let_91 7 12))))) (let ((_let_184 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_90)) (MACRO_SR_EQ_INTRO |:args| (_let_90 7 12))) (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 |: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_185 (EQ_RESOLVE (ASSUME |:args| (_let_89)) (MACRO_SR_EQ_INTRO _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_89 7 12))))) (let ((_let_186 (EQ_RESOLVE (ASSUME |:args| (_let_88)) (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 |:args| (_let_88 7 12))))) (let ((_let_187 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_87)) (MACRO_SR_EQ_INTRO |:args| (_let_87 7 12))) (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 |: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_188 (EQ_RESOLVE (ASSUME |:args| (_let_86)) (MACRO_SR_EQ_INTRO _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_86 7 12))))) (let ((_let_189 (EQ_RESOLVE (ASSUME |:args| (_let_85)) (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 |:args| (_let_85 7 12))))) (let ((_let_190 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_84)) (MACRO_SR_EQ_INTRO |:args| (_let_84 7 12))) (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 |: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_191 (EQ_RESOLVE (ASSUME |:args| (_let_83)) (MACRO_SR_EQ_INTRO _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_83 7 12))))) (let ((_let_192 (EQ_RESOLVE (ASSUME |:args| (_let_82)) (MACRO_SR_EQ_INTRO |:args| (_let_82 7 12))))) (let ((_let_193 (EQ_RESOLVE (ASSUME |:args| (_let_81)) (MACRO_SR_EQ_INTRO _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_81 7 12))))) (let ((_let_194 (EQ_RESOLVE (ASSUME |:args| (_let_80)) (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 |:args| (_let_80 7 12))))) (let ((_let_195 (EQ_RESOLVE (ASSUME |:args| (_let_79)) (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 |:args| (_let_79 7 12))))) (let ((_let_196 (EQ_RESOLVE (ASSUME |:args| (_let_77)) (MACRO_SR_EQ_INTRO |:args| (_let_77 7 12))))) (let ((_let_197 (EQ_RESOLVE (ASSUME |:args| (_let_76)) (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 |:args| (_let_76 7 12))))) (let ((_let_198 (EQ_RESOLVE (ASSUME |:args| (_let_75)) (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 |:args| (_let_75 7 12))))) (let ((_let_199 (EQ_RESOLVE (ASSUME |:args| (_let_73)) (MACRO_SR_EQ_INTRO |:args| (_let_73 7 12))))) (let ((_let_200 (ASSUME |:args| (_let_72)))) (let ((_let_201 (EQ_RESOLVE _let_200 (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 |:args| (_let_72 7 12))))) (let ((_let_202 (EQ_RESOLVE (ASSUME |:args| (_let_71)) (MACRO_SR_EQ_INTRO _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_71 7 12))))) (let ((_let_203 (EQ_RESOLVE (ASSUME |:args| (_let_69)) (MACRO_SR_EQ_INTRO |:args| (_let_69 7 12))))) (let ((_let_204 (EQ_RESOLVE (ASSUME |:args| (_let_68)) (MACRO_SR_EQ_INTRO _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_68 7 12))))) (let ((_let_205 (EQ_RESOLVE (ASSUME |:args| (_let_67)) (MACRO_SR_EQ_INTRO _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_67 7 12))))) (let ((_let_206 (EQ_RESOLVE (ASSUME |:args| (_let_66)) (MACRO_SR_EQ_INTRO |:args| (_let_66 7 12))))) (let ((_let_207 (EQ_RESOLVE (ASSUME |:args| (_let_65)) (MACRO_SR_EQ_INTRO _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_65 7 12))))) (let ((_let_208 (EQ_RESOLVE (ASSUME |:args| (_let_64)) (MACRO_SR_EQ_INTRO _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_64 7 12))))) (let ((_let_209 (ASSUME |:args| (_let_63)))) (let ((_let_210 (ASSUME |:args| (_let_62)))) (let ((_let_211 (ASSUME |:args| (_let_61)))) (let ((_let_212 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_60)) (MACRO_SR_EQ_INTRO |:args| (_let_60 7 12))) (MACRO_SR_EQ_INTRO _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasapinj1 (forall ((A term) (B term) (C term) (D term)) (let ((_let_1 (hoasap id))) (or (not (= (((_let_1 A) id) C) (((_let_1 B) id) D))) (= A B))))) 7 12))))) (let ((_let_213 (EQ_RESOLVE (ASSUME |:args| (_let_59)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_59 7 12))))) (let ((_let_214 (EQ_RESOLVE (ASSUME |:args| (_let_58)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_58 7 12))))) (let ((_let_215 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_57)) (MACRO_SR_EQ_INTRO |:args| (_let_57 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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasapinj2 (forall ((A term) (B term) (C term) (D term)) (let ((_let_1 (hoasap id))) (or (not (= (((_let_1 A) id) C) (((_let_1 B) id) D))) (= C D))))) 7 12))))) (let ((_let_216 (EQ_RESOLVE (ASSUME |:args| (_let_56)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_56 7 12))))) (let ((_let_217 (EQ_RESOLVE (ASSUME |:args| (_let_55)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_55 7 12))))) (let ((_let_218 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_54)) (MACRO_SR_EQ_INTRO |:args| (_let_54 7 12))) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoaslaminj (forall ((F (-> subst term term)) (BOUND_VARIABLE_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_219 (EQ_RESOLVE (ASSUME |:args| (_let_53)) (MACRO_SR_EQ_INTRO _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_53 7 12))))) (let ((_let_220 (EQ_RESOLVE (ASSUME |:args| (_let_52)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_52 7 12))))) (let ((_let_221 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_51)) (MACRO_SR_EQ_INTRO |:args| (_let_51 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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoaslamnotap (forall ((F (-> subst term term)) (BOUND_VARIABLE_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_222 (EQ_RESOLVE (ASSUME |:args| (_let_50)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_50 7 12))))) (let ((_let_223 (EQ_RESOLVE (ASSUME |:args| (_let_49)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_49 7 12))))) (let ((_let_224 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_48)) (MACRO_SR_EQ_INTRO |:args| (_let_48 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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoaslamnotvar (forall ((F (-> subst term term))) (or (not (forall ((M subst) (A term) (N subst)) (= ((sub ((F M) A)) N) ((F ((comp M) N)) ((sub A) N))))) (not (((hoasvar id) ((hoaslam id) (lambda ((M subst) (A term)) ((F M) A)))) id))))) 7 12))))) (let ((_let_225 (EQ_RESOLVE (ASSUME |:args| (_let_47)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_47 7 12))))) (let ((_let_226 (EQ_RESOLVE (ASSUME |:args| (_let_46)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_46 7 12))))) (let ((_let_227 (EQ_RESOLVE (ASSUME |:args| (_let_45)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_45 7 12))))) (let ((_let_228 (EQ_RESOLVE (ASSUME |:args| (_let_44)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_44 7 12))))) (let ((_let_229 (EQ_RESOLVE (ASSUME |:args| (_let_43)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_43 7 12))))) (let ((_let_230 (ASSUME |:args| (_let_42)))) (let ((_let_231 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_41)) (MACRO_SR_EQ_INTRO |:args| (_let_41 7 12))) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem0 (forall ((P (-> subst term subst Bool))) (not (forall ((Q (-> term Bool))) (not ((hoasinduction_p_and_p_prime P) Q)))))) 7 12))))) (let ((_let_232 (EQ_RESOLVE (ASSUME |:args| (_let_40)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_40 7 12))))) (let ((_let_233 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_39)) (MACRO_SR_EQ_INTRO |:args| (_let_39 7 12))) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem1v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_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_234 (EQ_RESOLVE (ASSUME |:args| (_let_38)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_38 7 12))))) (let ((_let_235 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_37)) (MACRO_SR_EQ_INTRO |:args| (_let_37 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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem2v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_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_236 (EQ_RESOLVE (ASSUME |:args| (_let_36)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_36 7 12))))) (let ((_let_237 (EQ_RESOLVE (ASSUME |:args| (_let_35)) (MACRO_SR_EQ_INTRO |:args| (_let_35 7 12))))) (let ((_let_238 (EQ_RESOLVE (ASSUME |:args| (_let_34)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_34 7 12))))) (let ((_let_239 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_33)) (MACRO_SR_EQ_INTRO |:args| (_let_33 7 12))) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem3v2 (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_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_240 (EQ_RESOLVE (ASSUME |:args| (_let_32)) (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_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_32 7 12))))) (let ((_let_241 (EQ_RESOLVE (ASSUME |:args| (_let_31)) (MACRO_SR_EQ_INTRO _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_31 7 12))))) (let ((_let_242 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_30)) (MACRO_SR_EQ_INTRO |:args| (_let_30 7 12))) (MACRO_SR_EQ_INTRO _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem3v2a (forall ((P (-> subst term subst Bool)) (Q (-> term Bool)) (BOUND_VARIABLE_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_243 (EQ_RESOLVE (ASSUME |:args| (_let_29)) (MACRO_SR_EQ_INTRO _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_29 7 12))))) (let ((_let_244 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_28)) (MACRO_SR_EQ_INTRO |:args| (_let_28 7 12))) (MACRO_SR_EQ_INTRO _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem1 (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_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_245 (EQ_RESOLVE (ASSUME |:args| (_let_27)) (MACRO_SR_EQ_INTRO _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_27 7 12))))) (let ((_let_246 (EQ_RESOLVE (ASSUME |:args| (_let_26)) (MACRO_SR_EQ_INTRO _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_26 7 12))))) (let ((_let_247 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_24)) (MACRO_SR_EQ_INTRO |:args| (_let_24 7 12))) (MACRO_SR_EQ_INTRO _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem2 (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_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_248 (EQ_RESOLVE (ASSUME |:args| (_let_23)) (MACRO_SR_EQ_INTRO _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_23 7 12))))) (let ((_let_249 (EQ_RESOLVE (ASSUME |:args| (_let_22)) (MACRO_SR_EQ_INTRO _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_22 7 12))))) (let ((_let_250 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_20)) (MACRO_SR_EQ_INTRO |:args| (_let_20 7 12))) (MACRO_SR_EQ_INTRO _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem3aa (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_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_251 (EQ_RESOLVE (ASSUME |:args| (_let_19)) (MACRO_SR_EQ_INTRO _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_19 7 12))))) (let ((_let_252 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_18)) (MACRO_SR_EQ_INTRO |:args| (_let_18 7 12))) (MACRO_SR_EQ_INTRO _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem3aaa (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_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_253 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_17)) (MACRO_SR_EQ_INTRO |:args| (_let_17 7 12))) (MACRO_SR_EQ_INTRO _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem3 (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_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_254 (EQ_RESOLVE (ASSUME |:args| (_let_16)) (MACRO_SR_EQ_INTRO _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_16 7 12))))) (let ((_let_255 (EQ_RESOLVE (ASSUME |:args| (_let_15)) (MACRO_SR_EQ_INTRO _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_15 7 12))))) (let ((_let_256 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_14)) (MACRO_SR_EQ_INTRO |:args| (_let_14 7 12))) (MACRO_SR_EQ_INTRO _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_lem3a (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_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_257 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (MACRO_SR_EQ_INTRO _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_13 7 12))))) (let ((_let_258 (EQ_RESOLVE (ASSUME |:args| (_let_12)) (MACRO_SR_EQ_INTRO _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_12 7 12))))) (let ((_let_259 (EQ_RESOLVE (ASSUME |:args| (_let_11)) (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12))))) (let ((_let_260 (EQ_RESOLVE (ASSUME |:args| (_let_10)) (MACRO_SR_EQ_INTRO _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_10 7 12))))) (let ((_let_261 (EQ_RESOLVE (ASSUME |:args| (_let_9)) (MACRO_SR_EQ_INTRO _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_9 7 12))))) (let ((_let_262 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_8)) (MACRO_SR_EQ_INTRO |:args| (_let_8 7 12))) (MACRO_SR_EQ_INTRO _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_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_263 (EQ_RESOLVE (ASSUME |:args| (_let_7)) (MACRO_SR_EQ_INTRO _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_7 7 12))))) (let ((_let_264 (EQ_RESOLVE (ASSUME |:args| (_let_6)) (MACRO_SR_EQ_INTRO _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_6 7 12))))) (let ((_let_265 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (MACRO_SR_EQ_INTRO _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_4 7 12))))) (let ((_let_266 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_3)) (MACRO_SR_EQ_INTRO |:args| (_let_3 7 12))) (MACRO_SR_EQ_INTRO _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| ((= hoasinduction_no_psi_cond (forall ((P (-> subst term subst Bool)) (BOUND_VARIABLE_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_267 (ASSUME |:args| (_let_1)))) (let ((_let_268 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE _let_267 (TRANS (MACRO_SR_EQ_INTRO (EQ_RESOLVE (NOT_IMPLIES_ELIM1 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (RESOLUTION (EQUIV_ELIM2 _let_200) _let_267 |:args| (true induction2_gthm))))))))))))) _let_164) (EQ_RESOLVE (ASSUME |:args| (_let_2)) (MACRO_SR_EQ_INTRO _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_2 7 12))) _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 |:args| (_let_1 7 12)) (PREPROCESS |:args| ((= (not (=> _let_128 (=> (forall ((A term) (M subst)) (= A ((sub one) ((push A) M)))) (=> (forall ((A term)) (= A ((sub A) ((push one) sh)))) (=> _let_124 (=> _let_122 (=> (forall ((M subst)) (= M ((comp ((push one) sh)) M))) (=> (forall ((A term) (M subst)) (= M ((comp sh) ((push A) M)))) (=> _let_118 (=> _let_116 (=> (forall ((M subst)) (= M ((comp M) ((push one) sh)))) (=> (forall ((M subst)) (= M ((push ((sub one) M)) ((comp sh) M)))) (=> _let_111 (=> (forall ((A term)) (or (not (var A)) (var ((sub A) sh)))) (=> (forall ((P (-> term Bool)) (BOUND_VARIABLE_3093 term)) (or (not (P one)) (not (forall ((A term)) (or (not (var A)) (not (P A)) (P ((sub A) sh))))) (not (var BOUND_VARIABLE_3093)) (P BOUND_VARIABLE_3093))) (=> (forall ((A term) (B term) (C term) (D term)) (or (not (= ((ap A) C) ((ap B) D))) (= A B))) (=> (forall ((A term) (B term) (C term) (D term)) (or (not (= ((ap A) C) ((ap B) D))) (= C D))) (=> (forall ((A term) (B term)) (or (not (= (lam A) (lam B))) (= A B))) (=> (forall ((A term) (B term)) (or (not (= ((sub A) sh) ((sub B) sh))) (= A B))) (=> _let_103 (=> _let_101 (=> _let_99 (=> (forall ((P (-> term Bool)) (BOUND_VARIABLE_3148 term)) (or (not (forall ((A term)) (or (not (var A)) (P A)))) (not (forall ((A term) (B term)) (or (not (P A)) (not (P B)) (P ((ap A) B))))) (not (forall ((A term)) (or (not (P A)) (P (lam A))))) (P BOUND_VARIABLE_3148))) (=> (forall ((P (-> term Bool)) (A term) (M subst) (BOUND_VARIABLE_3256 term)) (or (not (forall ((B term)) (or (not (var B)) (P ((sub B) M))))) (not (P A)) (not (var BOUND_VARIABLE_3256)) (P ((sub BOUND_VARIABLE_3256) ((push A) M))))) (=> (forall ((P (-> term Bool)) (BOUND_VARIABLE_3302 subst) (BOUND_VARIABLE_3300 term)) (or (not (forall ((A term) (B term)) (or (not (P A)) (not (P B)) (P ((ap A) B))))) (not (forall ((A term)) (or (not (forall ((B term)) (or (not (P B)) (P ((sub A) ((push B) ((push one) sh))))))) (P (lam A))))) (not (forall ((B term)) (or (not (var B)) (P ((sub B) BOUND_VARIABLE_3302))))) (P ((sub BOUND_VARIABLE_3300) BOUND_VARIABLE_3302)))) (forall ((P (-> term Bool)) (BOUND_VARIABLE_3347 term)) (or (not (forall ((A term)) (or (not (var A)) (P A)))) (not (forall ((A term) (B term)) (or (not (P A)) (not (P B)) (P ((ap A) B))))) (not (forall ((A term)) (or (not (forall ((B term)) (or (not (P B)) (P ((sub A) ((push B) ((push one) sh))))))) (P (lam A))))) (P BOUND_VARIABLE_3347)))))))))))))))))))))))))))) (not (=> (forall ((A term) (B term) (M subst)) (= (ho_16 (ho_15 k_14 (ho_11 (ho_10 k_9 A) M)) (ho_11 (ho_10 k_9 B) M)) (ho_11 (ho_10 k_9 (ho_16 (ho_15 k_14 A) B)) M))) (=> (forall ((A term) (M subst)) (= A (ho_11 (ho_10 k_9 one) (ho_3 (ho_2 k_1 A) M)))) (=> _let_153 (=> (forall ((A term) (M subst)) (= (ho_16 k_17 (ho_11 (ho_10 k_9 A) (ho_3 (ho_2 k_1 one) (ho_3 (ho_13 k_12 M) sh)))) (ho_11 (ho_10 k_9 (ho_16 k_17 A)) M))) (=> (forall ((A term) (M subst) (N subst)) (let ((_let_1 (ho_10 k_9 A))) (= (ho_11 _let_1 (ho_3 (ho_13 k_12 M) N)) (ho_11 (ho_10 k_9 (ho_11 _let_1 M)) N)))) (=> (forall ((M subst)) (= M (ho_3 (ho_13 k_12 (ho_3 (ho_2 k_1 one) sh)) M))) (=> (forall ((A term) (M subst)) (= M (ho_3 (ho_13 k_12 sh) (ho_3 (ho_2 k_1 A) M)))) (=> (forall ((M subst) (N subst) (K subst)) (let ((_let_1 (ho_13 k_12 M))) (= (ho_3 _let_1 (ho_3 (ho_13 k_12 N) K)) (ho_3 (ho_13 k_12 (ho_3 _let_1 N)) K)))) (=> (forall ((A term) (M subst) (N subst)) (= (ho_3 (ho_2 k_1 (ho_11 (ho_10 k_9 A) N)) (ho_3 (ho_13 k_12 M) N)) (ho_3 (ho_13 k_12 (ho_3 (ho_2 k_1 A) M)) N))) (=> (forall ((M subst)) (= M (ho_3 (ho_13 k_12 M) (ho_3 (ho_2 k_1 one) sh)))) (=> (forall ((M subst)) (= M (ho_3 (ho_2 k_1 (ho_11 (ho_10 k_9 one) M)) (ho_3 (ho_13 k_12 sh) M)))) (=> (ho_7 k_8 one) (=> (forall ((A term)) (or (not (ho_7 k_8 A)) (ho_7 k_8 (ho_11 (ho_10 k_9 A) sh)))) (=> (forall ((BOUND_VARIABLE_9069 |u_(-> term Bool)|) (BOUND_VARIABLE_3093 term)) (or (not (ho_7 BOUND_VARIABLE_9069 one)) (not (forall ((A term)) (or (not (ho_7 k_8 A)) (not (ho_7 BOUND_VARIABLE_9069 A)) (ho_7 BOUND_VARIABLE_9069 (ho_11 (ho_10 k_9 A) sh))))) (not (ho_7 k_8 BOUND_VARIABLE_3093)) (ho_7 BOUND_VARIABLE_9069 BOUND_VARIABLE_3093))) (=> (forall ((A term) (B term) (C term) (D term)) (or (not (= (ho_16 (ho_15 k_14 B) D) (ho_16 (ho_15 k_14 A) C))) (= A B))) (=> (forall ((A term) (B term) (C term) (D term)) (or (not (= (ho_16 (ho_15 k_14 B) D) (ho_16 (ho_15 k_14 A) C))) (= C D))) (=> (forall ((A term) (B term)) (or (not (= (ho_16 k_17 B) (ho_16 k_17 A))) (= A B))) (=> (forall ((A term) (B term)) (or (not (= (ho_11 (ho_10 k_9 B) sh) (ho_11 (ho_10 k_9 A) sh))) (= A B))) (=> (forall ((A term) (B term) (C term)) (not (= (ho_16 (ho_15 k_14 B) C) (ho_16 k_17 A)))) (=> (forall ((A term) (B term)) (not (ho_7 k_8 (ho_16 (ho_15 k_14 A) B)))) (=> (forall ((A term)) (not (ho_7 k_8 (ho_16 k_17 A)))) (=> _let_152 (=> _let_149 (=> _let_151 _let_150)))))))))))))))))))))))))))))))))) (let ((_let_269 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_268))))))))))))))))))))) (let ((_let_270 (NOT_IMPLIES_ELIM2 _let_269))) (let ((_let_271 (_let_149))) (let ((_let_272 (or _let_144 _let_142))) (let ((_let_273 (forall ((B term)) (or (not (ho_7 k_8 B)) (ho_7 skv_19 (ho_11 (ho_10 k_9 B) (ho_3 (ho_2 k_1 skv_26) (ho_3 (ho_2 k_1 one) sh)))))))) (let ((_let_274 (not _let_272))) (let ((_let_275 (ho_7 skv_19 (ho_11 (ho_10 k_9 skv_25) _let_141)))) (let ((_let_276 (not _let_273))) (let ((_let_277 (forall ((A term)) (or (not (forall ((B term)) (or (not (ho_7 skv_19 B)) (ho_7 skv_19 (ho_11 (ho_10 k_9 A) (ho_3 (ho_2 k_1 B) (ho_3 (ho_2 k_1 one) sh))))))) (ho_7 skv_19 (ho_16 k_17 A)))))) (let ((_let_278 (not _let_277))) (let ((_let_279 (forall ((A term) (B term)) (or (not (ho_7 skv_19 A)) (not (ho_7 skv_19 B)) (ho_7 skv_19 (ho_16 (ho_15 k_14 A) B)))))) (let ((_let_280 (not _let_279))) (let ((_let_281 (or _let_280 _let_278 _let_276 _let_275))) (let ((_let_282 (NOT_IMPLIES_ELIM2 _let_270))) (let ((_let_283 (_let_151))) (let ((_let_284 (forall ((A term)) (or (not (forall ((B term)) (or (not (ho_7 skv_19 B)) (ho_7 skv_19 (ho_11 (ho_10 k_9 A) (ho_3 (ho_2 k_1 B) (ho_3 (ho_2 k_1 one) sh))))))) (ho_7 skv_19 (ho_16 k_17 A)))))) (let ((_let_285 (ho_7 skv_19 skv_20))) (let ((_let_286 (not _let_284))) (let ((_let_287 (forall ((A term) (B term)) (or (not (ho_7 skv_19 A)) (not (ho_7 skv_19 B)) (ho_7 skv_19 (ho_16 (ho_15 k_14 A) B)))))) (let ((_let_288 (not _let_287))) (let ((_let_289 (forall ((A term)) (or (not (ho_7 k_8 A)) (ho_7 skv_19 A))))) (let ((_let_290 (not _let_289))) (let ((_let_291 (or _let_290 _let_288 _let_286 _let_285))) (let ((_let_292 (not _let_291))) (let ((_let_293 (20))) (let ((_let_294 (not _let_150))) (let ((_let_295 (_let_294))) (let ((_let_296 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_295)) |:args| _let_295)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_294) _let_150))) (REFL |:args| (_let_292)) |:args| _let_293)) (NOT_IMPLIES_ELIM2 _let_282) |:args| (_let_292 true _let_150)))) (let ((_let_297 (REFL |:args| (_let_291)))) (let ((_let_298 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_291 2)) (CONG _let_297 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_286) _let_284))) |:args| _let_293)) |:args| ((or _let_284 _let_291))) _let_296 |:args| (_let_284 true _let_291)))) (let ((_let_299 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_291 1)) (CONG _let_297 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_288) _let_287))) |:args| _let_293)) |:args| ((or _let_287 _let_291))) _let_296 |:args| (_let_287 true _let_291)))) (let ((_let_300 (or _let_146 _let_275))) (let ((_let_301 (forall ((B term)) (or (not (ho_7 skv_19 B)) (ho_7 skv_19 (ho_11 (ho_10 k_9 skv_25) (ho_3 (ho_2 k_1 B) (ho_3 (ho_2 k_1 one) sh)))))))) (let ((_let_302 (not _let_300))) (let ((_let_303 (ho_7 skv_19 (ho_16 k_17 skv_25)))) (let ((_let_304 (not _let_301))) (let ((_let_305 (or _let_304 _let_303))) (let ((_let_306 (_let_284))) (let ((_let_307 (or (not (ho_7 skv_19 skv_25)) _let_303))) (let ((_let_308 (forall ((A term)) (or (not (ho_7 skv_19 A)) (ho_7 skv_19 (ho_16 k_17 A)))))) (let ((_let_309 (not _let_307))) (let ((_let_310 (not _let_308))) (let ((_let_311 (forall ((A term) (B term)) (or (not (ho_7 skv_19 A)) (not (ho_7 skv_19 B)) (ho_7 skv_19 (ho_16 (ho_15 k_14 A) B)))))) (let ((_let_312 (not _let_311))) (let ((_let_313 (forall ((A term)) (or (not (ho_7 k_8 A)) (ho_7 skv_19 A))))) (let ((_let_314 (not _let_313))) (let ((_let_315 (or _let_314 _let_312 _let_310 _let_285))) (let ((_let_316 (_let_152))) (let ((_let_317 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_291 0)) (CONG _let_297 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_290) _let_289))) |:args| _let_293)) |:args| ((or _let_289 _let_291))) _let_296 |:args| (_let_289 true _let_291)))) (let ((_let_318 (_let_310))) (let ((_let_319 (_let_304))) (let ((_let_320 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_319)) |:args| _let_319)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_304) _let_301))) (REFL |:args| (_let_302)) |:args| _let_293)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_305)) |:args| ((or _let_303 _let_304 (not _let_305)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_307 1)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_318)) |:args| _let_318)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_310) _let_308))) (REFL |:args| (_let_309)) |:args| _let_293)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_315)) |:args| ((or _let_285 _let_314 _let_312 _let_310 (not _let_315)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_291 3)) _let_296 |:args| ((not _let_285) true _let_291)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM2 (THEORY_LEMMA |:args| ((= _let_313 _let_289) 12))) |:args| ((or _let_290 _let_313))) _let_317 |:args| (_let_313 false _let_289)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM2 (THEORY_LEMMA |:args| ((= _let_311 _let_287) 12))) |:args| ((or _let_288 _let_311))) _let_299 |:args| (_let_311 false _let_287)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_316) |:args| (skv_19 skv_20)) |:args| _let_316)) (NOT_IMPLIES_ELIM1 _let_269) |:args| (_let_315 false _let_152)) |:args| (_let_310 true _let_285 false _let_313 false _let_311 false _let_315)) |:args| (_let_309 true _let_308)) |:args| ((not _let_303) true _let_307)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_306) |:args| (skv_25)) |:args| _let_306)) _let_298 |:args| (_let_305 false _let_284)) |:args| (_let_304 true _let_303 false _let_305)) |:args| (_let_302 true _let_301)))) (let ((_let_321 (_let_276))) (let ((_let_322 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_321)) |:args| _let_321)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_276) _let_273))) (REFL |:args| (_let_274)) |:args| _let_293)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_281)) |:args| ((or _let_275 _let_280 _let_278 _let_276 (not _let_281)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_300 1)) _let_320 |:args| ((not _let_275) true _let_300)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM2 (THEORY_LEMMA |:args| ((= _let_279 _let_287) 12))) |:args| ((or _let_288 _let_279))) _let_299 |:args| (_let_279 false _let_287)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM2 (THEORY_LEMMA |:args| ((= _let_277 _let_284) 12))) |:args| ((or _let_286 _let_277))) _let_298 |:args| (_let_277 false _let_284)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_283) |:args| (skv_19 _let_141 skv_25)) |:args| _let_283)) (NOT_IMPLIES_ELIM1 _let_282) |:args| (_let_281 false _let_151)) |:args| (_let_276 true _let_275 false _let_279 false _let_277 false _let_281)) |:args| (_let_274 true _let_273)))) (let ((_let_323 (_let_147))) (let ((_let_324 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_323)) |:args| _let_323)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_147) _let_139))) (REFL |:args| (_let_140)) |:args| _let_293)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_148)) |:args| ((or _let_146 _let_147 _let_144 _let_142 (not _let_148)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_300 0)) (CONG (REFL |:args| (_let_300)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_146) _let_145))) |:args| _let_293)) |:args| ((or _let_145 _let_300))) _let_320 |:args| (_let_145 true _let_300)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_272 0)) (CONG (REFL |:args| (_let_272)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_144) _let_143))) |:args| _let_293)) |:args| ((or _let_143 _let_272))) _let_322 |:args| (_let_143 true _let_272)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_272 1)) _let_322 |:args| ((not _let_142) true _let_272)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_271) |:args| (skv_19 skv_26 _let_130 skv_29)) |:args| _let_271)) (NOT_IMPLIES_ELIM1 _let_270) |:args| (_let_148 false _let_149)) |:args| (_let_147 false _let_145 false _let_143 true _let_142 false _let_148)) |:args| (_let_140 true _let_139)))) (let ((_let_325 (_let_153))) (let ((_let_326 (skv_30))) (let ((_let_327 (or _let_136 _let_134))) (let ((_let_328 (_let_289))) (let ((_let_329 (not _let_134))) (let ((_let_330 (not _let_133))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME |:args| (_let_138)))) (CONG (REFL |:args| (skv_19)) (SYMM (ASSUME |:args| (_let_133))) |:args| (23 ho_7)) (TRUE_INTRO (ASSUME |:args| (_let_134))))) |:args| (_let_134 _let_133 _let_138))) (CONG (REFL |:args| (_let_329)) (REFL |:args| (_let_330)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_138) _let_132))) |:args| _let_293)) |:args| ((or _let_132 _let_330 _let_329))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_327)) |:args| ((or _let_136 _let_134 (not _let_327)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_137 0)) (CONG (REFL |:args| (_let_137)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_136) _let_135))) |:args| _let_293)) |:args| ((or _let_135 _let_137))) _let_324 |:args| (_let_135 true _let_137)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_328) |:args| _let_326) |:args| _let_328)) _let_317 |:args| (_let_327 false _let_289)) |:args| (_let_134 false _let_135 false _let_327)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_325) |:args| _let_326) |:args| _let_325)) (NOT_IMPLIES_ELIM1 _let_268) |:args| (_let_133 false _let_153)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_137 1)) _let_324 |:args| (_let_138 true _let_137)) |:args| (false false _let_134 false _let_133 true _let_132)) |:args| (_let_129 _let_127 _let_126 _let_125 _let_123 _let_121 _let_120 _let_119 _let_117 _let_115 _let_114 _let_113 _let_112 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_102 _let_100 _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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.59/0.78 ) 0.59/0.78 % SZS output end Proof for theBenchmark 0.59/0.78 EOF