0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.12/0.33 % Computer : n020.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 16:29:10 EDT 2019 0.12/0.33 % CPUTime : 4.47/4.63 % SZS status Theorem 4.47/4.63 4.47/4.63 % SZS output start Proof 4.47/4.63 Take the following subset of the input axioms: 4.47/4.64 fof(conj_1, conjecture, ?[B_c]: c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt, hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt), v_a), hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt), v_b), hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt), B_c), c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt)))))). 4.47/4.64 fof(fact_Suc__n__not__n, axiom, ![V_n]: hAPP(c_Nat_OSuc, V_n)!=V_n). 4.47/4.64 fof(fact_Suc__neq__Zero, axiom, ![V_m]: c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc, V_m)). 4.47/4.64 fof(fact_Suc__not__Zero, axiom, ![V_m]: c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc, V_m)). 4.47/4.64 fof(fact_Zero__neq__Suc, axiom, ![V_m]: hAPP(c_Nat_OSuc, V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). 4.47/4.64 fof(fact_Zero__not__Suc, axiom, ![V_m]: hAPP(c_Nat_OSuc, V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). 4.47/4.64 fof(fact_dropWhile__eq__Cons__conv, axiom, ![T_a, V_y_2, V_P_2, V_xs_2, V_ys_2]: (c_List_OdropWhile(T_a, V_P_2, V_xs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a), V_y_2), V_ys_2) <=> (~hBOOL(hAPP(V_P_2, V_y_2)) & V_xs_2=hAPP(hAPP(c_List_Oappend(T_a), c_List_OtakeWhile(T_a, V_P_2, V_xs_2)), hAPP(hAPP(c_List_Olist_OCons(T_a), V_y_2), V_ys_2))))). 4.47/4.64 fof(fact_ext, axiom, ![V_f_2, V_g_2]: (V_g_2=V_f_2 <= ![B_x]: hAPP(V_f_2, B_x)=hAPP(V_g_2, B_x))). 4.47/4.64 fof(fact_gr__implies__not0, axiom, ![V_m, V_n]: (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <= hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m), V_n)))). 4.47/4.64 fof(fact_insort__not__Nil, axiom, ![T_a, V_xs_2, V_aa_2, V_f_2, T_b]: (c_List_Olist_ONil(T_a)!=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a, T_b, V_f_2), V_aa_2), V_xs_2) <= class_Orderings_Olinorder(T_b))). 4.47/4.64 fof(fact_int__less__0__conv, axiom, ![V_k]: ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint, V_k)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 4.47/4.64 fof(fact_length__greater__0__conv, axiom, ![T_a, V_xs_2]: (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)), V_xs_2))) <=> V_xs_2!=c_List_Olist_ONil(T_a))). 4.47/4.64 fof(fact_less__imp__neq, axiom, ![V_y, V_x, T_a]: (class_Orderings_Oorder(T_a) => (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_x), V_y)) => V_x!=V_y))). 4.47/4.64 fof(fact_less__irrefl__nat, axiom, ![V_n]: ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n), V_n))). 4.47/4.64 fof(fact_less__nat__zero__code, axiom, ![V_n]: ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). 4.47/4.64 fof(fact_less__not__refl, axiom, ![V_n]: ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n), V_n))). 4.47/4.64 fof(fact_less__not__refl2, axiom, ![V_m, V_n]: (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n), V_m)) => V_n!=V_m)). 4.47/4.64 fof(fact_less__not__refl3, axiom, ![V_t, V_s]: (V_s!=V_t <= hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_s), V_t)))). 4.47/4.64 fof(fact_less__zeroE, axiom, ![V_n]: ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). 4.47/4.64 fof(fact_linorder__neq__iff, axiom, ![T_a, V_y_2, V_x_2]: (class_Orderings_Olinorder(T_a) => (V_y_2!=V_x_2 <=> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_y_2), V_x_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_x_2), V_y_2)))))). 4.47/4.64 fof(fact_list_Osimps_I2_J, axiom, ![T_a, V_list_H, V_a_H]: c_List_Olist_ONil(T_a)!=hAPP(hAPP(c_List_Olist_OCons(T_a), V_a_H), V_list_H)). 4.47/4.64 fof(fact_list_Osimps_I3_J, axiom, ![T_a, V_list_H, V_a_H]: hAPP(hAPP(c_List_Olist_OCons(T_a), V_a_H), V_list_H)!=c_List_Olist_ONil(T_a)). 4.47/4.64 fof(fact_list__ex1__simps_I1_J, axiom, ![T_a, V_P_2]: ~c_List_Olist__ex1(T_a, V_P_2, c_List_Olist_ONil(T_a))). 4.47/4.64 fof(fact_list__ex__simps_I2_J, axiom, ![T_a, V_P_2]: ~c_List_Olist__ex(T_a, V_P_2, c_List_Olist_ONil(T_a))). 4.47/4.64 fof(fact_member__rec_I2_J, axiom, ![V_y, T_a]: ~c_List_Omember(T_a, c_List_Olist_ONil(T_a), V_y)). 4.47/4.64 fof(fact_n__not__Suc__n, axiom, ![V_n]: V_n!=hAPP(c_Nat_OSuc, V_n)). 4.47/4.64 fof(fact_nat_Osimps_I2_J, axiom, ![V_nat_H]: hAPP(c_Nat_OSuc, V_nat_H)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). 4.47/4.64 fof(fact_nat_Osimps_I3_J, axiom, ![V_nat_H_1]: hAPP(c_Nat_OSuc, V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). 4.47/4.64 fof(fact_nat__less__cases, axiom, ![V_n_2, V_P_2, V_m_2]: ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2), V_n_2)) => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2))) => ((V_m_2=V_n_2 => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2))) => (hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2)) <= (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2), V_m_2)) => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2))))))). 4.47/4.64 fof(fact_nat__neq__iff, axiom, ![V_n_2, V_m_2]: ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2), V_n_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2), V_m_2))) <=> V_m_2!=V_n_2)). 4.47/4.64 fof(fact_neq0__conv, axiom, ![V_n_2]: (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), V_n_2)) <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=V_n_2)). 4.47/4.64 fof(fact_neq__Nil__conv, axiom, ![T_a, V_xs_2]: (?[B_y, B_ys]: hAPP(hAPP(c_List_Olist_OCons(T_a), B_y), B_ys)=V_xs_2 <=> V_xs_2!=c_List_Olist_ONil(T_a))). 4.47/4.64 fof(fact_not__Cons__self, axiom, ![V_x, T_a, V_xs]: V_xs!=hAPP(hAPP(c_List_Olist_OCons(T_a), V_x), V_xs)). 4.47/4.64 fof(fact_not__Cons__self2, axiom, ![V_x, T_a, V_xs]: hAPP(hAPP(c_List_Olist_OCons(T_a), V_x), V_xs)!=V_xs). 4.47/4.64 fof(fact_not__add__less1, axiom, ![V_i, V_j]: ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), V_i), V_j)), V_i))). 4.47/4.64 fof(fact_not__add__less2, axiom, ![V_i, V_j]: ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), V_j), V_i)), V_i))). 4.47/4.64 fof(fact_not__less0, axiom, ![V_n]: ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). 4.47/4.64 fof(fact_not__less__eq, axiom, ![V_n_2, V_m_2]: (~hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2), V_n_2)) <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2), hAPP(c_Nat_OSuc, V_m_2))))). 4.47/4.64 fof(fact_not__less__iff__gr__or__eq, axiom, ![T_a, V_y_2, V_x_2]: (class_Orderings_Olinorder(T_a) => (~hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_x_2), V_y_2)) <=> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_y_2), V_x_2)) | V_y_2=V_x_2)))). 4.47/4.64 fof(fact_nth__length__takeWhile, axiom, ![T_a, V_P_2, V_xs_2]: (~hBOOL(hAPP(V_P_2, hAPP(c_List_Onth(T_a, V_xs_2), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)), c_List_OtakeWhile(T_a, V_P_2, V_xs_2))))) <= hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)), c_List_OtakeWhile(T_a, V_P_2, V_xs_2))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)), V_xs_2))))). 4.47/4.64 fof(fact_null__rec_I1_J, axiom, ![V_x, T_a, V_xs]: ~c_List_Onull(T_a, hAPP(hAPP(c_List_Olist_OCons(T_a), V_x), V_xs))). 4.47/4.64 fof(fact_of__nat__less__0__iff, axiom, ![T_a, V_m]: (class_Rings_Olinordered__semidom(T_a) => ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, c_Nat_Osemiring__1__class_Oof__nat(T_a, V_m)), c_Groups_Ozero__class_Ozero(T_a))))). 4.47/4.64 fof(fact_order__less__asym, axiom, ![V_y, V_x, T_a]: (class_Orderings_Opreorder(T_a) => (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_x), V_y)) => ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_y), V_x))))). 4.47/4.64 fof(fact_order__less__asym_H, axiom, ![T_a, V_b, V_a]: (class_Orderings_Opreorder(T_a) => (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_a), V_b)) => ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_b), V_a))))). 4.47/4.64 fof(fact_order__less__imp__not__eq, axiom, ![V_y, V_x, T_a]: ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_x), V_y)) => V_x!=V_y) <= class_Orderings_Oorder(T_a))). 4.47/4.64 fof(fact_order__less__imp__not__eq2, axiom, ![V_y, V_x, T_a]: (class_Orderings_Oorder(T_a) => (V_y!=V_x <= hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_x), V_y))))). 4.47/4.64 fof(fact_order__less__imp__not__less, axiom, ![V_y, V_x, T_a]: ((~hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_y), V_x)) <= hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_x), V_y))) <= class_Orderings_Opreorder(T_a))). 4.47/4.64 fof(fact_order__less__irrefl, axiom, ![V_x, T_a]: (class_Orderings_Opreorder(T_a) => ~hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_x), V_x)))). 4.47/4.64 fof(fact_order__less__not__sym, axiom, ![V_y, V_x, T_a]: (class_Orderings_Opreorder(T_a) => (~hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_y), V_x)) <= hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_x), V_y))))). 4.47/4.64 fof(fact_snoc__eq__iff__butlast, axiom, ![T_a, V_x_2, V_xs_2, V_ys_2]: (V_ys_2=hAPP(hAPP(c_List_Oappend(T_a), V_xs_2), hAPP(hAPP(c_List_Olist_OCons(T_a), V_x_2), c_List_Olist_ONil(T_a))) <=> (c_List_Obutlast(T_a, V_ys_2)=V_xs_2 & (c_List_Olast(T_a, V_ys_2)=V_x_2 & V_ys_2!=c_List_Olist_ONil(T_a))))). 4.47/4.64 fof(fact_xt1_I9_J, axiom, ![T_a, V_b, V_a]: (class_Orderings_Oorder(T_a) => (~hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_a), V_b)) <= hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a, V_b), V_a))))). 4.47/4.64 fof(help_c__COMBI__1, axiom, ![T_a, V_P]: hAPP(c_COMBI(T_a), V_P)=V_P). 4.47/4.64 fof(help_c__COMBS__1, axiom, ![T_a, V_P_2, T_b, V_Q_2, V_R_2, T_c]: hAPP(c_COMBS(T_b, T_c, T_a, V_P_2, V_Q_2), V_R_2)=hAPP(hAPP(V_P_2, V_R_2), hAPP(V_Q_2, V_R_2))). 4.47/4.64 fof(help_c__fNot__1, axiom, ![V_P_2]: (~hBOOL(hAPP(c_fNot, V_P_2)) | ~hBOOL(V_P_2))). 4.47/4.64 4.47/4.64 Now clausify the problem and encode Horn clauses using encoding 3 of 4.47/4.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 4.47/4.64 We repeatedly replace C & s=t => u=v by the two clauses: 4.47/4.64 fresh(y, y, x1...xn) = u 4.47/4.64 C => fresh(s, t, x1...xn) = v 4.47/4.64 where fresh is a fresh function symbol and x1..xn are the free 4.47/4.64 variables of u and v. 4.47/4.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the 4.47/4.64 input problem has no model of domain size 1). 4.47/4.64 4.47/4.64 The encoding turns the above axioms into the following unit equations and goals: 4.47/4.64 4.47/4.64 Axiom 1 (fact_ext): fresh12(X, X, Y, Z) = Z. 4.47/4.64 Axiom 2 (help_c__COMBS__1): hAPP(c_COMBS(X, Y, Z, W, V), U) = hAPP(hAPP(W, U), hAPP(V, U)). 4.47/4.64 Axiom 3 (fact_ext): fresh12(hAPP(X, sK5_fact_ext_B_x(Y, X)), hAPP(Y, sK5_fact_ext_B_x(Y, X)), Y, X) = Y. 4.47/4.64 Axiom 4 (help_c__COMBI__1): hAPP(c_COMBI(X), Y) = Y. 4.47/4.64 4.47/4.64 Lemma 5: fresh12(sK5_fact_ext_B_x(X, c_COMBI(Y)), hAPP(X, sK5_fact_ext_B_x(X, c_COMBI(Y))), X, c_COMBI(Y)) = X. 4.47/4.64 Proof: 4.47/4.64 fresh12(sK5_fact_ext_B_x(X, c_COMBI(Y)), hAPP(X, sK5_fact_ext_B_x(X, c_COMBI(Y))), X, c_COMBI(Y)) 4.47/4.64 = { by axiom 4 (help_c__COMBI__1) } 4.47/4.64 fresh12(hAPP(c_COMBI(Y), sK5_fact_ext_B_x(X, c_COMBI(Y))), hAPP(X, sK5_fact_ext_B_x(X, c_COMBI(Y))), X, c_COMBI(Y)) 4.47/4.64 = { by axiom 3 (fact_ext) } 4.47/4.64 X 4.47/4.64 4.47/4.64 Lemma 6: c_COMBI(X) = c_COMBI(?). 4.47/4.64 Proof: 4.47/4.64 c_COMBI(X) 4.47/4.64 = { by lemma 5 } 4.47/4.64 fresh12(sK5_fact_ext_B_x(c_COMBI(X), c_COMBI(Y)), hAPP(c_COMBI(X), sK5_fact_ext_B_x(c_COMBI(X), c_COMBI(Y))), c_COMBI(X), c_COMBI(Y)) 4.47/4.64 = { by axiom 4 (help_c__COMBI__1) } 4.47/4.64 fresh12(sK5_fact_ext_B_x(c_COMBI(X), c_COMBI(Y)), sK5_fact_ext_B_x(c_COMBI(X), c_COMBI(Y)), c_COMBI(X), c_COMBI(Y)) 4.47/4.64 = { by axiom 1 (fact_ext) } 4.47/4.64 c_COMBI(Y) 4.47/4.64 = { by axiom 1 (fact_ext) } 4.47/4.64 fresh12(sK5_fact_ext_B_x(c_COMBI(?), c_COMBI(Y)), sK5_fact_ext_B_x(c_COMBI(?), c_COMBI(Y)), c_COMBI(?), c_COMBI(Y)) 4.47/4.64 = { by axiom 4 (help_c__COMBI__1) } 4.47/4.64 fresh12(sK5_fact_ext_B_x(c_COMBI(?), c_COMBI(Y)), hAPP(c_COMBI(?), sK5_fact_ext_B_x(c_COMBI(?), c_COMBI(Y))), c_COMBI(?), c_COMBI(Y)) 4.47/4.64 = { by lemma 5 } 4.47/4.64 c_COMBI(?) 4.47/4.64 4.47/4.64 Goal 1 (fact_not__Cons__self): X = hAPP(hAPP(c_List_Olist_OCons(Y), Z), X). 4.47/4.64 The goal is true when: 4.47/4.64 X = hAPP(c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?)), c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?)))) 4.47/4.64 Y = ? 4.47/4.64 Z = c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?))) 4.47/4.64 where "?" stands for an arbitrary term of your choice. 4.47/4.64 4.47/4.64 Proof: 4.47/4.64 hAPP(c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?)), c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?)))) 4.47/4.64 = { by axiom 2 (help_c__COMBS__1) } 4.47/4.64 hAPP(hAPP(c_COMBI(?), c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?)))), hAPP(c_COMBI(?), c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?))))) 4.47/4.64 = { by axiom 4 (help_c__COMBI__1) } 4.47/4.64 hAPP(c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?))), hAPP(c_COMBI(?), c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?))))) 4.47/4.64 = { by axiom 4 (help_c__COMBI__1) } 4.47/4.64 hAPP(c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?))), c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?)))) 4.47/4.64 = { by axiom 2 (help_c__COMBS__1) } 4.47/4.64 hAPP(hAPP(c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?)))), hAPP(c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?)), c_COMBS(?, ?, ?, c_List_Olist_OCons(?), c_COMBS(?, ?, ?, c_COMBI(?), c_COMBI(?))))) 4.47/4.64 % SZS output end Proof 4.47/4.64 4.47/4.64 RESULT: Theorem (the conjecture is true). 4.47/4.65 EOF