0.00/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.12 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.12/0.33 % Computer : n006.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 : 960 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Thu Jul 2 07:35:00 EDT 2020 0.12/0.33 % CPUTime : 48.73/6.62 % SZS status Theorem 48.73/6.62 48.73/6.62 % SZS output start Proof 48.73/6.62 Take the following subset of the input axioms: 48.73/6.62 fof(thm_2Ebool_2Ebool__case__thm, axiom, ![A_27a]: (![V0t1_2E0, V1t2_2E0]: s(A_27a, c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(A_27a, V0t1_2E0), s(A_27a, V1t2_2E0)))=s(A_27a, V0t1_2E0) & ![V2t1_2E0, V3t2_2E0]: s(A_27a, V3t2_2E0)=s(A_27a, c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0), s(A_27a, V2t1_2E0), s(A_27a, V3t2_2E0))))). 48.73/6.63 fof(thm_2Einteger_2EINT__LT__CALCULATE, axiom, ![V0n_2E0, V1m_2E0]: (s(tyop_2Emin_2Ebool, c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum, V1m_2E0), s(tyop_2Enum_2Enum, V0n_2E0)))=s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0))))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V1m_2E0))))))) & (s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V1m_2E0)))))))=s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) & (((s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)!=s(tyop_2Enum_2Enum, V1m_2E0) | s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)!=s(tyop_2Enum_2Enum, V0n_2E0)) <=> p(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0))))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V1m_2E0))))))) & s(tyop_2Emin_2Ebool, c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum, V0n_2E0), s(tyop_2Enum_2Enum, V1m_2E0)))=s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V1m_2E0))))))))). 48.73/6.63 fof(thm_2Einteger_2EINT__NEG__0, axiom, s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))=s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))). 48.73/6.63 fof(thm_2Einteger_2ENUM__OF__INT, axiom, ![V0n_2E0]: s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0)))))=s(tyop_2Enum_2Enum, V0n_2E0)). 48.73/6.63 fof(thm_2Einteger__word_2Ei2w__0, conjecture, ![A_27a]: s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))=s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))). 48.73/6.63 fof(thm_2Einteger__word_2Ei2w__def, axiom, ![A_27a, V0i_2E0]: s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, V0i_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, V0i_2E0))))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, V0i_2E0)))))))=s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, V0i_2E0)))). 48.73/6.63 48.73/6.63 Now clausify the problem and encode Horn clauses using encoding 3 of 48.73/6.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 48.73/6.63 We repeatedly replace C & s=t => u=v by the two clauses: 48.73/6.63 fresh(y, y, x1...xn) = u 48.73/6.63 C => fresh(s, t, x1...xn) = v 48.73/6.63 where fresh is a fresh function symbol and x1..xn are the free 48.73/6.63 variables of u and v. 48.73/6.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the 48.73/6.63 input problem has no model of domain size 1). 48.73/6.63 48.73/6.63 The encoding turns the above axioms into the following unit equations and goals: 48.73/6.63 48.73/6.63 Axiom 1 (thm_2Ebool_2ECOND__CONG_1): fresh39(X, X, Y, Z, W, V, U, T, S) = s(Y, c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, Z), s(Y, V), s(Y, T))). 48.73/6.63 Axiom 2 (thm_2Ewords_2En2w__11): fresh2(X, X, Y, Z, W) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, Z))). 48.73/6.63 Axiom 3 (thm_2Einteger__word_2Ei2w__def): s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, Y), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, Y))))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, Y))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, Y))). 48.73/6.63 Axiom 4 (thm_2Einteger_2EINT__NEG__0): s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))) = s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))). 48.73/6.63 Axiom 5 (thm_2Ebool_2Ebool__case__thm_1): s(X, Y) = s(X, c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0), s(X, Z), s(X, Y))). 48.73/6.63 Axiom 6 (thm_2Einteger_2ENUM__OF__INT): s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, X))))) = s(tyop_2Enum_2Enum, X). 48.73/6.63 Axiom 7 (thm_2Einteger_2EINT__LT__CALCULATE_4): s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, X))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, Y))))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0). 48.73/6.63 48.73/6.63 Goal 1 (thm_2Einteger__word_2Ei2w__0): s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))). 48.73/6.63 Proof: 48.73/6.63 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) 48.73/6.63 = { by axiom 3 (thm_2Einteger__word_2Ei2w__def) } 48.73/6.63 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))))) 48.73/6.63 = { by axiom 1 (thm_2Ebool_2ECOND__CONG_1) } 48.88/6.63 fresh39(?, ?, tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))), ?, c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))))), ?, c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), ?) 48.88/6.63 = { by axiom 4 (thm_2Einteger_2EINT__NEG__0) } 48.88/6.63 fresh39(?, ?, tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), ?, c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))))), ?, c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), ?) 48.88/6.63 = { by axiom 2 (thm_2Ewords_2En2w__11) } 48.88/6.63 fresh39(?, ?, tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), ?, c_2Ewords_2Eword__2comp_2E1(fresh2(?, ?, sK4_thm_2Einteger__word_2Ei2w__0_A_27a, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), ?)), ?, c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), ?) 48.88/6.63 = { by axiom 1 (thm_2Ebool_2ECOND__CONG_1) } 48.88/6.63 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2Eword__2comp_2E1(fresh2(?, ?, sK4_thm_2Einteger__word_2Ei2w__0_A_27a, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), ?))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))))) 48.88/6.63 = { by axiom 7 (thm_2Einteger_2EINT__LT__CALCULATE_4) } 48.88/6.63 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2Eword__2comp_2E1(fresh2(?, ?, sK4_thm_2Einteger__word_2Ei2w__0_A_27a, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), ?))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))))) 48.88/6.63 = { by axiom 5 (thm_2Ebool_2Ebool__case__thm_1) } 48.88/6.63 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))) 48.88/6.63 = { by axiom 6 (thm_2Einteger_2ENUM__OF__INT) } 48.88/6.63 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, sK4_thm_2Einteger__word_2Ei2w__0_A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))) 48.88/6.63 % SZS output end Proof 48.88/6.63 48.88/6.63 RESULT: Theorem (the conjecture is true). 48.88/6.64 EOF