%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG216+1 : TPTP v8.1.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 14 15:37:34 EDT 2022 % Result : Theorem 4.69s 1.70s % Output : Proof 9.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : ALG216+1 : TPTP v8.1.0. Released v3.4.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n021.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Thu Jun 9 06:14:53 EDT 2022 % 0.11/0.32 % CPUTime : % 0.18/0.58 ____ _ % 0.18/0.58 ___ / __ \_____(_)___ ________ __________ % 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.58 % 0.18/0.58 A Theorem Prover for First-Order Logic % 0.18/0.59 (ePrincess v.1.0) % 0.18/0.59 % 0.18/0.59 (c) Philipp Rümmer, 2009-2015 % 0.18/0.59 (c) Peter Backeman, 2014-2015 % 0.18/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.59 Bug reports to peter@backeman.se % 0.18/0.59 % 0.18/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.59 % 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.68/0.99 Prover 0: Preprocessing ... % 2.66/1.28 Prover 0: Warning: ignoring some quantifiers % 2.66/1.31 Prover 0: Constructing countermodel ... % 4.69/1.70 Prover 0: proved (1031ms) % 4.69/1.70 % 4.69/1.70 No countermodel exists, formula is valid % 4.69/1.70 % SZS status Theorem for theBenchmark % 4.69/1.70 % 4.69/1.70 Generating proof ... Warning: ignoring some quantifiers % 8.74/2.67 found it (size 78) % 8.74/2.67 % 8.74/2.67 % SZS output start Proof for theBenchmark % 8.74/2.67 Assumed formulas after preprocessing and simplification: % 8.74/2.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ( ~ (v2 = v1) & k2_group_1(v0) = v2 & k1_rlvect_1(v3) = v5 & k1_rlvect_1(v0) = v1 & k8_rlvect_2(v3, v6, v5) = v7 & k8_rlvect_2(v3, v5, v6) = v8 & u1_struct_0(v3) = v4 & l2_vectsp_1(v12) & l2_struct_0(v13) & l2_struct_0(v10) & l1_rlvect_1(v15) & l1_struct_0(v14) & l1_struct_0(v11) & l1_group_1(v16) & l1_vectsp_1(v19) & v1_xboole_0(v18) & v1_xboole_0(k1_xboole_0) & m1_subset_1(v6, v4) & l1_vectsp_2(v3, v0) & v5_vectsp_2(v3, v0) & l3_vectsp_1(v9) & l3_vectsp_1(v0) & v8_vectsp_1(v0) & v7_vectsp_1(v0) & v6_vectsp_1(v0) & v4_group_1(v0) & v6_rlvect_1(v3) & v6_rlvect_1(v0) & v5_rlvect_1(v3) & v5_rlvect_1(v0) & v4_rlvect_1(v3) & v4_rlvect_1(v0) & v3_rlvect_1(v3) & v3_rlvect_1(v0) & ~ v1_xboole_0(v17) & ~ v3_struct_0(v11) & ~ v3_struct_0(v10) & ~ v3_struct_0(v3) & ~ v3_struct_0(v0) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v21 = v20 | ~ (k8_rlvect_2(v24, v23, v22) = v21) | ~ (k8_rlvect_2(v24, v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (k2_tarski(v21, v22) = v24) | ~ (u1_struct_0(v20) = v23) | ~ l1_struct_0(v20) | ~ m1_subset_1(v22, v23) | ~ m1_subset_1(v21, v23) | k8_rlvect_2(v20, v21, v22) = v24 | v3_struct_0(v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (k2_tarski(v23, v22) = v21) | ~ (k2_tarski(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (k8_rlvect_2(v20, v22, v21) = v23) | ~ l1_struct_0(v20) | v3_struct_0(v20) | ? [v24] : ? [v25] : (k8_rlvect_2(v20, v21, v22) = v25 & u1_struct_0(v20) = v24 & (v25 = v23 | ~ m1_subset_1(v22, v24) | ~ m1_subset_1(v21, v24)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (k8_rlvect_2(v20, v21, v22) = v23) | ~ l1_struct_0(v20) | v3_struct_0(v20) | ? [v24] : ? [v25] : (k8_rlvect_2(v20, v22, v21) = v25 & u1_struct_0(v20) = v24 & (v25 = v23 | ~ m1_subset_1(v22, v24) | ~ m1_subset_1(v21, v24)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (k8_rlvect_2(v20, v21, v22) = v23) | ~ l1_struct_0(v20) | v3_struct_0(v20) | ? [v24] : ? [v25] : (k2_tarski(v21, v22) = v25 & u1_struct_0(v20) = v24 & (v25 = v23 | ~ m1_subset_1(v22, v24) | ~ m1_subset_1(v21, v24)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (k8_rlvect_2(v20, v21, v22) = v23) | ~ l1_struct_0(v20) | v3_struct_0(v20) | ? [v24] : ? [v25] : (u1_struct_0(v20) = v24 & k1_zfmisc_1(v24) = v25 & ( ~ m1_subset_1(v22, v24) | ~ m1_subset_1(v21, v24) | (v1_finset_1(v23) & m1_subset_1(v23, v25))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (k1_zfmisc_1(v22) = v23) | ~ v1_xboole_0(v22) | ~ r2_hidden(v20, v21) | ~ m1_subset_1(v21, v23)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (k1_zfmisc_1(v22) = v23) | ~ r2_hidden(v20, v21) | ~ m1_subset_1(v21, v23) | m1_subset_1(v20, v22)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (k2_group_1(v22) = v21) | ~ (k2_group_1(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (k1_rlvect_1(v22) = v21) | ~ (k1_rlvect_1(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (u1_struct_0(v22) = v21) | ~ (u1_struct_0(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (k1_zfmisc_1(v22) = v21) | ~ (k1_zfmisc_1(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (k2_tarski(v21, v20) = v22) | k2_tarski(v20, v21) = v22) & ! [v20] : ! [v21] : ! [v22] : ( ~ (k2_tarski(v20, v21) = v22) | ~ v1_xboole_0(v22)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (k2_tarski(v20, v21) = v22) | k2_tarski(v21, v20) = v22) & ! [v20] : ! [v21] : ! [v22] : ( ~ (k1_zfmisc_1(v21) = v22) | ~ r1_tarski(v20, v21) | m1_subset_1(v20, v22)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (k1_zfmisc_1(v21) = v22) | ~ m1_subset_1(v20, v22) | r1_tarski(v20, v21)) & ! [v20] : ! [v21] : (v21 = v20 | ~ v1_xboole_0(v21) | ~ v1_xboole_0(v20)) & ! [v20] : ! [v21] : ( ~ (k2_group_1(v20) = v21) | ~ l1_group_1(v20) | v3_struct_0(v20) | ? [v22] : (u1_struct_0(v20) = v22 & m1_subset_1(v21, v22))) & ! [v20] : ! [v21] : ( ~ (k2_group_1(v20) = v21) | ~ l3_vectsp_1(v20) | ~ v8_vectsp_1(v20) | ~ v7_vectsp_1(v20) | ~ v6_vectsp_1(v20) | ~ v4_group_1(v20) | ~ v6_rlvect_1(v20) | ~ v5_rlvect_1(v20) | ~ v4_rlvect_1(v20) | ~ v3_rlvect_1(v20) | v3_struct_0(v20) | ? [v22] : (k1_rlvect_1(v20) = v22 & ! [v23] : ! [v24] : ( ~ (k1_rlvect_1(v23) = v24) | ~ l1_vectsp_2(v23, v20) | ~ v5_vectsp_2(v23, v20) | ~ v6_rlvect_1(v23) | ~ v5_rlvect_1(v23) | ~ v4_rlvect_1(v23) | ~ v3_rlvect_1(v23) | v3_struct_0(v23) | ? [v25] : (u1_struct_0(v23) = v25 & ! [v26] : ! [v27] : (v22 = v21 | ~ (k8_rlvect_2(v23, v26, v24) = v27) | ~ v1_rmod_5(v27, v20, v23) | ~ m1_subset_1(v26, v25) | ~ m1_subset_1(v24, v25)) & ! [v26] : ! [v27] : (v22 = v21 | ~ (k8_rlvect_2(v23, v24, v26) = v27) | ~ v1_rmod_5(v27, v20, v23) | ~ m1_subset_1(v26, v25) | ~ m1_subset_1(v24, v25)))) & ! [v23] : ! [v24] : ( ~ (u1_struct_0(v23) = v24) | ~ l1_vectsp_2(v23, v20) | ~ v5_vectsp_2(v23, v20) | ~ v6_rlvect_1(v23) | ~ v5_rlvect_1(v23) | ~ v4_rlvect_1(v23) | ~ v3_rlvect_1(v23) | v3_struct_0(v23) | ? [v25] : (k1_rlvect_1(v23) = v25 & ! [v26] : ! [v27] : (v22 = v21 | ~ (k8_rlvect_2(v23, v26, v25) = v27) | ~ v1_rmod_5(v27, v20, v23) | ~ m1_subset_1(v26, v24) | ~ m1_subset_1(v25, v24)) & ! [v26] : ! [v27] : (v22 = v21 | ~ (k8_rlvect_2(v23, v25, v26) = v27) | ~ v1_rmod_5(v27, v20, v23) | ~ m1_subset_1(v26, v24) | ~ m1_subset_1(v25, v24)))))) & ! [v20] : ! [v21] : ( ~ (k1_rlvect_1(v20) = v21) | ~ l2_struct_0(v20) | ? [v22] : (u1_struct_0(v20) = v22 & m1_subset_1(v21, v22))) & ! [v20] : ! [v21] : ( ~ (k1_rlvect_1(v20) = v21) | ~ l3_vectsp_1(v20) | ~ v8_vectsp_1(v20) | ~ v7_vectsp_1(v20) | ~ v6_vectsp_1(v20) | ~ v4_group_1(v20) | ~ v6_rlvect_1(v20) | ~ v5_rlvect_1(v20) | ~ v4_rlvect_1(v20) | ~ v3_rlvect_1(v20) | v3_struct_0(v20) | ? [v22] : (k2_group_1(v20) = v22 & ! [v23] : ! [v24] : ( ~ (k1_rlvect_1(v23) = v24) | ~ l1_vectsp_2(v23, v20) | ~ v5_vectsp_2(v23, v20) | ~ v6_rlvect_1(v23) | ~ v5_rlvect_1(v23) | ~ v4_rlvect_1(v23) | ~ v3_rlvect_1(v23) | v3_struct_0(v23) | ? [v25] : (u1_struct_0(v23) = v25 & ! [v26] : ! [v27] : (v22 = v21 | ~ (k8_rlvect_2(v23, v26, v24) = v27) | ~ v1_rmod_5(v27, v20, v23) | ~ m1_subset_1(v26, v25) | ~ m1_subset_1(v24, v25)) & ! [v26] : ! [v27] : (v22 = v21 | ~ (k8_rlvect_2(v23, v24, v26) = v27) | ~ v1_rmod_5(v27, v20, v23) | ~ m1_subset_1(v26, v25) | ~ m1_subset_1(v24, v25)))) & ! [v23] : ! [v24] : ( ~ (u1_struct_0(v23) = v24) | ~ l1_vectsp_2(v23, v20) | ~ v5_vectsp_2(v23, v20) | ~ v6_rlvect_1(v23) | ~ v5_rlvect_1(v23) | ~ v4_rlvect_1(v23) | ~ v3_rlvect_1(v23) | v3_struct_0(v23) | ? [v25] : (k1_rlvect_1(v23) = v25 & ! [v26] : ! [v27] : (v22 = v21 | ~ (k8_rlvect_2(v23, v26, v25) = v27) | ~ v1_rmod_5(v27, v20, v23) | ~ m1_subset_1(v26, v24) | ~ m1_subset_1(v25, v24)) & ! [v26] : ! [v27] : (v22 = v21 | ~ (k8_rlvect_2(v23, v25, v26) = v27) | ~ v1_rmod_5(v27, v20, v23) | ~ m1_subset_1(v26, v24) | ~ m1_subset_1(v25, v24)))))) & ! [v20] : ! [v21] : ( ~ (u1_struct_0(v20) = v21) | ~ l2_struct_0(v20) | ? [v22] : (k1_rlvect_1(v20) = v22 & m1_subset_1(v22, v21))) & ! [v20] : ! [v21] : ( ~ (u1_struct_0(v20) = v21) | ~ l1_struct_0(v20) | ~ v1_xboole_0(v21) | v3_struct_0(v20)) & ! [v20] : ! [v21] : ( ~ (u1_struct_0(v20) = v21) | ~ l1_struct_0(v20) | v3_struct_0(v20) | ? [v22] : ? [v23] : (k1_zfmisc_1(v21) = v22 & v1_finset_1(v23) & m1_subset_1(v23, v22) & ~ v1_xboole_0(v23))) & ! [v20] : ! [v21] : ( ~ (u1_struct_0(v20) = v21) | ~ l1_struct_0(v20) | v3_struct_0(v20) | ? [v22] : ? [v23] : (k1_zfmisc_1(v21) = v22 & m1_subset_1(v23, v22) & ~ v1_xboole_0(v23))) & ! [v20] : ! [v21] : ( ~ (u1_struct_0(v20) = v21) | ~ l1_group_1(v20) | v3_struct_0(v20) | ? [v22] : (k2_group_1(v20) = v22 & m1_subset_1(v22, v21))) & ! [v20] : ! [v21] : ( ~ (k1_zfmisc_1(v20) = v21) | ~ v1_xboole_0(v21)) & ! [v20] : ! [v21] : ( ~ (k1_zfmisc_1(v20) = v21) | v1_xboole_0(v20) | ? [v22] : (m1_subset_1(v22, v21) & ~ v1_xboole_0(v22))) & ! [v20] : ! [v21] : ( ~ (k1_zfmisc_1(v20) = v21) | ? [v22] : (v1_xboole_0(v22) & m1_subset_1(v22, v21))) & ! [v20] : ! [v21] : ( ~ l1_struct_0(v20) | ~ l1_vectsp_2(v21, v20) | l1_rlvect_1(v21)) & ! [v20] : ! [v21] : ( ~ v1_xboole_0(v21) | ~ r2_hidden(v20, v21)) & ! [v20] : ! [v21] : ( ~ r2_hidden(v21, v20) | ~ r2_hidden(v20, v21)) & ! [v20] : ! [v21] : ( ~ r2_hidden(v20, v21) | m1_subset_1(v20, v21)) & ! [v20] : ! [v21] : ( ~ m1_subset_1(v20, v21) | v1_xboole_0(v21) | r2_hidden(v20, v21)) & ! [v20] : (v20 = k1_xboole_0 | ~ v1_xboole_0(v20)) & ! [v20] : ( ~ l2_vectsp_1(v20) | l2_struct_0(v20)) & ! [v20] : ( ~ l2_vectsp_1(v20) | l1_vectsp_1(v20)) & ! [v20] : ( ~ l2_struct_0(v20) | l1_struct_0(v20)) & ! [v20] : ( ~ l1_rlvect_1(v20) | l2_struct_0(v20)) & ! [v20] : ( ~ l1_struct_0(v20) | ? [v21] : (l1_vectsp_2(v21, v20) & ~ v3_struct_0(v21))) & ! [v20] : ( ~ l1_struct_0(v20) | ? [v21] : l1_vectsp_2(v21, v20)) & ! [v20] : ( ~ l1_group_1(v20) | l1_struct_0(v20)) & ! [v20] : ( ~ l1_vectsp_1(v20) | l1_group_1(v20)) & ! [v20] : ( ~ l3_vectsp_1(v20) | l2_vectsp_1(v20)) & ! [v20] : ( ~ l3_vectsp_1(v20) | l1_rlvect_1(v20)) & ? [v20] : ? [v21] : m1_subset_1(v21, v20) & ? [v20] : r1_tarski(v20, v20) & (v1_rmod_5(v8, v0, v3) | v1_rmod_5(v7, v0, v3))) % 9.12/2.72 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19 yields: % 9.12/2.72 | (1) ~ (all_0_17_17 = all_0_18_18) & k2_group_1(all_0_19_19) = all_0_17_17 & k1_rlvect_1(all_0_16_16) = all_0_14_14 & k1_rlvect_1(all_0_19_19) = all_0_18_18 & k8_rlvect_2(all_0_16_16, all_0_13_13, all_0_14_14) = all_0_12_12 & k8_rlvect_2(all_0_16_16, all_0_14_14, all_0_13_13) = all_0_11_11 & u1_struct_0(all_0_16_16) = all_0_15_15 & l2_vectsp_1(all_0_7_7) & l2_struct_0(all_0_6_6) & l2_struct_0(all_0_9_9) & l1_rlvect_1(all_0_4_4) & l1_struct_0(all_0_5_5) & l1_struct_0(all_0_8_8) & l1_group_1(all_0_3_3) & l1_vectsp_1(all_0_0_0) & v1_xboole_0(all_0_1_1) & v1_xboole_0(k1_xboole_0) & m1_subset_1(all_0_13_13, all_0_15_15) & l1_vectsp_2(all_0_16_16, all_0_19_19) & v5_vectsp_2(all_0_16_16, all_0_19_19) & l3_vectsp_1(all_0_10_10) & l3_vectsp_1(all_0_19_19) & v8_vectsp_1(all_0_19_19) & v7_vectsp_1(all_0_19_19) & v6_vectsp_1(all_0_19_19) & v4_group_1(all_0_19_19) & v6_rlvect_1(all_0_16_16) & v6_rlvect_1(all_0_19_19) & v5_rlvect_1(all_0_16_16) & v5_rlvect_1(all_0_19_19) & v4_rlvect_1(all_0_16_16) & v4_rlvect_1(all_0_19_19) & v3_rlvect_1(all_0_16_16) & v3_rlvect_1(all_0_19_19) & ~ v1_xboole_0(all_0_2_2) & ~ v3_struct_0(all_0_8_8) & ~ v3_struct_0(all_0_9_9) & ~ v3_struct_0(all_0_16_16) & ~ v3_struct_0(all_0_19_19) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k8_rlvect_2(v4, v3, v2) = v1) | ~ (k8_rlvect_2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k2_tarski(v1, v2) = v4) | ~ (u1_struct_0(v0) = v3) | ~ l1_struct_0(v0) | ~ m1_subset_1(v2, v3) | ~ m1_subset_1(v1, v3) | k8_rlvect_2(v0, v1, v2) = v4 | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_tarski(v3, v2) = v1) | ~ (k2_tarski(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_rlvect_2(v0, v2, v1) = v3) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : (k8_rlvect_2(v0, v1, v2) = v5 & u1_struct_0(v0) = v4 & (v5 = v3 | ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_rlvect_2(v0, v1, v2) = v3) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : (k8_rlvect_2(v0, v2, v1) = v5 & u1_struct_0(v0) = v4 & (v5 = v3 | ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_rlvect_2(v0, v1, v2) = v3) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : (k2_tarski(v1, v2) = v5 & u1_struct_0(v0) = v4 & (v5 = v3 | ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_rlvect_2(v0, v1, v2) = v3) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : (u1_struct_0(v0) = v4 & k1_zfmisc_1(v4) = v5 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4) | (v1_finset_1(v3) & m1_subset_1(v3, v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ v1_xboole_0(v2) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | m1_subset_1(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k2_group_1(v2) = v1) | ~ (k2_group_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_rlvect_1(v2) = v1) | ~ (k1_rlvect_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v1, v0) = v2) | k2_tarski(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | ~ v1_xboole_0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | k2_tarski(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : ( ~ (k2_group_1(v0) = v1) | ~ l1_group_1(v0) | v3_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & m1_subset_1(v1, v2))) & ! [v0] : ! [v1] : ( ~ (k2_group_1(v0) = v1) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (k1_rlvect_1(v0) = v2 & ! [v3] : ! [v4] : ( ~ (k1_rlvect_1(v3) = v4) | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5] : (u1_struct_0(v3) = v5 & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v4) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)) & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v4, v6) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)))) & ! [v3] : ! [v4] : ( ~ (u1_struct_0(v3) = v4) | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5] : (k1_rlvect_1(v3) = v5 & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v5) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4)) & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v5, v6) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4)))))) & ! [v0] : ! [v1] : ( ~ (k1_rlvect_1(v0) = v1) | ~ l2_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & m1_subset_1(v1, v2))) & ! [v0] : ! [v1] : ( ~ (k1_rlvect_1(v0) = v1) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (k2_group_1(v0) = v2 & ! [v3] : ! [v4] : ( ~ (k1_rlvect_1(v3) = v4) | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5] : (u1_struct_0(v3) = v5 & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v4) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)) & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v4, v6) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)))) & ! [v3] : ! [v4] : ( ~ (u1_struct_0(v3) = v4) | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5] : (k1_rlvect_1(v3) = v5 & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v5) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4)) & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v5, v6) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4)))))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l2_struct_0(v0) | ? [v2] : (k1_rlvect_1(v0) = v2 & m1_subset_1(v2, v1))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : (k1_zfmisc_1(v1) = v2 & v1_finset_1(v3) & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : (k1_zfmisc_1(v1) = v2 & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | v3_struct_0(v0) | ? [v2] : (k2_group_1(v0) = v2 & m1_subset_1(v2, v1))) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2))) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (v1_xboole_0(v2) & m1_subset_1(v2, v1))) & ! [v0] : ! [v1] : ( ~ l1_struct_0(v0) | ~ l1_vectsp_2(v1, v0) | l1_rlvect_1(v1)) & ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ! [v0] : ( ~ l2_vectsp_1(v0) | l2_struct_0(v0)) & ! [v0] : ( ~ l2_vectsp_1(v0) | l1_vectsp_1(v0)) & ! [v0] : ( ~ l2_struct_0(v0) | l1_struct_0(v0)) & ! [v0] : ( ~ l1_rlvect_1(v0) | l2_struct_0(v0)) & ! [v0] : ( ~ l1_struct_0(v0) | ? [v1] : (l1_vectsp_2(v1, v0) & ~ v3_struct_0(v1))) & ! [v0] : ( ~ l1_struct_0(v0) | ? [v1] : l1_vectsp_2(v1, v0)) & ! [v0] : ( ~ l1_group_1(v0) | l1_struct_0(v0)) & ! [v0] : ( ~ l1_vectsp_1(v0) | l1_group_1(v0)) & ! [v0] : ( ~ l3_vectsp_1(v0) | l2_vectsp_1(v0)) & ! [v0] : ( ~ l3_vectsp_1(v0) | l1_rlvect_1(v0)) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : r1_tarski(v0, v0) & (v1_rmod_5(all_0_11_11, all_0_19_19, all_0_16_16) | v1_rmod_5(all_0_12_12, all_0_19_19, all_0_16_16)) % 9.12/2.74 | % 9.12/2.74 | Applying alpha-rule on (1) yields: % 9.12/2.74 | (2) ! [v0] : ( ~ l2_vectsp_1(v0) | l2_struct_0(v0)) % 9.12/2.74 | (3) v3_rlvect_1(all_0_19_19) % 9.12/2.74 | (4) v5_vectsp_2(all_0_16_16, all_0_19_19) % 9.12/2.74 | (5) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1)) % 9.12/2.74 | (6) v6_vectsp_1(all_0_19_19) % 9.12/2.74 | (7) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) % 9.12/2.74 | (8) v4_rlvect_1(all_0_16_16) % 9.12/2.74 | (9) v6_rlvect_1(all_0_19_19) % 9.12/2.74 | (10) k1_rlvect_1(all_0_19_19) = all_0_18_18 % 9.12/2.74 | (11) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0)) % 9.12/2.74 | (12) l3_vectsp_1(all_0_19_19) % 9.12/2.74 | (13) l1_vectsp_1(all_0_0_0) % 9.12/2.74 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_rlvect_2(v0, v1, v2) = v3) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : (k8_rlvect_2(v0, v2, v1) = v5 & u1_struct_0(v0) = v4 & (v5 = v3 | ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))) % 9.12/2.74 | (15) v5_rlvect_1(all_0_19_19) % 9.12/2.74 | (16) l2_struct_0(all_0_9_9) % 9.12/2.74 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 9.12/2.74 | (18) l1_rlvect_1(all_0_4_4) % 9.12/2.74 | (19) ! [v0] : ( ~ l1_group_1(v0) | l1_struct_0(v0)) % 9.12/2.74 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | ~ v1_xboole_0(v2)) % 9.12/2.74 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) % 9.12/2.74 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ v1_xboole_0(v2) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3)) % 9.12/2.74 | (23) ~ v3_struct_0(all_0_8_8) % 9.12/2.74 | (24) ! [v0] : ( ~ l1_struct_0(v0) | ? [v1] : l1_vectsp_2(v1, v0)) % 9.12/2.74 | (25) ! [v0] : ( ~ l3_vectsp_1(v0) | l2_vectsp_1(v0)) % 9.12/2.74 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v0, v1) = v2) | k2_tarski(v1, v0) = v2) % 9.12/2.74 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_tarski(v1, v0) = v2) | k2_tarski(v0, v1) = v2) % 9.12/2.75 | (28) l1_struct_0(all_0_8_8) % 9.12/2.75 | (29) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) % 9.12/2.75 | (30) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : (k1_zfmisc_1(v1) = v2 & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3))) % 9.12/2.75 | (31) ~ v1_xboole_0(all_0_2_2) % 9.12/2.75 | (32) v6_rlvect_1(all_0_16_16) % 9.12/2.75 | (33) k1_rlvect_1(all_0_16_16) = all_0_14_14 % 9.12/2.75 | (34) ? [v0] : ? [v1] : m1_subset_1(v1, v0) % 9.12/2.75 | (35) ~ v3_struct_0(all_0_19_19) % 9.12/2.75 | (36) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1)) % 9.12/2.75 | (37) ? [v0] : r1_tarski(v0, v0) % 9.12/2.75 | (38) v7_vectsp_1(all_0_19_19) % 9.12/2.75 | (39) l1_struct_0(all_0_5_5) % 9.12/2.75 | (40) m1_subset_1(all_0_13_13, all_0_15_15) % 9.12/2.75 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_rlvect_2(v0, v1, v2) = v3) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : (k2_tarski(v1, v2) = v5 & u1_struct_0(v0) = v4 & (v5 = v3 | ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))) % 9.12/2.75 | (42) ! [v0] : ! [v1] : ( ~ (k1_rlvect_1(v0) = v1) | ~ l2_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & m1_subset_1(v1, v2))) % 9.12/2.75 | (43) ! [v0] : ( ~ l3_vectsp_1(v0) | l1_rlvect_1(v0)) % 9.12/2.75 | (44) ! [v0] : ( ~ l2_vectsp_1(v0) | l1_vectsp_1(v0)) % 9.12/2.75 | (45) k8_rlvect_2(all_0_16_16, all_0_13_13, all_0_14_14) = all_0_12_12 % 9.12/2.75 | (46) ! [v0] : ( ~ l2_struct_0(v0) | l1_struct_0(v0)) % 9.12/2.75 | (47) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) % 9.12/2.75 | (48) ! [v0] : ! [v1] : ( ~ (k2_group_1(v0) = v1) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (k1_rlvect_1(v0) = v2 & ! [v3] : ! [v4] : ( ~ (k1_rlvect_1(v3) = v4) | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5] : (u1_struct_0(v3) = v5 & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v4) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)) & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v4, v6) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)))) & ! [v3] : ! [v4] : ( ~ (u1_struct_0(v3) = v4) | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5] : (k1_rlvect_1(v3) = v5 & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v5) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4)) & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v5, v6) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4)))))) % 9.12/2.75 | (49) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | v3_struct_0(v0) | ? [v2] : (k2_group_1(v0) = v2 & m1_subset_1(v2, v1))) % 9.12/2.75 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 9.12/2.75 | (51) v4_group_1(all_0_19_19) % 9.12/2.75 | (52) ! [v0] : ( ~ l1_rlvect_1(v0) | l2_struct_0(v0)) % 9.12/2.75 | (53) ! [v0] : ! [v1] : ( ~ l1_struct_0(v0) | ~ l1_vectsp_2(v1, v0) | l1_rlvect_1(v1)) % 9.12/2.75 | (54) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (v1_xboole_0(v2) & m1_subset_1(v2, v1))) % 9.12/2.75 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | m1_subset_1(v0, v2)) % 9.12/2.75 | (56) k8_rlvect_2(all_0_16_16, all_0_14_14, all_0_13_13) = all_0_11_11 % 9.12/2.75 | (57) v1_xboole_0(k1_xboole_0) % 9.12/2.75 | (58) ! [v0] : ! [v1] : ( ~ (k2_group_1(v0) = v1) | ~ l1_group_1(v0) | v3_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & m1_subset_1(v1, v2))) % 9.12/2.75 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k2_tarski(v1, v2) = v4) | ~ (u1_struct_0(v0) = v3) | ~ l1_struct_0(v0) | ~ m1_subset_1(v2, v3) | ~ m1_subset_1(v1, v3) | k8_rlvect_2(v0, v1, v2) = v4 | v3_struct_0(v0)) % 9.12/2.75 | (60) l1_group_1(all_0_3_3) % 9.12/2.75 | (61) l2_vectsp_1(all_0_7_7) % 9.12/2.75 | (62) l2_struct_0(all_0_6_6) % 9.12/2.75 | (63) v4_rlvect_1(all_0_19_19) % 9.12/2.75 | (64) v5_rlvect_1(all_0_16_16) % 9.12/2.75 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k8_rlvect_2(v4, v3, v2) = v1) | ~ (k8_rlvect_2(v4, v3, v2) = v0)) % 9.12/2.76 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_tarski(v3, v2) = v1) | ~ (k2_tarski(v3, v2) = v0)) % 9.12/2.76 | (67) u1_struct_0(all_0_16_16) = all_0_15_15 % 9.12/2.76 | (68) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l2_struct_0(v0) | ? [v2] : (k1_rlvect_1(v0) = v2 & m1_subset_1(v2, v1))) % 9.12/2.76 | (69) ~ (all_0_17_17 = all_0_18_18) % 9.12/2.76 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_rlvect_1(v2) = v1) | ~ (k1_rlvect_1(v2) = v0)) % 9.12/2.76 | (71) v8_vectsp_1(all_0_19_19) % 9.12/2.76 | (72) k2_group_1(all_0_19_19) = all_0_17_17 % 9.12/2.76 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k2_group_1(v2) = v1) | ~ (k2_group_1(v2) = v0)) % 9.12/2.76 | (74) ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1)) % 9.12/2.76 | (75) ! [v0] : ( ~ l1_struct_0(v0) | ? [v1] : (l1_vectsp_2(v1, v0) & ~ v3_struct_0(v1))) % 9.12/2.76 | (76) v1_rmod_5(all_0_11_11, all_0_19_19, all_0_16_16) | v1_rmod_5(all_0_12_12, all_0_19_19, all_0_16_16) % 9.12/2.76 | (77) ~ v3_struct_0(all_0_9_9) % 9.12/2.76 | (78) v1_xboole_0(all_0_1_1) % 9.12/2.76 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_rlvect_2(v0, v1, v2) = v3) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : (u1_struct_0(v0) = v4 & k1_zfmisc_1(v4) = v5 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4) | (v1_finset_1(v3) & m1_subset_1(v3, v5))))) % 9.12/2.76 | (80) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v2] : ? [v3] : (k1_zfmisc_1(v1) = v2 & v1_finset_1(v3) & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3))) % 9.12/2.76 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k8_rlvect_2(v0, v2, v1) = v3) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : (k8_rlvect_2(v0, v1, v2) = v5 & u1_struct_0(v0) = v4 & (v5 = v3 | ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))) % 9.12/2.76 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1)) % 9.12/2.76 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2)) % 9.12/2.76 | (84) v3_rlvect_1(all_0_16_16) % 9.12/2.76 | (85) ! [v0] : ! [v1] : ( ~ (k1_rlvect_1(v0) = v1) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (k2_group_1(v0) = v2 & ! [v3] : ! [v4] : ( ~ (k1_rlvect_1(v3) = v4) | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5] : (u1_struct_0(v3) = v5 & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v4) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)) & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v4, v6) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)))) & ! [v3] : ! [v4] : ( ~ (u1_struct_0(v3) = v4) | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5] : (k1_rlvect_1(v3) = v5 & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v5) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4)) & ! [v6] : ! [v7] : (v2 = v1 | ~ (k8_rlvect_2(v3, v5, v6) = v7) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4)))))) % 9.12/2.76 | (86) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2))) % 9.12/2.76 | (87) ! [v0] : ( ~ l1_vectsp_1(v0) | l1_group_1(v0)) % 9.12/2.76 | (88) ~ v3_struct_0(all_0_16_16) % 9.12/2.76 | (89) l3_vectsp_1(all_0_10_10) % 9.12/2.76 | (90) l1_vectsp_2(all_0_16_16, all_0_19_19) % 9.12/2.76 | % 9.12/2.76 | Instantiating formula (43) with all_0_19_19 and discharging atoms l3_vectsp_1(all_0_19_19), yields: % 9.12/2.77 | (91) l1_rlvect_1(all_0_19_19) % 9.12/2.77 | % 9.12/2.77 | Instantiating formula (48) with all_0_17_17, all_0_19_19 and discharging atoms k2_group_1(all_0_19_19) = all_0_17_17, l3_vectsp_1(all_0_19_19), v8_vectsp_1(all_0_19_19), v7_vectsp_1(all_0_19_19), v6_vectsp_1(all_0_19_19), v4_group_1(all_0_19_19), v6_rlvect_1(all_0_19_19), v5_rlvect_1(all_0_19_19), v4_rlvect_1(all_0_19_19), v3_rlvect_1(all_0_19_19), ~ v3_struct_0(all_0_19_19), yields: % 9.12/2.77 | (92) ? [v0] : (k1_rlvect_1(all_0_19_19) = v0 & ! [v1] : ! [v2] : ( ~ (k1_rlvect_1(v1) = v2) | ~ l1_vectsp_2(v1, all_0_19_19) | ~ v5_vectsp_2(v1, all_0_19_19) | ~ v6_rlvect_1(v1) | ~ v5_rlvect_1(v1) | ~ v4_rlvect_1(v1) | ~ v3_rlvect_1(v1) | v3_struct_0(v1) | ? [v3] : (u1_struct_0(v1) = v3 & ! [v4] : ! [v5] : (v0 = all_0_17_17 | ~ (k8_rlvect_2(v1, v4, v2) = v5) | ~ v1_rmod_5(v5, all_0_19_19, v1) | ~ m1_subset_1(v4, v3) | ~ m1_subset_1(v2, v3)) & ! [v4] : ! [v5] : (v0 = all_0_17_17 | ~ (k8_rlvect_2(v1, v2, v4) = v5) | ~ v1_rmod_5(v5, all_0_19_19, v1) | ~ m1_subset_1(v4, v3) | ~ m1_subset_1(v2, v3)))) & ! [v1] : ! [v2] : ( ~ (u1_struct_0(v1) = v2) | ~ l1_vectsp_2(v1, all_0_19_19) | ~ v5_vectsp_2(v1, all_0_19_19) | ~ v6_rlvect_1(v1) | ~ v5_rlvect_1(v1) | ~ v4_rlvect_1(v1) | ~ v3_rlvect_1(v1) | v3_struct_0(v1) | ? [v3] : (k1_rlvect_1(v1) = v3 & ! [v4] : ! [v5] : (v0 = all_0_17_17 | ~ (k8_rlvect_2(v1, v4, v3) = v5) | ~ v1_rmod_5(v5, all_0_19_19, v1) | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2)) & ! [v4] : ! [v5] : (v0 = all_0_17_17 | ~ (k8_rlvect_2(v1, v3, v4) = v5) | ~ v1_rmod_5(v5, all_0_19_19, v1) | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2))))) % 9.12/2.77 | % 9.12/2.77 | Instantiating formula (85) with all_0_18_18, all_0_19_19 and discharging atoms k1_rlvect_1(all_0_19_19) = all_0_18_18, l3_vectsp_1(all_0_19_19), v8_vectsp_1(all_0_19_19), v7_vectsp_1(all_0_19_19), v6_vectsp_1(all_0_19_19), v4_group_1(all_0_19_19), v6_rlvect_1(all_0_19_19), v5_rlvect_1(all_0_19_19), v4_rlvect_1(all_0_19_19), v3_rlvect_1(all_0_19_19), ~ v3_struct_0(all_0_19_19), yields: % 9.12/2.77 | (93) ? [v0] : (k2_group_1(all_0_19_19) = v0 & ! [v1] : ! [v2] : ( ~ (k1_rlvect_1(v1) = v2) | ~ l1_vectsp_2(v1, all_0_19_19) | ~ v5_vectsp_2(v1, all_0_19_19) | ~ v6_rlvect_1(v1) | ~ v5_rlvect_1(v1) | ~ v4_rlvect_1(v1) | ~ v3_rlvect_1(v1) | v3_struct_0(v1) | ? [v3] : (u1_struct_0(v1) = v3 & ! [v4] : ! [v5] : (v0 = all_0_18_18 | ~ (k8_rlvect_2(v1, v4, v2) = v5) | ~ v1_rmod_5(v5, all_0_19_19, v1) | ~ m1_subset_1(v4, v3) | ~ m1_subset_1(v2, v3)) & ! [v4] : ! [v5] : (v0 = all_0_18_18 | ~ (k8_rlvect_2(v1, v2, v4) = v5) | ~ v1_rmod_5(v5, all_0_19_19, v1) | ~ m1_subset_1(v4, v3) | ~ m1_subset_1(v2, v3)))) & ! [v1] : ! [v2] : ( ~ (u1_struct_0(v1) = v2) | ~ l1_vectsp_2(v1, all_0_19_19) | ~ v5_vectsp_2(v1, all_0_19_19) | ~ v6_rlvect_1(v1) | ~ v5_rlvect_1(v1) | ~ v4_rlvect_1(v1) | ~ v3_rlvect_1(v1) | v3_struct_0(v1) | ? [v3] : (k1_rlvect_1(v1) = v3 & ! [v4] : ! [v5] : (v0 = all_0_18_18 | ~ (k8_rlvect_2(v1, v4, v3) = v5) | ~ v1_rmod_5(v5, all_0_19_19, v1) | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2)) & ! [v4] : ! [v5] : (v0 = all_0_18_18 | ~ (k8_rlvect_2(v1, v3, v4) = v5) | ~ v1_rmod_5(v5, all_0_19_19, v1) | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2))))) % 9.12/2.77 | % 9.12/2.77 | Instantiating (93) with all_25_0_27 yields: % 9.12/2.77 | (94) k2_group_1(all_0_19_19) = all_25_0_27 & ! [v0] : ! [v1] : ( ~ (k1_rlvect_1(v0) = v1) | ~ l1_vectsp_2(v0, all_0_19_19) | ~ v5_vectsp_2(v0, all_0_19_19) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & ! [v3] : ! [v4] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(v0, v3, v1) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v2) | ~ m1_subset_1(v1, v2)) & ! [v3] : ! [v4] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(v0, v1, v3) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v2) | ~ m1_subset_1(v1, v2)))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_vectsp_2(v0, all_0_19_19) | ~ v5_vectsp_2(v0, all_0_19_19) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (k1_rlvect_1(v0) = v2 & ! [v3] : ! [v4] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(v0, v3, v2) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1)) & ! [v3] : ! [v4] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(v0, v2, v3) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1)))) % 9.12/2.77 | % 9.12/2.77 | Applying alpha-rule on (94) yields: % 9.12/2.77 | (95) k2_group_1(all_0_19_19) = all_25_0_27 % 9.12/2.77 | (96) ! [v0] : ! [v1] : ( ~ (k1_rlvect_1(v0) = v1) | ~ l1_vectsp_2(v0, all_0_19_19) | ~ v5_vectsp_2(v0, all_0_19_19) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & ! [v3] : ! [v4] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(v0, v3, v1) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v2) | ~ m1_subset_1(v1, v2)) & ! [v3] : ! [v4] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(v0, v1, v3) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v2) | ~ m1_subset_1(v1, v2)))) % 9.12/2.77 | (97) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_vectsp_2(v0, all_0_19_19) | ~ v5_vectsp_2(v0, all_0_19_19) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (k1_rlvect_1(v0) = v2 & ! [v3] : ! [v4] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(v0, v3, v2) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1)) & ! [v3] : ! [v4] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(v0, v2, v3) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1)))) % 9.12/2.78 | % 9.12/2.78 | Instantiating formula (96) with all_0_14_14, all_0_16_16 and discharging atoms k1_rlvect_1(all_0_16_16) = all_0_14_14, l1_vectsp_2(all_0_16_16, all_0_19_19), v5_vectsp_2(all_0_16_16, all_0_19_19), v6_rlvect_1(all_0_16_16), v5_rlvect_1(all_0_16_16), v4_rlvect_1(all_0_16_16), v3_rlvect_1(all_0_16_16), ~ v3_struct_0(all_0_16_16), yields: % 9.12/2.78 | (98) ? [v0] : (u1_struct_0(all_0_16_16) = v0 & ! [v1] : ! [v2] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, v1, all_0_14_14) = v2) | ~ v1_rmod_5(v2, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v1, v0) | ~ m1_subset_1(all_0_14_14, v0)) & ! [v1] : ! [v2] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, all_0_14_14, v1) = v2) | ~ v1_rmod_5(v2, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v1, v0) | ~ m1_subset_1(all_0_14_14, v0))) % 9.12/2.78 | % 9.12/2.78 | Instantiating formula (97) with all_0_15_15, all_0_16_16 and discharging atoms u1_struct_0(all_0_16_16) = all_0_15_15, l1_vectsp_2(all_0_16_16, all_0_19_19), v5_vectsp_2(all_0_16_16, all_0_19_19), v6_rlvect_1(all_0_16_16), v5_rlvect_1(all_0_16_16), v4_rlvect_1(all_0_16_16), v3_rlvect_1(all_0_16_16), ~ v3_struct_0(all_0_16_16), yields: % 9.12/2.78 | (99) ? [v0] : (k1_rlvect_1(all_0_16_16) = v0 & ! [v1] : ! [v2] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, v1, v0) = v2) | ~ v1_rmod_5(v2, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v1, all_0_15_15) | ~ m1_subset_1(v0, all_0_15_15)) & ! [v1] : ! [v2] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, v0, v1) = v2) | ~ v1_rmod_5(v2, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v1, all_0_15_15) | ~ m1_subset_1(v0, all_0_15_15))) % 9.12/2.78 | % 9.12/2.78 | Instantiating (92) with all_28_0_28 yields: % 9.12/2.78 | (100) k1_rlvect_1(all_0_19_19) = all_28_0_28 & ! [v0] : ! [v1] : ( ~ (k1_rlvect_1(v0) = v1) | ~ l1_vectsp_2(v0, all_0_19_19) | ~ v5_vectsp_2(v0, all_0_19_19) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & ! [v3] : ! [v4] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(v0, v3, v1) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v2) | ~ m1_subset_1(v1, v2)) & ! [v3] : ! [v4] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(v0, v1, v3) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v2) | ~ m1_subset_1(v1, v2)))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_vectsp_2(v0, all_0_19_19) | ~ v5_vectsp_2(v0, all_0_19_19) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (k1_rlvect_1(v0) = v2 & ! [v3] : ! [v4] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(v0, v3, v2) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1)) & ! [v3] : ! [v4] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(v0, v2, v3) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1)))) % 9.12/2.78 | % 9.12/2.78 | Applying alpha-rule on (100) yields: % 9.12/2.78 | (101) k1_rlvect_1(all_0_19_19) = all_28_0_28 % 9.12/2.78 | (102) ! [v0] : ! [v1] : ( ~ (k1_rlvect_1(v0) = v1) | ~ l1_vectsp_2(v0, all_0_19_19) | ~ v5_vectsp_2(v0, all_0_19_19) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (u1_struct_0(v0) = v2 & ! [v3] : ! [v4] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(v0, v3, v1) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v2) | ~ m1_subset_1(v1, v2)) & ! [v3] : ! [v4] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(v0, v1, v3) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v2) | ~ m1_subset_1(v1, v2)))) % 9.12/2.78 | (103) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_vectsp_2(v0, all_0_19_19) | ~ v5_vectsp_2(v0, all_0_19_19) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2] : (k1_rlvect_1(v0) = v2 & ! [v3] : ! [v4] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(v0, v3, v2) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1)) & ! [v3] : ! [v4] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(v0, v2, v3) = v4) | ~ v1_rmod_5(v4, all_0_19_19, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1)))) % 9.61/2.78 | % 9.61/2.78 | Instantiating formula (102) with all_0_14_14, all_0_16_16 and discharging atoms k1_rlvect_1(all_0_16_16) = all_0_14_14, l1_vectsp_2(all_0_16_16, all_0_19_19), v5_vectsp_2(all_0_16_16, all_0_19_19), v6_rlvect_1(all_0_16_16), v5_rlvect_1(all_0_16_16), v4_rlvect_1(all_0_16_16), v3_rlvect_1(all_0_16_16), ~ v3_struct_0(all_0_16_16), yields: % 9.61/2.78 | (104) ? [v0] : (u1_struct_0(all_0_16_16) = v0 & ! [v1] : ! [v2] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, v1, all_0_14_14) = v2) | ~ v1_rmod_5(v2, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v1, v0) | ~ m1_subset_1(all_0_14_14, v0)) & ! [v1] : ! [v2] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, all_0_14_14, v1) = v2) | ~ v1_rmod_5(v2, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v1, v0) | ~ m1_subset_1(all_0_14_14, v0))) % 9.61/2.79 | % 9.61/2.79 | Instantiating formula (103) with all_0_15_15, all_0_16_16 and discharging atoms u1_struct_0(all_0_16_16) = all_0_15_15, l1_vectsp_2(all_0_16_16, all_0_19_19), v5_vectsp_2(all_0_16_16, all_0_19_19), v6_rlvect_1(all_0_16_16), v5_rlvect_1(all_0_16_16), v4_rlvect_1(all_0_16_16), v3_rlvect_1(all_0_16_16), ~ v3_struct_0(all_0_16_16), yields: % 9.61/2.79 | (105) ? [v0] : (k1_rlvect_1(all_0_16_16) = v0 & ! [v1] : ! [v2] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, v1, v0) = v2) | ~ v1_rmod_5(v2, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v1, all_0_15_15) | ~ m1_subset_1(v0, all_0_15_15)) & ! [v1] : ! [v2] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, v0, v1) = v2) | ~ v1_rmod_5(v2, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v1, all_0_15_15) | ~ m1_subset_1(v0, all_0_15_15))) % 9.61/2.79 | % 9.61/2.79 | Instantiating (99) with all_31_0_29 yields: % 9.61/2.79 | (106) k1_rlvect_1(all_0_16_16) = all_31_0_29 & ! [v0] : ! [v1] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, v0, all_31_0_29) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_0_15_15) | ~ m1_subset_1(all_31_0_29, all_0_15_15)) & ! [v0] : ! [v1] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, all_31_0_29, v0) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_0_15_15) | ~ m1_subset_1(all_31_0_29, all_0_15_15)) % 9.61/2.79 | % 9.61/2.79 | Applying alpha-rule on (106) yields: % 9.61/2.79 | (107) k1_rlvect_1(all_0_16_16) = all_31_0_29 % 9.61/2.79 | (108) ! [v0] : ! [v1] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, v0, all_31_0_29) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_0_15_15) | ~ m1_subset_1(all_31_0_29, all_0_15_15)) % 9.61/2.79 | (109) ! [v0] : ! [v1] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, all_31_0_29, v0) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_0_15_15) | ~ m1_subset_1(all_31_0_29, all_0_15_15)) % 9.61/2.79 | % 9.61/2.79 | Instantiating (98) with all_34_0_30 yields: % 9.61/2.79 | (110) u1_struct_0(all_0_16_16) = all_34_0_30 & ! [v0] : ! [v1] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, v0, all_0_14_14) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_34_0_30) | ~ m1_subset_1(all_0_14_14, all_34_0_30)) & ! [v0] : ! [v1] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, all_0_14_14, v0) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_34_0_30) | ~ m1_subset_1(all_0_14_14, all_34_0_30)) % 9.61/2.79 | % 9.61/2.79 | Applying alpha-rule on (110) yields: % 9.61/2.79 | (111) u1_struct_0(all_0_16_16) = all_34_0_30 % 9.61/2.79 | (112) ! [v0] : ! [v1] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, v0, all_0_14_14) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_34_0_30) | ~ m1_subset_1(all_0_14_14, all_34_0_30)) % 9.61/2.79 | (113) ! [v0] : ! [v1] : (all_25_0_27 = all_0_18_18 | ~ (k8_rlvect_2(all_0_16_16, all_0_14_14, v0) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_34_0_30) | ~ m1_subset_1(all_0_14_14, all_34_0_30)) % 9.61/2.79 | % 9.61/2.79 | Instantiating (105) with all_37_0_31 yields: % 9.61/2.79 | (114) k1_rlvect_1(all_0_16_16) = all_37_0_31 & ! [v0] : ! [v1] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, v0, all_37_0_31) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_0_15_15) | ~ m1_subset_1(all_37_0_31, all_0_15_15)) & ! [v0] : ! [v1] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, all_37_0_31, v0) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_0_15_15) | ~ m1_subset_1(all_37_0_31, all_0_15_15)) % 9.61/2.79 | % 9.61/2.79 | Applying alpha-rule on (114) yields: % 9.61/2.79 | (115) k1_rlvect_1(all_0_16_16) = all_37_0_31 % 9.61/2.79 | (116) ! [v0] : ! [v1] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, v0, all_37_0_31) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_0_15_15) | ~ m1_subset_1(all_37_0_31, all_0_15_15)) % 9.61/2.79 | (117) ! [v0] : ! [v1] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, all_37_0_31, v0) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_0_15_15) | ~ m1_subset_1(all_37_0_31, all_0_15_15)) % 9.61/2.79 | % 9.61/2.79 | Instantiating (104) with all_40_0_32 yields: % 9.61/2.79 | (118) u1_struct_0(all_0_16_16) = all_40_0_32 & ! [v0] : ! [v1] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, v0, all_0_14_14) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_40_0_32) | ~ m1_subset_1(all_0_14_14, all_40_0_32)) & ! [v0] : ! [v1] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, all_0_14_14, v0) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_40_0_32) | ~ m1_subset_1(all_0_14_14, all_40_0_32)) % 9.61/2.79 | % 9.61/2.79 | Applying alpha-rule on (118) yields: % 9.61/2.79 | (119) u1_struct_0(all_0_16_16) = all_40_0_32 % 9.61/2.79 | (120) ! [v0] : ! [v1] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, v0, all_0_14_14) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_40_0_32) | ~ m1_subset_1(all_0_14_14, all_40_0_32)) % 9.61/2.79 | (121) ! [v0] : ! [v1] : (all_28_0_28 = all_0_17_17 | ~ (k8_rlvect_2(all_0_16_16, all_0_14_14, v0) = v1) | ~ v1_rmod_5(v1, all_0_19_19, all_0_16_16) | ~ m1_subset_1(v0, all_40_0_32) | ~ m1_subset_1(all_0_14_14, all_40_0_32)) % 9.61/2.79 | % 9.61/2.79 | Instantiating formula (73) with all_0_19_19, all_25_0_27, all_0_17_17 and discharging atoms k2_group_1(all_0_19_19) = all_25_0_27, k2_group_1(all_0_19_19) = all_0_17_17, yields: % 9.61/2.79 | (122) all_25_0_27 = all_0_17_17 % 9.61/2.79 | % 9.61/2.79 | Instantiating formula (70) with all_0_16_16, all_37_0_31, all_0_14_14 and discharging atoms k1_rlvect_1(all_0_16_16) = all_37_0_31, k1_rlvect_1(all_0_16_16) = all_0_14_14, yields: % 9.61/2.79 | (123) all_37_0_31 = all_0_14_14 % 9.61/2.79 | % 9.61/2.79 | Instantiating formula (70) with all_0_16_16, all_31_0_29, all_37_0_31 and discharging atoms k1_rlvect_1(all_0_16_16) = all_37_0_31, k1_rlvect_1(all_0_16_16) = all_31_0_29, yields: % 9.61/2.79 | (124) all_37_0_31 = all_31_0_29 % 9.61/2.79 | % 9.61/2.79 | Instantiating formula (70) with all_0_19_19, all_28_0_28, all_0_18_18 and discharging atoms k1_rlvect_1(all_0_19_19) = all_28_0_28, k1_rlvect_1(all_0_19_19) = all_0_18_18, yields: % 9.61/2.79 | (125) all_28_0_28 = all_0_18_18 % 9.61/2.79 | % 9.61/2.79 | Instantiating formula (50) with all_0_16_16, all_40_0_32, all_0_15_15 and discharging atoms u1_struct_0(all_0_16_16) = all_40_0_32, u1_struct_0(all_0_16_16) = all_0_15_15, yields: % 9.61/2.79 | (126) all_40_0_32 = all_0_15_15 % 9.61/2.79 | % 9.61/2.79 | Instantiating formula (50) with all_0_16_16, all_34_0_30, all_40_0_32 and discharging atoms u1_struct_0(all_0_16_16) = all_40_0_32, u1_struct_0(all_0_16_16) = all_34_0_30, yields: % 9.61/2.79 | (127) all_40_0_32 = all_34_0_30 % 9.61/2.80 | % 9.61/2.80 | Combining equations (126,127) yields a new equation: % 9.61/2.80 | (128) all_34_0_30 = all_0_15_15 % 9.61/2.80 | % 9.61/2.80 | Combining equations (124,123) yields a new equation: % 9.61/2.80 | (129) all_31_0_29 = all_0_14_14 % 9.61/2.80 | % 9.61/2.80 | Simplifying 129 yields: % 9.61/2.80 | (130) all_31_0_29 = all_0_14_14 % 9.61/2.80 | % 9.61/2.80 | Combining equations (128,127) yields a new equation: % 9.61/2.80 | (126) all_40_0_32 = all_0_15_15 % 9.61/2.80 | % 9.61/2.80 | From (130) and (107) follows: % 9.68/2.80 | (33) k1_rlvect_1(all_0_16_16) = all_0_14_14 % 9.68/2.80 | % 9.68/2.80 | From (128) and (111) follows: % 9.68/2.80 | (67) u1_struct_0(all_0_16_16) = all_0_15_15 % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (52) with all_0_19_19 and discharging atoms l1_rlvect_1(all_0_19_19), yields: % 9.68/2.80 | (134) l2_struct_0(all_0_19_19) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (46) with all_0_19_19 and discharging atoms l2_struct_0(all_0_19_19), yields: % 9.68/2.80 | (135) l1_struct_0(all_0_19_19) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (53) with all_0_16_16, all_0_19_19 and discharging atoms l1_struct_0(all_0_19_19), l1_vectsp_2(all_0_16_16, all_0_19_19), yields: % 9.68/2.80 | (136) l1_rlvect_1(all_0_16_16) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (52) with all_0_16_16 and discharging atoms l1_rlvect_1(all_0_16_16), yields: % 9.68/2.80 | (137) l2_struct_0(all_0_16_16) % 9.68/2.80 | % 9.68/2.80 +-Applying beta-rule and splitting (76), into two cases. % 9.68/2.80 |-Branch one: % 9.68/2.80 | (138) v1_rmod_5(all_0_11_11, all_0_19_19, all_0_16_16) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (42) with all_0_14_14, all_0_16_16 and discharging atoms k1_rlvect_1(all_0_16_16) = all_0_14_14, l2_struct_0(all_0_16_16), yields: % 9.68/2.80 | (139) ? [v0] : (u1_struct_0(all_0_16_16) = v0 & m1_subset_1(all_0_14_14, v0)) % 9.68/2.80 | % 9.68/2.80 | Instantiating (139) with all_181_0_104 yields: % 9.68/2.80 | (140) u1_struct_0(all_0_16_16) = all_181_0_104 & m1_subset_1(all_0_14_14, all_181_0_104) % 9.68/2.80 | % 9.68/2.80 | Applying alpha-rule on (140) yields: % 9.68/2.80 | (141) u1_struct_0(all_0_16_16) = all_181_0_104 % 9.68/2.80 | (142) m1_subset_1(all_0_14_14, all_181_0_104) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (50) with all_0_16_16, all_181_0_104, all_0_15_15 and discharging atoms u1_struct_0(all_0_16_16) = all_181_0_104, u1_struct_0(all_0_16_16) = all_0_15_15, yields: % 9.68/2.80 | (143) all_181_0_104 = all_0_15_15 % 9.68/2.80 | % 9.68/2.80 | From (143) and (142) follows: % 9.68/2.80 | (144) m1_subset_1(all_0_14_14, all_0_15_15) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (121) with all_0_11_11, all_0_13_13 and discharging atoms k8_rlvect_2(all_0_16_16, all_0_14_14, all_0_13_13) = all_0_11_11, v1_rmod_5(all_0_11_11, all_0_19_19, all_0_16_16), yields: % 9.68/2.80 | (145) all_28_0_28 = all_0_17_17 | ~ m1_subset_1(all_0_13_13, all_40_0_32) | ~ m1_subset_1(all_0_14_14, all_40_0_32) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (113) with all_0_11_11, all_0_13_13 and discharging atoms k8_rlvect_2(all_0_16_16, all_0_14_14, all_0_13_13) = all_0_11_11, v1_rmod_5(all_0_11_11, all_0_19_19, all_0_16_16), yields: % 9.68/2.80 | (146) all_25_0_27 = all_0_18_18 | ~ m1_subset_1(all_0_13_13, all_34_0_30) | ~ m1_subset_1(all_0_14_14, all_34_0_30) % 9.68/2.80 | % 9.68/2.80 +-Applying beta-rule and splitting (146), into two cases. % 9.68/2.80 |-Branch one: % 9.68/2.80 | (147) ~ m1_subset_1(all_0_13_13, all_34_0_30) % 9.68/2.80 | % 9.68/2.80 | From (128) and (147) follows: % 9.68/2.80 | (148) ~ m1_subset_1(all_0_13_13, all_0_15_15) % 9.68/2.80 | % 9.68/2.80 | Using (40) and (148) yields: % 9.68/2.80 | (149) $false % 9.68/2.80 | % 9.68/2.80 |-The branch is then unsatisfiable % 9.68/2.80 |-Branch two: % 9.68/2.80 | (150) m1_subset_1(all_0_13_13, all_34_0_30) % 9.68/2.80 | (151) all_25_0_27 = all_0_18_18 | ~ m1_subset_1(all_0_14_14, all_34_0_30) % 9.68/2.80 | % 9.68/2.80 | From (128) and (150) follows: % 9.68/2.80 | (40) m1_subset_1(all_0_13_13, all_0_15_15) % 9.68/2.80 | % 9.68/2.80 +-Applying beta-rule and splitting (145), into two cases. % 9.68/2.80 |-Branch one: % 9.68/2.80 | (153) ~ m1_subset_1(all_0_13_13, all_40_0_32) % 9.68/2.80 | % 9.68/2.80 | From (126) and (153) follows: % 9.68/2.80 | (148) ~ m1_subset_1(all_0_13_13, all_0_15_15) % 9.68/2.80 | % 9.68/2.80 | Using (40) and (148) yields: % 9.68/2.80 | (149) $false % 9.68/2.80 | % 9.68/2.80 |-The branch is then unsatisfiable % 9.68/2.80 |-Branch two: % 9.68/2.80 | (156) m1_subset_1(all_0_13_13, all_40_0_32) % 9.68/2.80 | (157) all_28_0_28 = all_0_17_17 | ~ m1_subset_1(all_0_14_14, all_40_0_32) % 9.68/2.80 | % 9.68/2.80 +-Applying beta-rule and splitting (157), into two cases. % 9.68/2.80 |-Branch one: % 9.68/2.80 | (158) ~ m1_subset_1(all_0_14_14, all_40_0_32) % 9.68/2.80 | % 9.68/2.80 | From (126) and (158) follows: % 9.68/2.80 | (159) ~ m1_subset_1(all_0_14_14, all_0_15_15) % 9.68/2.80 | % 9.68/2.80 | Using (144) and (159) yields: % 9.68/2.80 | (149) $false % 9.68/2.80 | % 9.68/2.80 |-The branch is then unsatisfiable % 9.68/2.80 |-Branch two: % 9.68/2.80 | (161) m1_subset_1(all_0_14_14, all_40_0_32) % 9.68/2.80 | (162) all_28_0_28 = all_0_17_17 % 9.68/2.80 | % 9.68/2.80 | Combining equations (125,162) yields a new equation: % 9.68/2.80 | (163) all_0_17_17 = all_0_18_18 % 9.68/2.80 | % 9.68/2.80 | Equations (163) can reduce 69 to: % 9.68/2.80 | (164) $false % 9.68/2.80 | % 9.68/2.80 |-The branch is then unsatisfiable % 9.68/2.80 |-Branch two: % 9.68/2.80 | (165) ~ v1_rmod_5(all_0_11_11, all_0_19_19, all_0_16_16) % 9.68/2.80 | (166) v1_rmod_5(all_0_12_12, all_0_19_19, all_0_16_16) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (42) with all_0_14_14, all_0_16_16 and discharging atoms k1_rlvect_1(all_0_16_16) = all_0_14_14, l2_struct_0(all_0_16_16), yields: % 9.68/2.80 | (139) ? [v0] : (u1_struct_0(all_0_16_16) = v0 & m1_subset_1(all_0_14_14, v0)) % 9.68/2.80 | % 9.68/2.80 | Instantiating (139) with all_181_0_174 yields: % 9.68/2.80 | (168) u1_struct_0(all_0_16_16) = all_181_0_174 & m1_subset_1(all_0_14_14, all_181_0_174) % 9.68/2.80 | % 9.68/2.80 | Applying alpha-rule on (168) yields: % 9.68/2.80 | (169) u1_struct_0(all_0_16_16) = all_181_0_174 % 9.68/2.80 | (170) m1_subset_1(all_0_14_14, all_181_0_174) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (50) with all_0_16_16, all_181_0_174, all_0_15_15 and discharging atoms u1_struct_0(all_0_16_16) = all_181_0_174, u1_struct_0(all_0_16_16) = all_0_15_15, yields: % 9.68/2.80 | (171) all_181_0_174 = all_0_15_15 % 9.68/2.80 | % 9.68/2.80 | From (171) and (170) follows: % 9.68/2.80 | (144) m1_subset_1(all_0_14_14, all_0_15_15) % 9.68/2.80 | % 9.68/2.80 | Instantiating formula (112) with all_0_12_12, all_0_13_13 and discharging atoms k8_rlvect_2(all_0_16_16, all_0_13_13, all_0_14_14) = all_0_12_12, v1_rmod_5(all_0_12_12, all_0_19_19, all_0_16_16), yields: % 9.68/2.80 | (146) all_25_0_27 = all_0_18_18 | ~ m1_subset_1(all_0_13_13, all_34_0_30) | ~ m1_subset_1(all_0_14_14, all_34_0_30) % 9.68/2.80 | % 9.68/2.80 +-Applying beta-rule and splitting (146), into two cases. % 9.68/2.80 |-Branch one: % 9.68/2.80 | (147) ~ m1_subset_1(all_0_13_13, all_34_0_30) % 9.68/2.80 | % 9.68/2.80 | From (128) and (147) follows: % 9.68/2.80 | (148) ~ m1_subset_1(all_0_13_13, all_0_15_15) % 9.68/2.81 | % 9.68/2.81 | Using (40) and (148) yields: % 9.68/2.81 | (149) $false % 9.68/2.81 | % 9.68/2.81 |-The branch is then unsatisfiable % 9.68/2.81 |-Branch two: % 9.68/2.81 | (150) m1_subset_1(all_0_13_13, all_34_0_30) % 9.68/2.81 | (151) all_25_0_27 = all_0_18_18 | ~ m1_subset_1(all_0_14_14, all_34_0_30) % 9.68/2.81 | % 9.68/2.81 +-Applying beta-rule and splitting (151), into two cases. % 9.68/2.81 |-Branch one: % 9.68/2.81 | (179) ~ m1_subset_1(all_0_14_14, all_34_0_30) % 9.68/2.81 | % 9.68/2.81 | From (128) and (179) follows: % 9.68/2.81 | (159) ~ m1_subset_1(all_0_14_14, all_0_15_15) % 9.68/2.81 | % 9.68/2.81 | Using (144) and (159) yields: % 9.68/2.81 | (149) $false % 9.68/2.81 | % 9.68/2.81 |-The branch is then unsatisfiable % 9.68/2.81 |-Branch two: % 9.68/2.81 | (182) m1_subset_1(all_0_14_14, all_34_0_30) % 9.68/2.81 | (183) all_25_0_27 = all_0_18_18 % 9.68/2.81 | % 9.68/2.81 | Combining equations (183,122) yields a new equation: % 9.68/2.81 | (163) all_0_17_17 = all_0_18_18 % 9.68/2.81 | % 9.68/2.81 | Equations (163) can reduce 69 to: % 9.68/2.81 | (164) $false % 9.68/2.81 | % 9.68/2.81 |-The branch is then unsatisfiable % 9.68/2.81 % SZS output end Proof for theBenchmark % 9.68/2.81 % 9.68/2.81 2202ms %------------------------------------------------------------------------------