%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GRP618+1 : TPTP v8.1.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n009.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 : Sat Jul 16 08:43:00 EDT 2022 % Result : Theorem 17.23s 4.95s % Output : Proof 21.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : GRP618+1 : TPTP v8.1.0. Released v3.4.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n009.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 : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jun 13 19:42:08 EDT 2022 % 0.12/0.33 % 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 % 0.18/0.58 (ePrincess v.1.0) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2015 % 0.18/0.58 (c) Peter Backeman, 2014-2015 % 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.58 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.93/1.01 Prover 0: Preprocessing ... % 2.69/1.31 Prover 0: Warning: ignoring some quantifiers % 3.06/1.34 Prover 0: Constructing countermodel ... % 17.23/4.94 Prover 0: proved (4312ms) % 17.23/4.95 % 17.23/4.95 No countermodel exists, formula is valid % 17.23/4.95 % SZS status Theorem for theBenchmark % 17.23/4.95 % 17.23/4.95 Generating proof ... Warning: ignoring some quantifiers % 20.56/5.72 found it (size 20) % 20.56/5.72 % 20.56/5.72 % SZS output start Proof for theBenchmark % 20.56/5.72 Assumed formulas after preprocessing and simplification: % 20.56/5.72 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (u1_struct_0(v2) = v3 & u1_struct_0(v0) = v1 & v2_group_1(v11) & l1_struct_0(v12) & l1_struct_0(v10) & v1_xboole_0(v18) & v1_xboole_0(v15) & v1_xboole_0(v14) & v1_xboole_0(k1_xboole_0) & v2_funct_1(v18) & v2_funct_1(v17) & v1_funct_1(v18) & v1_funct_1(v17) & v1_funct_1(v16) & v1_funct_1(v15) & v1_relat_1(v18) & v1_relat_1(v17) & v1_relat_1(v16) & v1_relat_1(v15) & m1_group_2(v2, v0) & l1_group_1(v11) & l1_group_1(v9) & l1_group_1(v8) & l1_group_1(v7) & l1_group_1(v0) & v4_group_1(v11) & v4_group_1(v0) & v3_group_1(v11) & v3_group_1(v0) & v1_group_1(v11) & v1_group_1(v8) & v1_group_1(v7) & v1_group_1(v0) & ~ v1_xboole_0(v13) & ~ v3_struct_0(v11) & ~ v3_struct_0(v10) & ~ v3_struct_0(v7) & ~ v3_struct_0(v0) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (k2_group_3(v19, v24, v23) = v25) | ~ (u1_struct_0(v21) = v22) | ~ (u1_struct_0(v19) = v20) | ~ v1_group_3(v21, v19) | ~ m1_subset_1(v24, v22) | ~ m1_subset_1(v24, v20) | ~ m1_subset_1(v23, v20) | ~ m1_group_2(v21, v19) | ~ l1_group_1(v19) | ~ v4_group_1(v19) | ~ v3_group_1(v19) | ~ v1_group_1(v19) | r1_rlvect_1(v21, v25) | v3_struct_0(v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v20 | ~ (g1_group_1(v22, v23) = v21) | ~ (g1_group_1(v19, v20) = v21) | ~ v1_funct_1(v20) | ? [v24] : (k2_zfmisc_1(v19, v19) = v24 & ( ~ v1_funct_2(v20, v24, v19) | ~ m1_relset_1(v20, v24, v19)))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v22 = v19 | ~ (g1_group_1(v22, v23) = v21) | ~ (g1_group_1(v19, v20) = v21) | ~ v1_funct_1(v20) | ? [v24] : (k2_zfmisc_1(v19, v19) = v24 & ( ~ v1_funct_2(v20, v24, v19) | ~ m1_relset_1(v20, v24, v19)))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v20 = v19 | ~ (k2_group_3(v23, v22, v21) = v20) | ~ (k2_group_3(v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v19 | ~ (u1_group_1(v19) = v21) | ~ (g1_group_1(v20, v21) = v22) | ~ (u1_struct_0(v19) = v20) | ~ l1_group_1(v19) | ~ v1_group_1(v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (g1_group_1(v22, v21) = v20) | ~ (g1_group_1(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (k2_zfmisc_1(v22, v21) = v20) | ~ (k2_zfmisc_1(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k2_group_3(v19, v20, v21) = v22) | ~ l1_group_1(v19) | ~ v4_group_1(v19) | ~ v3_group_1(v19) | v3_struct_0(v19) | ? [v23] : (u1_struct_0(v19) = v23 & ( ~ m1_subset_1(v21, v23) | ~ m1_subset_1(v20, v23) | m1_subset_1(v22, v23)))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (u1_struct_0(v21) = v22) | ~ (u1_struct_0(v19) = v20) | ~ m1_group_2(v21, v19) | ~ l1_group_1(v19) | ~ v4_group_1(v19) | ~ v3_group_1(v19) | ~ v1_group_1(v19) | v1_group_3(v21, v19) | v3_struct_0(v19) | ? [v23] : ? [v24] : ? [v25] : (k2_group_3(v19, v24, v23) = v25 & m1_subset_1(v24, v22) & m1_subset_1(v24, v20) & m1_subset_1(v23, v20) & ~ r1_rlvect_1(v21, v25))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k2_zfmisc_1(v19, v20) = v22) | ~ m2_relset_1(v21, v19, v20) | ? [v23] : (k1_zfmisc_1(v22) = v23 & m1_subset_1(v21, v23))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k1_zfmisc_1(v21) = v22) | ~ r2_hidden(v19, v20) | ~ v1_xboole_0(v21) | ~ m1_subset_1(v20, v22)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k1_zfmisc_1(v21) = v22) | ~ r2_hidden(v19, v20) | ~ m1_subset_1(v20, v22) | m1_subset_1(v19, v21)) & ? [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (k2_zfmisc_1(v20, v21) = v22) | v1_relat_1(v19) | ? [v23] : (k1_zfmisc_1(v22) = v23 & ~ m1_subset_1(v19, v23))) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (u1_group_1(v21) = v20) | ~ (u1_group_1(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (u1_struct_0(v21) = v20) | ~ (u1_struct_0(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (k1_zfmisc_1(v21) = v20) | ~ (k1_zfmisc_1(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ( ~ (g1_group_1(v19, v20) = v21) | ~ v1_funct_1(v20) | ~ v3_struct_0(v21) | v1_xboole_0(v19) | ? [v22] : (k2_zfmisc_1(v19, v19) = v22 & ( ~ v1_funct_2(v20, v22, v19) | ~ m1_relset_1(v20, v22, v19)))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (g1_group_1(v19, v20) = v21) | ~ v1_funct_1(v20) | v1_xboole_0(v19) | v1_group_1(v21) | ? [v22] : (k2_zfmisc_1(v19, v19) = v22 & ( ~ v1_funct_2(v20, v22, v19) | ~ m1_relset_1(v20, v22, v19)))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (g1_group_1(v19, v20) = v21) | ~ v1_funct_1(v20) | l1_group_1(v21) | ? [v22] : (k2_zfmisc_1(v19, v19) = v22 & ( ~ v1_funct_2(v20, v22, v19) | ~ m1_relset_1(v20, v22, v19)))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (g1_group_1(v19, v20) = v21) | ~ v1_funct_1(v20) | v1_group_1(v21) | ? [v22] : (k2_zfmisc_1(v19, v19) = v22 & ( ~ v1_funct_2(v20, v22, v19) | ~ m1_relset_1(v20, v22, v19)))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (u1_struct_0(v19) = v20) | ~ (k2_zfmisc_1(v20, v20) = v21) | ~ l1_group_1(v19) | ? [v22] : (u1_group_1(v19) = v22 & m2_relset_1(v22, v21, v20) & v1_funct_2(v22, v21, v20) & v1_funct_1(v22))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (k1_zfmisc_1(v20) = v21) | ~ r1_tarski(v19, v20) | m1_subset_1(v19, v21)) & ! [v19] : ! [v20] : ! [v21] : ( ~ (k1_zfmisc_1(v20) = v21) | ~ m1_subset_1(v19, v21) | r1_tarski(v19, v20)) & ! [v19] : ! [v20] : ! [v21] : ( ~ m2_relset_1(v21, v19, v20) | m1_relset_1(v21, v19, v20)) & ! [v19] : ! [v20] : ! [v21] : ( ~ v1_partfun1(v21, v19, v20) | ~ m1_relset_1(v21, v19, v20) | ~ v1_funct_1(v21) | v1_funct_2(v21, v19, v20)) & ! [v19] : ! [v20] : ! [v21] : ( ~ v1_funct_2(v21, v19, v20) | ~ m1_relset_1(v21, v19, v20) | ~ v1_xboole_0(v21) | ~ v1_funct_1(v21) | v1_xboole_0(v20) | v1_xboole_0(v19)) & ! [v19] : ! [v20] : ! [v21] : ( ~ v1_funct_2(v21, v19, v20) | ~ m1_relset_1(v21, v19, v20) | ~ v1_funct_1(v21) | v1_partfun1(v21, v19, v20) | v1_xboole_0(v20) | v1_xboole_0(v19)) & ! [v19] : ! [v20] : ! [v21] : ( ~ v1_funct_2(v21, v19, v20) | ~ m1_relset_1(v21, v19, v20) | ~ v1_funct_1(v21) | v1_partfun1(v21, v19, v20) | v1_xboole_0(v20)) & ! [v19] : ! [v20] : ! [v21] : ( ~ m1_relset_1(v21, v19, v20) | m2_relset_1(v21, v19, v20)) & ! [v19] : ! [v20] : (v20 = v19 | ~ v1_xboole_0(v20) | ~ v1_xboole_0(v19)) & ! [v19] : ! [v20] : ( ~ (u1_group_1(v19) = v20) | ~ l1_group_1(v19) | v1_funct_1(v20)) & ! [v19] : ! [v20] : ( ~ (u1_group_1(v19) = v20) | ~ l1_group_1(v19) | ? [v21] : ? [v22] : (u1_struct_0(v19) = v21 & k2_zfmisc_1(v21, v21) = v22 & m2_relset_1(v20, v22, v21) & v1_funct_2(v20, v22, v21))) & ! [v19] : ! [v20] : ( ~ (u1_struct_0(v19) = v20) | ~ l1_struct_0(v19) | ~ v1_xboole_0(v20) | v3_struct_0(v19)) & ! [v19] : ! [v20] : ( ~ (u1_struct_0(v19) = v20) | ~ l1_struct_0(v19) | v3_struct_0(v19) | ? [v21] : ? [v22] : (k1_zfmisc_1(v20) = v21 & m1_subset_1(v22, v21) & ~ v1_xboole_0(v22))) & ! [v19] : ! [v20] : ( ~ (u1_struct_0(v19) = v20) | ~ l1_group_1(v19) | ? [v21] : ? [v22] : (u1_group_1(v19) = v21 & k2_zfmisc_1(v20, v20) = v22 & m2_relset_1(v21, v22, v20) & v1_funct_2(v21, v22, v20) & v1_funct_1(v21))) & ! [v19] : ! [v20] : ( ~ r2_hidden(v20, v19) | ~ r2_hidden(v19, v20)) & ! [v19] : ! [v20] : ( ~ r2_hidden(v19, v20) | ~ v1_xboole_0(v20)) & ! [v19] : ! [v20] : ( ~ r2_hidden(v19, v20) | m1_subset_1(v19, v20)) & ! [v19] : ! [v20] : ( ~ m1_subset_1(v19, v20) | r2_hidden(v19, v20) | v1_xboole_0(v20)) & ! [v19] : ! [v20] : ( ~ m1_group_2(v20, v19) | ~ l1_group_1(v19) | ~ v4_group_1(v19) | ~ v3_group_1(v19) | v4_group_1(v20) | v3_struct_0(v19)) & ! [v19] : ! [v20] : ( ~ m1_group_2(v20, v19) | ~ l1_group_1(v19) | ~ v3_group_1(v19) | ~ v3_struct_0(v20) | v3_struct_0(v19)) & ! [v19] : ! [v20] : ( ~ m1_group_2(v20, v19) | ~ l1_group_1(v19) | ~ v3_group_1(v19) | l1_group_1(v20) | v3_struct_0(v19)) & ! [v19] : ! [v20] : ( ~ m1_group_2(v20, v19) | ~ l1_group_1(v19) | ~ v3_group_1(v19) | v3_group_1(v20) | v3_struct_0(v19)) & ! [v19] : (v19 = k1_xboole_0 | ~ v1_xboole_0(v19)) & ! [v19] : ( ~ v1_xboole_0(v19) | ~ v1_funct_1(v19) | ~ v1_relat_1(v19) | v2_funct_1(v19)) & ! [v19] : ( ~ v1_xboole_0(v19) | v1_funct_1(v19)) & ! [v19] : ( ~ l1_group_1(v19) | ~ v4_group_1(v19) | ~ v3_group_1(v19) | v3_struct_0(v19) | ? [v20] : (v2_group_1(v20) & v1_group_3(v20, v19) & m1_group_2(v20, v19) & v4_group_1(v20) & v3_group_1(v20) & v1_group_1(v20) & ~ v3_struct_0(v20))) & ! [v19] : ( ~ l1_group_1(v19) | ~ v4_group_1(v19) | ~ v3_group_1(v19) | v3_struct_0(v19) | ? [v20] : (v2_group_1(v20) & m1_group_2(v20, v19) & v4_group_1(v20) & v3_group_1(v20) & v1_group_1(v20) & ~ v3_struct_0(v20))) & ! [v19] : ( ~ l1_group_1(v19) | ~ v3_group_1(v19) | v2_group_1(v19) | v3_struct_0(v19)) & ! [v19] : ( ~ l1_group_1(v19) | ~ v3_group_1(v19) | v3_struct_0(v19) | ? [v20] : m1_group_2(v20, v19)) & ! [v19] : ( ~ l1_group_1(v19) | l1_struct_0(v19)) & ? [v19] : ? [v20] : ? [v21] : m2_relset_1(v21, v19, v20) & ? [v19] : ? [v20] : ? [v21] : m1_relset_1(v21, v19, v20) & ? [v19] : ? [v20] : ? [v21] : (v1_funct_2(v21, v19, v20) & m1_relset_1(v21, v19, v20) & v1_funct_1(v21) & v1_relat_1(v21)) & ? [v19] : ? [v20] : ? [v21] : (m1_relset_1(v21, v19, v20) & v1_funct_1(v21) & v1_relat_1(v21)) & ? [v19] : ? [v20] : m1_subset_1(v20, v19) & ? [v19] : r1_tarski(v19, v19) & ((k2_group_3(v0, v5, v4) = v6 & v1_group_3(v2, v0) & m1_subset_1(v5, v3) & m1_subset_1(v5, v1) & m1_subset_1(v4, v1) & ~ r1_rlvect_1(v2, v6)) | ( ~ v1_group_3(v2, v0) & ! [v19] : ! [v20] : ( ~ m1_subset_1(v20, v3) | ~ m1_subset_1(v20, v1) | ~ m1_subset_1(v19, v1) | ? [v21] : (k2_group_3(v0, v20, v19) = v21 & r1_rlvect_1(v2, v21)))))) % 20.56/5.76 | 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 yields: % 20.56/5.76 | (1) u1_struct_0(all_0_16_16) = all_0_15_15 & u1_struct_0(all_0_18_18) = all_0_17_17 & v2_group_1(all_0_7_7) & l1_struct_0(all_0_6_6) & l1_struct_0(all_0_8_8) & v1_xboole_0(all_0_0_0) & v1_xboole_0(all_0_3_3) & v1_xboole_0(all_0_4_4) & v1_xboole_0(k1_xboole_0) & v2_funct_1(all_0_0_0) & v2_funct_1(all_0_1_1) & v1_funct_1(all_0_0_0) & v1_funct_1(all_0_1_1) & v1_funct_1(all_0_2_2) & v1_funct_1(all_0_3_3) & v1_relat_1(all_0_0_0) & v1_relat_1(all_0_1_1) & v1_relat_1(all_0_2_2) & v1_relat_1(all_0_3_3) & m1_group_2(all_0_16_16, all_0_18_18) & l1_group_1(all_0_7_7) & l1_group_1(all_0_9_9) & l1_group_1(all_0_10_10) & l1_group_1(all_0_11_11) & l1_group_1(all_0_18_18) & v4_group_1(all_0_7_7) & v4_group_1(all_0_18_18) & v3_group_1(all_0_7_7) & v3_group_1(all_0_18_18) & v1_group_1(all_0_7_7) & v1_group_1(all_0_10_10) & v1_group_1(all_0_11_11) & v1_group_1(all_0_18_18) & ~ v1_xboole_0(all_0_5_5) & ~ v3_struct_0(all_0_7_7) & ~ v3_struct_0(all_0_8_8) & ~ v3_struct_0(all_0_11_11) & ~ v3_struct_0(all_0_18_18) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k2_group_3(v0, v5, v4) = v6) | ~ (u1_struct_0(v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ v1_group_3(v2, v0) | ~ m1_subset_1(v5, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | ~ m1_group_2(v2, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | ~ v1_group_1(v0) | r1_rlvect_1(v2, v6) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (g1_group_1(v3, v4) = v2) | ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ? [v5] : (k2_zfmisc_1(v0, v0) = v5 & ( ~ v1_funct_2(v1, v5, v0) | ~ m1_relset_1(v1, v5, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | ~ (g1_group_1(v3, v4) = v2) | ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ? [v5] : (k2_zfmisc_1(v0, v0) = v5 & ( ~ v1_funct_2(v1, v5, v0) | ~ m1_relset_1(v1, v5, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k2_group_3(v4, v3, v2) = v1) | ~ (k2_group_3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (u1_group_1(v0) = v2) | ~ (g1_group_1(v1, v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ~ v1_group_1(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~ (g1_group_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_group_3(v0, v1, v2) = v3) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v4] : (u1_struct_0(v0) = v4 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4) | m1_subset_1(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u1_struct_0(v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ m1_group_2(v2, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | ~ v1_group_1(v0) | v1_group_3(v2, v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : ? [v6] : (k2_group_3(v0, v5, v4) = v6 & m1_subset_1(v5, v3) & m1_subset_1(v5, v1) & m1_subset_1(v4, v1) & ~ r1_rlvect_1(v2, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v1) = v3) | ~ m2_relset_1(v2, v0, v1) | ? [v4] : (k1_zfmisc_1(v3) = v4 & m1_subset_1(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v2) | ~ 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] : ! [v3] : ( ~ (k2_zfmisc_1(v1, v2) = v3) | v1_relat_1(v0) | ? [v4] : (k1_zfmisc_1(v3) = v4 & ~ m1_subset_1(v0, v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_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] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ~ v3_struct_0(v2) | v1_xboole_0(v0) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | v1_xboole_0(v0) | v1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | l1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | v1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (u1_struct_0(v0) = v1) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ l1_group_1(v0) | ? [v3] : (u1_group_1(v0) = v3 & m2_relset_1(v3, v2, v1) & v1_funct_2(v3, v2, v1) & v1_funct_1(v3))) & ! [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] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v1_partfun1(v2, v0, v1) | ~ m1_relset_1(v2, v0, v1) | ~ v1_funct_1(v2) | v1_funct_2(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ m1_relset_1(v2, v0, v1) | ~ v1_xboole_0(v2) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ m1_relset_1(v2, v0, v1) | ~ v1_funct_1(v2) | v1_partfun1(v2, v0, v1) | v1_xboole_0(v1) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ m1_relset_1(v2, v0, v1) | ~ v1_funct_1(v2) | v1_partfun1(v2, v0, v1) | v1_xboole_0(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : ( ~ (u1_group_1(v0) = v1) | ~ l1_group_1(v0) | v1_funct_1(v1)) & ! [v0] : ! [v1] : ( ~ (u1_group_1(v0) = v1) | ~ l1_group_1(v0) | ? [v2] : ? [v3] : (u1_struct_0(v0) = v2 & k2_zfmisc_1(v2, v2) = v3 & m2_relset_1(v1, v3, v2) & v1_funct_2(v1, v3, v2))) & ! [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 & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3))) & ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ? [v2] : ? [v3] : (u1_group_1(v0) = v2 & k2_zfmisc_1(v1, v1) = v3 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v4_group_1(v1) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | v3_struct_0(v0)) & ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_group_1(v1) | v3_struct_0(v0)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | ~ v1_funct_1(v0) | ~ v1_relat_1(v0) | v2_funct_1(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0)) & ! [v0] : ( ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v1] : (v2_group_1(v1) & v1_group_3(v1, v0) & m1_group_2(v1, v0) & v4_group_1(v1) & v3_group_1(v1) & v1_group_1(v1) & ~ v3_struct_0(v1))) & ! [v0] : ( ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v1] : (v2_group_1(v1) & m1_group_2(v1, v0) & v4_group_1(v1) & v3_group_1(v1) & v1_group_1(v1) & ~ v3_struct_0(v1))) & ! [v0] : ( ~ l1_group_1(v0) | ~ v3_group_1(v0) | v2_group_1(v0) | v3_struct_0(v0)) & ! [v0] : ( ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v1] : m1_group_2(v1, v0)) & ! [v0] : ( ~ l1_group_1(v0) | l1_struct_0(v0)) & ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : (v1_funct_2(v2, v0, v1) & m1_relset_1(v2, v0, v1) & v1_funct_1(v2) & v1_relat_1(v2)) & ? [v0] : ? [v1] : ? [v2] : (m1_relset_1(v2, v0, v1) & v1_funct_1(v2) & v1_relat_1(v2)) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : r1_tarski(v0, v0) & ((k2_group_3(all_0_18_18, all_0_13_13, all_0_14_14) = all_0_12_12 & v1_group_3(all_0_16_16, all_0_18_18) & m1_subset_1(all_0_13_13, all_0_15_15) & m1_subset_1(all_0_13_13, all_0_17_17) & m1_subset_1(all_0_14_14, all_0_17_17) & ~ r1_rlvect_1(all_0_16_16, all_0_12_12)) | ( ~ v1_group_3(all_0_16_16, all_0_18_18) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v1, all_0_15_15) | ~ m1_subset_1(v1, all_0_17_17) | ~ m1_subset_1(v0, all_0_17_17) | ? [v2] : (k2_group_3(all_0_18_18, v1, v0) = v2 & r1_rlvect_1(all_0_16_16, v2))))) % 20.56/5.78 | % 20.56/5.78 | Applying alpha-rule on (1) yields: % 20.56/5.78 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_partfun1(v2, v0, v1) | ~ m1_relset_1(v2, v0, v1) | ~ v1_funct_1(v2) | v1_funct_2(v2, v0, v1)) % 20.56/5.78 | (3) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v1, v2) = v3) | v1_relat_1(v0) | ? [v4] : (k1_zfmisc_1(v3) = v4 & ~ m1_subset_1(v0, v4))) % 20.56/5.78 | (4) v1_xboole_0(k1_xboole_0) % 20.56/5.78 | (5) l1_struct_0(all_0_6_6) % 20.56/5.78 | (6) v3_group_1(all_0_18_18) % 20.56/5.78 | (7) v1_relat_1(all_0_1_1) % 20.56/5.78 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | v1_xboole_0(v0) | v1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) % 21.01/5.78 | (9) v1_funct_1(all_0_1_1) % 21.01/5.78 | (10) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_group_1(v1) | v3_struct_0(v0)) % 21.01/5.78 | (11) v4_group_1(all_0_7_7) % 21.01/5.78 | (12) v1_funct_1(all_0_3_3) % 21.01/5.78 | (13) v1_relat_1(all_0_0_0) % 21.01/5.78 | (14) l1_group_1(all_0_18_18) % 21.01/5.78 | (15) v1_group_1(all_0_7_7) % 21.01/5.78 | (16) u1_struct_0(all_0_16_16) = all_0_15_15 % 21.01/5.78 | (17) l1_group_1(all_0_11_11) % 21.01/5.78 | (18) v1_relat_1(all_0_3_3) % 21.01/5.78 | (19) ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) % 21.01/5.78 | (20) ! [v0] : ( ~ v1_xboole_0(v0) | ~ v1_funct_1(v0) | ~ v1_relat_1(v0) | v2_funct_1(v0)) % 21.01/5.78 | (21) ! [v0] : ! [v1] : ( ~ (u1_group_1(v0) = v1) | ~ l1_group_1(v0) | ? [v2] : ? [v3] : (u1_struct_0(v0) = v2 & k2_zfmisc_1(v2, v2) = v3 & m2_relset_1(v1, v3, v2) & v1_funct_2(v1, v3, v2))) % 21.01/5.78 | (22) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1)) % 21.01/5.78 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (u1_struct_0(v0) = v1) | ~ (k2_zfmisc_1(v1, v1) = v2) | ~ l1_group_1(v0) | ? [v3] : (u1_group_1(v0) = v3 & m2_relset_1(v3, v2, v1) & v1_funct_2(v3, v2, v1) & v1_funct_1(v3))) % 21.01/5.78 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1)) % 21.01/5.78 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2)) % 21.01/5.78 | (26) l1_group_1(all_0_7_7) % 21.01/5.78 | (27) ? [v0] : r1_tarski(v0, v0) % 21.01/5.78 | (28) ! [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))) % 21.01/5.78 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_zfmisc_1(v0, v1) = v3) | ~ m2_relset_1(v2, v0, v1) | ? [v4] : (k1_zfmisc_1(v3) = v4 & m1_subset_1(v2, v4))) % 21.01/5.78 | (30) ~ v3_struct_0(all_0_7_7) % 21.01/5.78 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ~ v3_struct_0(v2) | v1_xboole_0(v0) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) % 21.01/5.78 | (32) v2_funct_1(all_0_1_1) % 21.01/5.78 | (33) ~ v1_xboole_0(all_0_5_5) % 21.01/5.79 | (34) m1_group_2(all_0_16_16, all_0_18_18) % 21.01/5.79 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v2) | ~ m1_subset_1(v1, v3)) % 21.01/5.79 | (36) v3_group_1(all_0_7_7) % 21.01/5.79 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (g1_group_1(v3, v4) = v2) | ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ? [v5] : (k2_zfmisc_1(v0, v0) = v5 & ( ~ v1_funct_2(v1, v5, v0) | ~ m1_relset_1(v1, v5, v0)))) % 21.01/5.79 | (38) ? [v0] : ? [v1] : m1_subset_1(v1, v0) % 21.01/5.79 | (39) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ? [v2] : ? [v3] : (u1_group_1(v0) = v2 & k2_zfmisc_1(v1, v1) = v3 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2))) % 21.01/5.79 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ m1_relset_1(v2, v0, v1) | ~ v1_funct_1(v2) | v1_partfun1(v2, v0, v1) | v1_xboole_0(v1)) % 21.01/5.79 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 21.01/5.79 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) % 21.01/5.79 | (43) ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0)) % 21.01/5.79 | (44) ! [v0] : ( ~ l1_group_1(v0) | ~ v3_group_1(v0) | v2_group_1(v0) | v3_struct_0(v0)) % 21.01/5.79 | (45) v1_xboole_0(all_0_4_4) % 21.01/5.79 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ m1_relset_1(v2, v0, v1) | ~ v1_xboole_0(v2) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0)) % 21.01/5.79 | (47) ! [v0] : ! [v1] : ( ~ (u1_struct_0(v0) = v1) | ~ l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0)) % 21.01/5.79 | (48) v2_group_1(all_0_7_7) % 21.01/5.79 | (49) ~ v3_struct_0(all_0_18_18) % 21.01/5.79 | (50) ? [v0] : ? [v1] : ? [v2] : (v1_funct_2(v2, v0, v1) & m1_relset_1(v2, v0, v1) & v1_funct_1(v2) & v1_relat_1(v2)) % 21.01/5.79 | (51) l1_group_1(all_0_9_9) % 21.01/5.79 | (52) v1_funct_1(all_0_2_2) % 21.01/5.79 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_1(v2) = v0)) % 21.01/5.79 | (54) v1_group_1(all_0_10_10) % 21.01/5.79 | (55) ! [v0] : ! [v1] : ( ~ (u1_group_1(v0) = v1) | ~ l1_group_1(v0) | v1_funct_1(v1)) % 21.01/5.79 | (56) v4_group_1(all_0_18_18) % 21.01/5.79 | (57) v1_funct_1(all_0_0_0) % 21.01/5.79 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~ (g1_group_1(v3, v2) = v0)) % 21.01/5.79 | (59) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) % 21.01/5.79 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | l1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) % 21.01/5.79 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1)) % 21.01/5.79 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1)) % 21.01/5.79 | (63) (k2_group_3(all_0_18_18, all_0_13_13, all_0_14_14) = all_0_12_12 & v1_group_3(all_0_16_16, all_0_18_18) & m1_subset_1(all_0_13_13, all_0_15_15) & m1_subset_1(all_0_13_13, all_0_17_17) & m1_subset_1(all_0_14_14, all_0_17_17) & ~ r1_rlvect_1(all_0_16_16, all_0_12_12)) | ( ~ v1_group_3(all_0_16_16, all_0_18_18) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v1, all_0_15_15) | ~ m1_subset_1(v1, all_0_17_17) | ~ m1_subset_1(v0, all_0_17_17) | ? [v2] : (k2_group_3(all_0_18_18, v1, v0) = v2 & r1_rlvect_1(all_0_16_16, v2)))) % 21.01/5.79 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 21.01/5.79 | (65) ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) % 21.01/5.79 | (66) ! [v0] : ( ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v1] : (v2_group_1(v1) & m1_group_2(v1, v0) & v4_group_1(v1) & v3_group_1(v1) & v1_group_1(v1) & ~ v3_struct_0(v1))) % 21.01/5.79 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | v1_group_1(v2) | ? [v3] : (k2_zfmisc_1(v0, v0) = v3 & ( ~ v1_funct_2(v1, v3, v0) | ~ m1_relset_1(v1, v3, v0)))) % 21.01/5.79 | (68) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | v3_struct_0(v0)) % 21.01/5.79 | (69) ? [v0] : ? [v1] : ? [v2] : (m1_relset_1(v2, v0, v1) & v1_funct_1(v2) & v1_relat_1(v2)) % 21.01/5.79 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u1_struct_0(v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ m1_group_2(v2, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | ~ v1_group_1(v0) | v1_group_3(v2, v0) | v3_struct_0(v0) | ? [v4] : ? [v5] : ? [v6] : (k2_group_3(v0, v5, v4) = v6 & m1_subset_1(v5, v3) & m1_subset_1(v5, v1) & m1_subset_1(v4, v1) & ~ r1_rlvect_1(v2, v6))) % 21.01/5.79 | (71) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) % 21.01/5.80 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k2_group_3(v4, v3, v2) = v1) | ~ (k2_group_3(v4, v3, v2) = v0)) % 21.01/5.80 | (73) v1_group_1(all_0_18_18) % 21.01/5.80 | (74) l1_struct_0(all_0_8_8) % 21.01/5.80 | (75) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | v3_struct_0(v0)) % 21.01/5.80 | (76) ~ v3_struct_0(all_0_11_11) % 21.01/5.80 | (77) u1_struct_0(all_0_18_18) = all_0_17_17 % 21.01/5.80 | (78) ! [v0] : ( ~ l1_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v1] : m1_group_2(v1, v0)) % 21.01/5.80 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (u1_group_1(v0) = v2) | ~ (g1_group_1(v1, v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ l1_group_1(v0) | ~ v1_group_1(v0)) % 21.01/5.80 | (80) v1_xboole_0(all_0_0_0) % 21.01/5.80 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (k2_group_3(v0, v5, v4) = v6) | ~ (u1_struct_0(v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ v1_group_3(v2, v0) | ~ m1_subset_1(v5, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | ~ m1_group_2(v2, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | ~ v1_group_1(v0) | r1_rlvect_1(v2, v6) | v3_struct_0(v0)) % 21.01/5.80 | (82) v1_group_1(all_0_11_11) % 21.01/5.80 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_group_3(v0, v1, v2) = v3) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v4] : (u1_struct_0(v0) = v4 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4) | m1_subset_1(v3, v4)))) % 21.01/5.80 | (84) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) % 21.01/5.80 | (85) ! [v0] : ( ~ l1_group_1(v0) | l1_struct_0(v0)) % 21.01/5.80 | (86) l1_group_1(all_0_10_10) % 21.01/5.80 | (87) ! [v0] : ! [v1] : ( ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v4_group_1(v1) | v3_struct_0(v0)) % 21.01/5.80 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | ~ (g1_group_1(v3, v4) = v2) | ~ (g1_group_1(v0, v1) = v2) | ~ v1_funct_1(v1) | ? [v5] : (k2_zfmisc_1(v0, v0) = v5 & ( ~ v1_funct_2(v1, v5, v0) | ~ m1_relset_1(v1, v5, v0)))) % 21.01/5.80 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_funct_2(v2, v0, v1) | ~ m1_relset_1(v2, v0, v1) | ~ v1_funct_1(v2) | v1_partfun1(v2, v0, v1) | v1_xboole_0(v1) | v1_xboole_0(v0)) % 21.01/5.80 | (90) ! [v0] : ( ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v1] : (v2_group_1(v1) & v1_group_3(v1, v0) & m1_group_2(v1, v0) & v4_group_1(v1) & v3_group_1(v1) & v1_group_1(v1) & ~ v3_struct_0(v1))) % 21.01/5.80 | (91) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1)) % 21.01/5.80 | (92) v1_relat_1(all_0_2_2) % 21.01/5.80 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ r2_hidden(v0, v1) | ~ m1_subset_1(v1, v3) | m1_subset_1(v0, v2)) % 21.01/5.80 | (94) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) % 21.01/5.80 | (95) ~ v3_struct_0(all_0_8_8) % 21.01/5.80 | (96) v2_funct_1(all_0_0_0) % 21.01/5.80 | (97) v1_xboole_0(all_0_3_3) % 21.01/5.80 | % 21.01/5.80 | Instantiating formula (70) with all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18 and discharging atoms u1_struct_0(all_0_16_16) = all_0_15_15, u1_struct_0(all_0_18_18) = all_0_17_17, m1_group_2(all_0_16_16, all_0_18_18), l1_group_1(all_0_18_18), v4_group_1(all_0_18_18), v3_group_1(all_0_18_18), v1_group_1(all_0_18_18), ~ v3_struct_0(all_0_18_18), yields: % 21.01/5.80 | (98) v1_group_3(all_0_16_16, all_0_18_18) | ? [v0] : ? [v1] : ? [v2] : (k2_group_3(all_0_18_18, v1, v0) = v2 & m1_subset_1(v1, all_0_15_15) & m1_subset_1(v1, all_0_17_17) & m1_subset_1(v0, all_0_17_17) & ~ r1_rlvect_1(all_0_16_16, v2)) % 21.01/5.80 | % 21.01/5.81 +-Applying beta-rule and splitting (63), into two cases. % 21.01/5.81 |-Branch one: % 21.01/5.81 | (99) k2_group_3(all_0_18_18, all_0_13_13, all_0_14_14) = all_0_12_12 & v1_group_3(all_0_16_16, all_0_18_18) & m1_subset_1(all_0_13_13, all_0_15_15) & m1_subset_1(all_0_13_13, all_0_17_17) & m1_subset_1(all_0_14_14, all_0_17_17) & ~ r1_rlvect_1(all_0_16_16, all_0_12_12) % 21.01/5.81 | % 21.01/5.81 | Applying alpha-rule on (99) yields: % 21.01/5.81 | (100) k2_group_3(all_0_18_18, all_0_13_13, all_0_14_14) = all_0_12_12 % 21.01/5.81 | (101) m1_subset_1(all_0_13_13, all_0_15_15) % 21.01/5.81 | (102) ~ r1_rlvect_1(all_0_16_16, all_0_12_12) % 21.01/5.81 | (103) v1_group_3(all_0_16_16, all_0_18_18) % 21.01/5.81 | (104) m1_subset_1(all_0_14_14, all_0_17_17) % 21.01/5.81 | (105) m1_subset_1(all_0_13_13, all_0_17_17) % 21.01/5.81 | % 21.01/5.81 | Instantiating formula (81) with 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 and discharging atoms k2_group_3(all_0_18_18, all_0_13_13, all_0_14_14) = all_0_12_12, u1_struct_0(all_0_16_16) = all_0_15_15, u1_struct_0(all_0_18_18) = all_0_17_17, v1_group_3(all_0_16_16, all_0_18_18), m1_subset_1(all_0_13_13, all_0_15_15), m1_subset_1(all_0_13_13, all_0_17_17), m1_subset_1(all_0_14_14, all_0_17_17), m1_group_2(all_0_16_16, all_0_18_18), l1_group_1(all_0_18_18), v4_group_1(all_0_18_18), v3_group_1(all_0_18_18), v1_group_1(all_0_18_18), ~ r1_rlvect_1(all_0_16_16, all_0_12_12), ~ v3_struct_0(all_0_18_18), yields: % 21.01/5.81 | (106) $false % 21.15/5.81 | % 21.15/5.81 |-The branch is then unsatisfiable % 21.15/5.81 |-Branch two: % 21.15/5.81 | (107) ~ v1_group_3(all_0_16_16, all_0_18_18) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v1, all_0_15_15) | ~ m1_subset_1(v1, all_0_17_17) | ~ m1_subset_1(v0, all_0_17_17) | ? [v2] : (k2_group_3(all_0_18_18, v1, v0) = v2 & r1_rlvect_1(all_0_16_16, v2))) % 21.15/5.81 | % 21.15/5.81 | Applying alpha-rule on (107) yields: % 21.15/5.81 | (108) ~ v1_group_3(all_0_16_16, all_0_18_18) % 21.15/5.81 | (109) ! [v0] : ! [v1] : ( ~ m1_subset_1(v1, all_0_15_15) | ~ m1_subset_1(v1, all_0_17_17) | ~ m1_subset_1(v0, all_0_17_17) | ? [v2] : (k2_group_3(all_0_18_18, v1, v0) = v2 & r1_rlvect_1(all_0_16_16, v2))) % 21.15/5.81 | % 21.15/5.81 +-Applying beta-rule and splitting (98), into two cases. % 21.15/5.81 |-Branch one: % 21.15/5.81 | (103) v1_group_3(all_0_16_16, all_0_18_18) % 21.15/5.81 | % 21.15/5.81 | Using (103) and (108) yields: % 21.15/5.81 | (106) $false % 21.15/5.81 | % 21.15/5.81 |-The branch is then unsatisfiable % 21.15/5.81 |-Branch two: % 21.15/5.81 | (108) ~ v1_group_3(all_0_16_16, all_0_18_18) % 21.15/5.81 | (113) ? [v0] : ? [v1] : ? [v2] : (k2_group_3(all_0_18_18, v1, v0) = v2 & m1_subset_1(v1, all_0_15_15) & m1_subset_1(v1, all_0_17_17) & m1_subset_1(v0, all_0_17_17) & ~ r1_rlvect_1(all_0_16_16, v2)) % 21.15/5.81 | % 21.15/5.81 | Instantiating (113) with all_158_0_88, all_158_1_89, all_158_2_90 yields: % 21.15/5.81 | (114) k2_group_3(all_0_18_18, all_158_1_89, all_158_2_90) = all_158_0_88 & m1_subset_1(all_158_1_89, all_0_15_15) & m1_subset_1(all_158_1_89, all_0_17_17) & m1_subset_1(all_158_2_90, all_0_17_17) & ~ r1_rlvect_1(all_0_16_16, all_158_0_88) % 21.15/5.81 | % 21.15/5.81 | Applying alpha-rule on (114) yields: % 21.15/5.81 | (115) m1_subset_1(all_158_1_89, all_0_17_17) % 21.15/5.81 | (116) m1_subset_1(all_158_1_89, all_0_15_15) % 21.15/5.81 | (117) m1_subset_1(all_158_2_90, all_0_17_17) % 21.15/5.81 | (118) ~ r1_rlvect_1(all_0_16_16, all_158_0_88) % 21.15/5.81 | (119) k2_group_3(all_0_18_18, all_158_1_89, all_158_2_90) = all_158_0_88 % 21.15/5.81 | % 21.15/5.81 | Instantiating formula (109) with all_158_1_89, all_158_2_90 and discharging atoms m1_subset_1(all_158_1_89, all_0_15_15), m1_subset_1(all_158_1_89, all_0_17_17), m1_subset_1(all_158_2_90, all_0_17_17), yields: % 21.15/5.81 | (120) ? [v0] : (k2_group_3(all_0_18_18, all_158_1_89, all_158_2_90) = v0 & r1_rlvect_1(all_0_16_16, v0)) % 21.15/5.81 | % 21.15/5.81 | Instantiating (120) with all_253_0_113 yields: % 21.15/5.81 | (121) k2_group_3(all_0_18_18, all_158_1_89, all_158_2_90) = all_253_0_113 & r1_rlvect_1(all_0_16_16, all_253_0_113) % 21.15/5.81 | % 21.15/5.81 | Applying alpha-rule on (121) yields: % 21.15/5.81 | (122) k2_group_3(all_0_18_18, all_158_1_89, all_158_2_90) = all_253_0_113 % 21.15/5.81 | (123) r1_rlvect_1(all_0_16_16, all_253_0_113) % 21.15/5.81 | % 21.15/5.81 | Instantiating formula (72) with all_0_18_18, all_158_1_89, all_158_2_90, all_253_0_113, all_158_0_88 and discharging atoms k2_group_3(all_0_18_18, all_158_1_89, all_158_2_90) = all_253_0_113, k2_group_3(all_0_18_18, all_158_1_89, all_158_2_90) = all_158_0_88, yields: % 21.15/5.81 | (124) all_253_0_113 = all_158_0_88 % 21.15/5.81 | % 21.15/5.81 | From (124) and (123) follows: % 21.15/5.81 | (125) r1_rlvect_1(all_0_16_16, all_158_0_88) % 21.15/5.81 | % 21.15/5.81 | Using (125) and (118) yields: % 21.15/5.81 | (106) $false % 21.15/5.81 | % 21.15/5.81 |-The branch is then unsatisfiable % 21.15/5.81 % SZS output end Proof for theBenchmark % 21.15/5.81 % 21.15/5.81 5222ms %------------------------------------------------------------------------------