%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : CAT025+1 : TPTP v8.1.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 23:59:08 EDT 2022 % Result : Theorem 4.44s 1.53s % Output : Proof 7.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : CAT025+1 : TPTP v8.1.0. Released v3.4.0. % 0.09/0.10 % Command : ePrincess-casc -timeout=%d %s % 0.09/0.29 % Computer : n032.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 600 % 0.09/0.29 % DateTime : Sun May 29 22:34:41 EDT 2022 % 0.09/0.29 % CPUTime : % 0.14/0.48 ____ _ % 0.14/0.48 ___ / __ \_____(_)___ ________ __________ % 0.14/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.14/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.14/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.14/0.48 % 0.14/0.48 A Theorem Prover for First-Order Logic % 0.14/0.48 (ePrincess v.1.0) % 0.14/0.48 % 0.14/0.48 (c) Philipp Rümmer, 2009-2015 % 0.14/0.48 (c) Peter Backeman, 2014-2015 % 0.14/0.48 (contributions by Angelo Brillout, Peter Baumgartner) % 0.14/0.48 Free software under GNU Lesser General Public License (LGPL). % 0.14/0.48 Bug reports to peter@backeman.se % 0.14/0.48 % 0.14/0.48 For more information, visit http://user.uu.se/~petba168/breu/ % 0.14/0.48 % 0.14/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.14/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.43/0.83 Prover 0: Preprocessing ... % 2.44/1.18 Prover 0: Warning: ignoring some quantifiers % 2.94/1.22 Prover 0: Constructing countermodel ... % 4.44/1.53 Prover 0: proved (1004ms) % 4.44/1.53 % 4.44/1.53 No countermodel exists, formula is valid % 4.44/1.53 % SZS status Theorem for theBenchmark % 4.44/1.53 % 4.44/1.53 Generating proof ... Warning: ignoring some quantifiers % 6.50/1.99 found it (size 49) % 6.50/1.99 % 6.50/1.99 % SZS output start Proof for theBenchmark % 6.50/1.99 Assumed formulas after preprocessing and simplification: % 6.50/1.99 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (k12_nattra_1(v2, v3) = v4 & k12_nattra_1(v1, v3) = v5 & k12_nattra_1(v0, v5) = v6 & k11_cat_2(v0, v1) = v2 & v1_xboole_0(v8) & v1_xboole_0(k1_xboole_0) & l1_cat_1(v9) & l1_cat_1(v3) & l1_cat_1(v1) & l1_cat_1(v0) & v2_cat_1(v3) & v2_cat_1(v1) & v2_cat_1(v0) & ~ v1_xboole_0(v7) & ~ r1_isocat_1(v4, v6) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v15 | ~ (g1_cat_1(v17, v18, v19, v20, v21, v22) = v16) | ~ (g1_cat_1(v10, v11, v12, v13, v14, v15) = v16) | ~ m1_relset_1(v15, v10, v11) | ~ m1_relset_1(v13, v11, v10) | ~ m1_relset_1(v12, v11, v10) | ~ v1_funct_2(v15, v10, v11) | ~ v1_funct_2(v13, v11, v10) | ~ v1_funct_2(v12, v11, v10) | ~ v1_funct_1(v15) | ~ v1_funct_1(v14) | ~ v1_funct_1(v13) | ~ v1_funct_1(v12) | v1_xboole_0(v11) | v1_xboole_0(v10) | ? [v23] : (k2_zfmisc_1(v11, v11) = v23 & ~ m1_relset_1(v14, v23, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = v14 | ~ (g1_cat_1(v17, v18, v19, v20, v21, v22) = v16) | ~ (g1_cat_1(v10, v11, v12, v13, v14, v15) = v16) | ~ m1_relset_1(v15, v10, v11) | ~ m1_relset_1(v13, v11, v10) | ~ m1_relset_1(v12, v11, v10) | ~ v1_funct_2(v15, v10, v11) | ~ v1_funct_2(v13, v11, v10) | ~ v1_funct_2(v12, v11, v10) | ~ v1_funct_1(v15) | ~ v1_funct_1(v14) | ~ v1_funct_1(v13) | ~ v1_funct_1(v12) | v1_xboole_0(v11) | v1_xboole_0(v10) | ? [v23] : (k2_zfmisc_1(v11, v11) = v23 & ~ m1_relset_1(v14, v23, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v13 | ~ (g1_cat_1(v17, v18, v19, v20, v21, v22) = v16) | ~ (g1_cat_1(v10, v11, v12, v13, v14, v15) = v16) | ~ m1_relset_1(v15, v10, v11) | ~ m1_relset_1(v13, v11, v10) | ~ m1_relset_1(v12, v11, v10) | ~ v1_funct_2(v15, v10, v11) | ~ v1_funct_2(v13, v11, v10) | ~ v1_funct_2(v12, v11, v10) | ~ v1_funct_1(v15) | ~ v1_funct_1(v14) | ~ v1_funct_1(v13) | ~ v1_funct_1(v12) | v1_xboole_0(v11) | v1_xboole_0(v10) | ? [v23] : (k2_zfmisc_1(v11, v11) = v23 & ~ m1_relset_1(v14, v23, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v12 | ~ (g1_cat_1(v17, v18, v19, v20, v21, v22) = v16) | ~ (g1_cat_1(v10, v11, v12, v13, v14, v15) = v16) | ~ m1_relset_1(v15, v10, v11) | ~ m1_relset_1(v13, v11, v10) | ~ m1_relset_1(v12, v11, v10) | ~ v1_funct_2(v15, v10, v11) | ~ v1_funct_2(v13, v11, v10) | ~ v1_funct_2(v12, v11, v10) | ~ v1_funct_1(v15) | ~ v1_funct_1(v14) | ~ v1_funct_1(v13) | ~ v1_funct_1(v12) | v1_xboole_0(v11) | v1_xboole_0(v10) | ? [v23] : (k2_zfmisc_1(v11, v11) = v23 & ~ m1_relset_1(v14, v23, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v18 = v11 | ~ (g1_cat_1(v17, v18, v19, v20, v21, v22) = v16) | ~ (g1_cat_1(v10, v11, v12, v13, v14, v15) = v16) | ~ m1_relset_1(v15, v10, v11) | ~ m1_relset_1(v13, v11, v10) | ~ m1_relset_1(v12, v11, v10) | ~ v1_funct_2(v15, v10, v11) | ~ v1_funct_2(v13, v11, v10) | ~ v1_funct_2(v12, v11, v10) | ~ v1_funct_1(v15) | ~ v1_funct_1(v14) | ~ v1_funct_1(v13) | ~ v1_funct_1(v12) | v1_xboole_0(v11) | v1_xboole_0(v10) | ? [v23] : (k2_zfmisc_1(v11, v11) = v23 & ~ m1_relset_1(v14, v23, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v17 = v10 | ~ (g1_cat_1(v17, v18, v19, v20, v21, v22) = v16) | ~ (g1_cat_1(v10, v11, v12, v13, v14, v15) = v16) | ~ m1_relset_1(v15, v10, v11) | ~ m1_relset_1(v13, v11, v10) | ~ m1_relset_1(v12, v11, v10) | ~ v1_funct_2(v15, v10, v11) | ~ v1_funct_2(v13, v11, v10) | ~ v1_funct_2(v12, v11, v10) | ~ v1_funct_1(v15) | ~ v1_funct_1(v14) | ~ v1_funct_1(v13) | ~ v1_funct_1(v12) | v1_xboole_0(v11) | v1_xboole_0(v10) | ? [v23] : (k2_zfmisc_1(v11, v11) = v23 & ~ m1_relset_1(v14, v23, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v10 | ~ (u1_cat_1(v10) = v11) | ~ (u2_cat_1(v10) = v12) | ~ (u3_cat_1(v10) = v13) | ~ (u4_cat_1(v10) = v14) | ~ (u5_cat_1(v10) = v15) | ~ (u6_cat_1(v10) = v16) | ~ (g1_cat_1(v11, v12, v13, v14, v15, v16) = v17) | ~ v1_cat_1(v10) | ~ l1_cat_1(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v11 = v10 | ~ (g1_cat_1(v17, v16, v15, v14, v13, v12) = v11) | ~ (g1_cat_1(v17, v16, v15, v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (g1_cat_1(v10, v11, v12, v13, v14, v15) = v16) | ~ m1_relset_1(v15, v10, v11) | ~ m1_relset_1(v13, v11, v10) | ~ m1_relset_1(v12, v11, v10) | ~ v1_funct_2(v15, v10, v11) | ~ v1_funct_2(v13, v11, v10) | ~ v1_funct_2(v12, v11, v10) | ~ v1_funct_1(v15) | ~ v1_funct_1(v14) | ~ v1_funct_1(v13) | ~ v1_funct_1(v12) | v1_xboole_0(v11) | v1_xboole_0(v10) | v1_cat_1(v16) | ? [v17] : (k2_zfmisc_1(v11, v11) = v17 & ~ m1_relset_1(v14, v17, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (g1_cat_1(v10, v11, v12, v13, v14, v15) = v16) | ~ m1_relset_1(v15, v10, v11) | ~ m1_relset_1(v13, v11, v10) | ~ m1_relset_1(v12, v11, v10) | ~ v1_funct_2(v15, v10, v11) | ~ v1_funct_2(v13, v11, v10) | ~ v1_funct_2(v12, v11, v10) | ~ v1_funct_1(v15) | ~ v1_funct_1(v14) | ~ v1_funct_1(v13) | ~ v1_funct_1(v12) | v1_xboole_0(v11) | v1_xboole_0(v10) | l1_cat_1(v16) | ? [v17] : (k2_zfmisc_1(v11, v11) = v17 & ~ m1_relset_1(v14, v17, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (k12_nattra_1(v11, v13) = v14) | ~ (k12_nattra_1(v10, v14) = v15) | ~ (k11_cat_2(v10, v11) = v12) | ~ l1_cat_1(v13) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v13) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | ? [v16] : ? [v17] : (k7_isocat_2(v10, v11, v13) = v16 & k12_nattra_1(v12, v13) = v17 & v8_cat_1(v16, v17, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (k7_isocat_2(v14, v13, v12) = v11) | ~ (k7_isocat_2(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (k7_isocat_2(v10, v11, v13) = v14) | ~ (k11_cat_2(v10, v11) = v12) | ~ l1_cat_1(v13) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v13) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | ? [v15] : ? [v16] : ? [v17] : (k12_nattra_1(v12, v13) = v15 & k12_nattra_1(v11, v13) = v16 & k12_nattra_1(v10, v16) = v17 & v8_cat_1(v14, v15, v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (k12_nattra_1(v13, v12) = v14) | ~ (k11_cat_2(v10, v11) = v13) | ~ l1_cat_1(v12) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v12) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | ? [v15] : ? [v16] : ? [v17] : (k7_isocat_2(v10, v11, v12) = v15 & k12_nattra_1(v11, v12) = v16 & k12_nattra_1(v10, v16) = v17 & m2_cat_1(v15, v14, v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (k12_nattra_1(v12, v13) = v14) | ~ (k11_cat_2(v10, v11) = v12) | ~ l1_cat_1(v13) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v13) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | ? [v15] : ? [v16] : ? [v17] : (k7_isocat_2(v10, v11, v13) = v15 & k12_nattra_1(v11, v13) = v16 & k12_nattra_1(v10, v16) = v17 & v8_cat_1(v15, v14, v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (k12_nattra_1(v11, v12) = v13) | ~ (k12_nattra_1(v10, v13) = v14) | ~ l1_cat_1(v12) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v12) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | ? [v15] : ? [v16] : ? [v17] : (k7_isocat_2(v10, v11, v12) = v15 & k12_nattra_1(v16, v12) = v17 & k11_cat_2(v10, v11) = v16 & m2_cat_1(v15, v17, v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (u2_cat_1(v11) = v13) | ~ (u2_cat_1(v10) = v12) | ~ m2_cat_1(v14, v10, v11) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | m2_relset_1(v14, v12, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (u2_cat_1(v11) = v13) | ~ (u2_cat_1(v10) = v12) | ~ m2_cat_1(v14, v10, v11) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | v1_funct_2(v14, v12, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (u2_cat_1(v11) = v13) | ~ (u2_cat_1(v10) = v12) | ~ m2_cat_1(v14, v10, v11) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | v1_funct_1(v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (k12_nattra_1(v13, v12) = v11) | ~ (k12_nattra_1(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (k11_cat_2(v13, v12) = v11) | ~ (k11_cat_2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (k2_zfmisc_1(v13, v12) = v11) | ~ (k2_zfmisc_1(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (k7_isocat_2(v10, v11, v12) = v13) | ~ l1_cat_1(v12) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v12) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (k12_nattra_1(v14, v12) = v15 & k12_nattra_1(v11, v12) = v16 & k12_nattra_1(v10, v16) = v17 & k11_cat_2(v10, v11) = v14 & m2_cat_1(v13, v15, v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (k2_zfmisc_1(v10, v11) = v13) | ~ m2_relset_1(v12, v10, v11) | ? [v14] : (k1_zfmisc_1(v13) = v14 & m1_subset_1(v12, v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (k1_zfmisc_1(v12) = v13) | ~ v1_xboole_0(v12) | ~ m1_subset_1(v11, v13) | ~ r2_hidden(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (k1_zfmisc_1(v12) = v13) | ~ m1_subset_1(v11, v13) | ~ r2_hidden(v10, v11) | m1_subset_1(v10, v12)) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (k2_zfmisc_1(v11, v12) = v13) | v1_relat_1(v10) | ? [v14] : (k1_zfmisc_1(v13) = v14 & ~ m1_subset_1(v10, v14))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (k1_zfmisc_1(v12) = v11) | ~ (k1_zfmisc_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (u1_cat_1(v12) = v11) | ~ (u1_cat_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (u2_cat_1(v12) = v11) | ~ (u2_cat_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (u3_cat_1(v12) = v11) | ~ (u3_cat_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (u4_cat_1(v12) = v11) | ~ (u4_cat_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (u5_cat_1(v12) = v11) | ~ (u5_cat_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (u6_cat_1(v12) = v11) | ~ (u6_cat_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k12_nattra_1(v10, v11) = v12) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | v1_cat_1(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k12_nattra_1(v10, v11) = v12) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | l1_cat_1(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k12_nattra_1(v10, v11) = v12) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | v2_cat_1(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k11_cat_2(v10, v11) = v12) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | l1_cat_1(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k11_cat_2(v10, v11) = v12) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | v2_cat_1(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k2_zfmisc_1(v11, v11) = v12) | ~ (u2_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v13] : (u5_cat_1(v10) = v13 & m2_relset_1(v13, v12, v11) & v1_funct_1(v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k2_zfmisc_1(v10, v11) = v12) | ~ v1_xboole_0(v12) | v1_xboole_0(v11) | v1_xboole_0(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k1_zfmisc_1(v11) = v12) | ~ r1_tarski(v10, v11) | m1_subset_1(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (k1_zfmisc_1(v11) = v12) | ~ m1_subset_1(v10, v12) | r1_tarski(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ m2_relset_1(v12, v10, v11) | m1_relset_1(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ m1_relset_1(v12, v10, v11) | m2_relset_1(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ v8_cat_1(v12, v10, v11) | ~ m2_cat_1(v12, v10, v11) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | r1_isocat_1(v10, v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ v1_xboole_0(v11) | ~ v1_xboole_0(v10)) & ! [v10] : ! [v11] : ( ~ (k1_zfmisc_1(v10) = v11) | ~ v1_xboole_0(v11)) & ! [v10] : ! [v11] : ( ~ (k1_zfmisc_1(v10) = v11) | v1_xboole_0(v10) | ? [v12] : (m1_subset_1(v12, v11) & ~ v1_xboole_0(v12))) & ! [v10] : ! [v11] : ( ~ (k1_zfmisc_1(v10) = v11) | ? [v12] : (v1_xboole_0(v12) & m1_subset_1(v12, v11))) & ! [v10] : ! [v11] : ( ~ (u1_cat_1(v10) = v11) | ~ v1_xboole_0(v11) | ~ l1_cat_1(v10)) & ! [v10] : ! [v11] : ( ~ (u1_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (u2_cat_1(v10) = v13 & u3_cat_1(v10) = v12 & m2_relset_1(v12, v13, v11) & v1_funct_2(v12, v13, v11) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (u1_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (u2_cat_1(v10) = v13 & u4_cat_1(v10) = v12 & m2_relset_1(v12, v13, v11) & v1_funct_2(v12, v13, v11) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (u1_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (u2_cat_1(v10) = v13 & u6_cat_1(v10) = v12 & m2_relset_1(v12, v11, v13) & v1_funct_2(v12, v11, v13) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (u2_cat_1(v10) = v11) | ~ v1_xboole_0(v11) | ~ l1_cat_1(v10)) & ! [v10] : ! [v11] : ( ~ (u2_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (k2_zfmisc_1(v11, v11) = v13 & u5_cat_1(v10) = v12 & m2_relset_1(v12, v13, v11) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (u2_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (u1_cat_1(v10) = v13 & u3_cat_1(v10) = v12 & m2_relset_1(v12, v11, v13) & v1_funct_2(v12, v11, v13) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (u2_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (u1_cat_1(v10) = v13 & u4_cat_1(v10) = v12 & m2_relset_1(v12, v11, v13) & v1_funct_2(v12, v11, v13) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (u2_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (u1_cat_1(v10) = v13 & u6_cat_1(v10) = v12 & m2_relset_1(v12, v13, v11) & v1_funct_2(v12, v13, v11) & v1_funct_1(v12))) & ! [v10] : ! [v11] : ( ~ (u3_cat_1(v10) = v11) | ~ l1_cat_1(v10) | v1_funct_1(v11)) & ! [v10] : ! [v11] : ( ~ (u3_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (u1_cat_1(v10) = v13 & u2_cat_1(v10) = v12 & m2_relset_1(v11, v12, v13) & v1_funct_2(v11, v12, v13))) & ! [v10] : ! [v11] : ( ~ (u4_cat_1(v10) = v11) | ~ l1_cat_1(v10) | v1_funct_1(v11)) & ! [v10] : ! [v11] : ( ~ (u4_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (u1_cat_1(v10) = v13 & u2_cat_1(v10) = v12 & m2_relset_1(v11, v12, v13) & v1_funct_2(v11, v12, v13))) & ! [v10] : ! [v11] : ( ~ (u5_cat_1(v10) = v11) | ~ l1_cat_1(v10) | v1_funct_1(v11)) & ! [v10] : ! [v11] : ( ~ (u5_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (k2_zfmisc_1(v12, v12) = v13 & u2_cat_1(v10) = v12 & m2_relset_1(v11, v13, v12))) & ! [v10] : ! [v11] : ( ~ (u6_cat_1(v10) = v11) | ~ l1_cat_1(v10) | v1_funct_1(v11)) & ! [v10] : ! [v11] : ( ~ (u6_cat_1(v10) = v11) | ~ l1_cat_1(v10) | ? [v12] : ? [v13] : (u1_cat_1(v10) = v12 & u2_cat_1(v10) = v13 & m2_relset_1(v11, v12, v13) & v1_funct_2(v11, v12, v13))) & ! [v10] : ! [v11] : ( ~ v1_xboole_0(v11) | ~ r2_hidden(v10, v11)) & ! [v10] : ! [v11] : ( ~ m1_subset_1(v10, v11) | v1_xboole_0(v11) | r2_hidden(v10, v11)) & ! [v10] : ! [v11] : ( ~ r2_hidden(v11, v10) | ~ r2_hidden(v10, v11)) & ! [v10] : ! [v11] : ( ~ r2_hidden(v10, v11) | m1_subset_1(v10, v11)) & ! [v10] : ! [v11] : ( ~ r1_isocat_1(v10, v11) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | r1_isocat_1(v11, v10)) & ! [v10] : ! [v11] : ( ~ r1_isocat_1(v10, v11) | ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | ? [v12] : (v8_cat_1(v12, v10, v11) & m2_cat_1(v12, v10, v11))) & ! [v10] : ! [v11] : ( ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | r1_isocat_1(v10, v10)) & ! [v10] : ! [v11] : ( ~ l1_cat_1(v11) | ~ l1_cat_1(v10) | ~ v2_cat_1(v11) | ~ v2_cat_1(v10) | ? [v12] : m2_cat_1(v12, v10, v11)) & ! [v10] : (v10 = k1_xboole_0 | ~ v1_xboole_0(v10)) & ? [v10] : ? [v11] : ? [v12] : m2_relset_1(v12, v10, v11) & ? [v10] : ? [v11] : ? [v12] : m1_relset_1(v12, v10, v11) & ? [v10] : ? [v11] : m1_subset_1(v11, v10) & ? [v10] : r1_tarski(v10, v10)) % 6.50/2.05 | 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 yields: % 6.50/2.05 | (1) k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5 & k12_nattra_1(all_0_8_8, all_0_6_6) = all_0_4_4 & k12_nattra_1(all_0_9_9, all_0_4_4) = all_0_3_3 & k11_cat_2(all_0_9_9, all_0_8_8) = all_0_7_7 & v1_xboole_0(all_0_1_1) & v1_xboole_0(k1_xboole_0) & l1_cat_1(all_0_0_0) & l1_cat_1(all_0_6_6) & l1_cat_1(all_0_8_8) & l1_cat_1(all_0_9_9) & v2_cat_1(all_0_6_6) & v2_cat_1(all_0_8_8) & v2_cat_1(all_0_9_9) & ~ v1_xboole_0(all_0_2_2) & ~ r1_isocat_1(all_0_5_5, all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v5 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v4 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v3 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v2 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v1 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v0 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v0 | ~ (u1_cat_1(v0) = v1) | ~ (u2_cat_1(v0) = v2) | ~ (u3_cat_1(v0) = v3) | ~ (u4_cat_1(v0) = v4) | ~ (u5_cat_1(v0) = v5) | ~ (u6_cat_1(v0) = v6) | ~ (g1_cat_1(v1, v2, v3, v4, v5, v6) = v7) | ~ v1_cat_1(v0) | ~ l1_cat_1(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (g1_cat_1(v7, v6, v5, v4, v3, v2) = v1) | ~ (g1_cat_1(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | v1_cat_1(v6) | ? [v7] : (k2_zfmisc_1(v1, v1) = v7 & ~ m1_relset_1(v4, v7, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | l1_cat_1(v6) | ? [v7] : (k2_zfmisc_1(v1, v1) = v7 & ~ m1_relset_1(v4, v7, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k12_nattra_1(v1, v3) = v4) | ~ (k12_nattra_1(v0, v4) = v5) | ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v6] : ? [v7] : (k7_isocat_2(v0, v1, v3) = v6 & k12_nattra_1(v2, v3) = v7 & v8_cat_1(v6, v7, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k7_isocat_2(v4, v3, v2) = v1) | ~ (k7_isocat_2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k7_isocat_2(v0, v1, v3) = v4) | ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5] : ? [v6] : ? [v7] : (k12_nattra_1(v2, v3) = v5 & k12_nattra_1(v1, v3) = v6 & k12_nattra_1(v0, v6) = v7 & v8_cat_1(v4, v5, v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k12_nattra_1(v3, v2) = v4) | ~ (k11_cat_2(v0, v1) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5] : ? [v6] : ? [v7] : (k7_isocat_2(v0, v1, v2) = v5 & k12_nattra_1(v1, v2) = v6 & k12_nattra_1(v0, v6) = v7 & m2_cat_1(v5, v4, v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k12_nattra_1(v2, v3) = v4) | ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5] : ? [v6] : ? [v7] : (k7_isocat_2(v0, v1, v3) = v5 & k12_nattra_1(v1, v3) = v6 & k12_nattra_1(v0, v6) = v7 & v8_cat_1(v5, v4, v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k12_nattra_1(v1, v2) = v3) | ~ (k12_nattra_1(v0, v3) = v4) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5] : ? [v6] : ? [v7] : (k7_isocat_2(v0, v1, v2) = v5 & k12_nattra_1(v6, v2) = v7 & k11_cat_2(v0, v1) = v6 & m2_cat_1(v5, v7, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_relset_1(v4, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_funct_2(v4, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_funct_1(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k12_nattra_1(v3, v2) = v1) | ~ (k12_nattra_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k11_cat_2(v3, v2) = v1) | ~ (k11_cat_2(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] : ( ~ (k7_isocat_2(v0, v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (k12_nattra_1(v4, v2) = v5 & k12_nattra_1(v1, v2) = v6 & k12_nattra_1(v0, v6) = v7 & k11_cat_2(v0, v1) = v4 & m2_cat_1(v3, v5, v7))) & ! [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) | ~ v1_xboole_0(v2) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1) | 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 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_cat_1(v2) = v1) | ~ (u1_cat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u2_cat_1(v2) = v1) | ~ (u2_cat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u3_cat_1(v2) = v1) | ~ (u3_cat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u4_cat_1(v2) = v1) | ~ (u4_cat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u5_cat_1(v2) = v1) | ~ (u5_cat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u6_cat_1(v2) = v1) | ~ (u6_cat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k12_nattra_1(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_cat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k12_nattra_1(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | l1_cat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k12_nattra_1(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v2_cat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | l1_cat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v2_cat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v1, v1) = v2) | ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v3] : (u5_cat_1(v0) = v3 & m2_relset_1(v3, v2, v1) & v1_funct_1(v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0)) & ! [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] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v8_cat_1(v2, v0, v1) | ~ m2_cat_1(v2, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r1_isocat_1(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [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] : ( ~ (u1_cat_1(v0) = v1) | ~ v1_xboole_0(v1) | ~ l1_cat_1(v0)) & ! [v0] : ! [v1] : ( ~ (u1_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u2_cat_1(v0) = v3 & u3_cat_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ (u1_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u2_cat_1(v0) = v3 & u4_cat_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ (u1_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u2_cat_1(v0) = v3 & u6_cat_1(v0) = v2 & m2_relset_1(v2, v1, v3) & v1_funct_2(v2, v1, v3) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ v1_xboole_0(v1) | ~ l1_cat_1(v0)) & ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (k2_zfmisc_1(v1, v1) = v3 & u5_cat_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u3_cat_1(v0) = v2 & m2_relset_1(v2, v1, v3) & v1_funct_2(v2, v1, v3) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u4_cat_1(v0) = v2 & m2_relset_1(v2, v1, v3) & v1_funct_2(v2, v1, v3) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u6_cat_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2))) & ! [v0] : ! [v1] : ( ~ (u3_cat_1(v0) = v1) | ~ l1_cat_1(v0) | v1_funct_1(v1)) & ! [v0] : ! [v1] : ( ~ (u3_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u2_cat_1(v0) = v2 & m2_relset_1(v1, v2, v3) & v1_funct_2(v1, v2, v3))) & ! [v0] : ! [v1] : ( ~ (u4_cat_1(v0) = v1) | ~ l1_cat_1(v0) | v1_funct_1(v1)) & ! [v0] : ! [v1] : ( ~ (u4_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u2_cat_1(v0) = v2 & m2_relset_1(v1, v2, v3) & v1_funct_2(v1, v2, v3))) & ! [v0] : ! [v1] : ( ~ (u5_cat_1(v0) = v1) | ~ l1_cat_1(v0) | v1_funct_1(v1)) & ! [v0] : ! [v1] : ( ~ (u5_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (k2_zfmisc_1(v2, v2) = v3 & u2_cat_1(v0) = v2 & m2_relset_1(v1, v3, v2))) & ! [v0] : ! [v1] : ( ~ (u6_cat_1(v0) = v1) | ~ l1_cat_1(v0) | v1_funct_1(v1)) & ! [v0] : ! [v1] : ( ~ (u6_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v2 & u2_cat_1(v0) = v3 & m2_relset_1(v1, v2, v3) & v1_funct_2(v1, v2, v3))) & ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_subset_1(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] : ( ~ r1_isocat_1(v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r1_isocat_1(v1, v0)) & ! [v0] : ! [v1] : ( ~ r1_isocat_1(v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v2] : (v8_cat_1(v2, v0, v1) & m2_cat_1(v2, v0, v1))) & ! [v0] : ! [v1] : ( ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r1_isocat_1(v0, v0)) & ! [v0] : ! [v1] : ( ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v2] : m2_cat_1(v2, v0, v1)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : r1_tarski(v0, v0) % 6.91/2.08 | % 6.91/2.08 | Applying alpha-rule on (1) yields: % 6.91/2.08 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k12_nattra_1(v3, v2) = v1) | ~ (k12_nattra_1(v3, v2) = v0)) % 6.91/2.08 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u4_cat_1(v2) = v1) | ~ (u4_cat_1(v2) = v0)) % 6.91/2.08 | (4) v2_cat_1(all_0_6_6) % 6.91/2.08 | (5) ! [v0] : ! [v1] : ( ~ (u5_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (k2_zfmisc_1(v2, v2) = v3 & u2_cat_1(v0) = v2 & m2_relset_1(v1, v3, v2))) % 6.91/2.08 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k12_nattra_1(v1, v2) = v3) | ~ (k12_nattra_1(v0, v3) = v4) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5] : ? [v6] : ? [v7] : (k7_isocat_2(v0, v1, v2) = v5 & k12_nattra_1(v6, v2) = v7 & k11_cat_2(v0, v1) = v6 & m2_cat_1(v5, v7, v4))) % 6.91/2.08 | (7) v1_xboole_0(all_0_1_1) % 6.91/2.08 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (g1_cat_1(v7, v6, v5, v4, v3, v2) = v1) | ~ (g1_cat_1(v7, v6, v5, v4, v3, v2) = v0)) % 6.91/2.08 | (9) ! [v0] : ! [v1] : ( ~ (u3_cat_1(v0) = v1) | ~ l1_cat_1(v0) | v1_funct_1(v1)) % 6.91/2.08 | (10) l1_cat_1(all_0_8_8) % 6.91/2.08 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_funct_2(v4, v2, v3)) % 6.91/2.08 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (k12_nattra_1(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v2_cat_1(v2)) % 6.91/2.08 | (13) ! [v0] : ! [v1] : ( ~ (u1_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u2_cat_1(v0) = v3 & u3_cat_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2))) % 6.91/2.08 | (14) ? [v0] : ? [v1] : m1_subset_1(v1, v0) % 6.91/2.08 | (15) ~ r1_isocat_1(all_0_5_5, all_0_3_3) % 6.91/2.08 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v2_cat_1(v2)) % 6.91/2.08 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v3 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) % 6.91/2.08 | (18) ! [v0] : ! [v1] : ( ~ (u5_cat_1(v0) = v1) | ~ l1_cat_1(v0) | v1_funct_1(v1)) % 6.91/2.08 | (19) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (v1_xboole_0(v2) & m1_subset_1(v2, v1))) % 6.91/2.08 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u5_cat_1(v2) = v1) | ~ (u5_cat_1(v2) = v0)) % 6.91/2.08 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v1 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) % 6.91/2.08 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k11_cat_2(v3, v2) = v1) | ~ (k11_cat_2(v3, v2) = v0)) % 6.91/2.08 | (23) ! [v0] : ! [v1] : ( ~ (u1_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u2_cat_1(v0) = v3 & u6_cat_1(v0) = v2 & m2_relset_1(v2, v1, v3) & v1_funct_2(v2, v1, v3) & v1_funct_1(v2))) % 6.91/2.08 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ v8_cat_1(v2, v0, v1) | ~ m2_cat_1(v2, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r1_isocat_1(v0, v1)) % 6.91/2.08 | (25) k12_nattra_1(all_0_9_9, all_0_4_4) = all_0_3_3 % 6.91/2.08 | (26) k11_cat_2(all_0_9_9, all_0_8_8) = all_0_7_7 % 6.91/2.08 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1)) % 6.91/2.08 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2)) % 6.91/2.08 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 6.91/2.08 | (30) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1)) % 6.91/2.08 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ v1_xboole_0(v2) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1)) % 7.02/2.08 | (32) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) % 7.02/2.09 | (33) k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5 % 7.02/2.09 | (34) ! [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))) % 7.02/2.09 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1) | m1_subset_1(v0, v2)) % 7.02/2.09 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0)) % 7.02/2.09 | (37) ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (k2_zfmisc_1(v1, v1) = v3 & u5_cat_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_1(v2))) % 7.02/2.09 | (38) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1)) % 7.02/2.09 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (k12_nattra_1(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_cat_1(v2)) % 7.02/2.09 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | v1_cat_1(v6) | ? [v7] : (k2_zfmisc_1(v1, v1) = v7 & ~ m1_relset_1(v4, v7, v1))) % 7.02/2.09 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k7_isocat_2(v0, v1, v2) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (k12_nattra_1(v4, v2) = v5 & k12_nattra_1(v1, v2) = v6 & k12_nattra_1(v0, v6) = v7 & k11_cat_2(v0, v1) = v4 & m2_cat_1(v3, v5, v7))) % 7.02/2.09 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u3_cat_1(v2) = v1) | ~ (u3_cat_1(v2) = v0)) % 7.02/2.09 | (43) ! [v0] : ! [v1] : ( ~ (u1_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u2_cat_1(v0) = v3 & u4_cat_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2))) % 7.02/2.09 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u1_cat_1(v2) = v1) | ~ (u1_cat_1(v2) = v0)) % 7.02/2.09 | (45) ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u6_cat_1(v0) = v2 & m2_relset_1(v2, v3, v1) & v1_funct_2(v2, v3, v1) & v1_funct_1(v2))) % 7.02/2.09 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k12_nattra_1(v2, v3) = v4) | ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5] : ? [v6] : ? [v7] : (k7_isocat_2(v0, v1, v3) = v5 & k12_nattra_1(v1, v3) = v6 & k12_nattra_1(v0, v6) = v7 & v8_cat_1(v5, v4, v7))) % 7.02/2.09 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | m2_relset_1(v4, v2, v3)) % 7.02/2.09 | (48) ? [v0] : r1_tarski(v0, v0) % 7.02/2.09 | (49) ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u3_cat_1(v0) = v2 & m2_relset_1(v2, v1, v3) & v1_funct_2(v2, v1, v3) & v1_funct_1(v2))) % 7.02/2.09 | (50) l1_cat_1(all_0_0_0) % 7.02/2.09 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v5 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) % 7.02/2.09 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k7_isocat_2(v4, v3, v2) = v1) | ~ (k7_isocat_2(v4, v3, v2) = v0)) % 7.02/2.09 | (53) v1_xboole_0(k1_xboole_0) % 7.02/2.09 | (54) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) % 7.02/2.09 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (k12_nattra_1(v1, v3) = v4) | ~ (k12_nattra_1(v0, v4) = v5) | ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v6] : ? [v7] : (k7_isocat_2(v0, v1, v3) = v6 & k12_nattra_1(v2, v3) = v7 & v8_cat_1(v6, v7, v5))) % 7.02/2.09 | (56) ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1)) % 7.02/2.09 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (k12_nattra_1(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | l1_cat_1(v2)) % 7.02/2.09 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v1, v1) = v2) | ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v3] : (u5_cat_1(v0) = v3 & m2_relset_1(v3, v2, v1) & v1_funct_1(v3))) % 7.02/2.09 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | l1_cat_1(v6) | ? [v7] : (k2_zfmisc_1(v1, v1) = v7 & ~ m1_relset_1(v4, v7, v1))) % 7.02/2.09 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) % 7.02/2.09 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u6_cat_1(v2) = v1) | ~ (u6_cat_1(v2) = v0)) % 7.02/2.09 | (62) ! [v0] : ! [v1] : ( ~ (u6_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v2 & u2_cat_1(v0) = v3 & m2_relset_1(v1, v2, v3) & v1_funct_2(v1, v2, v3))) % 7.02/2.09 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | l1_cat_1(v2)) % 7.02/2.09 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v4 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) % 7.02/2.10 | (65) ! [v0] : ! [v1] : ( ~ (u3_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u2_cat_1(v0) = v2 & m2_relset_1(v1, v2, v3) & v1_funct_2(v1, v2, v3))) % 7.02/2.10 | (66) l1_cat_1(all_0_9_9) % 7.02/2.10 | (67) v2_cat_1(all_0_9_9) % 7.02/2.10 | (68) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2))) % 7.02/2.10 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v2 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) % 7.02/2.10 | (70) v2_cat_1(all_0_8_8) % 7.02/2.10 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1)) % 7.02/2.10 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1)) % 7.02/2.10 | (73) ! [v0] : ! [v1] : ( ~ (u6_cat_1(v0) = v1) | ~ l1_cat_1(v0) | v1_funct_1(v1)) % 7.02/2.10 | (74) ? [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))) % 7.02/2.10 | (75) ~ v1_xboole_0(all_0_2_2) % 7.02/2.10 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v0 | ~ (g1_cat_1(v7, v8, v9, v10, v11, v12) = v6) | ~ (g1_cat_1(v0, v1, v2, v3, v4, v5) = v6) | ~ m1_relset_1(v5, v0, v1) | ~ m1_relset_1(v3, v1, v0) | ~ m1_relset_1(v2, v1, v0) | ~ v1_funct_2(v5, v0, v1) | ~ v1_funct_2(v3, v1, v0) | ~ v1_funct_2(v2, v1, v0) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~ v1_funct_1(v3) | ~ v1_funct_1(v2) | v1_xboole_0(v1) | v1_xboole_0(v0) | ? [v13] : (k2_zfmisc_1(v1, v1) = v13 & ~ m1_relset_1(v4, v13, v1))) % 7.02/2.10 | (77) ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ v1_xboole_0(v1) | ~ l1_cat_1(v0)) % 7.02/2.10 | (78) ! [v0] : ! [v1] : ( ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r1_isocat_1(v0, v0)) % 7.02/2.10 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k7_isocat_2(v0, v1, v3) = v4) | ~ (k11_cat_2(v0, v1) = v2) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5] : ? [v6] : ? [v7] : (k12_nattra_1(v2, v3) = v5 & k12_nattra_1(v1, v3) = v6 & k12_nattra_1(v0, v6) = v7 & v8_cat_1(v4, v5, v7))) % 7.02/2.10 | (80) ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) % 7.02/2.10 | (81) ! [v0] : ! [v1] : ( ~ r1_isocat_1(v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r1_isocat_1(v1, v0)) % 7.02/2.10 | (82) k12_nattra_1(all_0_8_8, all_0_6_6) = all_0_4_4 % 7.02/2.10 | (83) ! [v0] : ! [v1] : ( ~ (u1_cat_1(v0) = v1) | ~ v1_xboole_0(v1) | ~ l1_cat_1(v0)) % 7.02/2.10 | (84) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) % 7.02/2.10 | (85) ! [v0] : ! [v1] : ( ~ r1_isocat_1(v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v2] : (v8_cat_1(v2, v0, v1) & m2_cat_1(v2, v0, v1))) % 7.02/2.10 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (u2_cat_1(v1) = v3) | ~ (u2_cat_1(v0) = v2) | ~ m2_cat_1(v4, v0, v1) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v1_funct_1(v4)) % 7.02/2.10 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (u2_cat_1(v2) = v1) | ~ (u2_cat_1(v2) = v0)) % 7.02/2.10 | (88) ! [v0] : ! [v1] : ( ~ (u4_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u2_cat_1(v0) = v2 & m2_relset_1(v1, v2, v3) & v1_funct_2(v1, v2, v3))) % 7.02/2.10 | (89) l1_cat_1(all_0_6_6) % 7.02/2.10 | (90) ! [v0] : ! [v1] : ( ~ (u4_cat_1(v0) = v1) | ~ l1_cat_1(v0) | v1_funct_1(v1)) % 7.02/2.10 | (91) ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) % 7.02/2.10 | (92) ! [v0] : ! [v1] : ( ~ (u2_cat_1(v0) = v1) | ~ l1_cat_1(v0) | ? [v2] : ? [v3] : (u1_cat_1(v0) = v3 & u4_cat_1(v0) = v2 & m2_relset_1(v2, v1, v3) & v1_funct_2(v2, v1, v3) & v1_funct_1(v2))) % 7.02/2.10 | (93) ! [v0] : ! [v1] : ( ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v2] : m2_cat_1(v2, v0, v1)) % 7.02/2.10 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v0 | ~ (u1_cat_1(v0) = v1) | ~ (u2_cat_1(v0) = v2) | ~ (u3_cat_1(v0) = v3) | ~ (u4_cat_1(v0) = v4) | ~ (u5_cat_1(v0) = v5) | ~ (u6_cat_1(v0) = v6) | ~ (g1_cat_1(v1, v2, v3, v4, v5, v6) = v7) | ~ v1_cat_1(v0) | ~ l1_cat_1(v0)) % 7.02/2.10 | (95) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) % 7.02/2.10 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k12_nattra_1(v3, v2) = v4) | ~ (k11_cat_2(v0, v1) = v3) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5] : ? [v6] : ? [v7] : (k7_isocat_2(v0, v1, v2) = v5 & k12_nattra_1(v1, v2) = v6 & k12_nattra_1(v0, v6) = v7 & m2_cat_1(v5, v4, v7))) % 7.02/2.10 | % 7.02/2.10 | Instantiating formula (57) with all_0_4_4, all_0_6_6, all_0_8_8 and discharging atoms k12_nattra_1(all_0_8_8, all_0_6_6) = all_0_4_4, l1_cat_1(all_0_6_6), l1_cat_1(all_0_8_8), v2_cat_1(all_0_6_6), v2_cat_1(all_0_8_8), yields: % 7.02/2.10 | (97) l1_cat_1(all_0_4_4) % 7.02/2.10 | % 7.02/2.10 | Instantiating formula (12) with all_0_4_4, all_0_6_6, all_0_8_8 and discharging atoms k12_nattra_1(all_0_8_8, all_0_6_6) = all_0_4_4, l1_cat_1(all_0_6_6), l1_cat_1(all_0_8_8), v2_cat_1(all_0_6_6), v2_cat_1(all_0_8_8), yields: % 7.02/2.11 | (98) v2_cat_1(all_0_4_4) % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (96) with all_0_5_5, all_0_7_7, all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5, k11_cat_2(all_0_9_9, all_0_8_8) = all_0_7_7, l1_cat_1(all_0_6_6), l1_cat_1(all_0_8_8), l1_cat_1(all_0_9_9), v2_cat_1(all_0_6_6), v2_cat_1(all_0_8_8), v2_cat_1(all_0_9_9), yields: % 7.02/2.11 | (99) ? [v0] : ? [v1] : ? [v2] : (k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = v0 & k12_nattra_1(all_0_8_8, all_0_6_6) = v1 & k12_nattra_1(all_0_9_9, v1) = v2 & m2_cat_1(v0, all_0_5_5, v2)) % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (46) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5, k11_cat_2(all_0_9_9, all_0_8_8) = all_0_7_7, l1_cat_1(all_0_6_6), l1_cat_1(all_0_8_8), l1_cat_1(all_0_9_9), v2_cat_1(all_0_6_6), v2_cat_1(all_0_8_8), v2_cat_1(all_0_9_9), yields: % 7.02/2.11 | (100) ? [v0] : ? [v1] : ? [v2] : (k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = v0 & k12_nattra_1(all_0_8_8, all_0_6_6) = v1 & k12_nattra_1(all_0_9_9, v1) = v2 & v8_cat_1(v0, all_0_5_5, v2)) % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (55) with all_0_3_3, all_0_4_4, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms k12_nattra_1(all_0_8_8, all_0_6_6) = all_0_4_4, k12_nattra_1(all_0_9_9, all_0_4_4) = all_0_3_3, k11_cat_2(all_0_9_9, all_0_8_8) = all_0_7_7, l1_cat_1(all_0_6_6), l1_cat_1(all_0_8_8), l1_cat_1(all_0_9_9), v2_cat_1(all_0_6_6), v2_cat_1(all_0_8_8), v2_cat_1(all_0_9_9), yields: % 7.02/2.11 | (101) ? [v0] : ? [v1] : (k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = v0 & k12_nattra_1(all_0_7_7, all_0_6_6) = v1 & v8_cat_1(v0, v1, all_0_3_3)) % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (6) with all_0_3_3, all_0_4_4, all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms k12_nattra_1(all_0_8_8, all_0_6_6) = all_0_4_4, k12_nattra_1(all_0_9_9, all_0_4_4) = all_0_3_3, l1_cat_1(all_0_6_6), l1_cat_1(all_0_8_8), l1_cat_1(all_0_9_9), v2_cat_1(all_0_6_6), v2_cat_1(all_0_8_8), v2_cat_1(all_0_9_9), yields: % 7.02/2.11 | (102) ? [v0] : ? [v1] : ? [v2] : (k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = v0 & k12_nattra_1(v1, all_0_6_6) = v2 & k11_cat_2(all_0_9_9, all_0_8_8) = v1 & m2_cat_1(v0, v2, all_0_3_3)) % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (63) with all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms k11_cat_2(all_0_9_9, all_0_8_8) = all_0_7_7, l1_cat_1(all_0_8_8), l1_cat_1(all_0_9_9), v2_cat_1(all_0_8_8), v2_cat_1(all_0_9_9), yields: % 7.02/2.11 | (103) l1_cat_1(all_0_7_7) % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (16) with all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms k11_cat_2(all_0_9_9, all_0_8_8) = all_0_7_7, l1_cat_1(all_0_8_8), l1_cat_1(all_0_9_9), v2_cat_1(all_0_8_8), v2_cat_1(all_0_9_9), yields: % 7.02/2.11 | (104) v2_cat_1(all_0_7_7) % 7.02/2.11 | % 7.02/2.11 | Instantiating (102) with all_29_0_23, all_29_1_24, all_29_2_25 yields: % 7.02/2.11 | (105) k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_29_2_25 & k12_nattra_1(all_29_1_24, all_0_6_6) = all_29_0_23 & k11_cat_2(all_0_9_9, all_0_8_8) = all_29_1_24 & m2_cat_1(all_29_2_25, all_29_0_23, all_0_3_3) % 7.02/2.11 | % 7.02/2.11 | Applying alpha-rule on (105) yields: % 7.02/2.11 | (106) k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_29_2_25 % 7.02/2.11 | (107) k12_nattra_1(all_29_1_24, all_0_6_6) = all_29_0_23 % 7.02/2.11 | (108) k11_cat_2(all_0_9_9, all_0_8_8) = all_29_1_24 % 7.02/2.11 | (109) m2_cat_1(all_29_2_25, all_29_0_23, all_0_3_3) % 7.02/2.11 | % 7.02/2.11 | Instantiating (101) with all_31_0_26, all_31_1_27 yields: % 7.02/2.11 | (110) k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_31_1_27 & k12_nattra_1(all_0_7_7, all_0_6_6) = all_31_0_26 & v8_cat_1(all_31_1_27, all_31_0_26, all_0_3_3) % 7.02/2.11 | % 7.02/2.11 | Applying alpha-rule on (110) yields: % 7.02/2.11 | (111) k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_31_1_27 % 7.02/2.11 | (112) k12_nattra_1(all_0_7_7, all_0_6_6) = all_31_0_26 % 7.02/2.11 | (113) v8_cat_1(all_31_1_27, all_31_0_26, all_0_3_3) % 7.02/2.11 | % 7.02/2.11 | Instantiating (100) with all_43_0_33, all_43_1_34, all_43_2_35 yields: % 7.02/2.11 | (114) k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_43_2_35 & k12_nattra_1(all_0_8_8, all_0_6_6) = all_43_1_34 & k12_nattra_1(all_0_9_9, all_43_1_34) = all_43_0_33 & v8_cat_1(all_43_2_35, all_0_5_5, all_43_0_33) % 7.02/2.11 | % 7.02/2.11 | Applying alpha-rule on (114) yields: % 7.02/2.11 | (115) k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_43_2_35 % 7.02/2.11 | (116) k12_nattra_1(all_0_8_8, all_0_6_6) = all_43_1_34 % 7.02/2.11 | (117) k12_nattra_1(all_0_9_9, all_43_1_34) = all_43_0_33 % 7.02/2.11 | (118) v8_cat_1(all_43_2_35, all_0_5_5, all_43_0_33) % 7.02/2.11 | % 7.02/2.11 | Instantiating (99) with all_45_0_36, all_45_1_37, all_45_2_38 yields: % 7.02/2.11 | (119) k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_45_2_38 & k12_nattra_1(all_0_8_8, all_0_6_6) = all_45_1_37 & k12_nattra_1(all_0_9_9, all_45_1_37) = all_45_0_36 & m2_cat_1(all_45_2_38, all_0_5_5, all_45_0_36) % 7.02/2.11 | % 7.02/2.11 | Applying alpha-rule on (119) yields: % 7.02/2.11 | (120) k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_45_2_38 % 7.02/2.11 | (121) k12_nattra_1(all_0_8_8, all_0_6_6) = all_45_1_37 % 7.02/2.11 | (122) k12_nattra_1(all_0_9_9, all_45_1_37) = all_45_0_36 % 7.02/2.11 | (123) m2_cat_1(all_45_2_38, all_0_5_5, all_45_0_36) % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (52) with all_0_9_9, all_0_8_8, all_0_6_6, all_43_2_35, all_45_2_38 and discharging atoms k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_45_2_38, k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_43_2_35, yields: % 7.02/2.11 | (124) all_45_2_38 = all_43_2_35 % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (52) with all_0_9_9, all_0_8_8, all_0_6_6, all_29_2_25, all_45_2_38 and discharging atoms k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_45_2_38, k7_isocat_2(all_0_9_9, all_0_8_8, all_0_6_6) = all_29_2_25, yields: % 7.02/2.11 | (125) all_45_2_38 = all_29_2_25 % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (2) with all_0_7_7, all_0_6_6, all_31_0_26, all_0_5_5 and discharging atoms k12_nattra_1(all_0_7_7, all_0_6_6) = all_31_0_26, k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5, yields: % 7.02/2.11 | (126) all_31_0_26 = all_0_5_5 % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (2) with all_0_8_8, all_0_6_6, all_45_1_37, all_0_4_4 and discharging atoms k12_nattra_1(all_0_8_8, all_0_6_6) = all_45_1_37, k12_nattra_1(all_0_8_8, all_0_6_6) = all_0_4_4, yields: % 7.02/2.11 | (127) all_45_1_37 = all_0_4_4 % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (2) with all_0_8_8, all_0_6_6, all_43_1_34, all_45_1_37 and discharging atoms k12_nattra_1(all_0_8_8, all_0_6_6) = all_45_1_37, k12_nattra_1(all_0_8_8, all_0_6_6) = all_43_1_34, yields: % 7.02/2.11 | (128) all_45_1_37 = all_43_1_34 % 7.02/2.11 | % 7.02/2.11 | Instantiating formula (22) with all_0_9_9, all_0_8_8, all_29_1_24, all_0_7_7 and discharging atoms k11_cat_2(all_0_9_9, all_0_8_8) = all_29_1_24, k11_cat_2(all_0_9_9, all_0_8_8) = all_0_7_7, yields: % 7.02/2.11 | (129) all_29_1_24 = all_0_7_7 % 7.02/2.11 | % 7.02/2.11 | Combining equations (127,128) yields a new equation: % 7.02/2.11 | (130) all_43_1_34 = all_0_4_4 % 7.02/2.11 | % 7.02/2.12 | Combining equations (124,125) yields a new equation: % 7.02/2.12 | (131) all_43_2_35 = all_29_2_25 % 7.02/2.12 | % 7.02/2.12 | Simplifying 131 yields: % 7.02/2.12 | (132) all_43_2_35 = all_29_2_25 % 7.02/2.12 | % 7.02/2.12 | Combining equations (130,128) yields a new equation: % 7.02/2.12 | (127) all_45_1_37 = all_0_4_4 % 7.02/2.12 | % 7.02/2.12 | From (129) and (107) follows: % 7.02/2.12 | (134) k12_nattra_1(all_0_7_7, all_0_6_6) = all_29_0_23 % 7.02/2.12 | % 7.02/2.12 | From (126) and (112) follows: % 7.02/2.12 | (33) k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5 % 7.02/2.12 | % 7.02/2.12 | From (127) and (122) follows: % 7.02/2.12 | (136) k12_nattra_1(all_0_9_9, all_0_4_4) = all_45_0_36 % 7.02/2.12 | % 7.02/2.12 | From (130) and (117) follows: % 7.02/2.12 | (137) k12_nattra_1(all_0_9_9, all_0_4_4) = all_43_0_33 % 7.02/2.12 | % 7.02/2.12 | From (132) and (118) follows: % 7.02/2.12 | (138) v8_cat_1(all_29_2_25, all_0_5_5, all_43_0_33) % 7.02/2.12 | % 7.02/2.12 | From (125) and (123) follows: % 7.02/2.12 | (139) m2_cat_1(all_29_2_25, all_0_5_5, all_45_0_36) % 7.02/2.12 | % 7.02/2.12 | Instantiating formula (2) with all_0_7_7, all_0_6_6, all_29_0_23, all_0_5_5 and discharging atoms k12_nattra_1(all_0_7_7, all_0_6_6) = all_29_0_23, k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5, yields: % 7.02/2.12 | (140) all_29_0_23 = all_0_5_5 % 7.02/2.12 | % 7.02/2.12 | Instantiating formula (2) with all_0_9_9, all_0_4_4, all_45_0_36, all_0_3_3 and discharging atoms k12_nattra_1(all_0_9_9, all_0_4_4) = all_45_0_36, k12_nattra_1(all_0_9_9, all_0_4_4) = all_0_3_3, yields: % 7.02/2.12 | (141) all_45_0_36 = all_0_3_3 % 7.02/2.12 | % 7.02/2.12 | Instantiating formula (2) with all_0_9_9, all_0_4_4, all_43_0_33, all_45_0_36 and discharging atoms k12_nattra_1(all_0_9_9, all_0_4_4) = all_45_0_36, k12_nattra_1(all_0_9_9, all_0_4_4) = all_43_0_33, yields: % 7.02/2.12 | (142) all_45_0_36 = all_43_0_33 % 7.02/2.12 | % 7.02/2.12 | Combining equations (141,142) yields a new equation: % 7.02/2.12 | (143) all_43_0_33 = all_0_3_3 % 7.02/2.12 | % 7.02/2.12 | Combining equations (143,142) yields a new equation: % 7.02/2.12 | (141) all_45_0_36 = all_0_3_3 % 7.02/2.12 | % 7.02/2.12 | From (140) and (134) follows: % 7.02/2.12 | (33) k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5 % 7.02/2.12 | % 7.02/2.12 | From (143) and (137) follows: % 7.02/2.12 | (25) k12_nattra_1(all_0_9_9, all_0_4_4) = all_0_3_3 % 7.02/2.12 | % 7.02/2.12 | From (143) and (138) follows: % 7.02/2.12 | (147) v8_cat_1(all_29_2_25, all_0_5_5, all_0_3_3) % 7.02/2.12 | % 7.02/2.12 | From (141) and (139) follows: % 7.02/2.12 | (148) m2_cat_1(all_29_2_25, all_0_5_5, all_0_3_3) % 7.02/2.12 | % 7.02/2.12 | Instantiating formula (57) with all_0_3_3, all_0_4_4, all_0_9_9 and discharging atoms k12_nattra_1(all_0_9_9, all_0_4_4) = all_0_3_3, l1_cat_1(all_0_4_4), l1_cat_1(all_0_9_9), v2_cat_1(all_0_4_4), v2_cat_1(all_0_9_9), yields: % 7.02/2.12 | (149) l1_cat_1(all_0_3_3) % 7.02/2.12 | % 7.02/2.12 | Instantiating formula (12) with all_0_3_3, all_0_4_4, all_0_9_9 and discharging atoms k12_nattra_1(all_0_9_9, all_0_4_4) = all_0_3_3, l1_cat_1(all_0_4_4), l1_cat_1(all_0_9_9), v2_cat_1(all_0_4_4), v2_cat_1(all_0_9_9), yields: % 7.02/2.12 | (150) v2_cat_1(all_0_3_3) % 7.02/2.12 | % 7.02/2.12 | Instantiating formula (57) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5, l1_cat_1(all_0_6_6), l1_cat_1(all_0_7_7), v2_cat_1(all_0_6_6), v2_cat_1(all_0_7_7), yields: % 7.02/2.12 | (151) l1_cat_1(all_0_5_5) % 7.02/2.12 | % 7.02/2.12 | Instantiating formula (12) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms k12_nattra_1(all_0_7_7, all_0_6_6) = all_0_5_5, l1_cat_1(all_0_6_6), l1_cat_1(all_0_7_7), v2_cat_1(all_0_6_6), v2_cat_1(all_0_7_7), yields: % 7.19/2.12 | (152) v2_cat_1(all_0_5_5) % 7.19/2.12 | % 7.19/2.12 | Instantiating formula (24) with all_29_2_25, all_0_3_3, all_0_5_5 and discharging atoms v8_cat_1(all_29_2_25, all_0_5_5, all_0_3_3), m2_cat_1(all_29_2_25, all_0_5_5, all_0_3_3), l1_cat_1(all_0_3_3), l1_cat_1(all_0_5_5), v2_cat_1(all_0_3_3), v2_cat_1(all_0_5_5), ~ r1_isocat_1(all_0_5_5, all_0_3_3), yields: % 7.19/2.12 | (153) $false % 7.19/2.12 | % 7.19/2.12 |-The branch is then unsatisfiable % 7.19/2.12 % SZS output end Proof for theBenchmark % 7.19/2.12 % 7.19/2.12 1629ms %------------------------------------------------------------------------------