%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU444+1 : TPTP v8.1.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 : Tue Jul 19 08:50:08 EDT 2022 % Result : Theorem 2.97s 1.40s % Output : Proof 4.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU444+1 : TPTP v8.1.0. Released v3.4.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n019.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 20 10:51:39 EDT 2022 % 0.12/0.34 % CPUTime : % 0.54/0.58 ____ _ % 0.54/0.59 ___ / __ \_____(_)___ ________ __________ % 0.54/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.59 % 0.54/0.59 A Theorem Prover for First-Order Logic % 0.54/0.59 (ePrincess v.1.0) % 0.54/0.59 % 0.54/0.59 (c) Philipp Rümmer, 2009-2015 % 0.54/0.59 (c) Peter Backeman, 2014-2015 % 0.54/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.59 Bug reports to peter@backeman.se % 0.54/0.59 % 0.54/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.59 % 0.54/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.68/0.95 Prover 0: Preprocessing ... % 2.35/1.20 Prover 0: Warning: ignoring some quantifiers % 2.48/1.23 Prover 0: Constructing countermodel ... % 2.97/1.40 Prover 0: proved (761ms) % 2.97/1.40 % 2.97/1.40 No countermodel exists, formula is valid % 2.97/1.40 % SZS status Theorem for theBenchmark % 2.97/1.40 % 2.97/1.40 Generating proof ... Warning: ignoring some quantifiers % 4.13/1.66 found it (size 23) % 4.13/1.66 % 4.13/1.66 % SZS output start Proof for theBenchmark % 4.13/1.66 Assumed formulas after preprocessing and simplification: % 4.13/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (k1_funct_5(v2) = v3 & k2_funct_5(v2) = v8 & k10_relset_1(v1, v0, v2, v1) = v6 & k10_relset_1(v0, v1, v4, v8) = v9 & k10_relset_1(v0, v1, v4, v6) = v7 & k10_relset_1(v0, v1, v4, v0) = v5 & k6_relset_1(v1, v0, v2) = v4 & v1_xboole_0(v11) & v1_xboole_0(k1_xboole_0) & v3_relat_1(v12) & v3_relat_1(k1_xboole_0) & v1_relat_1(v12) & v1_relat_1(v11) & v1_relat_1(v10) & v1_relat_1(k1_xboole_0) & m2_relset_1(v2, v1, v0) & ~ v1_xboole_0(v10) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v14 = v13 | ~ (k10_relset_1(v18, v17, v16, v15) = v14) | ~ (k10_relset_1(v18, v17, v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (k6_relset_1(v13, v14, v16) = v17) | ~ (k6_relset_1(v13, v14, v15) = v16) | ~ m1_relset_1(v15, v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v14 = v13 | ~ (k6_relset_1(v17, v16, v15) = v14) | ~ (k6_relset_1(v17, v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k10_relset_1(v13, v14, v16, v13) = v17) | ~ (k6_relset_1(v14, v13, v15) = v16) | ~ m2_relset_1(v15, v14, v13) | ? [v18] : (k1_funct_5(v15) = v17 & k2_funct_5(v15) = v18 & k10_relset_1(v14, v13, v15, v14) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k10_relset_1(v13, v14, v15, v16) = v17) | ~ m1_relset_1(v15, v13, v14) | k9_relat_1(v15, v16) = v17) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (k10_relset_1(v13, v14, v15, v16) = v17) | ~ m1_relset_1(v15, v13, v14) | ? [v18] : (k1_zfmisc_1(v14) = v18 & m1_subset_1(v17, v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (k9_relat_1(v16, v15) = v14) | ~ (k9_relat_1(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (k2_zfmisc_1(v16, v15) = v14) | ~ (k2_zfmisc_1(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k10_relset_1(v14, v13, v15, v14) = v16) | ~ m2_relset_1(v15, v14, v13) | ? [v17] : ? [v18] : (k1_funct_5(v15) = v17 & k2_funct_5(v15) = v16 & k10_relset_1(v13, v14, v18, v13) = v17 & k6_relset_1(v14, v13, v15) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k6_relset_1(v13, v14, v15) = v16) | ~ m1_relset_1(v15, v13, v14) | k4_relat_1(v15) = v16) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k6_relset_1(v13, v14, v15) = v16) | ~ m1_relset_1(v15, v13, v14) | m2_relset_1(v16, v14, v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_zfmisc_1(v13, v14) = v16) | ~ m2_relset_1(v15, v13, v14) | ? [v17] : (k1_zfmisc_1(v16) = v17 & m1_subset_1(v15, v17))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_zfmisc_1(v15) = v16) | ~ m1_subset_1(v14, v16) | ~ v1_xboole_0(v15) | ~ r2_hidden(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k1_zfmisc_1(v15) = v16) | ~ m1_subset_1(v14, v16) | ~ r2_hidden(v13, v14) | m1_subset_1(v13, v15)) & ? [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (k2_zfmisc_1(v14, v15) = v16) | v1_relat_1(v13) | ? [v17] : (k1_zfmisc_1(v16) = v17 & ~ m1_subset_1(v13, v17))) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (k1_funct_5(v15) = v14) | ~ (k1_funct_5(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (k2_funct_5(v15) = v14) | ~ (k2_funct_5(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (k4_relat_1(v15) = v14) | ~ (k4_relat_1(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (k1_zfmisc_1(v15) = v14) | ~ (k1_zfmisc_1(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k2_zfmisc_1(v13, v14) = v15) | ~ v1_xboole_0(v15) | v1_xboole_0(v14) | v1_xboole_0(v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k2_zfmisc_1(v13, v14) = v15) | v1_relat_1(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ~ r1_tarski(v13, v14) | m1_subset_1(v13, v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (k1_zfmisc_1(v14) = v15) | ~ m1_subset_1(v13, v15) | r1_tarski(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ( ~ m1_relset_1(v15, v13, v14) | m2_relset_1(v15, v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ( ~ m2_relset_1(v15, v13, v14) | m1_relset_1(v15, v13, v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ v1_xboole_0(v14) | ~ v1_xboole_0(v13)) & ! [v13] : ! [v14] : ( ~ (k4_relat_1(v13) = v14) | ~ v1_xboole_0(v13) | v1_xboole_0(v14)) & ! [v13] : ! [v14] : ( ~ (k4_relat_1(v13) = v14) | ~ v1_xboole_0(v13) | v1_relat_1(v14)) & ! [v13] : ! [v14] : ( ~ (k4_relat_1(v13) = v14) | ~ v1_relat_1(v13) | k4_relat_1(v14) = v13) & ! [v13] : ! [v14] : ( ~ (k4_relat_1(v13) = v14) | ~ v1_relat_1(v13) | v1_relat_1(v14)) & ! [v13] : ! [v14] : ( ~ (k1_zfmisc_1(v13) = v14) | ~ v1_xboole_0(v14)) & ! [v13] : ! [v14] : ( ~ (k1_zfmisc_1(v13) = v14) | v1_xboole_0(v13) | ? [v15] : (m1_subset_1(v15, v14) & ~ v1_xboole_0(v15))) & ! [v13] : ! [v14] : ( ~ (k1_zfmisc_1(v13) = v14) | ? [v15] : (m1_subset_1(v15, v14) & v1_xboole_0(v15))) & ! [v13] : ! [v14] : ( ~ m1_subset_1(v13, v14) | v1_xboole_0(v14) | r2_hidden(v13, v14)) & ! [v13] : ! [v14] : ( ~ v1_xboole_0(v14) | ~ r2_hidden(v13, v14)) & ! [v13] : ! [v14] : ( ~ r2_hidden(v14, v13) | ~ r2_hidden(v13, v14)) & ! [v13] : ! [v14] : ( ~ r2_hidden(v13, v14) | m1_subset_1(v13, v14)) & ! [v13] : (v13 = k1_xboole_0 | ~ v1_xboole_0(v13)) & ! [v13] : ( ~ v1_xboole_0(v13) | v1_relat_1(v13)) & ? [v13] : ? [v14] : ? [v15] : m1_relset_1(v15, v13, v14) & ? [v13] : ? [v14] : ? [v15] : m2_relset_1(v15, v13, v14) & ? [v13] : ? [v14] : m1_subset_1(v14, v13) & ? [v13] : r1_tarski(v13, v13) & ( ~ (v9 = v7) | ~ (v5 = v3))) % 4.35/1.71 | 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 yields: % 4.35/1.71 | (1) k1_funct_5(all_0_10_10) = all_0_9_9 & k2_funct_5(all_0_10_10) = all_0_4_4 & k10_relset_1(all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11) = all_0_6_6 & k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_4_4) = all_0_3_3 & k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_6_6) = all_0_5_5 & k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_12_12) = all_0_7_7 & k6_relset_1(all_0_11_11, all_0_12_12, all_0_10_10) = all_0_8_8 & v1_xboole_0(all_0_1_1) & v1_xboole_0(k1_xboole_0) & v3_relat_1(all_0_0_0) & v3_relat_1(k1_xboole_0) & v1_relat_1(all_0_0_0) & v1_relat_1(all_0_1_1) & v1_relat_1(all_0_2_2) & v1_relat_1(k1_xboole_0) & m2_relset_1(all_0_10_10, all_0_11_11, all_0_12_12) & ~ v1_xboole_0(all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k10_relset_1(v5, v4, v3, v2) = v1) | ~ (k10_relset_1(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (k6_relset_1(v0, v1, v3) = v4) | ~ (k6_relset_1(v0, v1, v2) = v3) | ~ m1_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k6_relset_1(v4, v3, v2) = v1) | ~ (k6_relset_1(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k10_relset_1(v0, v1, v3, v0) = v4) | ~ (k6_relset_1(v1, v0, v2) = v3) | ~ m2_relset_1(v2, v1, v0) | ? [v5] : (k1_funct_5(v2) = v4 & k2_funct_5(v2) = v5 & k10_relset_1(v1, v0, v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k10_relset_1(v0, v1, v2, v3) = v4) | ~ m1_relset_1(v2, v0, v1) | k9_relat_1(v2, v3) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k10_relset_1(v0, v1, v2, v3) = v4) | ~ m1_relset_1(v2, v0, v1) | ? [v5] : (k1_zfmisc_1(v1) = v5 & m1_subset_1(v4, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1) | ~ (k9_relat_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] : ( ~ (k10_relset_1(v1, v0, v2, v1) = v3) | ~ m2_relset_1(v2, v1, v0) | ? [v4] : ? [v5] : (k1_funct_5(v2) = v4 & k2_funct_5(v2) = v3 & k10_relset_1(v0, v1, v5, v0) = v4 & k6_relset_1(v1, v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k6_relset_1(v0, v1, v2) = v3) | ~ m1_relset_1(v2, v0, v1) | k4_relat_1(v2) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k6_relset_1(v0, v1, v2) = v3) | ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v3, v1, v0)) & ! [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) | ~ m1_subset_1(v1, v3) | ~ v1_xboole_0(v2) | ~ 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_funct_5(v2) = v1) | ~ (k1_funct_5(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k2_funct_5(v2) = v1) | ~ (k2_funct_5(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k4_relat_1(v2) = v1) | ~ (k4_relat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | v1_relat_1(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : ( ~ (k4_relat_1(v0) = v1) | ~ v1_xboole_0(v0) | v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ (k4_relat_1(v0) = v1) | ~ v1_xboole_0(v0) | v1_relat_1(v1)) & ! [v0] : ! [v1] : ( ~ (k4_relat_1(v0) = v1) | ~ v1_relat_1(v0) | k4_relat_1(v1) = v0) & ! [v0] : ! [v1] : ( ~ (k4_relat_1(v0) = v1) | ~ v1_relat_1(v0) | v1_relat_1(v1)) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2))) & ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (m1_subset_1(v2, v1) & v1_xboole_0(v2))) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_relat_1(v0)) & ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : r1_tarski(v0, v0) & ( ~ (all_0_3_3 = all_0_5_5) | ~ (all_0_7_7 = all_0_9_9)) % 4.35/1.73 | % 4.35/1.73 | Applying alpha-rule on (1) yields: % 4.35/1.73 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (k10_relset_1(v5, v4, v3, v2) = v1) | ~ (k10_relset_1(v5, v4, v3, v2) = v0)) % 4.35/1.73 | (3) k1_funct_5(all_0_10_10) = all_0_9_9 % 4.35/1.73 | (4) ! [v0] : ! [v1] : ( ~ (k4_relat_1(v0) = v1) | ~ v1_xboole_0(v0) | v1_xboole_0(v1)) % 4.35/1.73 | (5) ! [v0] : ! [v1] : ( ~ (k4_relat_1(v0) = v1) | ~ v1_xboole_0(v0) | v1_relat_1(v1)) % 4.35/1.73 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) % 4.35/1.73 | (7) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ v1_xboole_0(v1)) % 4.35/1.73 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ m2_relset_1(v2, v0, v1) | m1_relset_1(v2, v0, v1)) % 4.35/1.73 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v2, v0, v1)) % 4.35/1.73 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ m1_subset_1(v0, v2) | r1_tarski(v0, v1)) % 4.35/1.73 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_zfmisc_1(v1) = v2) | ~ r1_tarski(v0, v1) | m1_subset_1(v0, v2)) % 4.35/1.73 | (12) k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_12_12) = all_0_7_7 % 4.35/1.73 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_funct_5(v2) = v1) | ~ (k1_funct_5(v2) = v0)) % 4.35/1.73 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k10_relset_1(v1, v0, v2, v1) = v3) | ~ m2_relset_1(v2, v1, v0) | ? [v4] : ? [v5] : (k1_funct_5(v2) = v4 & k2_funct_5(v2) = v3 & k10_relset_1(v0, v1, v5, v0) = v4 & k6_relset_1(v1, v0, v2) = v5)) % 4.35/1.73 | (15) ? [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))) % 4.35/1.73 | (16) ! [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))) % 4.35/1.73 | (17) v1_relat_1(all_0_2_2) % 4.35/1.73 | (18) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) % 4.35/1.73 | (19) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | ? [v2] : (m1_subset_1(v2, v1) & v1_xboole_0(v2))) % 4.35/1.74 | (20) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1)) % 4.35/1.74 | (21) ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1)) % 4.35/1.74 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (k6_relset_1(v0, v1, v3) = v4) | ~ (k6_relset_1(v0, v1, v2) = v3) | ~ m1_relset_1(v2, v0, v1)) % 4.35/1.74 | (23) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) % 4.35/1.74 | (24) m2_relset_1(all_0_10_10, all_0_11_11, all_0_12_12) % 4.35/1.74 | (25) ! [v0] : ! [v1] : ( ~ (k4_relat_1(v0) = v1) | ~ v1_relat_1(v0) | v1_relat_1(v1)) % 4.35/1.74 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (k6_relset_1(v4, v3, v2) = v1) | ~ (k6_relset_1(v4, v3, v2) = v0)) % 4.35/1.74 | (27) v1_relat_1(all_0_0_0) % 4.35/1.74 | (28) k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_4_4) = all_0_3_3 % 4.35/1.74 | (29) v3_relat_1(all_0_0_0) % 4.35/1.74 | (30) v1_relat_1(all_0_1_1) % 4.35/1.74 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k6_relset_1(v0, v1, v2) = v3) | ~ m1_relset_1(v2, v0, v1) | m2_relset_1(v3, v1, v0)) % 4.35/1.74 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1) | ~ (k9_relat_1(v3, v2) = v0)) % 4.35/1.74 | (33) k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_6_6) = all_0_5_5 % 4.35/1.74 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k10_relset_1(v0, v1, v2, v3) = v4) | ~ m1_relset_1(v2, v0, v1) | ? [v5] : (k1_zfmisc_1(v1) = v5 & m1_subset_1(v4, v5))) % 4.35/1.74 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k2_funct_5(v2) = v1) | ~ (k2_funct_5(v2) = v0)) % 4.35/1.74 | (36) ? [v0] : r1_tarski(v0, v0) % 4.35/1.74 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ r2_hidden(v0, v1) | m1_subset_1(v0, v2)) % 4.35/1.74 | (38) k2_funct_5(all_0_10_10) = all_0_4_4 % 4.35/1.74 | (39) k10_relset_1(all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11) = all_0_6_6 % 4.35/1.74 | (40) v1_xboole_0(all_0_1_1) % 4.35/1.74 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v1) | v1_xboole_0(v0)) % 4.35/1.74 | (42) ? [v0] : ? [v1] : ? [v2] : m1_relset_1(v2, v0, v1) % 4.35/1.74 | (43) ! [v0] : ! [v1] : ( ~ (k4_relat_1(v0) = v1) | ~ v1_relat_1(v0) | k4_relat_1(v1) = v0) % 4.35/1.74 | (44) ? [v0] : ? [v1] : m1_subset_1(v1, v0) % 4.35/1.74 | (45) v1_xboole_0(k1_xboole_0) % 4.35/1.74 | (46) ! [v0] : ( ~ v1_xboole_0(v0) | v1_relat_1(v0)) % 4.35/1.74 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 4.35/1.74 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) % 4.35/1.74 | (49) ? [v0] : ? [v1] : ? [v2] : m2_relset_1(v2, v0, v1) % 4.35/1.74 | (50) v3_relat_1(k1_xboole_0) % 4.35/1.74 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k1_zfmisc_1(v2) = v3) | ~ m1_subset_1(v1, v3) | ~ v1_xboole_0(v2) | ~ r2_hidden(v0, v1)) % 4.35/1.74 | (52) v1_relat_1(k1_xboole_0) % 4.35/1.75 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_zfmisc_1(v0, v1) = v2) | v1_relat_1(v2)) % 4.35/1.75 | (54) ! [v0] : ! [v1] : ( ~ (k1_zfmisc_1(v0) = v1) | v1_xboole_0(v0) | ? [v2] : (m1_subset_1(v2, v1) & ~ v1_xboole_0(v2))) % 4.35/1.75 | (55) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) % 4.35/1.75 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k10_relset_1(v0, v1, v3, v0) = v4) | ~ (k6_relset_1(v1, v0, v2) = v3) | ~ m2_relset_1(v2, v1, v0) | ? [v5] : (k1_funct_5(v2) = v4 & k2_funct_5(v2) = v5 & k10_relset_1(v1, v0, v2, v1) = v5)) % 4.35/1.75 | (57) k6_relset_1(all_0_11_11, all_0_12_12, all_0_10_10) = all_0_8_8 % 4.35/1.75 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (k10_relset_1(v0, v1, v2, v3) = v4) | ~ m1_relset_1(v2, v0, v1) | k9_relat_1(v2, v3) = v4) % 4.35/1.75 | (59) ~ v1_xboole_0(all_0_2_2) % 4.35/1.75 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k4_relat_1(v2) = v1) | ~ (k4_relat_1(v2) = v0)) % 4.35/1.75 | (61) ~ (all_0_3_3 = all_0_5_5) | ~ (all_0_7_7 = all_0_9_9) % 4.35/1.75 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k6_relset_1(v0, v1, v2) = v3) | ~ m1_relset_1(v2, v0, v1) | k4_relat_1(v2) = v3) % 4.35/1.75 | % 4.35/1.75 | Instantiating formula (14) with all_0_6_6, all_0_10_10, all_0_11_11, all_0_12_12 and discharging atoms k10_relset_1(all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11) = all_0_6_6, m2_relset_1(all_0_10_10, all_0_11_11, all_0_12_12), yields: % 4.35/1.75 | (63) ? [v0] : ? [v1] : (k1_funct_5(all_0_10_10) = v0 & k2_funct_5(all_0_10_10) = all_0_6_6 & k10_relset_1(all_0_12_12, all_0_11_11, v1, all_0_12_12) = v0 & k6_relset_1(all_0_11_11, all_0_12_12, all_0_10_10) = v1) % 4.35/1.75 | % 4.35/1.75 | Instantiating formula (56) with all_0_7_7, all_0_8_8, all_0_10_10, all_0_11_11, all_0_12_12 and discharging atoms k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_12_12) = all_0_7_7, k6_relset_1(all_0_11_11, all_0_12_12, all_0_10_10) = all_0_8_8, m2_relset_1(all_0_10_10, all_0_11_11, all_0_12_12), yields: % 4.35/1.75 | (64) ? [v0] : (k1_funct_5(all_0_10_10) = all_0_7_7 & k2_funct_5(all_0_10_10) = v0 & k10_relset_1(all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11) = v0) % 4.35/1.75 | % 4.35/1.75 | Instantiating (64) with all_23_0_23 yields: % 4.35/1.75 | (65) k1_funct_5(all_0_10_10) = all_0_7_7 & k2_funct_5(all_0_10_10) = all_23_0_23 & k10_relset_1(all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11) = all_23_0_23 % 4.35/1.75 | % 4.35/1.75 | Applying alpha-rule on (65) yields: % 4.35/1.75 | (66) k1_funct_5(all_0_10_10) = all_0_7_7 % 4.35/1.75 | (67) k2_funct_5(all_0_10_10) = all_23_0_23 % 4.35/1.75 | (68) k10_relset_1(all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11) = all_23_0_23 % 4.35/1.75 | % 4.35/1.75 | Instantiating (63) with all_25_0_24, all_25_1_25 yields: % 4.35/1.75 | (69) k1_funct_5(all_0_10_10) = all_25_1_25 & k2_funct_5(all_0_10_10) = all_0_6_6 & k10_relset_1(all_0_12_12, all_0_11_11, all_25_0_24, all_0_12_12) = all_25_1_25 & k6_relset_1(all_0_11_11, all_0_12_12, all_0_10_10) = all_25_0_24 % 4.35/1.75 | % 4.35/1.75 | Applying alpha-rule on (69) yields: % 4.35/1.75 | (70) k1_funct_5(all_0_10_10) = all_25_1_25 % 4.35/1.75 | (71) k2_funct_5(all_0_10_10) = all_0_6_6 % 4.35/1.75 | (72) k10_relset_1(all_0_12_12, all_0_11_11, all_25_0_24, all_0_12_12) = all_25_1_25 % 4.35/1.75 | (73) k6_relset_1(all_0_11_11, all_0_12_12, all_0_10_10) = all_25_0_24 % 4.35/1.75 | % 4.35/1.75 | Instantiating formula (13) with all_0_10_10, all_25_1_25, all_0_9_9 and discharging atoms k1_funct_5(all_0_10_10) = all_25_1_25, k1_funct_5(all_0_10_10) = all_0_9_9, yields: % 4.35/1.75 | (74) all_25_1_25 = all_0_9_9 % 4.35/1.76 | % 4.35/1.76 | Instantiating formula (13) with all_0_10_10, all_0_7_7, all_25_1_25 and discharging atoms k1_funct_5(all_0_10_10) = all_25_1_25, k1_funct_5(all_0_10_10) = all_0_7_7, yields: % 4.35/1.76 | (75) all_25_1_25 = all_0_7_7 % 4.35/1.76 | % 4.35/1.76 | Instantiating formula (35) with all_0_10_10, all_23_0_23, all_0_4_4 and discharging atoms k2_funct_5(all_0_10_10) = all_23_0_23, k2_funct_5(all_0_10_10) = all_0_4_4, yields: % 4.35/1.76 | (76) all_23_0_23 = all_0_4_4 % 4.35/1.76 | % 4.35/1.76 | Instantiating formula (2) with all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11, all_23_0_23, all_0_6_6 and discharging atoms k10_relset_1(all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11) = all_23_0_23, k10_relset_1(all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11) = all_0_6_6, yields: % 4.35/1.76 | (77) all_23_0_23 = all_0_6_6 % 4.35/1.76 | % 4.35/1.76 | Combining equations (75,74) yields a new equation: % 4.35/1.76 | (78) all_0_7_7 = all_0_9_9 % 4.35/1.76 | % 4.35/1.76 | Simplifying 78 yields: % 4.35/1.76 | (79) all_0_7_7 = all_0_9_9 % 4.35/1.76 | % 4.35/1.76 | Combining equations (76,77) yields a new equation: % 4.35/1.76 | (80) all_0_4_4 = all_0_6_6 % 4.35/1.76 | % 4.35/1.76 | Simplifying 80 yields: % 4.35/1.76 | (81) all_0_4_4 = all_0_6_6 % 4.35/1.76 | % 4.35/1.76 | From (81) and (28) follows: % 4.35/1.76 | (82) k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_6_6) = all_0_3_3 % 4.35/1.76 | % 4.35/1.76 +-Applying beta-rule and splitting (61), into two cases. % 4.35/1.76 |-Branch one: % 4.35/1.76 | (83) ~ (all_0_3_3 = all_0_5_5) % 4.35/1.76 | % 4.35/1.76 | Instantiating formula (2) with all_0_12_12, all_0_11_11, all_0_8_8, all_0_6_6, all_0_3_3, all_0_5_5 and discharging atoms k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_6_6) = all_0_3_3, k10_relset_1(all_0_12_12, all_0_11_11, all_0_8_8, all_0_6_6) = all_0_5_5, yields: % 4.35/1.76 | (84) all_0_3_3 = all_0_5_5 % 4.35/1.76 | % 4.72/1.76 | Equations (84) can reduce 83 to: % 4.72/1.76 | (85) $false % 4.72/1.76 | % 4.72/1.76 |-The branch is then unsatisfiable % 4.72/1.76 |-Branch two: % 4.72/1.76 | (84) all_0_3_3 = all_0_5_5 % 4.72/1.76 | (87) ~ (all_0_7_7 = all_0_9_9) % 4.72/1.76 | % 4.72/1.76 | Equations (79) can reduce 87 to: % 4.72/1.76 | (85) $false % 4.72/1.76 | % 4.72/1.76 |-The branch is then unsatisfiable % 4.72/1.76 % SZS output end Proof for theBenchmark % 4.72/1.76 % 4.72/1.76 1166ms %------------------------------------------------------------------------------