%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV403+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 : Wed Jul 20 17:51:16 EDT 2022 % Result : Theorem 8.21s 2.53s % Output : Proof 11.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV403+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n007.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Tue Jun 14 20:27:25 EDT 2022 % 0.12/0.34 % CPUTime : % 0.51/0.62 ____ _ % 0.51/0.62 ___ / __ \_____(_)___ ________ __________ % 0.51/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.62 % 0.51/0.62 A Theorem Prover for First-Order Logic % 0.51/0.62 (ePrincess v.1.0) % 0.51/0.62 % 0.51/0.62 (c) Philipp Rümmer, 2009-2015 % 0.51/0.62 (c) Peter Backeman, 2014-2015 % 0.51/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.62 Bug reports to peter@backeman.se % 0.51/0.62 % 0.51/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.62 % 0.51/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.78/0.96 Prover 0: Preprocessing ... % 2.37/1.18 Prover 0: Warning: ignoring some quantifiers % 2.45/1.20 Prover 0: Constructing countermodel ... % 6.46/2.21 Prover 0: gave up % 6.46/2.22 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 6.89/2.26 Prover 1: Preprocessing ... % 7.54/2.37 Prover 1: Constructing countermodel ... % 8.21/2.53 Prover 1: proved (312ms) % 8.21/2.53 % 8.21/2.53 No countermodel exists, formula is valid % 8.21/2.53 % SZS status Theorem for theBenchmark % 8.21/2.53 % 8.21/2.53 Generating proof ... found it (size 99) % 10.92/3.14 % 10.92/3.14 % SZS output start Proof for theBenchmark % 10.92/3.15 Assumed formulas after preprocessing and simplification: % 10.92/3.15 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & ~ (v0 = 0) & update_slb(v8, v4) = v9 & pair_in_list(v9, v2, v4) = v10 & pair_in_list(v8, v2, v3) = 0 & pair(v5, v6) = v7 & insert_slb(v1, v7) = v8 & isnonempty_slb(create_slb) = v0 & strictly_less_than(v3, v4) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (pair_in_list(v17, v13, v15) = v18) | ~ (pair(v12, v14) = v16) | ~ (insert_slb(v11, v16) = v17) | ? [v19] : ( ~ (v19 = 0) & pair_in_list(v11, v13, v15) = v19)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (contains_slb(v16, v13) = v17) | ~ (pair(v12, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : ( ~ (v18 = 0) & contains_slb(v11, v13) = v18)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (pair_in_list(v17, v13, v15) = 0) | ~ (pair(v12, v14) = v16) | ~ (insert_slb(v11, v16) = v17) | pair_in_list(v11, v13, v15) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v13 = v12 | ~ (lookup_slb(v16, v13) = v17) | ~ (pair(v12, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : ? [v19] : (lookup_slb(v11, v13) = v19 & contains_slb(v11, v13) = v18 & ( ~ (v18 = 0) | v19 = v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v13 = v12 | ~ (remove_slb(v16, v13) = v17) | ~ (pair(v12, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : (remove_slb(v11, v13) = v19 & contains_slb(v11, v13) = v18 & insert_slb(v19, v15) = v20 & ( ~ (v18 = 0) | v20 = v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v13 = v12 | ~ (pair_in_list(v17, v13, v15) = 0) | ~ (pair(v12, v14) = v16) | ~ (insert_slb(v11, v16) = v17) | pair_in_list(v11, v13, v15) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (update_slb(v16, v13) = v17) | ~ (pair(v12, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (update_slb(v11, v13) = v19 & pair(v12, v13) = v20 & insert_slb(v19, v20) = v21 & strictly_less_than(v14, v13) = v18 & ( ~ (v18 = 0) | v21 = v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (update_slb(v16, v13) = v17) | ~ (pair(v12, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : (update_slb(v11, v13) = v19 & insert_slb(v19, v15) = v20 & less_than(v13, v14) = v18 & ( ~ (v18 = 0) | v20 = v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v13 | ~ (lookup_slb(v15, v12) = v16) | ~ (pair(v12, v13) = v14) | ~ (insert_slb(v11, v14) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v11 | ~ (remove_slb(v15, v12) = v16) | ~ (pair(v12, v13) = v14) | ~ (insert_slb(v11, v14) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (pair_in_list(v15, v12, v13) = v16) | ~ (pair(v12, v13) = v14) | ~ (insert_slb(v11, v14) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (contains_slb(v15, v12) = v16) | ~ (pair(v12, v13) = v14) | ~ (insert_slb(v11, v14) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (contains_slb(v16, v13) = 0) | ~ (pair(v12, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | contains_slb(v11, v13) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (update_slb(v1, v13) = v14) | ~ (pair_in_list(v14, v11, v13) = v15) | ~ (strictly_less_than(v12, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & pair_in_list(v1, v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (pair_in_list(v15, v14, v13) = v12) | ~ (pair_in_list(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (pair(v12, v13) = v14) | ~ (insert_slb(v11, v14) = v15) | isnonempty_slb(v15) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (less_than(v11, v13) = v14) | ~ (less_than(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & less_than(v12, v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (update_slb(v14, v13) = v12) | ~ (update_slb(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (lookup_slb(v14, v13) = v12) | ~ (lookup_slb(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (remove_slb(v14, v13) = v12) | ~ (remove_slb(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (contains_slb(v14, v13) = v12) | ~ (contains_slb(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (pair(v14, v13) = v12) | ~ (pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (insert_slb(v14, v13) = v12) | ~ (insert_slb(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (strictly_less_than(v14, v13) = v12) | ~ (strictly_less_than(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (less_than(v14, v13) = v12) | ~ (less_than(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (strictly_less_than(v11, v12) = v13) | ? [v14] : ? [v15] : (less_than(v12, v11) = v15 & less_than(v11, v12) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (less_than(v11, v12) = v13) | less_than(v12, v11) = 0) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (isnonempty_slb(v13) = v12) | ~ (isnonempty_slb(v13) = v11)) & ! [v11] : ! [v12] : (v12 = create_slb | ~ (update_slb(create_slb, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (less_than(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (less_than(bottom, v11) = v12)) & ! [v11] : ! [v12] : ~ (pair_in_list(create_slb, v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (strictly_less_than(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & less_than(v12, v11) = v13 & less_than(v11, v12) = 0)) & ! [v11] : ~ (contains_slb(create_slb, v11) = 0)) % 10.95/3.18 | 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 yields: % 10.95/3.18 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_10_10 = 0) & update_slb(all_0_2_2, all_0_6_6) = all_0_1_1 & pair_in_list(all_0_1_1, all_0_8_8, all_0_6_6) = all_0_0_0 & pair_in_list(all_0_2_2, all_0_8_8, all_0_7_7) = 0 & pair(all_0_5_5, all_0_4_4) = all_0_3_3 & insert_slb(all_0_9_9, all_0_3_3) = all_0_2_2 & isnonempty_slb(create_slb) = all_0_10_10 & strictly_less_than(all_0_7_7, all_0_6_6) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & pair_in_list(v0, v2, v4) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : (lookup_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & ( ~ (v7 = 0) | v8 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (remove_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & insert_slb(v8, v4) = v9 & ( ~ (v7 = 0) | v9 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (update_slb(v0, v2) = v8 & pair(v1, v2) = v9 & insert_slb(v8, v9) = v10 & strictly_less_than(v3, v2) = v7 & ( ~ (v7 = 0) | v10 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (update_slb(v0, v2) = v8 & insert_slb(v8, v4) = v9 & less_than(v2, v3) = v7 & ( ~ (v7 = 0) | v9 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | contains_slb(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (update_slb(all_0_9_9, v2) = v3) | ~ (pair_in_list(v3, v0, v2) = v4) | ~ (strictly_less_than(v1, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & pair_in_list(all_0_9_9, v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ? [v4] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) & ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) & ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0] : ~ (contains_slb(create_slb, v0) = 0) % 10.95/3.19 | % 10.95/3.19 | Applying alpha-rule on (1) yields: % 10.95/3.19 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 10.95/3.19 | (3) update_slb(all_0_2_2, all_0_6_6) = all_0_1_1 % 10.95/3.19 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)) % 10.95/3.19 | (5) ! [v0] : ~ (contains_slb(create_slb, v0) = 0) % 10.95/3.19 | (6) ~ (all_0_10_10 = 0) % 10.95/3.19 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 10.95/3.19 | (8) strictly_less_than(all_0_7_7, all_0_6_6) = 0 % 10.95/3.19 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) % 10.95/3.19 | (10) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) % 10.95/3.19 | (11) pair(all_0_5_5, all_0_4_4) = all_0_3_3 % 10.95/3.20 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 10.95/3.20 | (13) pair_in_list(all_0_1_1, all_0_8_8, all_0_6_6) = all_0_0_0 % 10.95/3.20 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.95/3.20 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (update_slb(v0, v2) = v8 & pair(v1, v2) = v9 & insert_slb(v8, v9) = v10 & strictly_less_than(v3, v2) = v7 & ( ~ (v7 = 0) | v10 = v6))) % 10.95/3.20 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & pair_in_list(v0, v2, v4) = v8)) % 10.95/3.20 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) % 10.95/3.20 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.95/3.20 | (19) pair_in_list(all_0_2_2, all_0_8_8, all_0_7_7) = 0 % 10.95/3.20 | (20) ~ (all_0_0_0 = 0) % 10.95/3.20 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : (lookup_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & ( ~ (v7 = 0) | v8 = v6))) % 10.95/3.20 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) % 10.95/3.20 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 10.95/3.20 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (remove_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & insert_slb(v8, v4) = v9 & ( ~ (v7 = 0) | v9 = v6))) % 10.95/3.20 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) % 10.95/3.20 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | contains_slb(v0, v2) = 0) % 10.95/3.20 | (27) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) % 10.95/3.20 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ? [v4] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 10.95/3.20 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (update_slb(all_0_9_9, v2) = v3) | ~ (pair_in_list(v3, v0, v2) = v4) | ~ (strictly_less_than(v1, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & pair_in_list(all_0_9_9, v0, v1) = v5)) % 10.95/3.20 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) % 10.95/3.20 | (31) isnonempty_slb(create_slb) = all_0_10_10 % 10.95/3.20 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) % 10.95/3.20 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) % 11.22/3.20 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) % 11.22/3.20 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 11.22/3.20 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 11.22/3.20 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (update_slb(v0, v2) = v8 & insert_slb(v8, v4) = v9 & less_than(v2, v3) = v7 & ( ~ (v7 = 0) | v9 = v6))) % 11.22/3.20 | (38) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) % 11.22/3.20 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 11.22/3.20 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 11.22/3.20 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 11.22/3.20 | (42) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) % 11.22/3.20 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) % 11.22/3.21 | (44) insert_slb(all_0_9_9, all_0_3_3) = all_0_2_2 % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (33) with all_0_2_2, all_0_3_3, all_0_7_7, all_0_4_4, all_0_8_8, all_0_5_5, all_0_9_9 and discharging atoms pair_in_list(all_0_2_2, all_0_8_8, all_0_7_7) = 0, pair(all_0_5_5, all_0_4_4) = all_0_3_3, insert_slb(all_0_9_9, all_0_3_3) = all_0_2_2, yields: % 11.22/3.21 | (45) all_0_4_4 = all_0_7_7 | pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0 % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (43) with all_0_2_2, all_0_3_3, all_0_7_7, all_0_4_4, all_0_8_8, all_0_5_5, all_0_9_9 and discharging atoms pair_in_list(all_0_2_2, all_0_8_8, all_0_7_7) = 0, pair(all_0_5_5, all_0_4_4) = all_0_3_3, insert_slb(all_0_9_9, all_0_3_3) = all_0_2_2, yields: % 11.22/3.21 | (46) all_0_5_5 = all_0_8_8 | pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0 % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (15) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5, all_0_9_9 and discharging atoms update_slb(all_0_2_2, all_0_6_6) = all_0_1_1, pair(all_0_5_5, all_0_4_4) = all_0_3_3, insert_slb(all_0_9_9, all_0_3_3) = all_0_2_2, yields: % 11.22/3.21 | (47) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (update_slb(all_0_9_9, all_0_6_6) = v1 & pair(all_0_5_5, all_0_6_6) = v2 & insert_slb(v1, v2) = v3 & strictly_less_than(all_0_4_4, all_0_6_6) = v0 & ( ~ (v0 = 0) | v3 = all_0_1_1)) % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (37) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5, all_0_9_9 and discharging atoms update_slb(all_0_2_2, all_0_6_6) = all_0_1_1, pair(all_0_5_5, all_0_4_4) = all_0_3_3, insert_slb(all_0_9_9, all_0_3_3) = all_0_2_2, yields: % 11.22/3.21 | (48) ? [v0] : ? [v1] : ? [v2] : (update_slb(all_0_9_9, all_0_6_6) = v1 & insert_slb(v1, all_0_3_3) = v2 & less_than(all_0_6_6, all_0_4_4) = v0 & ( ~ (v0 = 0) | v2 = all_0_1_1)) % 11.22/3.21 | % 11.22/3.21 | Instantiating (48) with all_19_0_12, all_19_1_13, all_19_2_14 yields: % 11.22/3.21 | (49) update_slb(all_0_9_9, all_0_6_6) = all_19_1_13 & insert_slb(all_19_1_13, all_0_3_3) = all_19_0_12 & less_than(all_0_6_6, all_0_4_4) = all_19_2_14 & ( ~ (all_19_2_14 = 0) | all_19_0_12 = all_0_1_1) % 11.22/3.21 | % 11.22/3.21 | Applying alpha-rule on (49) yields: % 11.22/3.21 | (50) update_slb(all_0_9_9, all_0_6_6) = all_19_1_13 % 11.22/3.21 | (51) insert_slb(all_19_1_13, all_0_3_3) = all_19_0_12 % 11.22/3.21 | (52) less_than(all_0_6_6, all_0_4_4) = all_19_2_14 % 11.22/3.21 | (53) ~ (all_19_2_14 = 0) | all_19_0_12 = all_0_1_1 % 11.22/3.21 | % 11.22/3.21 | Instantiating (47) with all_21_0_15, all_21_1_16, all_21_2_17, all_21_3_18 yields: % 11.22/3.21 | (54) update_slb(all_0_9_9, all_0_6_6) = all_21_2_17 & pair(all_0_5_5, all_0_6_6) = all_21_1_16 & insert_slb(all_21_2_17, all_21_1_16) = all_21_0_15 & strictly_less_than(all_0_4_4, all_0_6_6) = all_21_3_18 & ( ~ (all_21_3_18 = 0) | all_21_0_15 = all_0_1_1) % 11.22/3.21 | % 11.22/3.21 | Applying alpha-rule on (54) yields: % 11.22/3.21 | (55) pair(all_0_5_5, all_0_6_6) = all_21_1_16 % 11.22/3.21 | (56) strictly_less_than(all_0_4_4, all_0_6_6) = all_21_3_18 % 11.22/3.21 | (57) insert_slb(all_21_2_17, all_21_1_16) = all_21_0_15 % 11.22/3.21 | (58) update_slb(all_0_9_9, all_0_6_6) = all_21_2_17 % 11.22/3.21 | (59) ~ (all_21_3_18 = 0) | all_21_0_15 = all_0_1_1 % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (12) with all_0_9_9, all_0_6_6, all_19_1_13, all_21_2_17 and discharging atoms update_slb(all_0_9_9, all_0_6_6) = all_21_2_17, update_slb(all_0_9_9, all_0_6_6) = all_19_1_13, yields: % 11.22/3.21 | (60) all_21_2_17 = all_19_1_13 % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (9) with all_0_7_7, all_0_6_6, all_21_3_18, 0 and discharging atoms strictly_less_than(all_0_7_7, all_0_6_6) = 0, yields: % 11.22/3.21 | (61) all_21_3_18 = 0 | ~ (strictly_less_than(all_0_7_7, all_0_6_6) = all_21_3_18) % 11.22/3.21 | % 11.22/3.21 | From (60) and (58) follows: % 11.22/3.21 | (50) update_slb(all_0_9_9, all_0_6_6) = all_19_1_13 % 11.22/3.21 | % 11.22/3.21 | From (60) and (57) follows: % 11.22/3.21 | (63) insert_slb(all_19_1_13, all_21_1_16) = all_21_0_15 % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_21_1_16, all_0_6_6, all_0_6_6, all_0_8_8, all_0_5_5, all_19_1_13 and discharging atoms pair_in_list(all_0_1_1, all_0_8_8, all_0_6_6) = all_0_0_0, pair(all_0_5_5, all_0_6_6) = all_21_1_16, yields: % 11.22/3.21 | (64) all_0_0_0 = 0 | ~ (insert_slb(all_19_1_13, all_21_1_16) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = v0) % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_6_6, all_0_4_4, all_0_8_8, all_0_5_5, all_19_1_13 and discharging atoms pair_in_list(all_0_1_1, all_0_8_8, all_0_6_6) = all_0_0_0, pair(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 11.22/3.21 | (65) all_0_0_0 = 0 | ~ (insert_slb(all_19_1_13, all_0_3_3) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = v0) % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (28) with all_21_3_18, all_0_6_6, all_0_4_4 and discharging atoms strictly_less_than(all_0_4_4, all_0_6_6) = all_21_3_18, yields: % 11.22/3.21 | (66) all_21_3_18 = 0 | ? [v0] : ? [v1] : (less_than(all_0_4_4, all_0_6_6) = v0 & less_than(all_0_6_6, all_0_4_4) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 11.22/3.21 | % 11.22/3.21 | Instantiating formula (34) with all_19_2_14, all_0_4_4, all_0_6_6 and discharging atoms less_than(all_0_6_6, all_0_4_4) = all_19_2_14, yields: % 11.22/3.21 | (67) all_19_2_14 = 0 | less_than(all_0_4_4, all_0_6_6) = 0 % 11.22/3.21 | % 11.22/3.21 +-Applying beta-rule and splitting (46), into two cases. % 11.22/3.21 |-Branch one: % 11.22/3.21 | (68) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0 % 11.22/3.21 | % 11.22/3.21 +-Applying beta-rule and splitting (53), into two cases. % 11.22/3.21 |-Branch one: % 11.22/3.21 | (69) ~ (all_19_2_14 = 0) % 11.22/3.21 | % 11.22/3.21 +-Applying beta-rule and splitting (67), into two cases. % 11.22/3.21 |-Branch one: % 11.22/3.21 | (70) less_than(all_0_4_4, all_0_6_6) = 0 % 11.22/3.21 | % 11.22/3.21 +-Applying beta-rule and splitting (66), into two cases. % 11.22/3.21 |-Branch one: % 11.22/3.21 | (71) all_21_3_18 = 0 % 11.22/3.21 | % 11.22/3.21 +-Applying beta-rule and splitting (59), into two cases. % 11.22/3.21 |-Branch one: % 11.22/3.21 | (72) ~ (all_21_3_18 = 0) % 11.22/3.21 | % 11.22/3.21 | Equations (71) can reduce 72 to: % 11.22/3.21 | (73) $false % 11.22/3.21 | % 11.22/3.22 |-The branch is then unsatisfiable % 11.22/3.22 |-Branch two: % 11.22/3.22 | (71) all_21_3_18 = 0 % 11.22/3.22 | (75) all_21_0_15 = all_0_1_1 % 11.22/3.22 | % 11.22/3.22 | From (75) and (63) follows: % 11.22/3.22 | (76) insert_slb(all_19_1_13, all_21_1_16) = all_0_1_1 % 11.22/3.22 | % 11.22/3.22 +-Applying beta-rule and splitting (64), into two cases. % 11.22/3.22 |-Branch one: % 11.22/3.22 | (77) ~ (insert_slb(all_19_1_13, all_21_1_16) = all_0_1_1) % 11.22/3.22 | % 11.22/3.22 | Using (76) and (77) yields: % 11.22/3.22 | (78) $false % 11.22/3.22 | % 11.22/3.22 |-The branch is then unsatisfiable % 11.22/3.22 |-Branch two: % 11.22/3.22 | (76) insert_slb(all_19_1_13, all_21_1_16) = all_0_1_1 % 11.22/3.22 | (80) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = v0) % 11.22/3.22 | % 11.22/3.22 +-Applying beta-rule and splitting (80), into two cases. % 11.22/3.22 |-Branch one: % 11.22/3.22 | (81) all_0_0_0 = 0 % 11.22/3.22 | % 11.22/3.22 | Equations (81) can reduce 20 to: % 11.22/3.22 | (73) $false % 11.22/3.22 | % 11.22/3.22 |-The branch is then unsatisfiable % 11.22/3.22 |-Branch two: % 11.22/3.22 | (20) ~ (all_0_0_0 = 0) % 11.22/3.22 | (84) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = v0) % 11.22/3.22 | % 11.22/3.22 | Instantiating (84) with all_162_0_19 yields: % 11.22/3.22 | (85) ~ (all_162_0_19 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = all_162_0_19 % 11.22/3.22 | % 11.22/3.22 | Applying alpha-rule on (85) yields: % 11.22/3.22 | (86) ~ (all_162_0_19 = 0) % 11.22/3.22 | (87) pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = all_162_0_19 % 11.22/3.22 | % 11.22/3.22 +-Applying beta-rule and splitting (61), into two cases. % 11.22/3.22 |-Branch one: % 11.22/3.22 | (88) ~ (strictly_less_than(all_0_7_7, all_0_6_6) = all_21_3_18) % 11.22/3.22 | % 11.22/3.22 | From (71) and (88) follows: % 11.22/3.22 | (89) ~ (strictly_less_than(all_0_7_7, all_0_6_6) = 0) % 11.22/3.22 | % 11.22/3.22 | Using (8) and (89) yields: % 11.22/3.22 | (78) $false % 11.22/3.22 | % 11.22/3.22 |-The branch is then unsatisfiable % 11.22/3.22 |-Branch two: % 11.22/3.22 | (91) strictly_less_than(all_0_7_7, all_0_6_6) = all_21_3_18 % 11.22/3.22 | (71) all_21_3_18 = 0 % 11.22/3.22 | % 11.22/3.22 | From (71) and (91) follows: % 11.22/3.22 | (8) strictly_less_than(all_0_7_7, all_0_6_6) = 0 % 11.22/3.22 | % 11.22/3.22 | Instantiating formula (29) with all_162_0_19, all_19_1_13, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms update_slb(all_0_9_9, all_0_6_6) = all_19_1_13, pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = all_162_0_19, strictly_less_than(all_0_7_7, all_0_6_6) = 0, yields: % 11.22/3.22 | (94) all_162_0_19 = 0 | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = v0) % 11.22/3.22 | % 11.22/3.22 +-Applying beta-rule and splitting (94), into two cases. % 11.22/3.22 |-Branch one: % 11.22/3.22 | (95) all_162_0_19 = 0 % 11.22/3.22 | % 11.22/3.22 | Equations (95) can reduce 86 to: % 11.22/3.22 | (73) $false % 11.22/3.22 | % 11.22/3.22 |-The branch is then unsatisfiable % 11.22/3.22 |-Branch two: % 11.22/3.22 | (86) ~ (all_162_0_19 = 0) % 11.22/3.22 | (98) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = v0) % 11.22/3.22 | % 11.22/3.22 | Instantiating (98) with all_201_0_20 yields: % 11.22/3.22 | (99) ~ (all_201_0_20 = 0) & pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_201_0_20 % 11.22/3.22 | % 11.22/3.22 | Applying alpha-rule on (99) yields: % 11.22/3.22 | (100) ~ (all_201_0_20 = 0) % 11.22/3.22 | (101) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_201_0_20 % 11.22/3.22 | % 11.22/3.22 | Instantiating formula (2) with all_0_9_9, all_0_8_8, all_0_7_7, all_201_0_20, 0 and discharging atoms pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_201_0_20, pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0, yields: % 11.22/3.22 | (102) all_201_0_20 = 0 % 11.22/3.22 | % 11.22/3.22 | Equations (102) can reduce 100 to: % 11.22/3.22 | (73) $false % 11.22/3.22 | % 11.22/3.22 |-The branch is then unsatisfiable % 11.22/3.22 |-Branch two: % 11.22/3.22 | (72) ~ (all_21_3_18 = 0) % 11.22/3.22 | (105) ? [v0] : ? [v1] : (less_than(all_0_4_4, all_0_6_6) = v0 & less_than(all_0_6_6, all_0_4_4) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 11.22/3.22 | % 11.22/3.22 | Instantiating (105) with all_150_0_22, all_150_1_23 yields: % 11.22/3.22 | (106) less_than(all_0_4_4, all_0_6_6) = all_150_1_23 & less_than(all_0_6_6, all_0_4_4) = all_150_0_22 & ( ~ (all_150_1_23 = 0) | all_150_0_22 = 0) % 11.22/3.22 | % 11.22/3.22 | Applying alpha-rule on (106) yields: % 11.22/3.22 | (107) less_than(all_0_4_4, all_0_6_6) = all_150_1_23 % 11.22/3.22 | (108) less_than(all_0_6_6, all_0_4_4) = all_150_0_22 % 11.22/3.22 | (109) ~ (all_150_1_23 = 0) | all_150_0_22 = 0 % 11.22/3.22 | % 11.22/3.22 | Instantiating formula (41) with all_0_4_4, all_0_6_6, 0, all_150_1_23 and discharging atoms less_than(all_0_4_4, all_0_6_6) = all_150_1_23, less_than(all_0_4_4, all_0_6_6) = 0, yields: % 11.22/3.22 | (110) all_150_1_23 = 0 % 11.22/3.22 | % 11.22/3.22 | Instantiating formula (41) with all_0_6_6, all_0_4_4, all_150_0_22, all_19_2_14 and discharging atoms less_than(all_0_6_6, all_0_4_4) = all_150_0_22, less_than(all_0_6_6, all_0_4_4) = all_19_2_14, yields: % 11.22/3.22 | (111) all_150_0_22 = all_19_2_14 % 11.22/3.22 | % 11.22/3.22 +-Applying beta-rule and splitting (109), into two cases. % 11.22/3.22 |-Branch one: % 11.22/3.22 | (112) ~ (all_150_1_23 = 0) % 11.22/3.22 | % 11.22/3.22 | Equations (110) can reduce 112 to: % 11.22/3.22 | (73) $false % 11.22/3.22 | % 11.22/3.22 |-The branch is then unsatisfiable % 11.22/3.22 |-Branch two: % 11.22/3.22 | (110) all_150_1_23 = 0 % 11.22/3.22 | (115) all_150_0_22 = 0 % 11.22/3.22 | % 11.22/3.22 | Combining equations (115,111) yields a new equation: % 11.22/3.22 | (116) all_19_2_14 = 0 % 11.22/3.22 | % 11.22/3.22 | Equations (116) can reduce 69 to: % 11.22/3.22 | (73) $false % 11.22/3.22 | % 11.22/3.22 |-The branch is then unsatisfiable % 11.22/3.22 |-Branch two: % 11.22/3.22 | (118) ~ (less_than(all_0_4_4, all_0_6_6) = 0) % 11.22/3.22 | (116) all_19_2_14 = 0 % 11.22/3.22 | % 11.22/3.22 | Equations (116) can reduce 69 to: % 11.22/3.22 | (73) $false % 11.22/3.22 | % 11.22/3.22 |-The branch is then unsatisfiable % 11.22/3.22 |-Branch two: % 11.22/3.22 | (116) all_19_2_14 = 0 % 11.22/3.22 | (122) all_19_0_12 = all_0_1_1 % 11.22/3.22 | % 11.22/3.22 | From (122) and (51) follows: % 11.22/3.22 | (123) insert_slb(all_19_1_13, all_0_3_3) = all_0_1_1 % 11.22/3.22 | % 11.22/3.22 +-Applying beta-rule and splitting (65), into two cases. % 11.22/3.22 |-Branch one: % 11.22/3.22 | (124) ~ (insert_slb(all_19_1_13, all_0_3_3) = all_0_1_1) % 11.22/3.23 | % 11.22/3.23 | Using (123) and (124) yields: % 11.22/3.23 | (78) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 |-Branch two: % 11.22/3.23 | (123) insert_slb(all_19_1_13, all_0_3_3) = all_0_1_1 % 11.22/3.23 | (80) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = v0) % 11.22/3.23 | % 11.22/3.23 +-Applying beta-rule and splitting (80), into two cases. % 11.22/3.23 |-Branch one: % 11.22/3.23 | (81) all_0_0_0 = 0 % 11.22/3.23 | % 11.22/3.23 | Equations (81) can reduce 20 to: % 11.22/3.23 | (73) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 |-Branch two: % 11.22/3.23 | (20) ~ (all_0_0_0 = 0) % 11.22/3.23 | (84) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = v0) % 11.22/3.23 | % 11.22/3.23 | Instantiating (84) with all_153_0_24 yields: % 11.22/3.23 | (132) ~ (all_153_0_24 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = all_153_0_24 % 11.22/3.23 | % 11.22/3.23 | Applying alpha-rule on (132) yields: % 11.22/3.23 | (133) ~ (all_153_0_24 = 0) % 11.22/3.23 | (134) pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = all_153_0_24 % 11.22/3.23 | % 11.22/3.23 | Instantiating formula (29) with all_153_0_24, all_19_1_13, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms update_slb(all_0_9_9, all_0_6_6) = all_19_1_13, pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = all_153_0_24, strictly_less_than(all_0_7_7, all_0_6_6) = 0, yields: % 11.22/3.23 | (135) all_153_0_24 = 0 | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = v0) % 11.22/3.23 | % 11.22/3.23 +-Applying beta-rule and splitting (135), into two cases. % 11.22/3.23 |-Branch one: % 11.22/3.23 | (136) all_153_0_24 = 0 % 11.22/3.23 | % 11.22/3.23 | Equations (136) can reduce 133 to: % 11.22/3.23 | (73) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 |-Branch two: % 11.22/3.23 | (133) ~ (all_153_0_24 = 0) % 11.22/3.23 | (98) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = v0) % 11.22/3.23 | % 11.22/3.23 | Instantiating (98) with all_216_0_28 yields: % 11.22/3.23 | (140) ~ (all_216_0_28 = 0) & pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_216_0_28 % 11.22/3.23 | % 11.22/3.23 | Applying alpha-rule on (140) yields: % 11.22/3.23 | (141) ~ (all_216_0_28 = 0) % 11.22/3.23 | (142) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_216_0_28 % 11.22/3.23 | % 11.22/3.23 | Instantiating formula (2) with all_0_9_9, all_0_8_8, all_0_7_7, all_216_0_28, 0 and discharging atoms pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_216_0_28, pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0, yields: % 11.22/3.23 | (143) all_216_0_28 = 0 % 11.22/3.23 | % 11.22/3.23 | Equations (143) can reduce 141 to: % 11.22/3.23 | (73) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 |-Branch two: % 11.22/3.23 | (145) ~ (pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0) % 11.22/3.23 | (146) all_0_5_5 = all_0_8_8 % 11.22/3.23 | % 11.22/3.23 | From (146) and (55) follows: % 11.22/3.23 | (147) pair(all_0_8_8, all_0_6_6) = all_21_1_16 % 11.22/3.23 | % 11.22/3.23 +-Applying beta-rule and splitting (45), into two cases. % 11.22/3.23 |-Branch one: % 11.22/3.23 | (68) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0 % 11.22/3.23 | % 11.22/3.23 | Using (68) and (145) yields: % 11.22/3.23 | (78) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 |-Branch two: % 11.22/3.23 | (145) ~ (pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0) % 11.22/3.23 | (151) all_0_4_4 = all_0_7_7 % 11.22/3.23 | % 11.22/3.23 | From (151) and (56) follows: % 11.22/3.23 | (91) strictly_less_than(all_0_7_7, all_0_6_6) = all_21_3_18 % 11.22/3.23 | % 11.22/3.23 +-Applying beta-rule and splitting (61), into two cases. % 11.22/3.23 |-Branch one: % 11.22/3.23 | (88) ~ (strictly_less_than(all_0_7_7, all_0_6_6) = all_21_3_18) % 11.22/3.23 | % 11.22/3.23 | Using (91) and (88) yields: % 11.22/3.23 | (78) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 |-Branch two: % 11.22/3.23 | (91) strictly_less_than(all_0_7_7, all_0_6_6) = all_21_3_18 % 11.22/3.23 | (71) all_21_3_18 = 0 % 11.22/3.23 | % 11.22/3.23 +-Applying beta-rule and splitting (59), into two cases. % 11.22/3.23 |-Branch one: % 11.22/3.23 | (72) ~ (all_21_3_18 = 0) % 11.22/3.23 | % 11.22/3.23 | Equations (71) can reduce 72 to: % 11.22/3.23 | (73) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 |-Branch two: % 11.22/3.23 | (71) all_21_3_18 = 0 % 11.22/3.23 | (75) all_21_0_15 = all_0_1_1 % 11.22/3.23 | % 11.22/3.23 | From (75) and (63) follows: % 11.22/3.23 | (76) insert_slb(all_19_1_13, all_21_1_16) = all_0_1_1 % 11.22/3.23 | % 11.22/3.23 +-Applying beta-rule and splitting (64), into two cases. % 11.22/3.23 |-Branch one: % 11.22/3.23 | (77) ~ (insert_slb(all_19_1_13, all_21_1_16) = all_0_1_1) % 11.22/3.23 | % 11.22/3.23 | Using (76) and (77) yields: % 11.22/3.23 | (78) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 |-Branch two: % 11.22/3.23 | (76) insert_slb(all_19_1_13, all_21_1_16) = all_0_1_1 % 11.22/3.23 | (80) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = v0) % 11.22/3.23 | % 11.22/3.23 +-Applying beta-rule and splitting (80), into two cases. % 11.22/3.23 |-Branch one: % 11.22/3.23 | (81) all_0_0_0 = 0 % 11.22/3.23 | % 11.22/3.23 | Equations (81) can reduce 20 to: % 11.22/3.23 | (73) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 |-Branch two: % 11.22/3.23 | (20) ~ (all_0_0_0 = 0) % 11.22/3.23 | (84) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_19_1_13, all_0_8_8, all_0_6_6) = v0) % 11.22/3.23 | % 11.22/3.23 | Instantiating formula (14) with all_0_0_0, all_0_1_1, all_21_1_16, all_0_6_6, all_0_8_8, all_19_1_13 and discharging atoms pair_in_list(all_0_1_1, all_0_8_8, all_0_6_6) = all_0_0_0, pair(all_0_8_8, all_0_6_6) = all_21_1_16, insert_slb(all_19_1_13, all_21_1_16) = all_0_1_1, yields: % 11.22/3.23 | (81) all_0_0_0 = 0 % 11.22/3.23 | % 11.22/3.23 | Equations (81) can reduce 20 to: % 11.22/3.23 | (73) $false % 11.22/3.23 | % 11.22/3.23 |-The branch is then unsatisfiable % 11.22/3.23 % SZS output end Proof for theBenchmark % 11.22/3.23 % 11.22/3.23 2607ms %------------------------------------------------------------------------------