%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV401+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 17:51:15 EDT 2022 % Result : Theorem 8.10s 2.56s % Output : Proof 10.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV401+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n024.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 : Tue Jun 14 17:50:18 EDT 2022 % 0.12/0.33 % CPUTime : % 0.53/0.58 ____ _ % 0.53/0.58 ___ / __ \_____(_)___ ________ __________ % 0.53/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.58 % 0.53/0.58 A Theorem Prover for First-Order Logic % 0.60/0.59 (ePrincess v.1.0) % 0.60/0.59 % 0.60/0.59 (c) Philipp Rümmer, 2009-2015 % 0.60/0.59 (c) Peter Backeman, 2014-2015 % 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.59 Bug reports to peter@backeman.se % 0.60/0.59 % 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.59 % 0.60/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.67/0.96 Prover 0: Preprocessing ... % 2.35/1.17 Prover 0: Warning: ignoring some quantifiers % 2.35/1.19 Prover 0: Constructing countermodel ... % 7.14/2.33 Prover 0: gave up % 7.14/2.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 7.14/2.36 Prover 1: Preprocessing ... % 7.57/2.44 Prover 1: Constructing countermodel ... % 8.10/2.56 Prover 1: proved (219ms) % 8.10/2.56 % 8.10/2.56 No countermodel exists, formula is valid % 8.10/2.56 % SZS status Theorem for theBenchmark % 8.10/2.56 % 8.10/2.56 Generating proof ... found it (size 112) % 10.87/3.13 % 10.87/3.13 % SZS output start Proof for theBenchmark % 10.87/3.13 Assumed formulas after preprocessing and simplification: % 10.87/3.13 | (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, v3) = v10 & pair_in_list(v8, v2, v3) = 0 & pair(v5, v6) = v7 & insert_slb(v1, v7) = v8 & isnonempty_slb(create_slb) = v0 & less_than(v4, v3) = 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, v12) = v15) | ? [v16] : ? [v17] : (pair_in_list(v1, v11, v12) = v16 & less_than(v13, v12) = v17 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [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)) % 10.87/3.17 | 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: % 10.87/3.17 | (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_7_7) = 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 & less_than(all_0_6_6, all_0_7_7) = 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, v1) = v4) | ? [v5] : ? [v6] : (pair_in_list(all_0_9_9, v0, v1) = v5 & less_than(v2, v1) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [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) % 10.87/3.18 | % 10.87/3.18 | Applying alpha-rule on (1) yields: % 10.87/3.18 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 10.87/3.18 | (3) update_slb(all_0_2_2, all_0_6_6) = all_0_1_1 % 10.87/3.18 | (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)) % 10.87/3.18 | (5) ! [v0] : ~ (contains_slb(create_slb, v0) = 0) % 10.87/3.18 | (6) ~ (all_0_10_10 = 0) % 10.87/3.18 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 10.87/3.18 | (8) less_than(all_0_6_6, all_0_7_7) = 0 % 10.87/3.18 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) % 10.87/3.18 | (10) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) % 10.87/3.18 | (11) pair(all_0_5_5, all_0_4_4) = all_0_3_3 % 10.87/3.18 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 10.87/3.18 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.87/3.18 | (14) ! [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))) % 10.87/3.18 | (15) ! [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)) % 10.87/3.18 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) % 10.87/3.18 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.87/3.18 | (18) pair_in_list(all_0_2_2, all_0_8_8, all_0_7_7) = 0 % 10.87/3.18 | (19) ~ (all_0_0_0 = 0) % 10.87/3.18 | (20) ! [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))) % 10.87/3.18 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) % 10.87/3.18 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 10.87/3.18 | (23) ! [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))) % 10.87/3.18 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (update_slb(all_0_9_9, v2) = v3) | ~ (pair_in_list(v3, v0, v1) = v4) | ? [v5] : ? [v6] : (pair_in_list(all_0_9_9, v0, v1) = v5 & less_than(v2, v1) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 10.87/3.18 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) % 10.87/3.18 | (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) % 10.87/3.18 | (27) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) % 10.87/3.19 | (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))) % 10.87/3.19 | (29) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) % 10.87/3.19 | (30) isnonempty_slb(create_slb) = all_0_10_10 % 10.87/3.19 | (31) pair_in_list(all_0_1_1, all_0_8_8, all_0_7_7) = all_0_0_0 % 10.87/3.19 | (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)) % 10.87/3.19 | (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) % 10.87/3.19 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) % 10.87/3.19 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.87/3.19 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.87/3.19 | (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))) % 10.87/3.19 | (38) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) % 10.87/3.19 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 10.87/3.19 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 10.87/3.19 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 10.87/3.19 | (42) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) % 10.87/3.19 | (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) % 10.87/3.19 | (44) insert_slb(all_0_9_9, all_0_3_3) = all_0_2_2 % 10.87/3.19 | % 10.87/3.19 | 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: % 10.87/3.19 | (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 % 10.87/3.19 | % 10.87/3.19 | 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: % 10.87/3.19 | (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 % 10.87/3.19 | % 10.87/3.19 | Instantiating formula (14) 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: % 10.87/3.19 | (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)) % 10.87/3.19 | % 10.87/3.19 | 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: % 10.87/3.19 | (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)) % 10.87/3.19 | % 10.87/3.19 | Instantiating (48) with all_17_0_11, all_17_1_12, all_17_2_13 yields: % 10.87/3.19 | (49) update_slb(all_0_9_9, all_0_6_6) = all_17_1_12 & insert_slb(all_17_1_12, all_0_3_3) = all_17_0_11 & less_than(all_0_6_6, all_0_4_4) = all_17_2_13 & ( ~ (all_17_2_13 = 0) | all_17_0_11 = all_0_1_1) % 10.87/3.19 | % 10.87/3.19 | Applying alpha-rule on (49) yields: % 10.87/3.19 | (50) update_slb(all_0_9_9, all_0_6_6) = all_17_1_12 % 10.87/3.19 | (51) insert_slb(all_17_1_12, all_0_3_3) = all_17_0_11 % 10.87/3.19 | (52) less_than(all_0_6_6, all_0_4_4) = all_17_2_13 % 10.87/3.19 | (53) ~ (all_17_2_13 = 0) | all_17_0_11 = all_0_1_1 % 10.87/3.19 | % 10.87/3.19 | Instantiating (47) with all_19_0_14, all_19_1_15, all_19_2_16, all_19_3_17 yields: % 10.87/3.19 | (54) update_slb(all_0_9_9, all_0_6_6) = all_19_2_16 & pair(all_0_5_5, all_0_6_6) = all_19_1_15 & insert_slb(all_19_2_16, all_19_1_15) = all_19_0_14 & strictly_less_than(all_0_4_4, all_0_6_6) = all_19_3_17 & ( ~ (all_19_3_17 = 0) | all_19_0_14 = all_0_1_1) % 10.87/3.19 | % 10.87/3.19 | Applying alpha-rule on (54) yields: % 10.87/3.19 | (55) update_slb(all_0_9_9, all_0_6_6) = all_19_2_16 % 10.87/3.19 | (56) strictly_less_than(all_0_4_4, all_0_6_6) = all_19_3_17 % 10.87/3.19 | (57) ~ (all_19_3_17 = 0) | all_19_0_14 = all_0_1_1 % 10.87/3.19 | (58) insert_slb(all_19_2_16, all_19_1_15) = all_19_0_14 % 10.87/3.19 | (59) pair(all_0_5_5, all_0_6_6) = all_19_1_15 % 10.87/3.19 | % 10.87/3.19 | Instantiating formula (12) with all_0_9_9, all_0_6_6, all_17_1_12, all_19_2_16 and discharging atoms update_slb(all_0_9_9, all_0_6_6) = all_19_2_16, update_slb(all_0_9_9, all_0_6_6) = all_17_1_12, yields: % 10.87/3.19 | (60) all_19_2_16 = all_17_1_12 % 10.87/3.19 | % 10.87/3.19 | Instantiating formula (41) with all_0_6_6, all_0_7_7, all_17_2_13, 0 and discharging atoms less_than(all_0_6_6, all_0_7_7) = 0, yields: % 10.87/3.19 | (61) all_17_2_13 = 0 | ~ (less_than(all_0_6_6, all_0_7_7) = all_17_2_13) % 10.87/3.20 | % 10.87/3.20 | From (60) and (55) follows: % 10.87/3.20 | (50) update_slb(all_0_9_9, all_0_6_6) = all_17_1_12 % 10.87/3.20 | % 10.87/3.20 | From (60) and (58) follows: % 10.87/3.20 | (63) insert_slb(all_17_1_12, all_19_1_15) = all_19_0_14 % 10.87/3.20 | % 10.87/3.20 | Instantiating formula (15) with all_0_0_0, all_0_1_1, all_19_1_15, all_0_7_7, all_0_6_6, all_0_8_8, all_0_5_5, all_17_1_12 and discharging atoms pair_in_list(all_0_1_1, all_0_8_8, all_0_7_7) = all_0_0_0, pair(all_0_5_5, all_0_6_6) = all_19_1_15, yields: % 10.87/3.20 | (64) all_0_0_0 = 0 | ~ (insert_slb(all_17_1_12, all_19_1_15) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = v0) % 10.87/3.20 | % 10.87/3.20 | Instantiating formula (15) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_7_7, all_0_4_4, all_0_8_8, all_0_5_5, all_17_1_12 and discharging atoms pair_in_list(all_0_1_1, all_0_8_8, all_0_7_7) = all_0_0_0, pair(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 10.87/3.20 | (65) all_0_0_0 = 0 | ~ (insert_slb(all_17_1_12, all_0_3_3) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = v0) % 10.87/3.20 | % 10.87/3.20 | Instantiating formula (28) with all_19_3_17, all_0_6_6, all_0_4_4 and discharging atoms strictly_less_than(all_0_4_4, all_0_6_6) = all_19_3_17, yields: % 10.87/3.20 | (66) all_19_3_17 = 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)) % 10.87/3.20 | % 10.87/3.20 | Instantiating formula (32) with all_17_2_13, all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms less_than(all_0_6_6, all_0_4_4) = all_17_2_13, less_than(all_0_6_6, all_0_7_7) = 0, yields: % 10.87/3.20 | (67) all_17_2_13 = 0 | ? [v0] : ( ~ (v0 = 0) & less_than(all_0_7_7, all_0_4_4) = v0) % 10.87/3.20 | % 10.87/3.20 | Instantiating formula (34) with all_17_2_13, all_0_4_4, all_0_6_6 and discharging atoms less_than(all_0_6_6, all_0_4_4) = all_17_2_13, yields: % 10.87/3.20 | (68) all_17_2_13 = 0 | less_than(all_0_4_4, all_0_6_6) = 0 % 10.87/3.20 | % 10.87/3.20 +-Applying beta-rule and splitting (45), into two cases. % 10.87/3.20 |-Branch one: % 10.87/3.20 | (69) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0 % 10.87/3.20 | % 10.87/3.20 +-Applying beta-rule and splitting (61), into two cases. % 10.87/3.20 |-Branch one: % 10.87/3.20 | (70) ~ (less_than(all_0_6_6, all_0_7_7) = all_17_2_13) % 10.87/3.20 | % 10.87/3.20 | Using (8) and (70) yields: % 10.87/3.20 | (71) ~ (all_17_2_13 = 0) % 10.87/3.20 | % 10.87/3.20 +-Applying beta-rule and splitting (68), into two cases. % 10.87/3.20 |-Branch one: % 10.87/3.20 | (72) less_than(all_0_4_4, all_0_6_6) = 0 % 10.87/3.20 | % 10.87/3.20 +-Applying beta-rule and splitting (67), into two cases. % 10.87/3.20 |-Branch one: % 10.87/3.20 | (73) all_17_2_13 = 0 % 10.87/3.20 | % 10.87/3.20 | Equations (73) can reduce 71 to: % 10.87/3.20 | (74) $false % 10.87/3.20 | % 10.87/3.20 |-The branch is then unsatisfiable % 10.87/3.20 |-Branch two: % 10.87/3.20 | (71) ~ (all_17_2_13 = 0) % 10.87/3.20 | (76) ? [v0] : ( ~ (v0 = 0) & less_than(all_0_7_7, all_0_4_4) = v0) % 10.87/3.20 | % 10.87/3.20 +-Applying beta-rule and splitting (66), into two cases. % 10.87/3.20 |-Branch one: % 10.87/3.20 | (77) all_19_3_17 = 0 % 10.87/3.20 | % 10.87/3.20 +-Applying beta-rule and splitting (57), into two cases. % 10.87/3.20 |-Branch one: % 10.87/3.20 | (78) ~ (all_19_3_17 = 0) % 10.87/3.20 | % 10.87/3.20 | Equations (77) can reduce 78 to: % 10.87/3.20 | (74) $false % 10.87/3.20 | % 10.87/3.20 |-The branch is then unsatisfiable % 10.87/3.20 |-Branch two: % 10.87/3.20 | (77) all_19_3_17 = 0 % 10.87/3.20 | (81) all_19_0_14 = all_0_1_1 % 10.87/3.20 | % 10.87/3.20 | From (81) and (63) follows: % 10.87/3.20 | (82) insert_slb(all_17_1_12, all_19_1_15) = all_0_1_1 % 10.87/3.20 | % 10.87/3.20 +-Applying beta-rule and splitting (64), into two cases. % 10.87/3.20 |-Branch one: % 10.87/3.20 | (83) ~ (insert_slb(all_17_1_12, all_19_1_15) = all_0_1_1) % 10.87/3.20 | % 10.87/3.20 | Using (82) and (83) yields: % 10.87/3.20 | (84) $false % 10.87/3.20 | % 10.87/3.20 |-The branch is then unsatisfiable % 10.87/3.20 |-Branch two: % 10.87/3.20 | (82) insert_slb(all_17_1_12, all_19_1_15) = all_0_1_1 % 10.87/3.20 | (86) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = v0) % 10.87/3.20 | % 10.87/3.20 +-Applying beta-rule and splitting (86), into two cases. % 10.87/3.20 |-Branch one: % 10.87/3.20 | (87) all_0_0_0 = 0 % 10.87/3.20 | % 10.87/3.20 | Equations (87) can reduce 19 to: % 10.87/3.20 | (74) $false % 10.87/3.20 | % 10.87/3.20 |-The branch is then unsatisfiable % 10.87/3.20 |-Branch two: % 10.87/3.20 | (19) ~ (all_0_0_0 = 0) % 10.87/3.20 | (90) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = v0) % 10.87/3.20 | % 10.87/3.20 | Instantiating (90) with all_144_0_19 yields: % 10.87/3.20 | (91) ~ (all_144_0_19 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = all_144_0_19 % 10.87/3.20 | % 10.87/3.20 | Applying alpha-rule on (91) yields: % 10.87/3.20 | (92) ~ (all_144_0_19 = 0) % 10.87/3.20 | (93) pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = all_144_0_19 % 10.87/3.20 | % 10.87/3.20 | Instantiating formula (24) with all_144_0_19, all_17_1_12, 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_17_1_12, pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = all_144_0_19, yields: % 10.87/3.20 | (94) all_144_0_19 = 0 | ? [v0] : ? [v1] : (pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = v0 & less_than(all_0_6_6, all_0_7_7) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.87/3.20 | % 10.87/3.20 +-Applying beta-rule and splitting (94), into two cases. % 10.87/3.20 |-Branch one: % 10.87/3.20 | (95) all_144_0_19 = 0 % 10.87/3.20 | % 10.87/3.20 | Equations (95) can reduce 92 to: % 10.87/3.20 | (74) $false % 10.87/3.20 | % 10.87/3.20 |-The branch is then unsatisfiable % 10.87/3.20 |-Branch two: % 10.87/3.20 | (92) ~ (all_144_0_19 = 0) % 10.87/3.20 | (98) ? [v0] : ? [v1] : (pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = v0 & less_than(all_0_6_6, all_0_7_7) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.87/3.20 | % 10.87/3.20 | Instantiating (98) with all_177_0_20, all_177_1_21 yields: % 10.87/3.20 | (99) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_177_1_21 & less_than(all_0_6_6, all_0_7_7) = all_177_0_20 & ( ~ (all_177_0_20 = 0) | ~ (all_177_1_21 = 0)) % 10.87/3.20 | % 10.87/3.20 | Applying alpha-rule on (99) yields: % 10.87/3.20 | (100) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_177_1_21 % 10.87/3.20 | (101) less_than(all_0_6_6, all_0_7_7) = all_177_0_20 % 10.87/3.20 | (102) ~ (all_177_0_20 = 0) | ~ (all_177_1_21 = 0) % 10.87/3.20 | % 10.87/3.20 | Instantiating formula (2) with all_0_9_9, all_0_8_8, all_0_7_7, all_177_1_21, 0 and discharging atoms pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_177_1_21, pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0, yields: % 10.87/3.21 | (103) all_177_1_21 = 0 % 10.87/3.21 | % 10.87/3.21 | Instantiating formula (41) with all_0_6_6, all_0_7_7, all_177_0_20, 0 and discharging atoms less_than(all_0_6_6, all_0_7_7) = all_177_0_20, less_than(all_0_6_6, all_0_7_7) = 0, yields: % 10.87/3.21 | (104) all_177_0_20 = 0 % 10.87/3.21 | % 10.87/3.21 +-Applying beta-rule and splitting (102), into two cases. % 10.87/3.21 |-Branch one: % 10.87/3.21 | (105) ~ (all_177_0_20 = 0) % 10.87/3.21 | % 10.87/3.21 | Equations (104) can reduce 105 to: % 10.87/3.21 | (74) $false % 10.87/3.21 | % 10.87/3.21 |-The branch is then unsatisfiable % 10.87/3.21 |-Branch two: % 10.87/3.21 | (104) all_177_0_20 = 0 % 10.87/3.21 | (108) ~ (all_177_1_21 = 0) % 10.87/3.21 | % 10.87/3.21 | Equations (103) can reduce 108 to: % 10.87/3.21 | (74) $false % 10.87/3.21 | % 10.87/3.21 |-The branch is then unsatisfiable % 10.87/3.21 |-Branch two: % 10.87/3.21 | (78) ~ (all_19_3_17 = 0) % 10.87/3.21 | (111) ? [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)) % 10.87/3.21 | % 10.87/3.21 | Instantiating (111) with all_132_0_22, all_132_1_23 yields: % 10.87/3.21 | (112) less_than(all_0_4_4, all_0_6_6) = all_132_1_23 & less_than(all_0_6_6, all_0_4_4) = all_132_0_22 & ( ~ (all_132_1_23 = 0) | all_132_0_22 = 0) % 10.87/3.21 | % 10.87/3.21 | Applying alpha-rule on (112) yields: % 10.87/3.21 | (113) less_than(all_0_4_4, all_0_6_6) = all_132_1_23 % 10.87/3.21 | (114) less_than(all_0_6_6, all_0_4_4) = all_132_0_22 % 10.87/3.21 | (115) ~ (all_132_1_23 = 0) | all_132_0_22 = 0 % 10.87/3.21 | % 10.87/3.21 | Instantiating formula (41) with all_0_4_4, all_0_6_6, 0, all_132_1_23 and discharging atoms less_than(all_0_4_4, all_0_6_6) = all_132_1_23, less_than(all_0_4_4, all_0_6_6) = 0, yields: % 10.87/3.21 | (116) all_132_1_23 = 0 % 10.87/3.21 | % 10.87/3.21 | Instantiating formula (41) with all_0_6_6, all_0_4_4, all_132_0_22, all_17_2_13 and discharging atoms less_than(all_0_6_6, all_0_4_4) = all_132_0_22, less_than(all_0_6_6, all_0_4_4) = all_17_2_13, yields: % 10.87/3.21 | (117) all_132_0_22 = all_17_2_13 % 10.87/3.21 | % 10.87/3.21 +-Applying beta-rule and splitting (115), into two cases. % 10.87/3.21 |-Branch one: % 10.87/3.21 | (118) ~ (all_132_1_23 = 0) % 10.87/3.21 | % 10.87/3.21 | Equations (116) can reduce 118 to: % 10.87/3.21 | (74) $false % 10.87/3.21 | % 10.87/3.21 |-The branch is then unsatisfiable % 10.87/3.21 |-Branch two: % 10.87/3.21 | (116) all_132_1_23 = 0 % 10.87/3.21 | (121) all_132_0_22 = 0 % 10.87/3.21 | % 10.87/3.21 | Combining equations (121,117) yields a new equation: % 10.87/3.21 | (73) all_17_2_13 = 0 % 10.87/3.21 | % 10.87/3.21 | Equations (73) can reduce 71 to: % 10.87/3.21 | (74) $false % 10.87/3.21 | % 10.87/3.21 |-The branch is then unsatisfiable % 10.87/3.21 |-Branch two: % 10.87/3.21 | (124) ~ (less_than(all_0_4_4, all_0_6_6) = 0) % 10.87/3.21 | (73) all_17_2_13 = 0 % 10.87/3.21 | % 10.87/3.21 | Equations (73) can reduce 71 to: % 10.87/3.21 | (74) $false % 10.87/3.21 | % 10.87/3.21 |-The branch is then unsatisfiable % 10.87/3.21 |-Branch two: % 10.87/3.21 | (127) less_than(all_0_6_6, all_0_7_7) = all_17_2_13 % 10.87/3.21 | (73) all_17_2_13 = 0 % 10.87/3.21 | % 10.87/3.21 | From (73) and (127) follows: % 10.87/3.21 | (8) less_than(all_0_6_6, all_0_7_7) = 0 % 10.87/3.21 | % 10.87/3.21 +-Applying beta-rule and splitting (53), into two cases. % 10.87/3.21 |-Branch one: % 10.87/3.21 | (71) ~ (all_17_2_13 = 0) % 10.87/3.21 | % 10.87/3.21 | Equations (73) can reduce 71 to: % 10.87/3.21 | (74) $false % 10.87/3.21 | % 10.87/3.21 |-The branch is then unsatisfiable % 10.87/3.21 |-Branch two: % 10.87/3.21 | (73) all_17_2_13 = 0 % 10.87/3.21 | (133) all_17_0_11 = all_0_1_1 % 10.87/3.21 | % 10.87/3.21 | From (133) and (51) follows: % 10.87/3.21 | (134) insert_slb(all_17_1_12, all_0_3_3) = all_0_1_1 % 10.87/3.21 | % 10.87/3.21 +-Applying beta-rule and splitting (65), into two cases. % 10.87/3.21 |-Branch one: % 10.87/3.21 | (135) ~ (insert_slb(all_17_1_12, all_0_3_3) = all_0_1_1) % 10.87/3.21 | % 10.87/3.21 | Using (134) and (135) yields: % 10.87/3.21 | (84) $false % 10.87/3.21 | % 10.87/3.21 |-The branch is then unsatisfiable % 10.87/3.21 |-Branch two: % 10.87/3.21 | (134) insert_slb(all_17_1_12, all_0_3_3) = all_0_1_1 % 10.87/3.21 | (86) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = v0) % 10.87/3.21 | % 10.87/3.21 +-Applying beta-rule and splitting (86), into two cases. % 10.87/3.21 |-Branch one: % 10.87/3.21 | (87) all_0_0_0 = 0 % 10.87/3.21 | % 10.87/3.21 | Equations (87) can reduce 19 to: % 10.87/3.21 | (74) $false % 10.87/3.21 | % 10.87/3.21 |-The branch is then unsatisfiable % 10.87/3.21 |-Branch two: % 10.87/3.21 | (19) ~ (all_0_0_0 = 0) % 10.87/3.21 | (90) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = v0) % 10.87/3.21 | % 10.87/3.21 | Instantiating (90) with all_123_0_24 yields: % 10.87/3.21 | (143) ~ (all_123_0_24 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = all_123_0_24 % 10.87/3.21 | % 10.87/3.21 | Applying alpha-rule on (143) yields: % 10.87/3.21 | (144) ~ (all_123_0_24 = 0) % 10.87/3.21 | (145) pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = all_123_0_24 % 10.87/3.21 | % 10.87/3.21 | Instantiating formula (24) with all_123_0_24, all_17_1_12, 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_17_1_12, pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = all_123_0_24, yields: % 10.87/3.21 | (146) all_123_0_24 = 0 | ? [v0] : ? [v1] : (pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = v0 & less_than(all_0_6_6, all_0_7_7) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.87/3.21 | % 10.87/3.21 +-Applying beta-rule and splitting (146), into two cases. % 10.87/3.21 |-Branch one: % 10.87/3.21 | (147) all_123_0_24 = 0 % 10.87/3.21 | % 10.87/3.21 | Equations (147) can reduce 144 to: % 10.87/3.21 | (74) $false % 10.87/3.21 | % 10.87/3.21 |-The branch is then unsatisfiable % 10.87/3.21 |-Branch two: % 10.87/3.21 | (144) ~ (all_123_0_24 = 0) % 10.87/3.21 | (98) ? [v0] : ? [v1] : (pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = v0 & less_than(all_0_6_6, all_0_7_7) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.87/3.21 | % 10.87/3.21 | Instantiating (98) with all_150_0_27, all_150_1_28 yields: % 10.87/3.21 | (151) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_150_1_28 & less_than(all_0_6_6, all_0_7_7) = all_150_0_27 & ( ~ (all_150_0_27 = 0) | ~ (all_150_1_28 = 0)) % 10.87/3.22 | % 10.87/3.22 | Applying alpha-rule on (151) yields: % 10.87/3.22 | (152) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_150_1_28 % 10.87/3.22 | (153) less_than(all_0_6_6, all_0_7_7) = all_150_0_27 % 10.87/3.22 | (154) ~ (all_150_0_27 = 0) | ~ (all_150_1_28 = 0) % 10.87/3.22 | % 10.87/3.22 | Instantiating formula (2) with all_0_9_9, all_0_8_8, all_0_7_7, all_150_1_28, 0 and discharging atoms pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = all_150_1_28, pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0, yields: % 10.87/3.22 | (155) all_150_1_28 = 0 % 10.87/3.22 | % 10.87/3.22 | Instantiating formula (41) with all_0_6_6, all_0_7_7, all_150_0_27, 0 and discharging atoms less_than(all_0_6_6, all_0_7_7) = all_150_0_27, less_than(all_0_6_6, all_0_7_7) = 0, yields: % 10.87/3.22 | (156) all_150_0_27 = 0 % 10.87/3.22 | % 10.87/3.22 +-Applying beta-rule and splitting (154), into two cases. % 10.87/3.22 |-Branch one: % 10.87/3.22 | (157) ~ (all_150_0_27 = 0) % 10.87/3.22 | % 10.87/3.22 | Equations (156) can reduce 157 to: % 10.87/3.22 | (74) $false % 10.87/3.22 | % 10.87/3.22 |-The branch is then unsatisfiable % 10.87/3.22 |-Branch two: % 10.87/3.22 | (156) all_150_0_27 = 0 % 10.87/3.22 | (160) ~ (all_150_1_28 = 0) % 10.87/3.22 | % 10.87/3.22 | Equations (155) can reduce 160 to: % 10.87/3.22 | (74) $false % 10.87/3.22 | % 10.87/3.22 |-The branch is then unsatisfiable % 10.87/3.22 |-Branch two: % 10.87/3.22 | (162) ~ (pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0) % 10.87/3.22 | (163) all_0_4_4 = all_0_7_7 % 10.87/3.22 | % 10.87/3.22 | From (163) and (11) follows: % 10.87/3.22 | (164) pair(all_0_5_5, all_0_7_7) = all_0_3_3 % 10.87/3.22 | % 10.87/3.22 | From (163) and (52) follows: % 10.87/3.22 | (127) less_than(all_0_6_6, all_0_7_7) = all_17_2_13 % 10.87/3.22 | % 10.87/3.22 +-Applying beta-rule and splitting (46), into two cases. % 10.87/3.22 |-Branch one: % 10.87/3.22 | (69) pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0 % 10.87/3.22 | % 10.87/3.22 | Using (69) and (162) yields: % 10.87/3.22 | (84) $false % 10.87/3.22 | % 10.87/3.22 |-The branch is then unsatisfiable % 10.87/3.22 |-Branch two: % 10.87/3.22 | (162) ~ (pair_in_list(all_0_9_9, all_0_8_8, all_0_7_7) = 0) % 10.87/3.22 | (169) all_0_5_5 = all_0_8_8 % 10.87/3.22 | % 10.87/3.22 | From (169) and (164) follows: % 10.87/3.22 | (170) pair(all_0_8_8, all_0_7_7) = all_0_3_3 % 10.87/3.22 | % 10.87/3.22 +-Applying beta-rule and splitting (61), into two cases. % 10.87/3.22 |-Branch one: % 10.87/3.22 | (70) ~ (less_than(all_0_6_6, all_0_7_7) = all_17_2_13) % 10.87/3.22 | % 10.87/3.22 | Using (127) and (70) yields: % 10.87/3.22 | (84) $false % 10.87/3.22 | % 10.87/3.22 |-The branch is then unsatisfiable % 10.87/3.22 |-Branch two: % 10.87/3.22 | (127) less_than(all_0_6_6, all_0_7_7) = all_17_2_13 % 10.87/3.22 | (73) all_17_2_13 = 0 % 10.87/3.22 | % 10.87/3.22 +-Applying beta-rule and splitting (53), into two cases. % 10.87/3.22 |-Branch one: % 10.87/3.22 | (71) ~ (all_17_2_13 = 0) % 10.87/3.22 | % 10.87/3.22 | Equations (73) can reduce 71 to: % 10.87/3.22 | (74) $false % 10.87/3.22 | % 10.87/3.22 |-The branch is then unsatisfiable % 10.87/3.22 |-Branch two: % 10.87/3.22 | (73) all_17_2_13 = 0 % 10.87/3.22 | (133) all_17_0_11 = all_0_1_1 % 10.87/3.22 | % 10.87/3.22 | From (133) and (51) follows: % 10.87/3.22 | (134) insert_slb(all_17_1_12, all_0_3_3) = all_0_1_1 % 10.87/3.22 | % 10.87/3.22 +-Applying beta-rule and splitting (65), into two cases. % 10.87/3.22 |-Branch one: % 10.87/3.22 | (135) ~ (insert_slb(all_17_1_12, all_0_3_3) = all_0_1_1) % 10.87/3.22 | % 10.87/3.22 | Using (134) and (135) yields: % 10.87/3.22 | (84) $false % 10.87/3.22 | % 10.87/3.22 |-The branch is then unsatisfiable % 10.87/3.22 |-Branch two: % 10.87/3.22 | (134) insert_slb(all_17_1_12, all_0_3_3) = all_0_1_1 % 10.87/3.22 | (86) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = v0) % 10.87/3.22 | % 10.87/3.22 +-Applying beta-rule and splitting (86), into two cases. % 10.87/3.22 |-Branch one: % 10.87/3.22 | (87) all_0_0_0 = 0 % 10.87/3.22 | % 10.87/3.22 | Equations (87) can reduce 19 to: % 10.87/3.22 | (74) $false % 10.87/3.22 | % 10.87/3.22 |-The branch is then unsatisfiable % 10.87/3.22 |-Branch two: % 10.87/3.22 | (19) ~ (all_0_0_0 = 0) % 10.87/3.22 | (90) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_17_1_12, all_0_8_8, all_0_7_7) = v0) % 10.87/3.22 | % 10.87/3.22 | Instantiating formula (13) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_7_7, all_0_8_8, all_17_1_12 and discharging atoms pair_in_list(all_0_1_1, all_0_8_8, all_0_7_7) = all_0_0_0, pair(all_0_8_8, all_0_7_7) = all_0_3_3, insert_slb(all_17_1_12, all_0_3_3) = all_0_1_1, yields: % 10.87/3.22 | (87) all_0_0_0 = 0 % 10.87/3.22 | % 10.87/3.22 | Equations (87) can reduce 19 to: % 10.87/3.22 | (74) $false % 10.87/3.22 | % 10.87/3.22 |-The branch is then unsatisfiable % 10.87/3.22 % SZS output end Proof for theBenchmark % 10.87/3.22 % 10.87/3.22 2627ms %------------------------------------------------------------------------------