%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV409+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n014.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 17:51:17 EDT 2022 % Result : Theorem 6.81s 2.19s % Output : Proof 9.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SWV409+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n014.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jun 14 17:12:36 EDT 2022 % 0.13/0.35 % CPUTime : % 0.61/0.60 ____ _ % 0.61/0.60 ___ / __ \_____(_)___ ________ __________ % 0.61/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic % 0.61/0.60 (ePrincess v.1.0) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2015 % 0.61/0.60 (c) Peter Backeman, 2014-2015 % 0.61/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.60 Bug reports to peter@backeman.se % 0.61/0.60 % 0.61/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.81/0.96 Prover 0: Preprocessing ... % 2.53/1.18 Prover 0: Warning: ignoring some quantifiers % 2.53/1.21 Prover 0: Constructing countermodel ... % 5.02/1.80 Prover 0: gave up % 5.02/1.80 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.02/1.83 Prover 1: Preprocessing ... % 5.60/1.92 Prover 1: Constructing countermodel ... % 5.60/1.99 Prover 1: gave up % 5.60/1.99 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.97/2.01 Prover 2: Preprocessing ... % 6.36/2.11 Prover 2: Warning: ignoring some quantifiers % 6.36/2.11 Prover 2: Constructing countermodel ... % 6.81/2.19 Prover 2: proved (202ms) % 6.81/2.19 % 6.81/2.19 No countermodel exists, formula is valid % 6.81/2.19 % SZS status Theorem for theBenchmark % 6.81/2.19 % 6.81/2.19 Generating proof ... Warning: ignoring some quantifiers % 8.68/2.61 found it (size 66) % 8.68/2.61 % 8.68/2.62 % SZS output start Proof for theBenchmark % 8.68/2.62 Assumed formulas after preprocessing and simplification: % 8.68/2.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v0 = 0) & update_slb(v1, v3) = v4 & pair_in_list(v4, v2, v3) = v5 & contains_slb(v1, v2) = 0 & isnonempty_slb(create_slb) = v0 & strictly_less_than(v2, v3) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (pair_in_list(v12, v8, v10) = v13) | ~ (pair(v7, v9) = v11) | ~ (insert_slb(v6, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & pair_in_list(v6, v8, v10) = v14)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (contains_slb(v11, v8) = v12) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & contains_slb(v6, v8) = v13)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (pair_in_list(v12, v8, v10) = 0) | ~ (pair(v7, v9) = v11) | ~ (insert_slb(v6, v11) = v12) | pair_in_list(v6, v8, v10) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (lookup_slb(v11, v8) = v12) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ? [v13] : ((v13 = v12 & lookup_slb(v6, v8) = v12) | ( ~ (v13 = 0) & contains_slb(v6, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (remove_slb(v11, v8) = v12) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ? [v13] : ? [v14] : ((v14 = v12 & remove_slb(v6, v8) = v13 & insert_slb(v13, v10) = v12) | ( ~ (v13 = 0) & contains_slb(v6, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (remove_slb(v6, v8) = v11) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v11, v10) = v12) | ? [v13] : ? [v14] : ((v14 = v12 & remove_slb(v13, v8) = v12 & insert_slb(v6, v10) = v13) | ( ~ (v13 = 0) & contains_slb(v6, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (pair_in_list(v12, v8, v10) = 0) | ~ (pair(v7, v9) = v11) | ~ (insert_slb(v6, v11) = v12) | pair_in_list(v6, v8, v10) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (update_slb(v11, v8) = v12) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ? [v13] : ? [v14] : ? [v15] : ((v15 = v12 & update_slb(v6, v8) = v13 & pair(v7, v8) = v14 & insert_slb(v13, v14) = v12) | ( ~ (v13 = 0) & strictly_less_than(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (update_slb(v11, v8) = v12) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ? [v13] : ? [v14] : ((v14 = v12 & update_slb(v6, v8) = v13 & insert_slb(v13, v10) = v12) | ( ~ (v13 = 0) & less_than(v8, v9) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (update_slb(v6, v8) = v11) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v11, v10) = v12) | ? [v13] : ? [v14] : ((v14 = v12 & update_slb(v13, v8) = v12 & insert_slb(v6, v10) = v13) | ( ~ (v13 = 0) & less_than(v8, v9) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (update_slb(v6, v9) = v10) | ~ (pair_in_list(v10, v7, v9) = v11) | ~ (pair_in_list(v6, v7, v8) = 0) | ? [v12] : (( ~ (v12 = 0) & strictly_less_than(v8, v9) = v12) | ( ~ (v12 = 0) & strictly_less_than(v7, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (update_slb(v6, v9) = v10) | ~ (pair_in_list(v10, v7, v9) = v11) | ~ (strictly_less_than(v8, v9) = 0) | ? [v12] : (( ~ (v12 = 0) & pair_in_list(v6, v7, v8) = v12) | ( ~ (v12 = 0) & strictly_less_than(v7, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (pair_in_list(v10, v7, v8) = v11) | ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (contains_slb(v10, v7) = v11) | ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (contains_slb(v11, v8) = 0) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | contains_slb(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (pair_in_list(v10, v9, v8) = v7) | ~ (pair_in_list(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (update_slb(v6, v9) = v10) | ~ (pair_in_list(v6, v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & pair_in_list(v10, v7, v11) = 0 & less_than(v9, v11) = 0) | ( ~ (v11 = 0) & strictly_less_than(v7, v9) = v11) | ( ~ (v11 = 0) & less_than(v9, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (update_slb(v6, v9) = v10) | ~ (strictly_less_than(v7, v9) = 0) | ~ (less_than(v9, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & pair_in_list(v10, v7, v11) = 0 & less_than(v9, v11) = 0) | ( ~ (v11 = 0) & pair_in_list(v6, v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10) | lookup_slb(v10, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10) | remove_slb(v10, v7) = v6) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10) | isnonempty_slb(v10) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(v7, v8) = 0) | ~ (less_than(v6, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & less_than(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(v6, v8) = v9) | ~ (less_than(v6, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & less_than(v7, v8) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (update_slb(v9, v8) = v7) | ~ (update_slb(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (lookup_slb(v9, v8) = v7) | ~ (lookup_slb(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (remove_slb(v9, v8) = v7) | ~ (remove_slb(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (contains_slb(v9, v8) = v7) | ~ (contains_slb(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (pair(v9, v8) = v7) | ~ (pair(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (insert_slb(v9, v8) = v7) | ~ (insert_slb(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (strictly_less_than(v9, v8) = v7) | ~ (strictly_less_than(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (less_than(v9, v8) = v7) | ~ (less_than(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (pair_in_list(v6, v7, v8) = 0) | ~ (strictly_less_than(v8, v9) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & update_slb(v6, v9) = v10 & pair_in_list(v10, v7, v9) = 0) | ( ~ (v10 = 0) & strictly_less_than(v7, v9) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (pair_in_list(v6, v7, v8) = 0) | ~ (strictly_less_than(v7, v9) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & update_slb(v6, v9) = v10 & pair_in_list(v10, v7, v11) = 0 & less_than(v9, v11) = 0) | ( ~ (v10 = 0) & less_than(v9, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (pair_in_list(v6, v7, v8) = 0) | ~ (strictly_less_than(v7, v9) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & update_slb(v6, v9) = v10 & pair_in_list(v10, v7, v9) = 0) | ( ~ (v10 = 0) & strictly_less_than(v8, v9) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (pair_in_list(v6, v7, v8) = 0) | ~ (less_than(v9, v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & update_slb(v6, v9) = v10 & pair_in_list(v10, v7, v11) = 0 & less_than(v9, v11) = 0) | ( ~ (v10 = 0) & strictly_less_than(v7, v9) = v10))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (strictly_less_than(v6, v7) = v8) | ? [v9] : ((v9 = 0 & less_than(v7, v6) = 0) | ( ~ (v9 = 0) & less_than(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (less_than(v7, v6) = v8) | less_than(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (less_than(v7, v6) = v8) | ? [v9] : ((v9 = 0 & strictly_less_than(v6, v7) = 0) | ( ~ (v9 = 0) & less_than(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (less_than(v6, v7) = v8) | less_than(v7, v6) = 0) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (isnonempty_slb(v8) = v7) | ~ (isnonempty_slb(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (less_than(v7, v8) = 0) | ~ (less_than(v6, v7) = 0) | less_than(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (less_than(v7, v6) = v8) | ? [v9] : ((v9 = 0 & ~ (v8 = 0) & less_than(v6, v7) = 0) | ( ~ (v9 = 0) & strictly_less_than(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (less_than(v6, v7) = v8) | ? [v9] : ((v8 = 0 & ~ (v9 = 0) & less_than(v7, v6) = v9) | ( ~ (v9 = 0) & strictly_less_than(v6, v7) = v9))) & ! [v6] : ! [v7] : (v7 = create_slb | ~ (update_slb(create_slb, v6) = v7)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (less_than(v6, v6) = v7)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (less_than(bottom, v6) = v7)) & ! [v6] : ! [v7] : ~ (pair_in_list(create_slb, v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (contains_slb(v6, v7) = 0) | ? [v8] : pair_in_list(v6, v7, v8) = 0) & ! [v6] : ! [v7] : ( ~ (strictly_less_than(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & less_than(v7, v6) = v8 & less_than(v6, v7) = 0)) & ! [v6] : ! [v7] : ( ~ (less_than(v6, v7) = 0) | ? [v8] : ((v8 = 0 & strictly_less_than(v6, v7) = 0) | (v8 = 0 & less_than(v7, v6) = 0))) & ! [v6] : ( ~ (pair_in_list(v4, v2, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & less_than(v3, v6) = v7)) & ! [v6] : ~ (contains_slb(create_slb, v6) = 0) & ! [v6] : ( ~ (less_than(v3, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & pair_in_list(v4, v2, v6) = v7)) & ? [v6] : ? [v7] : ? [v8] : ? [v9] : pair_in_list(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : update_slb(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : lookup_slb(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : remove_slb(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : contains_slb(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : pair(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : insert_slb(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : strictly_less_than(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : less_than(v7, v6) = v8 & ? [v6] : ? [v7] : isnonempty_slb(v6) = v7) % 8.68/2.66 | 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 yields: % 8.68/2.66 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_5_5 = 0) & update_slb(all_0_4_4, all_0_2_2) = all_0_1_1 & pair_in_list(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0 & contains_slb(all_0_4_4, all_0_3_3) = 0 & isnonempty_slb(create_slb) = all_0_5_5 & strictly_less_than(all_0_3_3, all_0_2_2) = 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] : ((v7 = v6 & lookup_slb(v0, v2) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) & ! [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] : ((v8 = v6 & remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) & ! [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] : ((v9 = v6 & update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6) | ( ~ (v7 = 0) & strictly_less_than(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & less_than(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & less_than(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) = v5) | ~ (pair_in_list(v0, v1, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & strictly_less_than(v2, v3) = v6) | ( ~ (v6 = 0) & strictly_less_than(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) = v5) | ~ (strictly_less_than(v2, v3) = 0) | ? [v6] : (( ~ (v6 = 0) & pair_in_list(v0, v1, v2) = v6) | ( ~ (v6 = 0) & strictly_less_than(v1, v3) = v6))) & ! [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] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v0, v1, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & pair_in_list(v4, v1, v5) = 0 & less_than(v3, v5) = 0) | ( ~ (v5 = 0) & strictly_less_than(v1, v3) = v5) | ( ~ (v5 = 0) & less_than(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (update_slb(v0, v3) = v4) | ~ (strictly_less_than(v1, v3) = 0) | ~ (less_than(v3, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & pair_in_list(v4, v1, v5) = 0 & less_than(v3, v5) = 0) | ( ~ (v5 = 0) & pair_in_list(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | lookup_slb(v4, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | remove_slb(v4, v1) = 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(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & less_than(v0, v1) = v4)) & ! [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] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = 0) | ( ~ (v4 = 0) & strictly_less_than(v1, v3) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v1, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v5) = 0 & less_than(v3, v5) = 0) | ( ~ (v4 = 0) & less_than(v3, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v1, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = 0) | ( ~ (v4 = 0) & strictly_less_than(v2, v3) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (less_than(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v5) = 0 & less_than(v3, v5) = 0) | ( ~ (v4 = 0) & strictly_less_than(v1, v3) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ((v3 = 0 & less_than(v1, v0) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | less_than(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & strictly_less_than(v0, v1) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3))) & ! [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] : ! [v2] : ( ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v1) = 0) | less_than(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ~ (v2 = 0) & less_than(v0, v1) = 0) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v0, v1) = v2) | ? [v3] : ((v2 = 0 & ~ (v3 = 0) & less_than(v1, v0) = v3) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3))) & ! [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] : ( ~ (contains_slb(v0, v1) = 0) | ? [v2] : pair_in_list(v0, v1, v2) = 0) & ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (less_than(v0, v1) = 0) | ? [v2] : ((v2 = 0 & strictly_less_than(v0, v1) = 0) | (v2 = 0 & less_than(v1, v0) = 0))) & ! [v0] : ( ~ (pair_in_list(all_0_1_1, all_0_3_3, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & less_than(all_0_2_2, v0) = v1)) & ! [v0] : ~ (contains_slb(create_slb, v0) = 0) & ! [v0] : ( ~ (less_than(all_0_2_2, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & pair_in_list(all_0_1_1, all_0_3_3, v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : update_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : lookup_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : remove_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : contains_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : strictly_less_than(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : less_than(v1, v0) = v2 & ? [v0] : ? [v1] : isnonempty_slb(v0) = v1 % 8.68/2.68 | % 8.68/2.68 | Applying alpha-rule on (1) yields: % 8.68/2.68 | (2) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) % 8.68/2.68 | (3) ! [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) % 8.68/2.68 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) % 8.68/2.68 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (less_than(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v5) = 0 & less_than(v3, v5) = 0) | ( ~ (v4 = 0) & strictly_less_than(v1, v3) = v4))) % 8.68/2.68 | (6) ! [v0] : ! [v1] : ( ~ (contains_slb(v0, v1) = 0) | ? [v2] : pair_in_list(v0, v1, v2) = 0) % 8.68/2.68 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) % 8.68/2.68 | (8) ! [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)) % 8.68/2.68 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v0, v1, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & pair_in_list(v4, v1, v5) = 0 & less_than(v3, v5) = 0) | ( ~ (v5 = 0) & strictly_less_than(v1, v3) = v5) | ( ~ (v5 = 0) & less_than(v3, v2) = v5))) % 8.68/2.69 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 8.68/2.69 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6) | ( ~ (v7 = 0) & strictly_less_than(v3, v2) = v7))) % 8.68/2.69 | (12) contains_slb(all_0_4_4, all_0_3_3) = 0 % 8.68/2.69 | (13) ! [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)) % 8.68/2.69 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | lookup_slb(v4, v1) = v2) % 8.68/2.69 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) % 8.68/2.69 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & less_than(v2, v3) = v7))) % 8.68/2.69 | (17) ? [v0] : ? [v1] : ? [v2] : insert_slb(v1, v0) = v2 % 8.68/2.69 | (18) ? [v0] : ? [v1] : ? [v2] : less_than(v1, v0) = v2 % 8.68/2.69 | (19) ? [v0] : ? [v1] : ? [v2] : contains_slb(v1, v0) = v2 % 8.68/2.69 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & strictly_less_than(v0, v1) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3))) % 8.68/2.69 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 8.68/2.69 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 8.68/2.69 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ~ (v2 = 0) & less_than(v0, v1) = 0) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3))) % 8.68/2.69 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (update_slb(v0, v3) = v4) | ~ (strictly_less_than(v1, v3) = 0) | ~ (less_than(v3, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & pair_in_list(v4, v1, v5) = 0 & less_than(v3, v5) = 0) | ( ~ (v5 = 0) & pair_in_list(v0, v1, v2) = v5))) % 8.68/2.69 | (25) ~ (all_0_0_0 = 0) % 8.68/2.69 | (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) % 8.68/2.69 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) = v5) | ~ (pair_in_list(v0, v1, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & strictly_less_than(v2, v3) = v6) | ( ~ (v6 = 0) & strictly_less_than(v1, v3) = v6))) % 8.68/2.69 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = 0) | ( ~ (v4 = 0) & strictly_less_than(v1, v3) = v4))) % 8.68/2.69 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & less_than(v2, v3) = v7))) % 9.12/2.69 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) % 9.12/2.69 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | less_than(v0, v1) = 0) % 9.12/2.69 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) % 9.12/2.69 | (33) ! [v0] : ! [v1] : ( ~ (less_than(v0, v1) = 0) | ? [v2] : ((v2 = 0 & strictly_less_than(v0, v1) = 0) | (v2 = 0 & less_than(v1, v0) = 0))) % 9.12/2.69 | (34) ? [v0] : ? [v1] : isnonempty_slb(v0) = v1 % 9.12/2.69 | (35) ? [v0] : ? [v1] : ? [v2] : update_slb(v1, v0) = v2 % 9.12/2.69 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) % 9.12/2.69 | (37) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) % 9.12/2.69 | (38) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) % 9.12/2.70 | (39) ~ (all_0_5_5 = 0) % 9.12/2.70 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 9.12/2.70 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | remove_slb(v4, v1) = v0) % 9.12/2.70 | (42) ? [v0] : ? [v1] : ? [v2] : remove_slb(v1, v0) = v2 % 9.12/2.70 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 9.12/2.70 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v1, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = 0) | ( ~ (v4 = 0) & strictly_less_than(v2, v3) = v4))) % 9.12/2.70 | (45) ? [v0] : ? [v1] : ? [v2] : pair(v1, v0) = v2 % 9.12/2.70 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ((v7 = v6 & lookup_slb(v0, v2) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) % 9.12/2.70 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v0, v1) = v2) | ? [v3] : ((v2 = 0 & ~ (v3 = 0) & less_than(v1, v0) = v3) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3))) % 9.12/2.70 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 9.12/2.70 | (49) isnonempty_slb(create_slb) = all_0_5_5 % 9.12/2.70 | (50) ! [v0] : ( ~ (less_than(all_0_2_2, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & pair_in_list(all_0_1_1, all_0_3_3, v0) = v1)) % 9.12/2.70 | (51) ! [v0] : ( ~ (pair_in_list(all_0_1_1, all_0_3_3, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & less_than(all_0_2_2, v0) = v1)) % 9.12/2.70 | (52) ? [v0] : ? [v1] : ? [v2] : strictly_less_than(v1, v0) = v2 % 9.12/2.70 | (53) ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3 % 9.12/2.70 | (54) pair_in_list(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0 % 9.12/2.70 | (55) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ((v3 = 0 & less_than(v1, v0) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3))) % 9.12/2.70 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & less_than(v0, v1) = v4)) % 9.12/2.70 | (57) ! [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) % 9.12/2.70 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) % 9.12/2.70 | (59) ! [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] : ((v8 = v6 & remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) % 9.12/2.70 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v1) = 0) | less_than(v0, v2) = 0) % 9.12/2.70 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 9.12/2.70 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) = v5) | ~ (strictly_less_than(v2, v3) = 0) | ? [v6] : (( ~ (v6 = 0) & pair_in_list(v0, v1, v2) = v6) | ( ~ (v6 = 0) & strictly_less_than(v1, v3) = v6))) % 9.12/2.70 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) % 9.12/2.70 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v1, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v5) = 0 & less_than(v3, v5) = 0) | ( ~ (v4 = 0) & less_than(v3, v2) = v4))) % 9.12/2.70 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) % 9.12/2.70 | (66) ? [v0] : ? [v1] : ? [v2] : lookup_slb(v1, v0) = v2 % 9.12/2.70 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 9.12/2.70 | (68) ! [v0] : ~ (contains_slb(create_slb, v0) = 0) % 9.12/2.70 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 9.12/2.70 | (70) update_slb(all_0_4_4, all_0_2_2) = all_0_1_1 % 9.12/2.70 | (71) strictly_less_than(all_0_3_3, all_0_2_2) = 0 % 9.12/2.70 | % 9.12/2.70 | Instantiating formula (6) with all_0_3_3, all_0_4_4 and discharging atoms contains_slb(all_0_4_4, all_0_3_3) = 0, yields: % 9.12/2.70 | (72) ? [v0] : pair_in_list(all_0_4_4, all_0_3_3, v0) = 0 % 9.12/2.70 | % 9.12/2.70 | Instantiating formula (62) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms update_slb(all_0_4_4, all_0_2_2) = all_0_1_1, pair_in_list(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0, strictly_less_than(all_0_3_3, all_0_2_2) = 0, yields: % 9.12/2.70 | (73) all_0_0_0 = 0 | ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_4_4, all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & strictly_less_than(all_0_3_3, all_0_2_2) = v0)) % 9.12/2.70 | % 9.12/2.70 | Instantiating (72) with all_30_0_37 yields: % 9.12/2.70 | (74) pair_in_list(all_0_4_4, all_0_3_3, all_30_0_37) = 0 % 9.12/2.70 | % 9.12/2.70 +-Applying beta-rule and splitting (73), into two cases. % 9.12/2.70 |-Branch one: % 9.12/2.70 | (75) all_0_0_0 = 0 % 9.12/2.70 | % 9.12/2.70 | Equations (75) can reduce 25 to: % 9.12/2.70 | (76) $false % 9.12/2.70 | % 9.12/2.71 |-The branch is then unsatisfiable % 9.12/2.71 |-Branch two: % 9.12/2.71 | (25) ~ (all_0_0_0 = 0) % 9.12/2.71 | (78) ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_4_4, all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & strictly_less_than(all_0_3_3, all_0_2_2) = v0)) % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (27) with all_0_0_0, all_0_1_1, all_0_2_2, all_30_0_37, all_0_3_3, all_0_4_4 and discharging atoms update_slb(all_0_4_4, all_0_2_2) = all_0_1_1, pair_in_list(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0, pair_in_list(all_0_4_4, all_0_3_3, all_30_0_37) = 0, yields: % 9.12/2.71 | (79) all_0_0_0 = 0 | ? [v0] : (( ~ (v0 = 0) & strictly_less_than(all_30_0_37, all_0_2_2) = v0) | ( ~ (v0 = 0) & strictly_less_than(all_0_3_3, all_0_2_2) = v0)) % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (64) with all_0_2_2, all_30_0_37, all_0_3_3, all_0_4_4 and discharging atoms pair_in_list(all_0_4_4, all_0_3_3, all_30_0_37) = 0, strictly_less_than(all_0_3_3, all_0_2_2) = 0, yields: % 9.12/2.71 | (80) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & update_slb(all_0_4_4, all_0_2_2) = v0 & pair_in_list(v0, all_0_3_3, v1) = 0 & less_than(all_0_2_2, v1) = 0) | ( ~ (v0 = 0) & less_than(all_0_2_2, all_30_0_37) = v0)) % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (44) with all_0_2_2, all_30_0_37, all_0_3_3, all_0_4_4 and discharging atoms pair_in_list(all_0_4_4, all_0_3_3, all_30_0_37) = 0, strictly_less_than(all_0_3_3, all_0_2_2) = 0, yields: % 9.12/2.71 | (81) ? [v0] : ? [v1] : ((v1 = 0 & update_slb(all_0_4_4, all_0_2_2) = v0 & pair_in_list(v0, all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & strictly_less_than(all_30_0_37, all_0_2_2) = v0)) % 9.12/2.71 | % 9.12/2.71 | Instantiating (81) with all_48_0_40, all_48_1_41 yields: % 9.12/2.71 | (82) (all_48_0_40 = 0 & update_slb(all_0_4_4, all_0_2_2) = all_48_1_41 & pair_in_list(all_48_1_41, all_0_3_3, all_0_2_2) = 0) | ( ~ (all_48_1_41 = 0) & strictly_less_than(all_30_0_37, all_0_2_2) = all_48_1_41) % 9.12/2.71 | % 9.12/2.71 | Instantiating (80) with all_50_0_45, all_50_1_46, all_50_2_47, all_50_3_48 yields: % 9.12/2.71 | (83) (all_50_0_45 = 0 & all_50_1_46 = 0 & update_slb(all_0_4_4, all_0_2_2) = all_50_3_48 & pair_in_list(all_50_3_48, all_0_3_3, all_50_2_47) = 0 & less_than(all_0_2_2, all_50_2_47) = 0) | ( ~ (all_50_3_48 = 0) & less_than(all_0_2_2, all_30_0_37) = all_50_3_48) % 9.12/2.71 | % 9.12/2.71 +-Applying beta-rule and splitting (82), into two cases. % 9.12/2.71 |-Branch one: % 9.12/2.71 | (84) all_48_0_40 = 0 & update_slb(all_0_4_4, all_0_2_2) = all_48_1_41 & pair_in_list(all_48_1_41, all_0_3_3, all_0_2_2) = 0 % 9.12/2.71 | % 9.12/2.71 | Applying alpha-rule on (84) yields: % 9.12/2.71 | (85) all_48_0_40 = 0 % 9.12/2.71 | (86) update_slb(all_0_4_4, all_0_2_2) = all_48_1_41 % 9.12/2.71 | (87) pair_in_list(all_48_1_41, all_0_3_3, all_0_2_2) = 0 % 9.12/2.71 | % 9.12/2.71 +-Applying beta-rule and splitting (79), into two cases. % 9.12/2.71 |-Branch one: % 9.12/2.71 | (75) all_0_0_0 = 0 % 9.12/2.71 | % 9.12/2.71 | Equations (75) can reduce 25 to: % 9.12/2.71 | (76) $false % 9.12/2.71 | % 9.12/2.71 |-The branch is then unsatisfiable % 9.12/2.71 |-Branch two: % 9.12/2.71 | (25) ~ (all_0_0_0 = 0) % 9.12/2.71 | (91) ? [v0] : (( ~ (v0 = 0) & strictly_less_than(all_30_0_37, all_0_2_2) = v0) | ( ~ (v0 = 0) & strictly_less_than(all_0_3_3, all_0_2_2) = v0)) % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (69) with all_0_4_4, all_0_2_2, all_48_1_41, all_0_1_1 and discharging atoms update_slb(all_0_4_4, all_0_2_2) = all_48_1_41, update_slb(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 9.12/2.71 | (92) all_48_1_41 = all_0_1_1 % 9.12/2.71 | % 9.12/2.71 | From (92) and (87) follows: % 9.12/2.71 | (93) pair_in_list(all_0_1_1, all_0_3_3, all_0_2_2) = 0 % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (61) with all_0_1_1, all_0_3_3, all_0_2_2, 0, all_0_0_0 and discharging atoms pair_in_list(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0, pair_in_list(all_0_1_1, all_0_3_3, all_0_2_2) = 0, yields: % 9.12/2.71 | (75) all_0_0_0 = 0 % 9.12/2.71 | % 9.12/2.71 | Equations (75) can reduce 25 to: % 9.12/2.71 | (76) $false % 9.12/2.71 | % 9.12/2.71 |-The branch is then unsatisfiable % 9.12/2.71 |-Branch two: % 9.12/2.71 | (96) ~ (all_48_1_41 = 0) & strictly_less_than(all_30_0_37, all_0_2_2) = all_48_1_41 % 9.12/2.71 | % 9.12/2.71 | Applying alpha-rule on (96) yields: % 9.12/2.71 | (97) ~ (all_48_1_41 = 0) % 9.12/2.71 | (98) strictly_less_than(all_30_0_37, all_0_2_2) = all_48_1_41 % 9.12/2.71 | % 9.12/2.71 +-Applying beta-rule and splitting (79), into two cases. % 9.12/2.71 |-Branch one: % 9.12/2.71 | (75) all_0_0_0 = 0 % 9.12/2.71 | % 9.12/2.71 | Equations (75) can reduce 25 to: % 9.12/2.71 | (76) $false % 9.12/2.71 | % 9.12/2.71 |-The branch is then unsatisfiable % 9.12/2.71 |-Branch two: % 9.12/2.71 | (25) ~ (all_0_0_0 = 0) % 9.12/2.71 | (91) ? [v0] : (( ~ (v0 = 0) & strictly_less_than(all_30_0_37, all_0_2_2) = v0) | ( ~ (v0 = 0) & strictly_less_than(all_0_3_3, all_0_2_2) = v0)) % 9.12/2.71 | % 9.12/2.71 | Instantiating (91) with all_63_0_51 yields: % 9.12/2.71 | (103) ( ~ (all_63_0_51 = 0) & strictly_less_than(all_30_0_37, all_0_2_2) = all_63_0_51) | ( ~ (all_63_0_51 = 0) & strictly_less_than(all_0_3_3, all_0_2_2) = all_63_0_51) % 9.12/2.71 | % 9.12/2.71 +-Applying beta-rule and splitting (103), into two cases. % 9.12/2.71 |-Branch one: % 9.12/2.71 | (104) ~ (all_63_0_51 = 0) & strictly_less_than(all_30_0_37, all_0_2_2) = all_63_0_51 % 9.12/2.71 | % 9.12/2.71 | Applying alpha-rule on (104) yields: % 9.12/2.71 | (105) ~ (all_63_0_51 = 0) % 9.12/2.71 | (106) strictly_less_than(all_30_0_37, all_0_2_2) = all_63_0_51 % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (32) with all_30_0_37, all_0_2_2, all_48_1_41, all_63_0_51 and discharging atoms strictly_less_than(all_30_0_37, all_0_2_2) = all_63_0_51, strictly_less_than(all_30_0_37, all_0_2_2) = all_48_1_41, yields: % 9.12/2.71 | (107) all_63_0_51 = all_48_1_41 % 9.12/2.71 | % 9.12/2.71 | Equations (107) can reduce 105 to: % 9.12/2.71 | (97) ~ (all_48_1_41 = 0) % 9.12/2.71 | % 9.12/2.71 | From (107) and (106) follows: % 9.12/2.71 | (98) strictly_less_than(all_30_0_37, all_0_2_2) = all_48_1_41 % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (55) with all_48_1_41, all_0_2_2, all_30_0_37 and discharging atoms strictly_less_than(all_30_0_37, all_0_2_2) = all_48_1_41, yields: % 9.12/2.71 | (110) all_48_1_41 = 0 | ? [v0] : ((v0 = 0 & less_than(all_0_2_2, all_30_0_37) = 0) | ( ~ (v0 = 0) & less_than(all_30_0_37, all_0_2_2) = v0)) % 9.12/2.71 | % 9.12/2.71 +-Applying beta-rule and splitting (83), into two cases. % 9.12/2.71 |-Branch one: % 9.12/2.71 | (111) all_50_0_45 = 0 & all_50_1_46 = 0 & update_slb(all_0_4_4, all_0_2_2) = all_50_3_48 & pair_in_list(all_50_3_48, all_0_3_3, all_50_2_47) = 0 & less_than(all_0_2_2, all_50_2_47) = 0 % 9.12/2.71 | % 9.12/2.71 | Applying alpha-rule on (111) yields: % 9.12/2.71 | (112) all_50_1_46 = 0 % 9.12/2.71 | (113) all_50_0_45 = 0 % 9.12/2.71 | (114) pair_in_list(all_50_3_48, all_0_3_3, all_50_2_47) = 0 % 9.12/2.71 | (115) less_than(all_0_2_2, all_50_2_47) = 0 % 9.12/2.71 | (116) update_slb(all_0_4_4, all_0_2_2) = all_50_3_48 % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (69) with all_0_4_4, all_0_2_2, all_50_3_48, all_0_1_1 and discharging atoms update_slb(all_0_4_4, all_0_2_2) = all_50_3_48, update_slb(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 9.12/2.71 | (117) all_50_3_48 = all_0_1_1 % 9.12/2.71 | % 9.12/2.71 | From (117) and (114) follows: % 9.12/2.71 | (118) pair_in_list(all_0_1_1, all_0_3_3, all_50_2_47) = 0 % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (50) with all_50_2_47 and discharging atoms less_than(all_0_2_2, all_50_2_47) = 0, yields: % 9.12/2.71 | (119) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_1_1, all_0_3_3, all_50_2_47) = v0) % 9.12/2.71 | % 9.12/2.71 | Instantiating (119) with all_98_0_54 yields: % 9.12/2.71 | (120) ~ (all_98_0_54 = 0) & pair_in_list(all_0_1_1, all_0_3_3, all_50_2_47) = all_98_0_54 % 9.12/2.71 | % 9.12/2.71 | Applying alpha-rule on (120) yields: % 9.12/2.71 | (121) ~ (all_98_0_54 = 0) % 9.12/2.71 | (122) pair_in_list(all_0_1_1, all_0_3_3, all_50_2_47) = all_98_0_54 % 9.12/2.71 | % 9.12/2.71 | Instantiating formula (61) with all_0_1_1, all_0_3_3, all_50_2_47, all_98_0_54, 0 and discharging atoms pair_in_list(all_0_1_1, all_0_3_3, all_50_2_47) = all_98_0_54, pair_in_list(all_0_1_1, all_0_3_3, all_50_2_47) = 0, yields: % 9.12/2.72 | (123) all_98_0_54 = 0 % 9.12/2.72 | % 9.12/2.72 | Equations (123) can reduce 121 to: % 9.12/2.72 | (76) $false % 9.12/2.72 | % 9.12/2.72 |-The branch is then unsatisfiable % 9.12/2.72 |-Branch two: % 9.12/2.72 | (125) ~ (all_50_3_48 = 0) & less_than(all_0_2_2, all_30_0_37) = all_50_3_48 % 9.12/2.72 | % 9.12/2.72 | Applying alpha-rule on (125) yields: % 9.12/2.72 | (126) ~ (all_50_3_48 = 0) % 9.12/2.72 | (127) less_than(all_0_2_2, all_30_0_37) = all_50_3_48 % 9.12/2.72 | % 9.12/2.72 +-Applying beta-rule and splitting (110), into two cases. % 9.12/2.72 |-Branch one: % 9.12/2.72 | (128) all_48_1_41 = 0 % 9.12/2.72 | % 9.12/2.72 | Equations (128) can reduce 97 to: % 9.12/2.72 | (76) $false % 9.12/2.72 | % 9.12/2.72 |-The branch is then unsatisfiable % 9.12/2.72 |-Branch two: % 9.12/2.72 | (97) ~ (all_48_1_41 = 0) % 9.12/2.72 | (131) ? [v0] : ((v0 = 0 & less_than(all_0_2_2, all_30_0_37) = 0) | ( ~ (v0 = 0) & less_than(all_30_0_37, all_0_2_2) = v0)) % 9.12/2.72 | % 9.12/2.72 | Instantiating (131) with all_83_0_73 yields: % 9.12/2.72 | (132) (all_83_0_73 = 0 & less_than(all_0_2_2, all_30_0_37) = 0) | ( ~ (all_83_0_73 = 0) & less_than(all_30_0_37, all_0_2_2) = all_83_0_73) % 9.12/2.72 | % 9.12/2.72 +-Applying beta-rule and splitting (132), into two cases. % 9.12/2.72 |-Branch one: % 9.12/2.72 | (133) all_83_0_73 = 0 & less_than(all_0_2_2, all_30_0_37) = 0 % 9.12/2.72 | % 9.12/2.72 | Applying alpha-rule on (133) yields: % 9.12/2.72 | (134) all_83_0_73 = 0 % 9.12/2.72 | (135) less_than(all_0_2_2, all_30_0_37) = 0 % 9.12/2.72 | % 9.12/2.72 | Instantiating formula (21) with all_0_2_2, all_30_0_37, 0, all_50_3_48 and discharging atoms less_than(all_0_2_2, all_30_0_37) = all_50_3_48, less_than(all_0_2_2, all_30_0_37) = 0, yields: % 9.12/2.72 | (136) all_50_3_48 = 0 % 9.12/2.72 | % 9.12/2.72 | Equations (136) can reduce 126 to: % 9.12/2.72 | (76) $false % 9.12/2.72 | % 9.12/2.72 |-The branch is then unsatisfiable % 9.12/2.72 |-Branch two: % 9.12/2.72 | (138) ~ (all_83_0_73 = 0) & less_than(all_30_0_37, all_0_2_2) = all_83_0_73 % 9.12/2.72 | % 9.12/2.72 | Applying alpha-rule on (138) yields: % 9.12/2.72 | (139) ~ (all_83_0_73 = 0) % 9.12/2.72 | (140) less_than(all_30_0_37, all_0_2_2) = all_83_0_73 % 9.12/2.72 | % 9.12/2.72 | Instantiating formula (31) with all_83_0_73, all_30_0_37, all_0_2_2 and discharging atoms less_than(all_30_0_37, all_0_2_2) = all_83_0_73, yields: % 9.12/2.72 | (141) all_83_0_73 = 0 | less_than(all_0_2_2, all_30_0_37) = 0 % 9.12/2.72 | % 9.12/2.72 +-Applying beta-rule and splitting (141), into two cases. % 9.12/2.72 |-Branch one: % 9.12/2.72 | (135) less_than(all_0_2_2, all_30_0_37) = 0 % 9.12/2.72 | % 9.12/2.72 | Instantiating formula (21) with all_0_2_2, all_30_0_37, 0, all_50_3_48 and discharging atoms less_than(all_0_2_2, all_30_0_37) = all_50_3_48, less_than(all_0_2_2, all_30_0_37) = 0, yields: % 9.12/2.72 | (136) all_50_3_48 = 0 % 9.12/2.72 | % 9.12/2.72 | Equations (136) can reduce 126 to: % 9.12/2.72 | (76) $false % 9.12/2.72 | % 9.12/2.72 |-The branch is then unsatisfiable % 9.12/2.72 |-Branch two: % 9.12/2.72 | (145) ~ (less_than(all_0_2_2, all_30_0_37) = 0) % 9.12/2.72 | (134) all_83_0_73 = 0 % 9.12/2.72 | % 9.12/2.72 | Equations (134) can reduce 139 to: % 9.12/2.72 | (76) $false % 9.12/2.72 | % 9.12/2.72 |-The branch is then unsatisfiable % 9.12/2.72 |-Branch two: % 9.12/2.72 | (148) ~ (all_63_0_51 = 0) & strictly_less_than(all_0_3_3, all_0_2_2) = all_63_0_51 % 9.12/2.72 | % 9.12/2.72 | Applying alpha-rule on (148) yields: % 9.12/2.72 | (105) ~ (all_63_0_51 = 0) % 9.12/2.72 | (150) strictly_less_than(all_0_3_3, all_0_2_2) = all_63_0_51 % 9.12/2.72 | % 9.12/2.72 | Instantiating formula (32) with all_0_3_3, all_0_2_2, all_63_0_51, 0 and discharging atoms strictly_less_than(all_0_3_3, all_0_2_2) = all_63_0_51, strictly_less_than(all_0_3_3, all_0_2_2) = 0, yields: % 9.12/2.72 | (151) all_63_0_51 = 0 % 9.12/2.72 | % 9.12/2.72 | Equations (151) can reduce 105 to: % 9.12/2.72 | (76) $false % 9.12/2.72 | % 9.12/2.72 |-The branch is then unsatisfiable % 9.12/2.72 % SZS output end Proof for theBenchmark % 9.12/2.72 % 9.12/2.72 2107ms %------------------------------------------------------------------------------