%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV399+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 8.65s 2.88s % Output : Proof 11.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SWV399+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n021.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Wed Jun 15 18:09:59 EDT 2022 % 0.11/0.32 % CPUTime : % 0.17/0.57 ____ _ % 0.17/0.57 ___ / __ \_____(_)___ ________ __________ % 0.17/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.17/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.17/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.17/0.57 % 0.17/0.57 A Theorem Prover for First-Order Logic % 0.17/0.57 (ePrincess v.1.0) % 0.17/0.57 % 0.17/0.57 (c) Philipp Rümmer, 2009-2015 % 0.17/0.57 (c) Peter Backeman, 2014-2015 % 0.17/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.17/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.17/0.58 Bug reports to peter@backeman.se % 0.17/0.58 % 0.17/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.17/0.58 % 0.17/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.64/0.99 Prover 0: Preprocessing ... % 2.57/1.30 Prover 0: Warning: ignoring some quantifiers % 2.75/1.34 Prover 0: Constructing countermodel ... % 6.10/2.24 Prover 0: gave up % 6.10/2.24 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 6.10/2.28 Prover 1: Preprocessing ... % 6.98/2.44 Prover 1: Constructing countermodel ... % 7.33/2.56 Prover 1: gave up % 7.33/2.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 7.68/2.62 Prover 2: Preprocessing ... % 8.19/2.75 Prover 2: Warning: ignoring some quantifiers % 8.19/2.76 Prover 2: Constructing countermodel ... % 8.65/2.88 Prover 2: proved (314ms) % 8.65/2.88 % 8.65/2.88 No countermodel exists, formula is valid % 8.65/2.88 % SZS status Theorem for theBenchmark % 8.65/2.88 % 8.65/2.88 Generating proof ... Warning: ignoring some quantifiers % 10.80/3.30 found it (size 71) % 10.80/3.30 % 10.80/3.30 % SZS output start Proof for theBenchmark % 10.80/3.30 Assumed formulas after preprocessing and simplification: % 10.80/3.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v0 = 0) & update_slb(v1, v2) = v3 & pair_in_list(v1, v4, v5) = 0 & isnonempty_slb(create_slb) = v0 & strictly_less_than(v4, v5) = 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)) & ! [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)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (update_slb(v6, v9) = v10) | ~ (pair_in_list(v10, v7, v8) = v11) | ? [v12] : (( ~ (v12 = 0) & pair_in_list(v6, v7, v8) = v12) | ( ~ (v12 = 0) & less_than(v9, v8) = 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] : ( ~ (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] : (update_slb(v6, v9) = v10 & pair_in_list(v10, v7, v9) = 0)) & ! [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(v3, v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & strictly_less_than(v6, v7) = v8)) & ! [v6] : ! [v7] : ~ (pair_in_list(create_slb, v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (strictly_less_than(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & pair_in_list(v3, v6, v7) = v8)) & ! [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] : ~ (contains_slb(create_slb, v6) = 0) & ? [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) % 10.92/3.35 | 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: % 10.92/3.35 | (1) ~ (all_0_5_5 = 0) & update_slb(all_0_4_4, all_0_3_3) = all_0_2_2 & pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = 0 & isnonempty_slb(create_slb) = all_0_5_5 & strictly_less_than(all_0_1_1, all_0_0_0) = 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)) & ! [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)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v2) = v5) | ? [v6] : (( ~ (v6 = 0) & pair_in_list(v0, v1, v2) = v6) | ( ~ (v6 = 0) & less_than(v3, v2) = 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] : ( ~ (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] : (update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = 0)) & ! [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(all_0_2_2, v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & strictly_less_than(v0, v1) = v2)) & ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & pair_in_list(all_0_2_2, v0, v1) = v2)) & ! [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] : ~ (contains_slb(create_slb, v0) = 0) & ? [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 % 10.92/3.38 | % 10.92/3.38 | Applying alpha-rule on (1) yields: % 10.92/3.38 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) % 10.92/3.38 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) % 10.92/3.38 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | less_than(v0, v1) = 0) % 10.92/3.38 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) % 10.92/3.38 | (6) ? [v0] : ? [v1] : isnonempty_slb(v0) = v1 % 10.92/3.38 | (7) ! [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) % 10.92/3.38 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) % 10.92/3.38 | (9) pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = 0 % 10.92/3.38 | (10) ! [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)) % 10.92/3.38 | (11) ? [v0] : ? [v1] : ? [v2] : remove_slb(v1, v0) = v2 % 10.92/3.38 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 10.92/3.38 | (13) ! [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)) % 10.92/3.38 | (14) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & pair_in_list(all_0_2_2, v0, v1) = v2)) % 10.92/3.38 | (15) ! [v0] : ! [v1] : ( ~ (pair_in_list(all_0_2_2, v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & strictly_less_than(v0, v1) = v2)) % 10.92/3.38 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.92/3.39 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | lookup_slb(v4, v1) = v2) % 10.92/3.39 | (18) ? [v0] : ? [v1] : ? [v2] : contains_slb(v1, v0) = v2 % 10.92/3.39 | (19) ? [v0] : ? [v1] : ? [v2] : insert_slb(v1, v0) = v2 % 10.92/3.39 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 10.92/3.39 | (21) ? [v0] : ? [v1] : ? [v2] : update_slb(v1, v0) = v2 % 10.92/3.39 | (22) strictly_less_than(all_0_1_1, all_0_0_0) = 0 % 10.92/3.39 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.92/3.39 | (24) ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3 % 10.92/3.39 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v2, v3) = 0) | ? [v4] : (update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = 0)) % 10.92/3.39 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 10.92/3.39 | (27) ? [v0] : ? [v1] : ? [v2] : strictly_less_than(v1, v0) = v2 % 10.92/3.39 | (28) ! [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))) % 10.92/3.39 | (29) ! [v0] : ~ (contains_slb(create_slb, v0) = 0) % 10.92/3.39 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & less_than(v0, v1) = v4)) % 10.92/3.39 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) % 10.92/3.39 | (32) ~ (all_0_5_5 = 0) % 10.92/3.39 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | remove_slb(v4, v1) = v0) % 10.92/3.39 | (34) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) % 10.92/3.39 | (35) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) % 10.92/3.39 | (36) ! [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) % 10.92/3.39 | (37) ! [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) % 10.92/3.39 | (38) isnonempty_slb(create_slb) = all_0_5_5 % 10.92/3.39 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 10.92/3.40 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) % 10.92/3.40 | (41) ? [v0] : ? [v1] : ? [v2] : less_than(v1, v0) = v2 % 10.92/3.40 | (42) ! [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))) % 10.92/3.40 | (43) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) % 10.92/3.40 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 10.92/3.40 | (45) ? [v0] : ? [v1] : ? [v2] : pair(v1, v0) = v2 % 10.92/3.40 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v1) = 0) | less_than(v0, v2) = 0) % 10.92/3.40 | (47) ! [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))) % 10.92/3.40 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 10.92/3.40 | (49) ! [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))) % 10.92/3.40 | (50) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) % 10.92/3.40 | (51) ! [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)) % 10.92/3.40 | (52) ! [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))) % 10.92/3.40 | (53) ! [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))) % 10.92/3.40 | (54) ! [v0] : ! [v1] : ( ~ (less_than(v0, v1) = 0) | ? [v2] : ((v2 = 0 & strictly_less_than(v0, v1) = 0) | (v2 = 0 & less_than(v1, v0) = 0))) % 10.92/3.40 | (55) ? [v0] : ? [v1] : ? [v2] : lookup_slb(v1, v0) = v2 % 10.92/3.40 | (56) ! [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))) % 11.35/3.40 | (57) ! [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))) % 11.35/3.40 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v2) = v5) | ? [v6] : (( ~ (v6 = 0) & pair_in_list(v0, v1, v2) = v6) | ( ~ (v6 = 0) & less_than(v3, v2) = v6))) % 11.35/3.40 | (59) ! [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))) % 11.35/3.41 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 11.35/3.41 | (61) update_slb(all_0_4_4, all_0_3_3) = all_0_2_2 % 11.35/3.41 | (62) ! [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))) % 11.35/3.41 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) % 11.35/3.41 | (64) ! [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)) % 11.35/3.41 | % 11.35/3.41 | Instantiating formula (14) with all_0_0_0, all_0_1_1 and discharging atoms strictly_less_than(all_0_1_1, all_0_0_0) = 0, yields: % 11.35/3.41 | (65) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_2_2, all_0_1_1, all_0_0_0) = v0) % 11.35/3.41 | % 11.35/3.41 | Instantiating formula (34) with all_0_0_0, all_0_1_1 and discharging atoms strictly_less_than(all_0_1_1, all_0_0_0) = 0, yields: % 11.35/3.41 | (66) ? [v0] : ( ~ (v0 = 0) & less_than(all_0_0_0, all_0_1_1) = v0 & less_than(all_0_1_1, all_0_0_0) = 0) % 11.35/3.41 | % 11.35/3.41 | Instantiating (66) with all_28_0_36 yields: % 11.35/3.41 | (67) ~ (all_28_0_36 = 0) & less_than(all_0_0_0, all_0_1_1) = all_28_0_36 & less_than(all_0_1_1, all_0_0_0) = 0 % 11.35/3.41 | % 11.35/3.41 | Applying alpha-rule on (67) yields: % 11.35/3.41 | (68) ~ (all_28_0_36 = 0) % 11.35/3.41 | (69) less_than(all_0_0_0, all_0_1_1) = all_28_0_36 % 11.35/3.41 | (70) less_than(all_0_1_1, all_0_0_0) = 0 % 11.35/3.41 | % 11.35/3.41 | Instantiating (65) with all_30_0_37 yields: % 11.35/3.41 | (71) ~ (all_30_0_37 = 0) & pair_in_list(all_0_2_2, all_0_1_1, all_0_0_0) = all_30_0_37 % 11.35/3.41 | % 11.35/3.41 | Applying alpha-rule on (71) yields: % 11.35/3.41 | (72) ~ (all_30_0_37 = 0) % 11.35/3.41 | (73) pair_in_list(all_0_2_2, all_0_1_1, all_0_0_0) = all_30_0_37 % 11.35/3.41 | % 11.35/3.41 | Instantiating formula (58) with all_30_0_37, all_0_2_2, all_0_3_3, all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms update_slb(all_0_4_4, all_0_3_3) = all_0_2_2, pair_in_list(all_0_2_2, all_0_1_1, all_0_0_0) = all_30_0_37, yields: % 11.35/3.41 | (74) all_30_0_37 = 0 | ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & less_than(all_0_3_3, all_0_0_0) = v0)) % 11.35/3.41 | % 11.35/3.41 +-Applying beta-rule and splitting (74), into two cases. % 11.35/3.41 |-Branch one: % 11.35/3.41 | (75) all_30_0_37 = 0 % 11.35/3.41 | % 11.35/3.41 | Equations (75) can reduce 72 to: % 11.35/3.41 | (76) $false % 11.35/3.41 | % 11.35/3.41 |-The branch is then unsatisfiable % 11.35/3.41 |-Branch two: % 11.35/3.41 | (72) ~ (all_30_0_37 = 0) % 11.35/3.41 | (78) ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & less_than(all_0_3_3, all_0_0_0) = v0)) % 11.35/3.41 | % 11.35/3.41 | Instantiating (78) with all_47_0_40 yields: % 11.35/3.41 | (79) ( ~ (all_47_0_40 = 0) & pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = all_47_0_40) | ( ~ (all_47_0_40 = 0) & less_than(all_0_3_3, all_0_0_0) = all_47_0_40) % 11.35/3.41 | % 11.35/3.41 +-Applying beta-rule and splitting (79), into two cases. % 11.35/3.41 |-Branch one: % 11.35/3.41 | (80) ~ (all_47_0_40 = 0) & pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = all_47_0_40 % 11.35/3.41 | % 11.35/3.42 | Applying alpha-rule on (80) yields: % 11.35/3.42 | (81) ~ (all_47_0_40 = 0) % 11.35/3.42 | (82) pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = all_47_0_40 % 11.35/3.42 | % 11.35/3.42 | Instantiating formula (60) with all_0_4_4, all_0_1_1, all_0_0_0, all_47_0_40, 0 and discharging atoms pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = all_47_0_40, pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = 0, yields: % 11.35/3.42 | (83) all_47_0_40 = 0 % 11.35/3.42 | % 11.35/3.42 | Equations (83) can reduce 81 to: % 11.35/3.42 | (76) $false % 11.35/3.42 | % 11.35/3.42 |-The branch is then unsatisfiable % 11.35/3.42 |-Branch two: % 11.35/3.42 | (85) ~ (all_47_0_40 = 0) & less_than(all_0_3_3, all_0_0_0) = all_47_0_40 % 11.35/3.42 | % 11.35/3.42 | Applying alpha-rule on (85) yields: % 11.35/3.42 | (81) ~ (all_47_0_40 = 0) % 11.35/3.42 | (87) less_than(all_0_3_3, all_0_0_0) = all_47_0_40 % 11.35/3.42 | % 11.35/3.42 | Instantiating formula (30) with all_47_0_40, all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms less_than(all_0_1_1, all_0_0_0) = 0, less_than(all_0_3_3, all_0_0_0) = all_47_0_40, yields: % 11.35/3.42 | (88) all_47_0_40 = 0 | ? [v0] : ( ~ (v0 = 0) & less_than(all_0_3_3, all_0_1_1) = v0) % 11.35/3.42 | % 11.35/3.42 | Instantiating formula (4) with all_47_0_40, all_0_3_3, all_0_0_0 and discharging atoms less_than(all_0_3_3, all_0_0_0) = all_47_0_40, yields: % 11.35/3.42 | (89) all_47_0_40 = 0 | less_than(all_0_0_0, all_0_3_3) = 0 % 11.35/3.42 | % 11.35/3.42 | Instantiating formula (52) with all_47_0_40, all_0_3_3, all_0_0_0 and discharging atoms less_than(all_0_3_3, all_0_0_0) = all_47_0_40, yields: % 11.35/3.42 | (90) all_47_0_40 = 0 | ? [v0] : ((v0 = 0 & strictly_less_than(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & less_than(all_0_0_0, all_0_3_3) = v0)) % 11.35/3.42 | % 11.35/3.42 | Instantiating formula (59) with all_47_0_40, all_0_3_3, all_0_0_0 and discharging atoms less_than(all_0_3_3, all_0_0_0) = all_47_0_40, yields: % 11.35/3.42 | (91) ? [v0] : ((v0 = 0 & ~ (all_47_0_40 = 0) & less_than(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & strictly_less_than(all_0_0_0, all_0_3_3) = v0)) % 11.35/3.42 | % 11.35/3.42 | Instantiating (91) with all_62_0_42 yields: % 11.35/3.42 | (92) (all_62_0_42 = 0 & ~ (all_47_0_40 = 0) & less_than(all_0_0_0, all_0_3_3) = 0) | ( ~ (all_62_0_42 = 0) & strictly_less_than(all_0_0_0, all_0_3_3) = all_62_0_42) % 11.35/3.42 | % 11.35/3.42 +-Applying beta-rule and splitting (89), into two cases. % 11.35/3.42 |-Branch one: % 11.35/3.42 | (93) less_than(all_0_0_0, all_0_3_3) = 0 % 11.35/3.42 | % 11.35/3.42 +-Applying beta-rule and splitting (90), into two cases. % 11.35/3.42 |-Branch one: % 11.35/3.42 | (83) all_47_0_40 = 0 % 11.35/3.42 | % 11.35/3.42 | Equations (83) can reduce 81 to: % 11.35/3.42 | (76) $false % 11.35/3.42 | % 11.35/3.42 |-The branch is then unsatisfiable % 11.35/3.42 |-Branch two: % 11.35/3.42 | (81) ~ (all_47_0_40 = 0) % 11.35/3.42 | (97) ? [v0] : ((v0 = 0 & strictly_less_than(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & less_than(all_0_0_0, all_0_3_3) = v0)) % 11.35/3.42 | % 11.35/3.42 | Instantiating (97) with all_69_0_43 yields: % 11.35/3.42 | (98) (all_69_0_43 = 0 & strictly_less_than(all_0_0_0, all_0_3_3) = 0) | ( ~ (all_69_0_43 = 0) & less_than(all_0_0_0, all_0_3_3) = all_69_0_43) % 11.35/3.42 | % 11.35/3.42 +-Applying beta-rule and splitting (88), into two cases. % 11.35/3.42 |-Branch one: % 11.35/3.42 | (83) all_47_0_40 = 0 % 11.35/3.42 | % 11.35/3.42 | Equations (83) can reduce 81 to: % 11.35/3.42 | (76) $false % 11.35/3.42 | % 11.35/3.42 |-The branch is then unsatisfiable % 11.35/3.42 |-Branch two: % 11.35/3.42 | (81) ~ (all_47_0_40 = 0) % 11.35/3.42 | (102) ? [v0] : ( ~ (v0 = 0) & less_than(all_0_3_3, all_0_1_1) = v0) % 11.35/3.42 | % 11.35/3.42 | Instantiating (102) with all_77_0_45 yields: % 11.35/3.42 | (103) ~ (all_77_0_45 = 0) & less_than(all_0_3_3, all_0_1_1) = all_77_0_45 % 11.35/3.42 | % 11.35/3.42 | Applying alpha-rule on (103) yields: % 11.35/3.42 | (104) ~ (all_77_0_45 = 0) % 11.35/3.42 | (105) less_than(all_0_3_3, all_0_1_1) = all_77_0_45 % 11.35/3.42 | % 11.35/3.42 +-Applying beta-rule and splitting (98), into two cases. % 11.35/3.42 |-Branch one: % 11.35/3.42 | (106) all_69_0_43 = 0 & strictly_less_than(all_0_0_0, all_0_3_3) = 0 % 11.35/3.42 | % 11.35/3.42 | Applying alpha-rule on (106) yields: % 11.35/3.42 | (107) all_69_0_43 = 0 % 11.35/3.42 | (108) strictly_less_than(all_0_0_0, all_0_3_3) = 0 % 11.35/3.42 | % 11.35/3.42 +-Applying beta-rule and splitting (92), into two cases. % 11.35/3.42 |-Branch one: % 11.35/3.42 | (109) all_62_0_42 = 0 & ~ (all_47_0_40 = 0) & less_than(all_0_0_0, all_0_3_3) = 0 % 11.35/3.42 | % 11.35/3.42 | Applying alpha-rule on (109) yields: % 11.35/3.42 | (110) all_62_0_42 = 0 % 11.35/3.42 | (81) ~ (all_47_0_40 = 0) % 11.35/3.42 | (93) less_than(all_0_0_0, all_0_3_3) = 0 % 11.35/3.42 | % 11.35/3.42 | Instantiating formula (25) with all_0_3_3, all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms pair_in_list(all_0_4_4, all_0_1_1, all_0_0_0) = 0, strictly_less_than(all_0_0_0, all_0_3_3) = 0, yields: % 11.35/3.42 | (113) ? [v0] : (update_slb(all_0_4_4, all_0_3_3) = v0 & pair_in_list(v0, all_0_1_1, all_0_3_3) = 0) % 11.35/3.42 | % 11.35/3.42 | Instantiating formula (46) with all_0_3_3, all_0_0_0, all_0_1_1 and discharging atoms less_than(all_0_0_0, all_0_3_3) = 0, less_than(all_0_1_1, all_0_0_0) = 0, yields: % 11.35/3.42 | (114) less_than(all_0_1_1, all_0_3_3) = 0 % 11.35/3.42 | % 11.35/3.42 | Instantiating formula (52) with all_77_0_45, all_0_3_3, all_0_1_1 and discharging atoms less_than(all_0_3_3, all_0_1_1) = all_77_0_45, yields: % 11.35/3.42 | (115) all_77_0_45 = 0 | ? [v0] : ((v0 = 0 & strictly_less_than(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & less_than(all_0_1_1, all_0_3_3) = v0)) % 11.35/3.43 | % 11.35/3.43 | Instantiating (113) with all_99_0_47 yields: % 11.35/3.43 | (116) update_slb(all_0_4_4, all_0_3_3) = all_99_0_47 & pair_in_list(all_99_0_47, all_0_1_1, all_0_3_3) = 0 % 11.35/3.43 | % 11.35/3.43 | Applying alpha-rule on (116) yields: % 11.35/3.43 | (117) update_slb(all_0_4_4, all_0_3_3) = all_99_0_47 % 11.35/3.43 | (118) pair_in_list(all_99_0_47, all_0_1_1, all_0_3_3) = 0 % 11.35/3.43 | % 11.35/3.43 +-Applying beta-rule and splitting (115), into two cases. % 11.35/3.43 |-Branch one: % 11.35/3.43 | (119) all_77_0_45 = 0 % 11.35/3.43 | % 11.35/3.43 | Equations (119) can reduce 104 to: % 11.35/3.43 | (76) $false % 11.35/3.43 | % 11.35/3.43 |-The branch is then unsatisfiable % 11.35/3.43 |-Branch two: % 11.35/3.43 | (104) ~ (all_77_0_45 = 0) % 11.35/3.43 | (122) ? [v0] : ((v0 = 0 & strictly_less_than(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & less_than(all_0_1_1, all_0_3_3) = v0)) % 11.35/3.43 | % 11.35/3.43 | Instantiating (122) with all_107_0_50 yields: % 11.35/3.43 | (123) (all_107_0_50 = 0 & strictly_less_than(all_0_1_1, all_0_3_3) = 0) | ( ~ (all_107_0_50 = 0) & less_than(all_0_1_1, all_0_3_3) = all_107_0_50) % 11.35/3.43 | % 11.35/3.43 +-Applying beta-rule and splitting (123), into two cases. % 11.35/3.43 |-Branch one: % 11.35/3.43 | (124) all_107_0_50 = 0 & strictly_less_than(all_0_1_1, all_0_3_3) = 0 % 11.35/3.43 | % 11.35/3.43 | Applying alpha-rule on (124) yields: % 11.35/3.43 | (125) all_107_0_50 = 0 % 11.35/3.43 | (126) strictly_less_than(all_0_1_1, all_0_3_3) = 0 % 11.35/3.43 | % 11.35/3.43 | Instantiating formula (48) with all_0_4_4, all_0_3_3, all_99_0_47, all_0_2_2 and discharging atoms update_slb(all_0_4_4, all_0_3_3) = all_99_0_47, update_slb(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 11.35/3.43 | (127) all_99_0_47 = all_0_2_2 % 11.35/3.43 | % 11.35/3.43 | From (127) and (118) follows: % 11.35/3.43 | (128) pair_in_list(all_0_2_2, all_0_1_1, all_0_3_3) = 0 % 11.35/3.43 | % 11.35/3.43 | Instantiating formula (14) with all_0_3_3, all_0_1_1 and discharging atoms strictly_less_than(all_0_1_1, all_0_3_3) = 0, yields: % 11.35/3.43 | (129) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_2_2, all_0_1_1, all_0_3_3) = v0) % 11.35/3.43 | % 11.35/3.43 | Instantiating (129) with all_133_0_52 yields: % 11.35/3.43 | (130) ~ (all_133_0_52 = 0) & pair_in_list(all_0_2_2, all_0_1_1, all_0_3_3) = all_133_0_52 % 11.35/3.43 | % 11.35/3.43 | Applying alpha-rule on (130) yields: % 11.35/3.43 | (131) ~ (all_133_0_52 = 0) % 11.35/3.43 | (132) pair_in_list(all_0_2_2, all_0_1_1, all_0_3_3) = all_133_0_52 % 11.35/3.43 | % 11.35/3.43 | Instantiating formula (60) with all_0_2_2, all_0_1_1, all_0_3_3, all_133_0_52, 0 and discharging atoms pair_in_list(all_0_2_2, all_0_1_1, all_0_3_3) = all_133_0_52, pair_in_list(all_0_2_2, all_0_1_1, all_0_3_3) = 0, yields: % 11.35/3.43 | (133) all_133_0_52 = 0 % 11.35/3.43 | % 11.35/3.43 | Equations (133) can reduce 131 to: % 11.35/3.43 | (76) $false % 11.35/3.43 | % 11.35/3.43 |-The branch is then unsatisfiable % 11.35/3.43 |-Branch two: % 11.35/3.43 | (135) ~ (all_107_0_50 = 0) & less_than(all_0_1_1, all_0_3_3) = all_107_0_50 % 11.35/3.43 | % 11.35/3.43 | Applying alpha-rule on (135) yields: % 11.35/3.43 | (136) ~ (all_107_0_50 = 0) % 11.35/3.43 | (137) less_than(all_0_1_1, all_0_3_3) = all_107_0_50 % 11.35/3.43 | % 11.35/3.43 | Instantiating formula (12) with all_0_1_1, all_0_3_3, 0, all_107_0_50 and discharging atoms less_than(all_0_1_1, all_0_3_3) = all_107_0_50, less_than(all_0_1_1, all_0_3_3) = 0, yields: % 11.35/3.43 | (125) all_107_0_50 = 0 % 11.35/3.43 | % 11.35/3.43 | Equations (125) can reduce 136 to: % 11.35/3.43 | (76) $false % 11.35/3.43 | % 11.35/3.43 |-The branch is then unsatisfiable % 11.35/3.43 |-Branch two: % 11.35/3.43 | (140) ~ (all_62_0_42 = 0) & strictly_less_than(all_0_0_0, all_0_3_3) = all_62_0_42 % 11.35/3.43 | % 11.35/3.43 | Applying alpha-rule on (140) yields: % 11.35/3.43 | (141) ~ (all_62_0_42 = 0) % 11.35/3.43 | (142) strictly_less_than(all_0_0_0, all_0_3_3) = all_62_0_42 % 11.35/3.43 | % 11.35/3.43 | Instantiating formula (40) with all_0_0_0, all_0_3_3, 0, all_62_0_42 and discharging atoms strictly_less_than(all_0_0_0, all_0_3_3) = all_62_0_42, strictly_less_than(all_0_0_0, all_0_3_3) = 0, yields: % 11.35/3.43 | (110) all_62_0_42 = 0 % 11.35/3.43 | % 11.35/3.43 | Equations (110) can reduce 141 to: % 11.35/3.43 | (76) $false % 11.35/3.43 | % 11.35/3.43 |-The branch is then unsatisfiable % 11.35/3.43 |-Branch two: % 11.35/3.43 | (145) ~ (all_69_0_43 = 0) & less_than(all_0_0_0, all_0_3_3) = all_69_0_43 % 11.35/3.43 | % 11.35/3.43 | Applying alpha-rule on (145) yields: % 11.35/3.43 | (146) ~ (all_69_0_43 = 0) % 11.35/3.43 | (147) less_than(all_0_0_0, all_0_3_3) = all_69_0_43 % 11.35/3.43 | % 11.35/3.43 | Instantiating formula (12) with all_0_0_0, all_0_3_3, 0, all_69_0_43 and discharging atoms less_than(all_0_0_0, all_0_3_3) = all_69_0_43, less_than(all_0_0_0, all_0_3_3) = 0, yields: % 11.35/3.43 | (107) all_69_0_43 = 0 % 11.35/3.43 | % 11.35/3.43 | Equations (107) can reduce 146 to: % 11.35/3.43 | (76) $false % 11.35/3.43 | % 11.35/3.43 |-The branch is then unsatisfiable % 11.35/3.43 |-Branch two: % 11.35/3.43 | (150) ~ (less_than(all_0_0_0, all_0_3_3) = 0) % 11.35/3.43 | (83) all_47_0_40 = 0 % 11.35/3.43 | % 11.35/3.43 | Equations (83) can reduce 81 to: % 11.35/3.43 | (76) $false % 11.35/3.43 | % 11.35/3.43 |-The branch is then unsatisfiable % 11.35/3.43 % SZS output end Proof for theBenchmark % 11.35/3.43 % 11.35/3.44 2847ms %------------------------------------------------------------------------------