%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV378+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 17:51:10 EDT 2022 % Result : Theorem 7.61s 2.32s % Output : Proof 11.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWV378+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n006.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 : Wed Jun 15 18:30:41 EDT 2022 % 0.12/0.33 % CPUTime : % 0.57/0.58 ____ _ % 0.57/0.58 ___ / __ \_____(_)___ ________ __________ % 0.57/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.58 % 0.57/0.58 A Theorem Prover for First-Order Logic % 0.57/0.58 (ePrincess v.1.0) % 0.57/0.58 % 0.57/0.58 (c) Philipp Rümmer, 2009-2015 % 0.57/0.58 (c) Peter Backeman, 2014-2015 % 0.57/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.58 Bug reports to peter@backeman.se % 0.57/0.58 % 0.57/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.58 % 0.57/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.61/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.91/0.95 Prover 0: Preprocessing ... % 2.96/1.28 Prover 0: Warning: ignoring some quantifiers % 2.96/1.31 Prover 0: Constructing countermodel ... % 5.86/1.97 Prover 0: gave up % 5.86/1.97 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 6.21/2.02 Prover 1: Preprocessing ... % 6.84/2.16 Prover 1: Constructing countermodel ... % 7.61/2.32 Prover 1: proved (347ms) % 7.61/2.32 % 7.61/2.32 No countermodel exists, formula is valid % 7.61/2.32 % SZS status Theorem for theBenchmark % 7.61/2.32 % 7.61/2.32 Generating proof ... found it (size 131) % 10.77/2.99 % 10.77/2.99 % SZS output start Proof for theBenchmark % 10.77/2.99 Assumed formulas after preprocessing and simplification: % 10.77/2.99 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & ~ (v0 = 0) & ok(v7) = 0 & ok(v5) = v6 & triple(v1, v2, v3) = v5 & remove_cpq(v5, v4) = v7 & isnonempty_slb(create_slb) = v0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (pair_in_list(v14, v10, v12) = v15) | ~ (pair(v9, v11) = v13) | ~ (insert_slb(v8, v13) = v14) | ? [v16] : ( ~ (v16 = 0) & pair_in_list(v8, v10, v12) = v16)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (insert_pqp(v8, v11) = v12) | ~ (triple(v12, v14, v10) = v15) | ~ (pair(v11, bottom) = v13) | ~ (insert_slb(v9, v13) = v14) | ? [v16] : (triple(v8, v9, v10) = v16 & insert_cpq(v16, v11) = v15)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v8, v14, v10) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (triple(v8, v9, v10) = v18 & check_cpq(v18) = v19 & check_cpq(v15) = v17 & less_than(v12, v11) = v16 & ( ~ (v16 = 0) | (( ~ (v19 = 0) | v17 = 0) & ( ~ (v17 = 0) | v19 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v8, v14, v10) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ? [v16] : ? [v17] : (check_cpq(v15) = v17 & strictly_less_than(v11, v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (contains_slb(v13, v10) = v14) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & contains_slb(v8, v10) = v15)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (pair_in_list(v14, v10, v12) = 0) | ~ (pair(v9, v11) = v13) | ~ (insert_slb(v8, v13) = v14) | pair_in_list(v8, v10, v12) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (lookup_slb(v13, v10) = v14) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : ? [v16] : (lookup_slb(v8, v10) = v16 & contains_slb(v8, v10) = v15 & ( ~ (v15 = 0) | v16 = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (remove_slb(v13, v10) = v14) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : ? [v16] : ? [v17] : (remove_slb(v8, v10) = v16 & contains_slb(v8, v10) = v15 & insert_slb(v16, v12) = v17 & ( ~ (v15 = 0) | v17 = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (pair_in_list(v14, v10, v12) = 0) | ~ (pair(v9, v11) = v13) | ~ (insert_slb(v8, v13) = v14) | pair_in_list(v8, v10, v12) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (remove_pqp(v8, v11) = v12) | ~ (triple(v12, v13, v10) = v14) | ~ (remove_slb(v9, v11) = v13) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (triple(v8, v9, v10) = v18 & remove_cpq(v18, v11) = v19 & lookup_slb(v9, v11) = v16 & contains_slb(v9, v11) = v15 & less_than(v16, v11) = v17 & ( ~ (v17 = 0) | ~ (v15 = 0) | v19 = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (update_slb(v13, v10) = v14) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (update_slb(v8, v10) = v16 & pair(v9, v10) = v17 & insert_slb(v16, v17) = v18 & strictly_less_than(v11, v10) = v15 & ( ~ (v15 = 0) | v18 = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (update_slb(v13, v10) = v14) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : ? [v16] : ? [v17] : (update_slb(v8, v10) = v16 & insert_slb(v16, v12) = v17 & less_than(v10, v11) = v15 & ( ~ (v15 = 0) | v17 = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (lookup_slb(v12, v9) = v13) | ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v8 | ~ (remove_slb(v12, v9) = v13) | ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (contains_cpq(v12, v11) = v13) | ~ (triple(v8, v9, v10) = v12) | ? [v14] : ( ~ (v14 = 0) & contains_slb(v9, v11) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (pair_in_list(v12, v9, v10) = v13) | ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (contains_slb(v12, v9) = v13) | ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (contains_slb(v13, v10) = 0) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | contains_slb(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = create_slb | ~ (findmin_pqp_res(v8) = v11) | ~ (triple(v8, v12, v10) = v13) | ~ (update_slb(v9, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (triple(v8, v9, v10) = v17 & findmin_cpq_eff(v17) = v18 & lookup_slb(v9, v11) = v15 & contains_slb(v9, v11) = v14 & less_than(v15, v11) = v16 & ( ~ (v16 = 0) | ~ (v14 = 0) | v18 = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v8, v9, v10) = v12) | ~ (remove_cpq(v12, v11) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (remove_pqp(v8, v11) = v17 & triple(v17, v18, bad) = v19 & lookup_slb(v9, v11) = v15 & remove_slb(v9, v11) = v18 & contains_slb(v9, v11) = v14 & strictly_less_than(v11, v15) = v16 & ( ~ (v16 = 0) | ~ (v14 = 0) | v19 = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v8, v9, v10) = v12) | ~ (remove_cpq(v12, v11) = v13) | ? [v14] : ? [v15] : (triple(v8, v9, bad) = v15 & contains_slb(v9, v11) = v14 & (v15 = v13 | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (remove_cpq(v9, v10) = v11) | ~ (succ_cpq(v8, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & succ_cpq(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (insert_cpq(v9, v10) = v11) | ~ (succ_cpq(v8, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & succ_cpq(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (triple(v12, v11, v10) = v9) | ~ (triple(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (pair_in_list(v12, v11, v10) = v9) | ~ (pair_in_list(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (contains_cpq(v12, v11) = 0) | ~ (triple(v8, v9, v10) = v12) | contains_slb(v9, v11) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12) | isnonempty_slb(v12) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (removemin_cpq_eff(v9) = v10) | ~ (succ_cpq(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & succ_cpq(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (findmin_cpq_eff(v9) = v10) | ~ (succ_cpq(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & succ_cpq(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (less_than(v8, v10) = v11) | ~ (less_than(v8, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & less_than(v9, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = bad | ~ (triple(v8, v9, v10) = v11) | ok(v11) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (remove_pqp(v11, v10) = v9) | ~ (remove_pqp(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (insert_pqp(v11, v10) = v9) | ~ (insert_pqp(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (contains_cpq(v11, v10) = v9) | ~ (contains_cpq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (remove_cpq(v11, v10) = v9) | ~ (remove_cpq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (insert_cpq(v11, v10) = v9) | ~ (insert_cpq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (succ_cpq(v11, v10) = v9) | ~ (succ_cpq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (update_slb(v11, v10) = v9) | ~ (update_slb(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (lookup_slb(v11, v10) = v9) | ~ (lookup_slb(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (remove_slb(v11, v10) = v9) | ~ (remove_slb(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (contains_slb(v11, v10) = v9) | ~ (contains_slb(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (pair(v11, v10) = v9) | ~ (pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (insert_slb(v11, v10) = v9) | ~ (insert_slb(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (strictly_less_than(v11, v10) = v9) | ~ (strictly_less_than(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (less_than(v11, v10) = v9) | ~ (less_than(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = create_slb | ~ (triple(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (findmin_pqp_res(v8) = v12 & triple(v8, v17, bad) = v18 & findmin_cpq_eff(v11) = v16 & update_slb(v9, v12) = v17 & lookup_slb(v9, v12) = v14 & contains_slb(v9, v12) = v13 & strictly_less_than(v12, v14) = v15 & ( ~ (v15 = 0) | ~ (v13 = 0) | v18 = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = create_slb | ~ (triple(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (findmin_pqp_res(v8) = v12 & triple(v8, v15, bad) = v16 & findmin_cpq_eff(v11) = v14 & update_slb(v9, v12) = v15 & contains_slb(v9, v12) = v13 & (v16 = v14 | v13 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = create_slb | ~ (triple(v8, v9, v10) = v11) | ? [v12] : (findmin_cpq_res(v11) = v12 & findmin_pqp_res(v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (findmin_cpq_res(v8) = v10) | ~ (findmin_cpq_eff(v8) = v9) | ~ (remove_cpq(v9, v10) = v11) | removemin_cpq_eff(v8) = v11) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (strictly_less_than(v8, v9) = v10) | ? [v11] : ? [v12] : (less_than(v9, v8) = v12 & less_than(v8, v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (less_than(v8, v9) = v10) | less_than(v9, v8) = 0) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (removemin_cpq_res(v10) = v9) | ~ (removemin_cpq_res(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (findmin_cpq_res(v10) = v9) | ~ (findmin_cpq_res(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (findmin_pqp_res(v10) = v9) | ~ (findmin_pqp_res(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ok(v10) = v9) | ~ (ok(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (check_cpq(v10) = v9) | ~ (check_cpq(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (removemin_cpq_eff(v10) = v9) | ~ (removemin_cpq_eff(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (findmin_cpq_eff(v10) = v9) | ~ (findmin_cpq_eff(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (isnonempty_slb(v10) = v9) | ~ (isnonempty_slb(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v8, v9, bad) = v10) | ? [v11] : ( ~ (v11 = 0) & ok(v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v8, create_slb, v9) = v10) | findmin_cpq_res(v10) = bottom) & ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v8, create_slb, v9) = v10) | check_cpq(v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v8, create_slb, v9) = v10) | ? [v11] : (triple(v8, create_slb, bad) = v11 & findmin_cpq_eff(v10) = v11)) & ! [v8] : ! [v9] : (v9 = create_slb | ~ (update_slb(create_slb, v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (succ_cpq(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(bottom, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (removemin_cpq_res(v8) = v9) | findmin_cpq_res(v8) = v9) & ! [v8] : ! [v9] : ~ (pair_in_list(create_slb, v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (strictly_less_than(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & less_than(v9, v8) = v10 & less_than(v8, v9) = 0)) & ! [v8] : ~ (contains_slb(create_slb, v8) = 0)) % 10.77/3.07 | 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 yields: % 10.77/3.07 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_7_7 = 0) & ok(all_0_0_0) = 0 & ok(all_0_2_2) = all_0_1_1 & triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_2_2 & remove_cpq(all_0_2_2, all_0_3_3) = all_0_0_0 & isnonempty_slb(create_slb) = all_0_7_7 & ! [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] : ! [v7] : ( ~ (insert_pqp(v0, v3) = v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 & check_cpq(v7) = v9 & less_than(v4, v3) = v8 & ( ~ (v8 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : (check_cpq(v7) = v9 & strictly_less_than(v3, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [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] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v11 & lookup_slb(v1, v3) = v8 & contains_slb(v1, v3) = v7 & less_than(v8, v3) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = 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] : ? [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 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ( ~ (v6 = 0) & contains_slb(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] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v11 & lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & strictly_less_than(v3, v7) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v11 = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 & (v7 = v5 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (remove_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (insert_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [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] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(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] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [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] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (findmin_pqp_res(v0) = v4 & triple(v0, v9, bad) = v10 & findmin_cpq_eff(v3) = v8 & update_slb(v1, v4) = v9 & lookup_slb(v1, v4) = v6 & contains_slb(v1, v4) = v5 & strictly_less_than(v4, v6) = v7 & ( ~ (v7 = 0) | ~ (v5 = 0) | v10 = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, bad) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & contains_slb(v1, v4) = v5 & (v8 = v6 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3) & ! [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 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) & ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(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) % 11.26/3.09 | % 11.26/3.09 | Applying alpha-rule on (1) yields: % 11.26/3.09 | (2) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) % 11.26/3.09 | (3) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) % 11.26/3.09 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) % 11.26/3.09 | (5) triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_2_2 % 11.26/3.09 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) % 11.26/3.09 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) % 11.26/3.09 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 11.26/3.09 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4)) % 11.26/3.09 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 11.26/3.09 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) % 11.26/3.09 | (12) ! [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))) % 11.26/3.09 | (13) isnonempty_slb(create_slb) = all_0_7_7 % 11.26/3.09 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) % 11.26/3.09 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 11.26/3.09 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 11.26/3.09 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (remove_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) % 11.26/3.09 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) % 11.26/3.09 | (19) ! [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)) % 11.26/3.10 | (20) ! [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))) % 11.26/3.10 | (21) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) % 11.26/3.10 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 11.26/3.10 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3)) % 11.26/3.10 | (24) ! [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))) % 11.26/3.10 | (25) ! [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))) % 11.26/3.10 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) % 11.26/3.10 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) % 11.26/3.10 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) % 11.26/3.10 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) % 11.26/3.10 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)) % 11.26/3.10 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) % 11.26/3.10 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) % 11.26/3.10 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 11.26/3.10 | (34) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) % 11.26/3.10 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 11.26/3.10 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 11.26/3.10 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 11.26/3.10 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) % 11.26/3.10 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 11.26/3.10 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) % 11.26/3.10 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0) % 11.26/3.10 | (42) ! [v0] : ~ (contains_slb(create_slb, v0) = 0) % 11.26/3.10 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v11 & lookup_slb(v1, v3) = v8 & contains_slb(v1, v3) = v7 & less_than(v8, v3) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = v6))) % 11.33/3.10 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (insert_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) % 11.33/3.10 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (findmin_pqp_res(v0) = v4 & triple(v0, v9, bad) = v10 & findmin_cpq_eff(v3) = v8 & update_slb(v1, v4) = v9 & lookup_slb(v1, v4) = v6 & contains_slb(v1, v4) = v5 & strictly_less_than(v4, v6) = v7 & ( ~ (v7 = 0) | ~ (v5 = 0) | v10 = v8))) % 11.33/3.10 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4)) % 11.33/3.11 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3) % 11.33/3.11 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 11.33/3.11 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, bad) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & contains_slb(v1, v4) = v5 & (v8 = v6 | v5 = 0))) % 11.33/3.11 | (50) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) % 11.33/3.11 | (51) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) % 11.33/3.11 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (update_slb(v0, v2) = v8 & insert_slb(v8, v4) = v9 & less_than(v2, v3) = v7 & ( ~ (v7 = 0) | v9 = v6))) % 11.33/3.11 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 11.33/3.11 | (54) remove_cpq(all_0_2_2, all_0_3_3) = all_0_0_0 % 11.33/3.11 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 11.33/3.11 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) % 11.33/3.11 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) % 11.33/3.11 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 11.33/3.11 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 & (v7 = v5 | v6 = 0))) % 11.33/3.11 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v11 & lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & strictly_less_than(v3, v7) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v11 = v5))) % 11.33/3.11 | (61) ok(all_0_0_0) = 0 % 11.33/3.11 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 11.33/3.11 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) % 11.33/3.11 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : (check_cpq(v7) = v9 & strictly_less_than(v3, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) % 11.38/3.11 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0) % 11.38/3.11 | (66) ! [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)) % 11.38/3.11 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) % 11.38/3.11 | (68) ~ (all_0_7_7 = 0) % 11.38/3.11 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 & check_cpq(v7) = v9 & less_than(v4, v3) = v8 & ( ~ (v8 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) % 11.38/3.11 | (70) ! [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) % 11.38/3.11 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4)) % 11.38/3.12 | (72) ~ (all_0_1_1 = 0) % 11.38/3.12 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) % 11.38/3.12 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) % 11.38/3.12 | (75) ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1)) % 11.38/3.12 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0) % 11.38/3.12 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (insert_pqp(v0, v3) = v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7)) % 11.38/3.12 | (78) ok(all_0_2_2) = all_0_1_1 % 11.38/3.12 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) % 11.38/3.12 | % 11.38/3.12 | Instantiating formula (62) with all_0_2_2, all_0_1_1, 0 and discharging atoms ok(all_0_2_2) = all_0_1_1, yields: % 11.38/3.12 | (80) all_0_1_1 = 0 | ~ (ok(all_0_2_2) = 0) % 11.38/3.12 | % 11.38/3.12 | Instantiating formula (41) with all_0_2_2, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 11.38/3.12 | (81) all_0_4_4 = bad | ok(all_0_2_2) = 0 % 11.38/3.12 | % 11.38/3.12 | Instantiating formula (45) with all_0_2_2, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 11.38/3.12 | (82) all_0_5_5 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v5, bad) = v6 & findmin_cpq_eff(all_0_2_2) = v4 & update_slb(all_0_5_5, v0) = v5 & lookup_slb(all_0_5_5, v0) = v2 & contains_slb(all_0_5_5, v0) = v1 & strictly_less_than(v0, v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0) | v6 = v4)) % 11.38/3.12 | % 11.38/3.12 | Instantiating formula (49) with all_0_2_2, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 11.38/3.12 | (83) all_0_5_5 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v3, bad) = v4 & findmin_cpq_eff(all_0_2_2) = v2 & update_slb(all_0_5_5, v0) = v3 & contains_slb(all_0_5_5, v0) = v1 & (v4 = v2 | v1 = 0)) % 11.38/3.12 | % 11.38/3.12 | Instantiating formula (9) with all_0_2_2, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 11.38/3.12 | (84) all_0_5_5 = create_slb | ? [v0] : (findmin_cpq_res(all_0_2_2) = v0 & findmin_pqp_res(all_0_6_6) = v0) % 11.38/3.12 | % 11.38/3.12 | Instantiating formula (60) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_2_2, remove_cpq(all_0_2_2, all_0_3_3) = all_0_0_0, yields: % 11.38/3.12 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (remove_pqp(all_0_6_6, all_0_3_3) = v3 & triple(v3, v4, bad) = v5 & lookup_slb(all_0_5_5, all_0_3_3) = v1 & remove_slb(all_0_5_5, all_0_3_3) = v4 & contains_slb(all_0_5_5, all_0_3_3) = v0 & strictly_less_than(all_0_3_3, v1) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0) | v5 = all_0_0_0)) % 11.38/3.12 | % 11.38/3.12 | Instantiating formula (59) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_2_2, remove_cpq(all_0_2_2, all_0_3_3) = all_0_0_0, yields: % 11.38/3.12 | (86) ? [v0] : ? [v1] : (triple(all_0_6_6, all_0_5_5, bad) = v1 & contains_slb(all_0_5_5, all_0_3_3) = v0 & (v1 = all_0_0_0 | v0 = 0)) % 11.38/3.12 | % 11.38/3.12 | Instantiating (86) with all_8_0_8, all_8_1_9 yields: % 11.38/3.12 | (87) triple(all_0_6_6, all_0_5_5, bad) = all_8_0_8 & contains_slb(all_0_5_5, all_0_3_3) = all_8_1_9 & (all_8_0_8 = all_0_0_0 | all_8_1_9 = 0) % 11.38/3.12 | % 11.38/3.12 | Applying alpha-rule on (87) yields: % 11.38/3.12 | (88) triple(all_0_6_6, all_0_5_5, bad) = all_8_0_8 % 11.38/3.12 | (89) contains_slb(all_0_5_5, all_0_3_3) = all_8_1_9 % 11.38/3.12 | (90) all_8_0_8 = all_0_0_0 | all_8_1_9 = 0 % 11.38/3.12 | % 11.38/3.12 | Instantiating (85) with all_10_0_10, all_10_1_11, all_10_2_12, all_10_3_13, all_10_4_14, all_10_5_15 yields: % 11.38/3.12 | (91) remove_pqp(all_0_6_6, all_0_3_3) = all_10_2_12 & triple(all_10_2_12, all_10_1_11, bad) = all_10_0_10 & lookup_slb(all_0_5_5, all_0_3_3) = all_10_4_14 & remove_slb(all_0_5_5, all_0_3_3) = all_10_1_11 & contains_slb(all_0_5_5, all_0_3_3) = all_10_5_15 & strictly_less_than(all_0_3_3, all_10_4_14) = all_10_3_13 & ( ~ (all_10_3_13 = 0) | ~ (all_10_5_15 = 0) | all_10_0_10 = all_0_0_0) % 11.38/3.12 | % 11.38/3.12 | Applying alpha-rule on (91) yields: % 11.38/3.12 | (92) ~ (all_10_3_13 = 0) | ~ (all_10_5_15 = 0) | all_10_0_10 = all_0_0_0 % 11.38/3.12 | (93) lookup_slb(all_0_5_5, all_0_3_3) = all_10_4_14 % 11.38/3.12 | (94) remove_slb(all_0_5_5, all_0_3_3) = all_10_1_11 % 11.38/3.12 | (95) triple(all_10_2_12, all_10_1_11, bad) = all_10_0_10 % 11.38/3.12 | (96) strictly_less_than(all_0_3_3, all_10_4_14) = all_10_3_13 % 11.38/3.12 | (97) remove_pqp(all_0_6_6, all_0_3_3) = all_10_2_12 % 11.38/3.12 | (98) contains_slb(all_0_5_5, all_0_3_3) = all_10_5_15 % 11.38/3.12 | % 11.38/3.12 +-Applying beta-rule and splitting (81), into two cases. % 11.38/3.12 |-Branch one: % 11.38/3.12 | (99) ok(all_0_2_2) = 0 % 11.38/3.12 | % 11.38/3.12 +-Applying beta-rule and splitting (80), into two cases. % 11.38/3.12 |-Branch one: % 11.38/3.12 | (100) ~ (ok(all_0_2_2) = 0) % 11.38/3.12 | % 11.38/3.12 | Using (99) and (100) yields: % 11.38/3.12 | (101) $false % 11.38/3.12 | % 11.38/3.12 |-The branch is then unsatisfiable % 11.38/3.12 |-Branch two: % 11.38/3.12 | (99) ok(all_0_2_2) = 0 % 11.38/3.12 | (103) all_0_1_1 = 0 % 11.38/3.12 | % 11.38/3.12 | Equations (103) can reduce 72 to: % 11.38/3.12 | (104) $false % 11.38/3.12 | % 11.38/3.12 |-The branch is then unsatisfiable % 11.38/3.12 |-Branch two: % 11.38/3.12 | (100) ~ (ok(all_0_2_2) = 0) % 11.38/3.12 | (106) all_0_4_4 = bad % 11.38/3.12 | % 11.38/3.12 | From (106) and (5) follows: % 11.38/3.13 | (107) triple(all_0_6_6, all_0_5_5, bad) = all_0_2_2 % 11.38/3.13 | % 11.38/3.13 | Instantiating formula (18) with all_0_6_6, all_0_5_5, bad, all_0_2_2, all_8_0_8 and discharging atoms triple(all_0_6_6, all_0_5_5, bad) = all_8_0_8, triple(all_0_6_6, all_0_5_5, bad) = all_0_2_2, yields: % 11.38/3.13 | (108) all_8_0_8 = all_0_2_2 % 11.38/3.13 | % 11.38/3.13 | Instantiating formula (39) with all_0_5_5, all_0_3_3, all_8_1_9, all_10_5_15 and discharging atoms contains_slb(all_0_5_5, all_0_3_3) = all_10_5_15, contains_slb(all_0_5_5, all_0_3_3) = all_8_1_9, yields: % 11.38/3.13 | (109) all_10_5_15 = all_8_1_9 % 11.38/3.13 | % 11.38/3.13 | Using (61) and (100) yields: % 11.38/3.13 | (110) ~ (all_0_0_0 = all_0_2_2) % 11.38/3.13 | % 11.38/3.13 | From (108) and (88) follows: % 11.38/3.13 | (107) triple(all_0_6_6, all_0_5_5, bad) = all_0_2_2 % 11.38/3.13 | % 11.38/3.13 | From (109) and (98) follows: % 11.38/3.13 | (89) contains_slb(all_0_5_5, all_0_3_3) = all_8_1_9 % 11.38/3.13 | % 11.38/3.13 +-Applying beta-rule and splitting (90), into two cases. % 11.38/3.13 |-Branch one: % 11.38/3.13 | (113) all_8_1_9 = 0 % 11.38/3.13 | % 11.38/3.13 | Combining equations (113,109) yields a new equation: % 11.38/3.13 | (114) all_10_5_15 = 0 % 11.38/3.13 | % 11.38/3.13 | From (113) and (89) follows: % 11.38/3.13 | (115) contains_slb(all_0_5_5, all_0_3_3) = 0 % 11.38/3.13 | % 11.38/3.13 | Instantiating formula (42) with all_0_3_3 yields: % 11.38/3.13 | (116) ~ (contains_slb(create_slb, all_0_3_3) = 0) % 11.38/3.13 | % 11.38/3.13 | Using (115) and (116) yields: % 11.38/3.13 | (117) ~ (all_0_5_5 = create_slb) % 11.38/3.13 | % 11.38/3.13 +-Applying beta-rule and splitting (82), into two cases. % 11.38/3.13 |-Branch one: % 11.38/3.13 | (118) all_0_5_5 = create_slb % 11.38/3.13 | % 11.38/3.13 | Equations (118) can reduce 117 to: % 11.38/3.13 | (104) $false % 11.38/3.13 | % 11.38/3.13 |-The branch is then unsatisfiable % 11.38/3.13 |-Branch two: % 11.38/3.13 | (117) ~ (all_0_5_5 = create_slb) % 11.38/3.13 | (121) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v5, bad) = v6 & findmin_cpq_eff(all_0_2_2) = v4 & update_slb(all_0_5_5, v0) = v5 & lookup_slb(all_0_5_5, v0) = v2 & contains_slb(all_0_5_5, v0) = v1 & strictly_less_than(v0, v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0) | v6 = v4)) % 11.38/3.13 | % 11.38/3.13 | Instantiating (121) with all_36_0_16, all_36_1_17, all_36_2_18, all_36_3_19, all_36_4_20, all_36_5_21, all_36_6_22 yields: % 11.38/3.13 | (122) findmin_pqp_res(all_0_6_6) = all_36_6_22 & triple(all_0_6_6, all_36_1_17, bad) = all_36_0_16 & findmin_cpq_eff(all_0_2_2) = all_36_2_18 & update_slb(all_0_5_5, all_36_6_22) = all_36_1_17 & lookup_slb(all_0_5_5, all_36_6_22) = all_36_4_20 & contains_slb(all_0_5_5, all_36_6_22) = all_36_5_21 & strictly_less_than(all_36_6_22, all_36_4_20) = all_36_3_19 & ( ~ (all_36_3_19 = 0) | ~ (all_36_5_21 = 0) | all_36_0_16 = all_36_2_18) % 11.38/3.13 | % 11.38/3.13 | Applying alpha-rule on (122) yields: % 11.38/3.13 | (123) lookup_slb(all_0_5_5, all_36_6_22) = all_36_4_20 % 11.38/3.13 | (124) update_slb(all_0_5_5, all_36_6_22) = all_36_1_17 % 11.38/3.13 | (125) strictly_less_than(all_36_6_22, all_36_4_20) = all_36_3_19 % 11.38/3.13 | (126) findmin_pqp_res(all_0_6_6) = all_36_6_22 % 11.38/3.13 | (127) contains_slb(all_0_5_5, all_36_6_22) = all_36_5_21 % 11.38/3.13 | (128) findmin_cpq_eff(all_0_2_2) = all_36_2_18 % 11.38/3.13 | (129) triple(all_0_6_6, all_36_1_17, bad) = all_36_0_16 % 11.38/3.13 | (130) ~ (all_36_3_19 = 0) | ~ (all_36_5_21 = 0) | all_36_0_16 = all_36_2_18 % 11.38/3.13 | % 11.38/3.13 +-Applying beta-rule and splitting (84), into two cases. % 11.38/3.13 |-Branch one: % 11.38/3.13 | (118) all_0_5_5 = create_slb % 11.38/3.13 | % 11.38/3.13 | Equations (118) can reduce 117 to: % 11.38/3.13 | (104) $false % 11.38/3.13 | % 11.38/3.13 |-The branch is then unsatisfiable % 11.38/3.13 |-Branch two: % 11.38/3.13 | (117) ~ (all_0_5_5 = create_slb) % 11.38/3.13 | (134) ? [v0] : (findmin_cpq_res(all_0_2_2) = v0 & findmin_pqp_res(all_0_6_6) = v0) % 11.38/3.13 | % 11.38/3.13 | Instantiating (134) with all_41_0_23 yields: % 11.38/3.13 | (135) findmin_cpq_res(all_0_2_2) = all_41_0_23 & findmin_pqp_res(all_0_6_6) = all_41_0_23 % 11.38/3.13 | % 11.38/3.13 | Applying alpha-rule on (135) yields: % 11.38/3.13 | (136) findmin_cpq_res(all_0_2_2) = all_41_0_23 % 11.38/3.13 | (137) findmin_pqp_res(all_0_6_6) = all_41_0_23 % 11.38/3.13 | % 11.38/3.13 +-Applying beta-rule and splitting (83), into two cases. % 11.38/3.13 |-Branch one: % 11.38/3.13 | (118) all_0_5_5 = create_slb % 11.38/3.13 | % 11.38/3.13 | Equations (118) can reduce 117 to: % 11.38/3.13 | (104) $false % 11.38/3.13 | % 11.38/3.13 |-The branch is then unsatisfiable % 11.38/3.13 |-Branch two: % 11.38/3.13 | (117) ~ (all_0_5_5 = create_slb) % 11.38/3.13 | (141) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v3, bad) = v4 & findmin_cpq_eff(all_0_2_2) = v2 & update_slb(all_0_5_5, v0) = v3 & contains_slb(all_0_5_5, v0) = v1 & (v4 = v2 | v1 = 0)) % 11.38/3.13 | % 11.38/3.13 | Instantiating (141) with all_46_0_24, all_46_1_25, all_46_2_26, all_46_3_27, all_46_4_28 yields: % 11.38/3.13 | (142) findmin_pqp_res(all_0_6_6) = all_46_4_28 & triple(all_0_6_6, all_46_1_25, bad) = all_46_0_24 & findmin_cpq_eff(all_0_2_2) = all_46_2_26 & update_slb(all_0_5_5, all_46_4_28) = all_46_1_25 & contains_slb(all_0_5_5, all_46_4_28) = all_46_3_27 & (all_46_0_24 = all_46_2_26 | all_46_3_27 = 0) % 11.38/3.13 | % 11.38/3.13 | Applying alpha-rule on (142) yields: % 11.38/3.13 | (143) findmin_pqp_res(all_0_6_6) = all_46_4_28 % 11.38/3.13 | (144) findmin_cpq_eff(all_0_2_2) = all_46_2_26 % 11.38/3.13 | (145) update_slb(all_0_5_5, all_46_4_28) = all_46_1_25 % 11.38/3.13 | (146) contains_slb(all_0_5_5, all_46_4_28) = all_46_3_27 % 11.38/3.13 | (147) triple(all_0_6_6, all_46_1_25, bad) = all_46_0_24 % 11.38/3.13 | (148) all_46_0_24 = all_46_2_26 | all_46_3_27 = 0 % 11.38/3.13 | % 11.38/3.13 | Instantiating formula (8) with all_0_6_6, all_41_0_23, all_46_4_28 and discharging atoms findmin_pqp_res(all_0_6_6) = all_46_4_28, findmin_pqp_res(all_0_6_6) = all_41_0_23, yields: % 11.38/3.13 | (149) all_46_4_28 = all_41_0_23 % 11.38/3.13 | % 11.38/3.13 | Instantiating formula (8) with all_0_6_6, all_36_6_22, all_46_4_28 and discharging atoms findmin_pqp_res(all_0_6_6) = all_46_4_28, findmin_pqp_res(all_0_6_6) = all_36_6_22, yields: % 11.38/3.13 | (150) all_46_4_28 = all_36_6_22 % 11.38/3.13 | % 11.38/3.13 | Instantiating formula (18) with all_0_6_6, all_36_1_17, bad, all_36_0_16, all_46_0_24 and discharging atoms triple(all_0_6_6, all_36_1_17, bad) = all_36_0_16, yields: % 11.38/3.13 | (151) all_46_0_24 = all_36_0_16 | ~ (triple(all_0_6_6, all_36_1_17, bad) = all_46_0_24) % 11.38/3.13 | % 11.38/3.13 | Instantiating formula (15) with all_0_5_5, all_36_6_22, all_36_1_17, all_46_1_25 and discharging atoms update_slb(all_0_5_5, all_36_6_22) = all_36_1_17, yields: % 11.38/3.13 | (152) all_46_1_25 = all_36_1_17 | ~ (update_slb(all_0_5_5, all_36_6_22) = all_46_1_25) % 11.38/3.13 | % 11.38/3.13 | Combining equations (150,149) yields a new equation: % 11.38/3.13 | (153) all_41_0_23 = all_36_6_22 % 11.38/3.13 | % 11.38/3.13 | Combining equations (153,149) yields a new equation: % 11.38/3.13 | (150) all_46_4_28 = all_36_6_22 % 11.38/3.13 | % 11.38/3.13 | From (153) and (137) follows: % 11.38/3.13 | (126) findmin_pqp_res(all_0_6_6) = all_36_6_22 % 11.38/3.13 | % 11.38/3.13 | From (150) and (145) follows: % 11.38/3.13 | (156) update_slb(all_0_5_5, all_36_6_22) = all_46_1_25 % 11.38/3.13 | % 11.38/3.13 +-Applying beta-rule and splitting (152), into two cases. % 11.38/3.13 |-Branch one: % 11.38/3.13 | (157) ~ (update_slb(all_0_5_5, all_36_6_22) = all_46_1_25) % 11.38/3.13 | % 11.38/3.13 | Using (156) and (157) yields: % 11.38/3.13 | (101) $false % 11.38/3.13 | % 11.38/3.13 |-The branch is then unsatisfiable % 11.38/3.13 |-Branch two: % 11.38/3.13 | (156) update_slb(all_0_5_5, all_36_6_22) = all_46_1_25 % 11.38/3.13 | (160) all_46_1_25 = all_36_1_17 % 11.38/3.13 | % 11.38/3.13 | From (160) and (147) follows: % 11.38/3.13 | (161) triple(all_0_6_6, all_36_1_17, bad) = all_46_0_24 % 11.38/3.13 | % 11.38/3.13 | From (160) and (156) follows: % 11.38/3.13 | (124) update_slb(all_0_5_5, all_36_6_22) = all_36_1_17 % 11.38/3.13 | % 11.38/3.13 +-Applying beta-rule and splitting (151), into two cases. % 11.38/3.13 |-Branch one: % 11.38/3.13 | (163) ~ (triple(all_0_6_6, all_36_1_17, bad) = all_46_0_24) % 11.38/3.13 | % 11.38/3.13 | Using (161) and (163) yields: % 11.38/3.13 | (101) $false % 11.38/3.13 | % 11.38/3.13 |-The branch is then unsatisfiable % 11.38/3.13 |-Branch two: % 11.38/3.13 | (161) triple(all_0_6_6, all_36_1_17, bad) = all_46_0_24 % 11.38/3.13 | (166) all_46_0_24 = all_36_0_16 % 11.38/3.13 | % 11.38/3.13 | From (166) and (161) follows: % 11.38/3.13 | (129) triple(all_0_6_6, all_36_1_17, bad) = all_36_0_16 % 11.38/3.13 | % 11.38/3.13 | Instantiating formula (23) with all_10_0_10, all_10_1_11, all_10_2_12 and discharging atoms triple(all_10_2_12, all_10_1_11, bad) = all_10_0_10, yields: % 11.38/3.14 | (168) ? [v0] : ( ~ (v0 = 0) & ok(all_10_0_10) = v0) % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (6) with all_36_0_16, all_36_1_17, all_36_6_22, bad, all_0_5_5, all_0_6_6 and discharging atoms findmin_pqp_res(all_0_6_6) = all_36_6_22, triple(all_0_6_6, all_36_1_17, bad) = all_36_0_16, update_slb(all_0_5_5, all_36_6_22) = all_36_1_17, yields: % 11.38/3.14 | (169) all_0_5_5 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (triple(all_0_6_6, all_0_5_5, bad) = v3 & findmin_cpq_eff(v3) = v4 & lookup_slb(all_0_5_5, all_36_6_22) = v1 & contains_slb(all_0_5_5, all_36_6_22) = v0 & less_than(v1, all_36_6_22) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = all_36_0_16)) % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (43) with all_10_0_10, all_10_1_11, all_10_2_12, all_0_3_3, bad, all_0_5_5, all_0_6_6 and discharging atoms remove_pqp(all_0_6_6, all_0_3_3) = all_10_2_12, triple(all_10_2_12, all_10_1_11, bad) = all_10_0_10, remove_slb(all_0_5_5, all_0_3_3) = all_10_1_11, yields: % 11.38/3.14 | (170) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (triple(all_0_6_6, all_0_5_5, bad) = v3 & remove_cpq(v3, all_0_3_3) = v4 & lookup_slb(all_0_5_5, all_0_3_3) = v1 & contains_slb(all_0_5_5, all_0_3_3) = v0 & less_than(v1, all_0_3_3) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = all_10_0_10)) % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (25) with all_10_3_13, all_10_4_14, all_0_3_3 and discharging atoms strictly_less_than(all_0_3_3, all_10_4_14) = all_10_3_13, yields: % 11.38/3.14 | (171) all_10_3_13 = 0 | ? [v0] : ? [v1] : (less_than(all_10_4_14, all_0_3_3) = v1 & less_than(all_0_3_3, all_10_4_14) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 11.38/3.14 | % 11.38/3.14 | Instantiating (170) with all_69_0_29, all_69_1_30, all_69_2_31, all_69_3_32, all_69_4_33 yields: % 11.38/3.14 | (172) triple(all_0_6_6, all_0_5_5, bad) = all_69_1_30 & remove_cpq(all_69_1_30, all_0_3_3) = all_69_0_29 & lookup_slb(all_0_5_5, all_0_3_3) = all_69_3_32 & contains_slb(all_0_5_5, all_0_3_3) = all_69_4_33 & less_than(all_69_3_32, all_0_3_3) = all_69_2_31 & ( ~ (all_69_2_31 = 0) | ~ (all_69_4_33 = 0) | all_69_0_29 = all_10_0_10) % 11.38/3.14 | % 11.38/3.14 | Applying alpha-rule on (172) yields: % 11.38/3.14 | (173) remove_cpq(all_69_1_30, all_0_3_3) = all_69_0_29 % 11.38/3.14 | (174) lookup_slb(all_0_5_5, all_0_3_3) = all_69_3_32 % 11.38/3.14 | (175) ~ (all_69_2_31 = 0) | ~ (all_69_4_33 = 0) | all_69_0_29 = all_10_0_10 % 11.38/3.14 | (176) less_than(all_69_3_32, all_0_3_3) = all_69_2_31 % 11.38/3.14 | (177) triple(all_0_6_6, all_0_5_5, bad) = all_69_1_30 % 11.38/3.14 | (178) contains_slb(all_0_5_5, all_0_3_3) = all_69_4_33 % 11.38/3.14 | % 11.38/3.14 | Instantiating (168) with all_73_0_35 yields: % 11.38/3.14 | (179) ~ (all_73_0_35 = 0) & ok(all_10_0_10) = all_73_0_35 % 11.38/3.14 | % 11.38/3.14 | Applying alpha-rule on (179) yields: % 11.38/3.14 | (180) ~ (all_73_0_35 = 0) % 11.38/3.14 | (181) ok(all_10_0_10) = all_73_0_35 % 11.38/3.14 | % 11.38/3.14 +-Applying beta-rule and splitting (169), into two cases. % 11.38/3.14 |-Branch one: % 11.38/3.14 | (118) all_0_5_5 = create_slb % 11.38/3.14 | % 11.38/3.14 | Equations (118) can reduce 117 to: % 11.38/3.14 | (104) $false % 11.38/3.14 | % 11.38/3.14 |-The branch is then unsatisfiable % 11.38/3.14 |-Branch two: % 11.38/3.14 | (117) ~ (all_0_5_5 = create_slb) % 11.38/3.14 | (185) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (triple(all_0_6_6, all_0_5_5, bad) = v3 & findmin_cpq_eff(v3) = v4 & lookup_slb(all_0_5_5, all_36_6_22) = v1 & contains_slb(all_0_5_5, all_36_6_22) = v0 & less_than(v1, all_36_6_22) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = all_36_0_16)) % 11.38/3.14 | % 11.38/3.14 | Instantiating (185) with all_79_0_36, all_79_1_37, all_79_2_38, all_79_3_39, all_79_4_40 yields: % 11.38/3.14 | (186) triple(all_0_6_6, all_0_5_5, bad) = all_79_1_37 & findmin_cpq_eff(all_79_1_37) = all_79_0_36 & lookup_slb(all_0_5_5, all_36_6_22) = all_79_3_39 & contains_slb(all_0_5_5, all_36_6_22) = all_79_4_40 & less_than(all_79_3_39, all_36_6_22) = all_79_2_38 & ( ~ (all_79_2_38 = 0) | ~ (all_79_4_40 = 0) | all_79_0_36 = all_36_0_16) % 11.38/3.14 | % 11.38/3.14 | Applying alpha-rule on (186) yields: % 11.38/3.14 | (187) triple(all_0_6_6, all_0_5_5, bad) = all_79_1_37 % 11.38/3.14 | (188) less_than(all_79_3_39, all_36_6_22) = all_79_2_38 % 11.38/3.14 | (189) ~ (all_79_2_38 = 0) | ~ (all_79_4_40 = 0) | all_79_0_36 = all_36_0_16 % 11.38/3.14 | (190) contains_slb(all_0_5_5, all_36_6_22) = all_79_4_40 % 11.38/3.14 | (191) lookup_slb(all_0_5_5, all_36_6_22) = all_79_3_39 % 11.38/3.14 | (192) findmin_cpq_eff(all_79_1_37) = all_79_0_36 % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (62) with all_0_0_0, all_73_0_35, 0 and discharging atoms ok(all_0_0_0) = 0, yields: % 11.38/3.14 | (193) all_73_0_35 = 0 | ~ (ok(all_0_0_0) = all_73_0_35) % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (18) with all_0_6_6, all_0_5_5, bad, all_79_1_37, all_0_2_2 and discharging atoms triple(all_0_6_6, all_0_5_5, bad) = all_79_1_37, triple(all_0_6_6, all_0_5_5, bad) = all_0_2_2, yields: % 11.38/3.14 | (194) all_79_1_37 = all_0_2_2 % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (18) with all_0_6_6, all_0_5_5, bad, all_69_1_30, all_79_1_37 and discharging atoms triple(all_0_6_6, all_0_5_5, bad) = all_79_1_37, triple(all_0_6_6, all_0_5_5, bad) = all_69_1_30, yields: % 11.38/3.14 | (195) all_79_1_37 = all_69_1_30 % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (31) with all_0_2_2, all_0_3_3, all_69_0_29, all_0_0_0 and discharging atoms remove_cpq(all_0_2_2, all_0_3_3) = all_0_0_0, yields: % 11.38/3.14 | (196) all_69_0_29 = all_0_0_0 | ~ (remove_cpq(all_0_2_2, all_0_3_3) = all_69_0_29) % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (22) with all_0_5_5, all_0_3_3, all_69_3_32, all_10_4_14 and discharging atoms lookup_slb(all_0_5_5, all_0_3_3) = all_69_3_32, lookup_slb(all_0_5_5, all_0_3_3) = all_10_4_14, yields: % 11.38/3.14 | (197) all_69_3_32 = all_10_4_14 % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (39) with all_0_5_5, all_0_3_3, all_69_4_33, 0 and discharging atoms contains_slb(all_0_5_5, all_0_3_3) = all_69_4_33, contains_slb(all_0_5_5, all_0_3_3) = 0, yields: % 11.38/3.14 | (198) all_69_4_33 = 0 % 11.38/3.14 | % 11.38/3.14 | Combining equations (195,194) yields a new equation: % 11.38/3.14 | (199) all_69_1_30 = all_0_2_2 % 11.38/3.14 | % 11.38/3.14 | Simplifying 199 yields: % 11.38/3.14 | (200) all_69_1_30 = all_0_2_2 % 11.38/3.14 | % 11.38/3.14 | From (200) and (173) follows: % 11.38/3.14 | (201) remove_cpq(all_0_2_2, all_0_3_3) = all_69_0_29 % 11.38/3.14 | % 11.38/3.14 | From (197) and (176) follows: % 11.38/3.14 | (202) less_than(all_10_4_14, all_0_3_3) = all_69_2_31 % 11.38/3.14 | % 11.38/3.14 +-Applying beta-rule and splitting (196), into two cases. % 11.38/3.14 |-Branch one: % 11.38/3.14 | (203) ~ (remove_cpq(all_0_2_2, all_0_3_3) = all_69_0_29) % 11.38/3.14 | % 11.38/3.14 | Using (201) and (203) yields: % 11.38/3.14 | (101) $false % 11.38/3.14 | % 11.38/3.14 |-The branch is then unsatisfiable % 11.38/3.14 |-Branch two: % 11.38/3.14 | (201) remove_cpq(all_0_2_2, all_0_3_3) = all_69_0_29 % 11.38/3.14 | (206) all_69_0_29 = all_0_0_0 % 11.38/3.14 | % 11.38/3.14 +-Applying beta-rule and splitting (92), into two cases. % 11.38/3.14 |-Branch one: % 11.38/3.14 | (207) ~ (all_10_3_13 = 0) % 11.38/3.14 | % 11.38/3.14 +-Applying beta-rule and splitting (171), into two cases. % 11.38/3.14 |-Branch one: % 11.38/3.14 | (208) all_10_3_13 = 0 % 11.38/3.14 | % 11.38/3.14 | Equations (208) can reduce 207 to: % 11.38/3.14 | (104) $false % 11.38/3.14 | % 11.38/3.14 |-The branch is then unsatisfiable % 11.38/3.14 |-Branch two: % 11.38/3.14 | (207) ~ (all_10_3_13 = 0) % 11.38/3.14 | (211) ? [v0] : ? [v1] : (less_than(all_10_4_14, all_0_3_3) = v1 & less_than(all_0_3_3, all_10_4_14) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 11.38/3.14 | % 11.38/3.14 | Instantiating (211) with all_118_0_41, all_118_1_42 yields: % 11.38/3.14 | (212) less_than(all_10_4_14, all_0_3_3) = all_118_0_41 & less_than(all_0_3_3, all_10_4_14) = all_118_1_42 & ( ~ (all_118_1_42 = 0) | all_118_0_41 = 0) % 11.38/3.14 | % 11.38/3.14 | Applying alpha-rule on (212) yields: % 11.38/3.14 | (213) less_than(all_10_4_14, all_0_3_3) = all_118_0_41 % 11.38/3.14 | (214) less_than(all_0_3_3, all_10_4_14) = all_118_1_42 % 11.38/3.14 | (215) ~ (all_118_1_42 = 0) | all_118_0_41 = 0 % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (48) with all_10_4_14, all_0_3_3, all_118_0_41, all_69_2_31 and discharging atoms less_than(all_10_4_14, all_0_3_3) = all_118_0_41, less_than(all_10_4_14, all_0_3_3) = all_69_2_31, yields: % 11.38/3.14 | (216) all_118_0_41 = all_69_2_31 % 11.38/3.14 | % 11.38/3.14 | From (216) and (213) follows: % 11.38/3.14 | (202) less_than(all_10_4_14, all_0_3_3) = all_69_2_31 % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (27) with all_118_1_42, all_10_4_14, all_0_3_3 and discharging atoms less_than(all_0_3_3, all_10_4_14) = all_118_1_42, yields: % 11.38/3.14 | (218) all_118_1_42 = 0 | less_than(all_10_4_14, all_0_3_3) = 0 % 11.38/3.14 | % 11.38/3.14 +-Applying beta-rule and splitting (175), into two cases. % 11.38/3.14 |-Branch one: % 11.38/3.14 | (219) ~ (all_69_2_31 = 0) % 11.38/3.14 | % 11.38/3.14 +-Applying beta-rule and splitting (218), into two cases. % 11.38/3.14 |-Branch one: % 11.38/3.14 | (220) less_than(all_10_4_14, all_0_3_3) = 0 % 11.38/3.14 | % 11.38/3.14 | Instantiating formula (48) with all_10_4_14, all_0_3_3, 0, all_69_2_31 and discharging atoms less_than(all_10_4_14, all_0_3_3) = all_69_2_31, less_than(all_10_4_14, all_0_3_3) = 0, yields: % 11.38/3.14 | (221) all_69_2_31 = 0 % 11.38/3.14 | % 11.38/3.14 | Equations (221) can reduce 219 to: % 11.38/3.14 | (104) $false % 11.38/3.14 | % 11.38/3.14 |-The branch is then unsatisfiable % 11.38/3.14 |-Branch two: % 11.38/3.14 | (223) ~ (less_than(all_10_4_14, all_0_3_3) = 0) % 11.38/3.14 | (224) all_118_1_42 = 0 % 11.38/3.14 | % 11.38/3.14 +-Applying beta-rule and splitting (215), into two cases. % 11.38/3.14 |-Branch one: % 11.38/3.14 | (225) ~ (all_118_1_42 = 0) % 11.38/3.14 | % 11.38/3.14 | Equations (224) can reduce 225 to: % 11.38/3.14 | (104) $false % 11.38/3.14 | % 11.38/3.14 |-The branch is then unsatisfiable % 11.38/3.14 |-Branch two: % 11.38/3.14 | (224) all_118_1_42 = 0 % 11.38/3.14 | (228) all_118_0_41 = 0 % 11.38/3.14 | % 11.38/3.14 | Combining equations (216,228) yields a new equation: % 11.38/3.14 | (229) all_69_2_31 = 0 % 11.38/3.15 | % 11.38/3.15 | Simplifying 229 yields: % 11.38/3.15 | (221) all_69_2_31 = 0 % 11.38/3.15 | % 11.38/3.15 | Equations (221) can reduce 219 to: % 11.38/3.15 | (104) $false % 11.38/3.15 | % 11.38/3.15 |-The branch is then unsatisfiable % 11.38/3.15 |-Branch two: % 11.38/3.15 | (221) all_69_2_31 = 0 % 11.38/3.15 | (233) ~ (all_69_4_33 = 0) | all_69_0_29 = all_10_0_10 % 11.38/3.15 | % 11.38/3.15 +-Applying beta-rule and splitting (233), into two cases. % 11.38/3.15 |-Branch one: % 11.38/3.15 | (234) ~ (all_69_4_33 = 0) % 11.38/3.15 | % 11.38/3.15 | Equations (198) can reduce 234 to: % 11.38/3.15 | (104) $false % 11.38/3.15 | % 11.38/3.15 |-The branch is then unsatisfiable % 11.38/3.15 |-Branch two: % 11.38/3.15 | (198) all_69_4_33 = 0 % 11.38/3.15 | (237) all_69_0_29 = all_10_0_10 % 11.38/3.15 | % 11.38/3.15 | Combining equations (206,237) yields a new equation: % 11.38/3.15 | (238) all_10_0_10 = all_0_0_0 % 11.38/3.15 | % 11.38/3.15 | From (238) and (181) follows: % 11.38/3.15 | (239) ok(all_0_0_0) = all_73_0_35 % 11.38/3.15 | % 11.38/3.15 +-Applying beta-rule and splitting (193), into two cases. % 11.38/3.15 |-Branch one: % 11.38/3.15 | (240) ~ (ok(all_0_0_0) = all_73_0_35) % 11.38/3.15 | % 11.38/3.15 | Using (239) and (240) yields: % 11.38/3.15 | (101) $false % 11.38/3.15 | % 11.38/3.15 |-The branch is then unsatisfiable % 11.38/3.15 |-Branch two: % 11.38/3.15 | (239) ok(all_0_0_0) = all_73_0_35 % 11.38/3.15 | (243) all_73_0_35 = 0 % 11.38/3.15 | % 11.38/3.15 | Equations (243) can reduce 180 to: % 11.38/3.15 | (104) $false % 11.38/3.15 | % 11.38/3.15 |-The branch is then unsatisfiable % 11.38/3.15 |-Branch two: % 11.38/3.15 | (208) all_10_3_13 = 0 % 11.38/3.15 | (246) ~ (all_10_5_15 = 0) | all_10_0_10 = all_0_0_0 % 11.38/3.15 | % 11.38/3.15 +-Applying beta-rule and splitting (246), into two cases. % 11.38/3.15 |-Branch one: % 11.38/3.15 | (247) ~ (all_10_5_15 = 0) % 11.38/3.15 | % 11.38/3.15 | Equations (114) can reduce 247 to: % 11.38/3.15 | (104) $false % 11.38/3.15 | % 11.38/3.15 |-The branch is then unsatisfiable % 11.38/3.15 |-Branch two: % 11.38/3.15 | (114) all_10_5_15 = 0 % 11.38/3.15 | (238) all_10_0_10 = all_0_0_0 % 11.38/3.15 | % 11.38/3.15 | From (238) and (181) follows: % 11.38/3.15 | (239) ok(all_0_0_0) = all_73_0_35 % 11.38/3.15 | % 11.38/3.15 +-Applying beta-rule and splitting (193), into two cases. % 11.38/3.15 |-Branch one: % 11.38/3.15 | (240) ~ (ok(all_0_0_0) = all_73_0_35) % 11.38/3.15 | % 11.38/3.15 | Using (239) and (240) yields: % 11.38/3.15 | (101) $false % 11.38/3.15 | % 11.38/3.15 |-The branch is then unsatisfiable % 11.38/3.15 |-Branch two: % 11.38/3.15 | (239) ok(all_0_0_0) = all_73_0_35 % 11.38/3.15 | (243) all_73_0_35 = 0 % 11.38/3.15 | % 11.38/3.15 | Equations (243) can reduce 180 to: % 11.38/3.15 | (104) $false % 11.38/3.15 | % 11.38/3.15 |-The branch is then unsatisfiable % 11.38/3.15 |-Branch two: % 11.38/3.15 | (257) ~ (all_8_1_9 = 0) % 11.38/3.15 | (258) all_8_0_8 = all_0_0_0 % 11.38/3.15 | % 11.38/3.15 | Combining equations (108,258) yields a new equation: % 11.38/3.15 | (259) all_0_0_0 = all_0_2_2 % 11.38/3.15 | % 11.38/3.15 | Equations (259) can reduce 110 to: % 11.38/3.15 | (104) $false % 11.38/3.15 | % 11.38/3.15 |-The branch is then unsatisfiable % 11.38/3.15 % SZS output end Proof for theBenchmark % 11.38/3.15 % 11.38/3.15 2558ms %------------------------------------------------------------------------------