%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV380+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.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 17:51:11 EDT 2022 % Result : Theorem 7.85s 2.41s % Output : Proof 10.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SWV380+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.35 % Computer : n027.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Thu Jun 16 07:09:50 EDT 2022 % 0.14/0.36 % CPUTime : % 0.54/0.62 ____ _ % 0.54/0.62 ___ / __ \_____(_)___ ________ __________ % 0.54/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.62 % 0.54/0.62 A Theorem Prover for First-Order Logic % 0.54/0.62 (ePrincess v.1.0) % 0.54/0.62 % 0.54/0.62 (c) Philipp Rümmer, 2009-2015 % 0.54/0.62 (c) Peter Backeman, 2014-2015 % 0.54/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.62 Bug reports to peter@backeman.se % 0.54/0.62 % 0.54/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.62 % 0.54/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.90/1.03 Prover 0: Preprocessing ... % 3.01/1.39 Prover 0: Warning: ignoring some quantifiers % 3.27/1.42 Prover 0: Constructing countermodel ... % 5.16/1.86 Prover 0: gave up % 5.16/1.86 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.16/1.90 Prover 1: Preprocessing ... % 6.01/2.03 Prover 1: Constructing countermodel ... % 6.45/2.10 Prover 1: gave up % 6.45/2.10 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 6.55/2.13 Prover 2: Preprocessing ... % 7.06/2.25 Prover 2: Warning: ignoring some quantifiers % 7.06/2.26 Prover 2: Constructing countermodel ... % 7.85/2.41 Prover 2: proved (310ms) % 7.85/2.41 % 7.85/2.41 No countermodel exists, formula is valid % 7.85/2.41 % SZS status Theorem for theBenchmark % 7.85/2.41 % 7.85/2.41 Generating proof ... Warning: ignoring some quantifiers % 10.12/2.99 found it (size 168) % 10.12/2.99 % 10.12/2.99 % SZS output start Proof for theBenchmark % 10.12/2.99 Assumed formulas after preprocessing and simplification: % 10.12/2.99 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v0 = 0) & ok(v6) = 0 & ok(v4) = v5 & triple(v1, v2, v3) = v4 & removemin_cpq_eff(v4) = v6 & isnonempty_slb(create_slb) = v0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (pair_in_list(v13, v9, v11) = v14) | ~ (pair(v8, v10) = v12) | ~ (insert_slb(v7, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & pair_in_list(v7, v9, v11) = v15)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (insert_pqp(v7, v10) = v11) | ~ (triple(v11, v13, v9) = v14) | ~ (pair(v10, bottom) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : (triple(v7, v8, v9) = v15 & insert_cpq(v15, v10) = v14)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v7, v13, v9) = v14) | ~ (pair(v10, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : ? [v16] : ? [v17] : (( ~ (v15 = 0) & less_than(v11, v10) = v15) | (((v17 = 0 & triple(v7, v8, v9) = v16 & check_cpq(v16) = 0) | ( ~ (v15 = 0) & check_cpq(v14) = v15)) & ((v15 = 0 & check_cpq(v14) = 0) | ( ~ (v17 = 0) & triple(v7, v8, v9) = v16 & check_cpq(v16) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v7, v13, v9) = v14) | ~ (pair(v10, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & check_cpq(v14) = v15) | ( ~ (v15 = 0) & strictly_less_than(v10, v11) = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (contains_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & contains_slb(v7, v9) = v14)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (pair_in_list(v13, v9, v11) = 0) | ~ (pair(v8, v10) = v12) | ~ (insert_slb(v7, v12) = v13) | pair_in_list(v7, v9, v11) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (lookup_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ((v14 = v13 & lookup_slb(v7, v9) = v13) | ( ~ (v14 = 0) & contains_slb(v7, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (remove_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ? [v15] : ((v15 = v13 & remove_slb(v7, v9) = v14 & insert_slb(v14, v11) = v13) | ( ~ (v14 = 0) & contains_slb(v7, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (remove_slb(v7, v9) = v12) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v12, v11) = v13) | ? [v14] : ? [v15] : ((v15 = v13 & remove_slb(v14, v9) = v13 & insert_slb(v7, v11) = v14) | ( ~ (v14 = 0) & contains_slb(v7, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (pair_in_list(v13, v9, v11) = 0) | ~ (pair(v8, v10) = v12) | ~ (insert_slb(v7, v12) = v13) | pair_in_list(v7, v9, v11) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (remove_pqp(v7, v10) = v11) | ~ (triple(v11, v12, v9) = v13) | ~ (remove_slb(v8, v10) = v12) | ? [v14] : ? [v15] : ((v15 = v13 & triple(v7, v8, v9) = v14 & remove_cpq(v14, v10) = v13) | ( ~ (v15 = 0) & lookup_slb(v8, v10) = v14 & less_than(v14, v10) = v15) | ( ~ (v14 = 0) & contains_slb(v8, v10) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : ((v16 = v13 & update_slb(v7, v9) = v14 & pair(v8, v9) = v15 & insert_slb(v14, v15) = v13) | ( ~ (v14 = 0) & strictly_less_than(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ? [v15] : ((v15 = v13 & update_slb(v7, v9) = v14 & insert_slb(v14, v11) = v13) | ( ~ (v14 = 0) & less_than(v9, v10) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v7, v9) = v12) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v12, v11) = v13) | ? [v14] : ? [v15] : ((v15 = v13 & update_slb(v14, v9) = v13 & insert_slb(v7, v11) = v14) | ( ~ (v14 = 0) & less_than(v9, v10) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (contains_cpq(v11, v10) = v12) | ~ (triple(v7, v8, v9) = v11) | ? [v13] : ( ~ (v13 = 0) & contains_slb(v8, v10) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (pair_in_list(v11, v8, v9) = v12) | ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (contains_slb(v11, v8) = v12) | ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (contains_slb(v12, v9) = 0) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | contains_slb(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = create_slb | ~ (findmin_pqp_res(v7) = v10) | ~ (triple(v7, v11, v9) = v12) | ~ (update_slb(v8, v10) = v11) | ? [v13] : ? [v14] : ((v14 = v12 & triple(v7, v8, v9) = v13 & findmin_cpq_eff(v13) = v12) | ( ~ (v14 = 0) & lookup_slb(v8, v10) = v13 & less_than(v13, v10) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v15 = v12 & remove_pqp(v7, v10) = v13 & triple(v13, v14, v9) = v12 & remove_slb(v8, v10) = v14) | ( ~ (v14 = 0) & lookup_slb(v8, v10) = v13 & less_than(v13, v10) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v15 = v12 & remove_pqp(v7, v10) = v13 & triple(v13, v14, bad) = v12 & remove_slb(v8, v10) = v14) | ( ~ (v14 = 0) & lookup_slb(v8, v10) = v13 & strictly_less_than(v10, v13) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ((v13 = v12 & triple(v7, v8, bad) = v12) | (v13 = 0 & contains_slb(v8, v10) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ((v13 = 0 & ok(v11) = 0) | ( ~ (v13 = 0) & ok(v12) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (insert_cpq(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : (insert_pqp(v7, v10) = v13 & triple(v13, v15, v9) = v12 & pair(v10, bottom) = v14 & insert_slb(v8, v14) = v15)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (remove_cpq(v8, v9) = v10) | ~ (succ_cpq(v7, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & succ_cpq(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (insert_cpq(v8, v9) = v10) | ~ (succ_cpq(v7, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & succ_cpq(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (triple(v11, v10, v9) = v8) | ~ (triple(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (pair_in_list(v11, v10, v9) = v8) | ~ (pair_in_list(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = create_slb | ~ (findmin_cpq_res(v10) = v11) | ~ (triple(v7, v8, v9) = v10) | findmin_pqp_res(v7) = v11) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ~ (findmin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (findmin_pqp_res(v7) = v12 & ((v14 = v11 & triple(v7, v13, v9) = v11 & update_slb(v8, v12) = v13) | ( ~ (v14 = 0) & lookup_slb(v8, v12) = v13 & less_than(v13, v12) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v12) = v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ~ (findmin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (findmin_pqp_res(v7) = v12 & ((v14 = v11 & triple(v7, v13, bad) = v11 & update_slb(v8, v12) = v13) | (v13 = 0 & contains_slb(v8, v12) = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ~ (findmin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (findmin_pqp_res(v7) = v12 & ((v14 = v11 & triple(v7, v13, bad) = v11 & update_slb(v8, v12) = v13) | ( ~ (v14 = 0) & lookup_slb(v8, v12) = v13 & strictly_less_than(v12, v13) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v12) = v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (contains_cpq(v11, v10) = 0) | ~ (triple(v7, v8, v9) = v11) | contains_slb(v8, v10) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11) | lookup_slb(v11, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11) | remove_slb(v11, v8) = v7) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11) | isnonempty_slb(v11) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (removemin_cpq_eff(v8) = v9) | ~ (succ_cpq(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & succ_cpq(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (findmin_cpq_eff(v8) = v9) | ~ (succ_cpq(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & succ_cpq(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (less_than(v8, v9) = 0) | ~ (less_than(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & less_than(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (less_than(v7, v9) = v10) | ~ (less_than(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & less_than(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = bad | ~ (triple(v7, v8, v9) = v10) | ok(v10) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (remove_pqp(v10, v9) = v8) | ~ (remove_pqp(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (insert_pqp(v10, v9) = v8) | ~ (insert_pqp(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (contains_cpq(v10, v9) = v8) | ~ (contains_cpq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (remove_cpq(v10, v9) = v8) | ~ (remove_cpq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (insert_cpq(v10, v9) = v8) | ~ (insert_cpq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (succ_cpq(v10, v9) = v8) | ~ (succ_cpq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (update_slb(v10, v9) = v8) | ~ (update_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (lookup_slb(v10, v9) = v8) | ~ (lookup_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (remove_slb(v10, v9) = v8) | ~ (remove_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (contains_slb(v10, v9) = v8) | ~ (contains_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (pair(v10, v9) = v8) | ~ (pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (insert_slb(v10, v9) = v8) | ~ (insert_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (strictly_less_than(v10, v9) = v8) | ~ (strictly_less_than(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (less_than(v10, v9) = v8) | ~ (less_than(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (strictly_less_than(v7, v8) = v9) | ? [v10] : ((v10 = 0 & less_than(v8, v7) = 0) | ( ~ (v10 = 0) & less_than(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(v8, v7) = v9) | less_than(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(v8, v7) = v9) | ? [v10] : ((v10 = 0 & strictly_less_than(v7, v8) = 0) | ( ~ (v10 = 0) & less_than(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(v7, v8) = v9) | less_than(v8, v7) = 0) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (removemin_cpq_res(v9) = v8) | ~ (removemin_cpq_res(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (findmin_cpq_res(v9) = v8) | ~ (findmin_cpq_res(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (findmin_pqp_res(v9) = v8) | ~ (findmin_pqp_res(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (ok(v9) = v8) | ~ (ok(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (check_cpq(v9) = v8) | ~ (check_cpq(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (removemin_cpq_eff(v9) = v8) | ~ (removemin_cpq_eff(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (findmin_cpq_eff(v9) = v8) | ~ (findmin_cpq_eff(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (isnonempty_slb(v9) = v8) | ~ (isnonempty_slb(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, v8, bad) = v9) | ? [v10] : ( ~ (v10 = 0) & ok(v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, create_slb, v8) = v9) | findmin_cpq_res(v9) = bottom) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, create_slb, v8) = v9) | check_cpq(v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, create_slb, v8) = v9) | ? [v10] : (triple(v7, create_slb, bad) = v10 & findmin_cpq_eff(v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (less_than(v8, v9) = 0) | ~ (less_than(v7, v8) = 0) | less_than(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (less_than(v8, v7) = v9) | ? [v10] : ((v10 = 0 & ~ (v9 = 0) & less_than(v7, v8) = 0) | ( ~ (v10 = 0) & strictly_less_than(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (less_than(v7, v8) = v9) | ? [v10] : ((v9 = 0 & ~ (v10 = 0) & less_than(v8, v7) = v10) | ( ~ (v10 = 0) & strictly_less_than(v7, v8) = v10))) & ! [v7] : ! [v8] : (v8 = create_slb | ~ (update_slb(create_slb, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (succ_cpq(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (less_than(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (less_than(bottom, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (removemin_cpq_res(v7) = v8) | findmin_cpq_res(v7) = v8) & ! [v7] : ! [v8] : ( ~ (findmin_cpq_res(v7) = v8) | removemin_cpq_res(v7) = v8) & ! [v7] : ! [v8] : ( ~ (findmin_cpq_res(v7) = v8) | ? [v9] : ? [v10] : (removemin_cpq_eff(v7) = v9 & findmin_cpq_eff(v7) = v10 & remove_cpq(v10, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (removemin_cpq_eff(v7) = v8) | ? [v9] : ? [v10] : (findmin_cpq_res(v7) = v10 & findmin_cpq_eff(v7) = v9 & remove_cpq(v9, v10) = v8)) & ! [v7] : ! [v8] : ( ~ (findmin_cpq_eff(v7) = v8) | ? [v9] : ? [v10] : (findmin_cpq_res(v7) = v10 & removemin_cpq_eff(v7) = v9 & remove_cpq(v8, v10) = v9)) & ! [v7] : ! [v8] : ( ~ (succ_cpq(v7, v8) = 0) | ? [v9] : (removemin_cpq_eff(v8) = v9 & succ_cpq(v7, v9) = 0)) & ! [v7] : ! [v8] : ( ~ (succ_cpq(v7, v8) = 0) | ? [v9] : (findmin_cpq_eff(v8) = v9 & succ_cpq(v7, v9) = 0)) & ! [v7] : ! [v8] : ~ (pair_in_list(create_slb, v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (strictly_less_than(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & less_than(v8, v7) = v9 & less_than(v7, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (less_than(v7, v8) = 0) | ? [v9] : ((v9 = 0 & strictly_less_than(v7, v8) = 0) | (v9 = 0 & less_than(v8, v7) = 0))) & ! [v7] : ~ (contains_slb(create_slb, v7) = 0) & ? [v7] : ? [v8] : ? [v9] : ? [v10] : triple(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : pair_in_list(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : remove_pqp(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : insert_pqp(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : contains_cpq(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : remove_cpq(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : insert_cpq(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : succ_cpq(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : update_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : lookup_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : remove_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : contains_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : pair(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : insert_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : strictly_less_than(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : less_than(v8, v7) = v9 & ? [v7] : ? [v8] : removemin_cpq_res(v7) = v8 & ? [v7] : ? [v8] : findmin_cpq_res(v7) = v8 & ? [v7] : ? [v8] : findmin_pqp_res(v7) = v8 & ? [v7] : ? [v8] : ok(v7) = v8 & ? [v7] : ? [v8] : check_cpq(v7) = v8 & ? [v7] : ? [v8] : removemin_cpq_eff(v7) = v8 & ? [v7] : ? [v8] : findmin_cpq_eff(v7) = v8 & ? [v7] : ? [v8] : isnonempty_slb(v7) = v8) % 10.48/3.07 | 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 yields: % 10.48/3.07 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_6_6 = 0) & ok(all_0_0_0) = 0 & ok(all_0_2_2) = all_0_1_1 & triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2 & removemin_cpq_eff(all_0_2_2) = all_0_0_0 & isnonempty_slb(create_slb) = all_0_6_6 & ! [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] : (( ~ (v8 = 0) & less_than(v4, v3) = v8) | (((v10 = 0 & triple(v0, v1, v2) = v9 & check_cpq(v9) = 0) | ( ~ (v8 = 0) & check_cpq(v7) = v8)) & ((v8 = 0 & check_cpq(v7) = 0) | ( ~ (v10 = 0) & triple(v0, v1, v2) = v9 & check_cpq(v9) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (( ~ (v8 = 0) & check_cpq(v7) = v8) | ( ~ (v8 = 0) & strictly_less_than(v3, 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] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & triple(v0, v1, v2) = v7 & remove_cpq(v7, v3) = v6) | ( ~ (v8 = 0) & lookup_slb(v1, v3) = v7 & less_than(v7, v3) = v8) | ( ~ (v7 = 0) & contains_slb(v1, v3) = v7))) & ! [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 | ~ (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] : ((v7 = v5 & triple(v0, v1, v2) = v6 & findmin_cpq_eff(v6) = v5) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, v2) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, bad) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & strictly_less_than(v3, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = v5 & triple(v0, v1, bad) = v5) | (v6 = 0 & contains_slb(v1, v3) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = 0 & ok(v4) = 0) | ( ~ (v6 = 0) & ok(v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8)) & ! [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] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, v2) = v3) | findmin_pqp_res(v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, v2) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & less_than(v6, v5) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | (v6 = 0 & contains_slb(v1, v5) = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & strictly_less_than(v5, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6)))) & ! [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) | 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 | ~ (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(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] : (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] : (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 | ~ (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] : ! [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 | ~ (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] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | ? [v2] : ? [v3] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (findmin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2)) & ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (removemin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (findmin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0)) & ! [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] : ! [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] : triple(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : remove_pqp(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_pqp(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : contains_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : remove_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : succ_cpq(v1, v0) = v2 & ? [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] : removemin_cpq_res(v0) = v1 & ? [v0] : ? [v1] : findmin_cpq_res(v0) = v1 & ? [v0] : ? [v1] : findmin_pqp_res(v0) = v1 & ? [v0] : ? [v1] : ok(v0) = v1 & ? [v0] : ? [v1] : check_cpq(v0) = v1 & ? [v0] : ? [v1] : removemin_cpq_eff(v0) = v1 & ? [v0] : ? [v1] : findmin_cpq_eff(v0) = v1 & ? [v0] : ? [v1] : isnonempty_slb(v0) = v1 % 10.85/3.09 | % 10.85/3.09 | Applying alpha-rule on (1) yields: % 10.85/3.09 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (( ~ (v8 = 0) & check_cpq(v7) = v8) | ( ~ (v8 = 0) & strictly_less_than(v3, v4) = v8))) % 10.85/3.09 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) % 10.85/3.09 | (4) ? [v0] : ? [v1] : ? [v2] : insert_cpq(v1, v0) = v2 % 10.85/3.09 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = v5 & triple(v0, v1, bad) = v5) | (v6 = 0 & contains_slb(v1, v3) = 0))) % 10.85/3.09 | (6) ? [v0] : ? [v1] : ? [v2] : less_than(v1, v0) = v2 % 10.85/3.09 | (7) ? [v0] : ? [v1] : ? [v2] : contains_cpq(v1, v0) = v2 % 10.85/3.10 | (8) ? [v0] : ? [v1] : check_cpq(v0) = v1 % 10.85/3.10 | (9) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) % 10.85/3.10 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 10.85/3.10 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) % 10.85/3.10 | (12) ! [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))) % 10.85/3.10 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0) % 10.85/3.10 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) % 10.85/3.10 | (15) ? [v0] : ? [v1] : findmin_cpq_eff(v0) = v1 % 10.85/3.10 | (16) ? [v0] : ? [v1] : isnonempty_slb(v0) = v1 % 10.85/3.10 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) % 10.85/3.10 | (18) ! [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] : ((v7 = v5 & triple(v0, v1, v2) = v6 & findmin_cpq_eff(v6) = v5) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) % 10.85/3.10 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0) % 10.85/3.10 | (20) ? [v0] : ? [v1] : findmin_cpq_res(v0) = v1 % 10.85/3.10 | (21) ? [v0] : ? [v1] : ? [v2] : succ_cpq(v1, v0) = v2 % 10.85/3.10 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) % 10.85/3.10 | (23) ! [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))) % 10.85/3.10 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, v2) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & less_than(v6, v5) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6)))) % 10.85/3.10 | (25) ? [v0] : ? [v1] : ? [v2] : update_slb(v1, v0) = v2 % 10.85/3.10 | (26) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) % 10.85/3.10 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) % 10.85/3.10 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & triple(v0, v1, v2) = v7 & remove_cpq(v7, v3) = v6) | ( ~ (v8 = 0) & lookup_slb(v1, v3) = v7 & less_than(v7, v3) = v8) | ( ~ (v7 = 0) & contains_slb(v1, v3) = v7))) % 10.85/3.10 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) % 10.85/3.10 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) % 10.85/3.10 | (31) ! [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) % 10.85/3.10 | (32) ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (findmin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0)) % 10.85/3.10 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, v2) = v3) | findmin_pqp_res(v0) = v4) % 10.85/3.10 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & strictly_less_than(v5, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6)))) % 10.85/3.10 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) % 10.85/3.10 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) % 10.85/3.10 | (37) ! [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))) % 10.85/3.10 | (38) ? [v0] : ? [v1] : ? [v2] : strictly_less_than(v1, v0) = v2 % 10.85/3.10 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | remove_slb(v4, v1) = v0) % 10.85/3.10 | (40) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) % 10.85/3.10 | (41) ? [v0] : ? [v1] : removemin_cpq_eff(v0) = v1 % 10.85/3.10 | (42) ! [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))) % 10.85/3.10 | (43) ! [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)) % 10.85/3.10 | (44) ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1)) % 10.85/3.10 | (45) ! [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))) % 10.85/3.10 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) % 10.85/3.10 | (47) ! [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)) % 10.85/3.10 | (48) ! [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)) % 10.85/3.10 | (49) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) % 10.85/3.10 | (50) ! [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)) % 10.85/3.10 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 10.85/3.10 | (52) ~ (all_0_6_6 = 0) % 10.85/3.11 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8)) % 10.85/3.11 | (54) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 10.85/3.11 | (55) ? [v0] : ? [v1] : ? [v2] : insert_slb(v1, v0) = v2 % 10.85/3.11 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & less_than(v0, v1) = v4)) % 10.85/3.11 | (57) ? [v0] : ? [v1] : removemin_cpq_res(v0) = v1 % 10.85/3.11 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4)) % 10.85/3.11 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.85/3.11 | (60) ok(all_0_2_2) = all_0_1_1 % 10.85/3.11 | (61) ! [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) % 10.85/3.11 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) % 10.85/3.11 | (63) ? [v0] : ? [v1] : ? [v2] : insert_pqp(v1, v0) = v2 % 10.85/3.11 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 10.85/3.11 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) % 10.85/3.11 | (66) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | ? [v2] : ? [v3] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2)) % 10.85/3.11 | (67) removemin_cpq_eff(all_0_2_2) = all_0_0_0 % 10.85/3.11 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & pair_in_list(v0, v2, v4) = v8)) % 10.85/3.11 | (69) ? [v0] : ? [v1] : ok(v0) = v1 % 10.85/3.11 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) % 10.85/3.11 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0) % 10.85/3.11 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, v2) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) % 10.85/3.11 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4)) % 10.85/3.11 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = 0 & ok(v4) = 0) | ( ~ (v6 = 0) & ok(v5) = v6))) % 10.85/3.11 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 10.85/3.11 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 10.85/3.11 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 10.85/3.11 | (78) ? [v0] : ? [v1] : ? [v2] : remove_cpq(v1, v0) = v2 % 10.85/3.11 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 10.85/3.11 | (80) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) % 10.85/3.11 | (81) ! [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))) % 10.85/3.11 | (82) ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3 % 10.85/3.11 | (83) ! [v0] : ! [v1] : ( ~ (findmin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2)) % 10.85/3.11 | (84) ? [v0] : ? [v1] : ? [v2] : contains_slb(v1, v0) = v2 % 10.85/3.11 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | (v6 = 0 & contains_slb(v1, v5) = 0)))) % 10.85/3.11 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 10.85/3.11 | (87) ! [v0] : ! [v1] : ( ~ (less_than(v0, v1) = 0) | ? [v2] : ((v2 = 0 & strictly_less_than(v0, v1) = 0) | (v2 = 0 & less_than(v1, v0) = 0))) % 10.85/3.11 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) % 10.85/3.11 | (89) ! [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)) % 10.85/3.11 | (90) triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2 % 10.85/3.11 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) % 10.85/3.11 | (92) ? [v0] : ? [v1] : ? [v2] : remove_slb(v1, v0) = v2 % 10.85/3.11 | (93) ~ (all_0_1_1 = 0) % 10.85/3.11 | (94) ? [v0] : ? [v1] : ? [v2] : remove_pqp(v1, v0) = v2 % 10.85/3.11 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, bad) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & strictly_less_than(v3, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) % 10.85/3.11 | (96) ! [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))) % 10.85/3.11 | (97) ! [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))) % 10.85/3.11 | (98) ? [v0] : ? [v1] : ? [v2] : pair(v1, v0) = v2 % 10.85/3.11 | (99) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1) % 10.85/3.12 | (100) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) % 10.85/3.12 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) % 10.85/3.12 | (102) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v1) = 0) | less_than(v0, v2) = 0) % 10.85/3.12 | (103) ! [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))) % 10.85/3.12 | (104) ok(all_0_0_0) = 0 % 10.85/3.12 | (105) ? [v0] : ? [v1] : findmin_pqp_res(v0) = v1 % 10.85/3.12 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | lookup_slb(v4, v1) = v2) % 10.85/3.12 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 10.85/3.12 | (108) ! [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))) % 10.85/3.12 | (109) ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (removemin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0)) % 10.85/3.12 | (110) ? [v0] : ? [v1] : ? [v2] : lookup_slb(v1, v0) = v2 % 10.85/3.12 | (111) ! [v0] : ~ (contains_slb(create_slb, v0) = 0) % 10.85/3.12 | (112) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) % 10.85/3.12 | (113) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | less_than(v0, v1) = 0) % 10.85/3.12 | (114) ! [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] : (( ~ (v8 = 0) & less_than(v4, v3) = v8) | (((v10 = 0 & triple(v0, v1, v2) = v9 & check_cpq(v9) = 0) | ( ~ (v8 = 0) & check_cpq(v7) = v8)) & ((v8 = 0 & check_cpq(v7) = 0) | ( ~ (v10 = 0) & triple(v0, v1, v2) = v9 & check_cpq(v9) = v10))))) % 10.85/3.12 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 10.85/3.12 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3)) % 10.85/3.12 | (117) ! [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) % 10.85/3.12 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 10.85/3.12 | (119) isnonempty_slb(create_slb) = all_0_6_6 % 10.85/3.12 | (120) ? [v0] : ? [v1] : ? [v2] : ? [v3] : triple(v2, v1, v0) = v3 % 10.85/3.12 | (121) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) % 10.85/3.12 | % 10.85/3.12 | Instantiating formula (71) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 10.85/3.12 | (122) all_0_3_3 = bad | ok(all_0_2_2) = 0 % 10.85/3.12 | % 10.85/3.12 | Instantiating formula (26) with all_0_0_0, all_0_2_2 and discharging atoms removemin_cpq_eff(all_0_2_2) = all_0_0_0, yields: % 10.85/3.12 | (123) ? [v0] : ? [v1] : (findmin_cpq_res(all_0_2_2) = v1 & findmin_cpq_eff(all_0_2_2) = v0 & remove_cpq(v0, v1) = all_0_0_0) % 10.85/3.12 | % 10.85/3.12 | Instantiating (123) with all_56_0_73, all_56_1_74 yields: % 10.85/3.12 | (124) findmin_cpq_res(all_0_2_2) = all_56_0_73 & findmin_cpq_eff(all_0_2_2) = all_56_1_74 & remove_cpq(all_56_1_74, all_56_0_73) = all_0_0_0 % 10.85/3.12 | % 10.85/3.12 | Applying alpha-rule on (124) yields: % 10.85/3.12 | (125) findmin_cpq_res(all_0_2_2) = all_56_0_73 % 10.85/3.12 | (126) findmin_cpq_eff(all_0_2_2) = all_56_1_74 % 10.85/3.12 | (127) remove_cpq(all_56_1_74, all_56_0_73) = all_0_0_0 % 10.85/3.12 | % 10.85/3.12 +-Applying beta-rule and splitting (122), into two cases. % 10.85/3.12 |-Branch one: % 10.85/3.12 | (128) ok(all_0_2_2) = 0 % 10.85/3.12 | % 10.85/3.12 | Instantiating formula (77) with all_0_2_2, 0, all_0_1_1 and discharging atoms ok(all_0_2_2) = all_0_1_1, ok(all_0_2_2) = 0, yields: % 10.85/3.12 | (129) all_0_1_1 = 0 % 10.85/3.12 | % 10.85/3.12 | Equations (129) can reduce 93 to: % 10.85/3.12 | (130) $false % 10.85/3.12 | % 10.85/3.12 |-The branch is then unsatisfiable % 10.85/3.12 |-Branch two: % 10.85/3.12 | (131) ~ (ok(all_0_2_2) = 0) % 10.85/3.12 | (132) all_0_3_3 = bad % 10.85/3.12 | % 10.85/3.12 | From (132) and (90) follows: % 10.85/3.12 | (133) triple(all_0_5_5, all_0_4_4, bad) = all_0_2_2 % 10.85/3.12 | % 10.85/3.12 | Instantiating formula (33) with all_56_0_73, all_0_2_2, bad, all_0_4_4, all_0_5_5 and discharging atoms findmin_cpq_res(all_0_2_2) = all_56_0_73, triple(all_0_5_5, all_0_4_4, bad) = all_0_2_2, yields: % 10.85/3.12 | (134) all_0_4_4 = create_slb | findmin_pqp_res(all_0_5_5) = all_56_0_73 % 10.85/3.12 | % 10.85/3.12 | Instantiating formula (24) with all_56_1_74, all_0_2_2, bad, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, bad) = all_0_2_2, findmin_cpq_eff(all_0_2_2) = all_56_1_74, yields: % 10.85/3.12 | (135) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | ( ~ (v2 = 0) & lookup_slb(all_0_4_4, v0) = v1 & less_than(v1, v0) = v2) | ( ~ (v1 = 0) & contains_slb(all_0_4_4, v0) = v1))) % 10.85/3.12 | % 10.85/3.12 | Instantiating formula (85) with all_56_1_74, all_0_2_2, bad, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, bad) = all_0_2_2, findmin_cpq_eff(all_0_2_2) = all_56_1_74, yields: % 10.85/3.12 | (136) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | (v1 = 0 & contains_slb(all_0_4_4, v0) = 0))) % 10.85/3.12 | % 10.85/3.12 | Instantiating formula (34) with all_56_1_74, all_0_2_2, bad, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, bad) = all_0_2_2, findmin_cpq_eff(all_0_2_2) = all_56_1_74, yields: % 10.85/3.12 | (137) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | ( ~ (v2 = 0) & lookup_slb(all_0_4_4, v0) = v1 & strictly_less_than(v0, v1) = v2) | ( ~ (v1 = 0) & contains_slb(all_0_4_4, v0) = v1))) % 10.85/3.12 | % 10.85/3.12 +-Applying beta-rule and splitting (134), into two cases. % 10.85/3.12 |-Branch one: % 10.85/3.12 | (138) findmin_pqp_res(all_0_5_5) = all_56_0_73 % 10.85/3.12 | % 10.85/3.12 +-Applying beta-rule and splitting (136), into two cases. % 10.85/3.12 |-Branch one: % 10.85/3.12 | (139) all_0_4_4 = create_slb % 10.85/3.12 | % 10.85/3.12 | From (139) and (133) follows: % 10.85/3.12 | (140) triple(all_0_5_5, create_slb, bad) = all_0_2_2 % 10.85/3.12 | % 10.85/3.12 | Instantiating formula (11) with all_0_2_2, bad, all_0_5_5 and discharging atoms triple(all_0_5_5, create_slb, bad) = all_0_2_2, yields: % 10.85/3.13 | (141) findmin_cpq_res(all_0_2_2) = bottom % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (14) with all_0_2_2, bad, all_0_5_5 and discharging atoms triple(all_0_5_5, create_slb, bad) = all_0_2_2, yields: % 10.85/3.13 | (142) ? [v0] : (triple(all_0_5_5, create_slb, bad) = v0 & findmin_cpq_eff(all_0_2_2) = v0) % 10.85/3.13 | % 10.85/3.13 | Instantiating (142) with all_88_0_75 yields: % 10.85/3.13 | (143) triple(all_0_5_5, create_slb, bad) = all_88_0_75 & findmin_cpq_eff(all_0_2_2) = all_88_0_75 % 10.85/3.13 | % 10.85/3.13 | Applying alpha-rule on (143) yields: % 10.85/3.13 | (144) triple(all_0_5_5, create_slb, bad) = all_88_0_75 % 10.85/3.13 | (145) findmin_cpq_eff(all_0_2_2) = all_88_0_75 % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (17) with all_0_2_2, bottom, all_56_0_73 and discharging atoms findmin_cpq_res(all_0_2_2) = all_56_0_73, findmin_cpq_res(all_0_2_2) = bottom, yields: % 10.85/3.13 | (146) all_56_0_73 = bottom % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (101) with all_0_5_5, create_slb, bad, all_88_0_75, all_0_2_2 and discharging atoms triple(all_0_5_5, create_slb, bad) = all_88_0_75, triple(all_0_5_5, create_slb, bad) = all_0_2_2, yields: % 10.85/3.13 | (147) all_88_0_75 = all_0_2_2 % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (10) with all_0_2_2, all_88_0_75, all_56_1_74 and discharging atoms findmin_cpq_eff(all_0_2_2) = all_88_0_75, findmin_cpq_eff(all_0_2_2) = all_56_1_74, yields: % 10.85/3.13 | (148) all_88_0_75 = all_56_1_74 % 10.85/3.13 | % 10.85/3.13 | Combining equations (147,148) yields a new equation: % 10.85/3.13 | (149) all_56_1_74 = all_0_2_2 % 10.85/3.13 | % 10.85/3.13 | Combining equations (149,148) yields a new equation: % 10.85/3.13 | (147) all_88_0_75 = all_0_2_2 % 10.85/3.13 | % 10.85/3.13 | From (147) and (144) follows: % 10.85/3.13 | (140) triple(all_0_5_5, create_slb, bad) = all_0_2_2 % 10.85/3.13 | % 10.85/3.13 | From (149)(146) and (127) follows: % 10.85/3.13 | (152) remove_cpq(all_0_2_2, bottom) = all_0_0_0 % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (74) with all_0_0_0, all_0_2_2, bottom, bad, create_slb, all_0_5_5 and discharging atoms triple(all_0_5_5, create_slb, bad) = all_0_2_2, remove_cpq(all_0_2_2, bottom) = all_0_0_0, yields: % 10.85/3.13 | (153) ? [v0] : ((v0 = 0 & ok(all_0_2_2) = 0) | ( ~ (v0 = 0) & ok(all_0_0_0) = v0)) % 10.85/3.13 | % 10.85/3.13 | Instantiating (153) with all_99_0_76 yields: % 10.85/3.13 | (154) (all_99_0_76 = 0 & ok(all_0_2_2) = 0) | ( ~ (all_99_0_76 = 0) & ok(all_0_0_0) = all_99_0_76) % 10.85/3.13 | % 10.85/3.13 +-Applying beta-rule and splitting (154), into two cases. % 10.85/3.13 |-Branch one: % 10.85/3.13 | (155) all_99_0_76 = 0 & ok(all_0_2_2) = 0 % 10.85/3.13 | % 10.85/3.13 | Applying alpha-rule on (155) yields: % 10.85/3.13 | (156) all_99_0_76 = 0 % 10.85/3.13 | (128) ok(all_0_2_2) = 0 % 10.85/3.13 | % 10.85/3.13 | Using (128) and (131) yields: % 10.85/3.13 | (158) $false % 10.85/3.13 | % 10.85/3.13 |-The branch is then unsatisfiable % 10.85/3.13 |-Branch two: % 10.85/3.13 | (159) ~ (all_99_0_76 = 0) & ok(all_0_0_0) = all_99_0_76 % 10.85/3.13 | % 10.85/3.13 | Applying alpha-rule on (159) yields: % 10.85/3.13 | (160) ~ (all_99_0_76 = 0) % 10.85/3.13 | (161) ok(all_0_0_0) = all_99_0_76 % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (77) with all_0_0_0, all_99_0_76, 0 and discharging atoms ok(all_0_0_0) = all_99_0_76, ok(all_0_0_0) = 0, yields: % 10.85/3.13 | (156) all_99_0_76 = 0 % 10.85/3.13 | % 10.85/3.13 | Equations (156) can reduce 160 to: % 10.85/3.13 | (130) $false % 10.85/3.13 | % 10.85/3.13 |-The branch is then unsatisfiable % 10.85/3.13 |-Branch two: % 10.85/3.13 | (164) ~ (all_0_4_4 = create_slb) % 10.85/3.13 | (165) ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | (v1 = 0 & contains_slb(all_0_4_4, v0) = 0))) % 10.85/3.13 | % 10.85/3.13 | Instantiating (165) with all_82_0_84, all_82_1_85, all_82_2_86 yields: % 10.85/3.13 | (166) findmin_pqp_res(all_0_5_5) = all_82_2_86 & ((all_82_0_84 = all_56_1_74 & triple(all_0_5_5, all_82_1_85, bad) = all_56_1_74 & update_slb(all_0_4_4, all_82_2_86) = all_82_1_85) | (all_82_1_85 = 0 & contains_slb(all_0_4_4, all_82_2_86) = 0)) % 10.85/3.13 | % 10.85/3.13 | Applying alpha-rule on (166) yields: % 10.85/3.13 | (167) findmin_pqp_res(all_0_5_5) = all_82_2_86 % 10.85/3.13 | (168) (all_82_0_84 = all_56_1_74 & triple(all_0_5_5, all_82_1_85, bad) = all_56_1_74 & update_slb(all_0_4_4, all_82_2_86) = all_82_1_85) | (all_82_1_85 = 0 & contains_slb(all_0_4_4, all_82_2_86) = 0) % 10.85/3.13 | % 10.85/3.13 +-Applying beta-rule and splitting (135), into two cases. % 10.85/3.13 |-Branch one: % 10.85/3.13 | (139) all_0_4_4 = create_slb % 10.85/3.13 | % 10.85/3.13 | Equations (139) can reduce 164 to: % 10.85/3.13 | (130) $false % 10.85/3.13 | % 10.85/3.13 |-The branch is then unsatisfiable % 10.85/3.13 |-Branch two: % 10.85/3.13 | (164) ~ (all_0_4_4 = create_slb) % 10.85/3.13 | (172) ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | ( ~ (v2 = 0) & lookup_slb(all_0_4_4, v0) = v1 & less_than(v1, v0) = v2) | ( ~ (v1 = 0) & contains_slb(all_0_4_4, v0) = v1))) % 10.85/3.13 | % 10.85/3.13 | Instantiating (172) with all_88_0_87, all_88_1_88, all_88_2_89 yields: % 10.85/3.13 | (173) findmin_pqp_res(all_0_5_5) = all_88_2_89 & ((all_88_0_87 = all_56_1_74 & triple(all_0_5_5, all_88_1_88, bad) = all_56_1_74 & update_slb(all_0_4_4, all_88_2_89) = all_88_1_88) | ( ~ (all_88_0_87 = 0) & lookup_slb(all_0_4_4, all_88_2_89) = all_88_1_88 & less_than(all_88_1_88, all_88_2_89) = all_88_0_87) | ( ~ (all_88_1_88 = 0) & contains_slb(all_0_4_4, all_88_2_89) = all_88_1_88)) % 10.85/3.13 | % 10.85/3.13 | Applying alpha-rule on (173) yields: % 10.85/3.13 | (174) findmin_pqp_res(all_0_5_5) = all_88_2_89 % 10.85/3.13 | (175) (all_88_0_87 = all_56_1_74 & triple(all_0_5_5, all_88_1_88, bad) = all_56_1_74 & update_slb(all_0_4_4, all_88_2_89) = all_88_1_88) | ( ~ (all_88_0_87 = 0) & lookup_slb(all_0_4_4, all_88_2_89) = all_88_1_88 & less_than(all_88_1_88, all_88_2_89) = all_88_0_87) | ( ~ (all_88_1_88 = 0) & contains_slb(all_0_4_4, all_88_2_89) = all_88_1_88) % 10.85/3.13 | % 10.85/3.13 +-Applying beta-rule and splitting (137), into two cases. % 10.85/3.13 |-Branch one: % 10.85/3.13 | (139) all_0_4_4 = create_slb % 10.85/3.13 | % 10.85/3.13 | Equations (139) can reduce 164 to: % 10.85/3.13 | (130) $false % 10.85/3.13 | % 10.85/3.13 |-The branch is then unsatisfiable % 10.85/3.13 |-Branch two: % 10.85/3.13 | (164) ~ (all_0_4_4 = create_slb) % 10.85/3.13 | (179) ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | ( ~ (v2 = 0) & lookup_slb(all_0_4_4, v0) = v1 & strictly_less_than(v0, v1) = v2) | ( ~ (v1 = 0) & contains_slb(all_0_4_4, v0) = v1))) % 10.85/3.13 | % 10.85/3.13 | Instantiating (179) with all_93_0_90, all_93_1_91, all_93_2_92 yields: % 10.85/3.13 | (180) findmin_pqp_res(all_0_5_5) = all_93_2_92 & ((all_93_0_90 = all_56_1_74 & triple(all_0_5_5, all_93_1_91, bad) = all_56_1_74 & update_slb(all_0_4_4, all_93_2_92) = all_93_1_91) | ( ~ (all_93_0_90 = 0) & lookup_slb(all_0_4_4, all_93_2_92) = all_93_1_91 & strictly_less_than(all_93_2_92, all_93_1_91) = all_93_0_90) | ( ~ (all_93_1_91 = 0) & contains_slb(all_0_4_4, all_93_2_92) = all_93_1_91)) % 10.85/3.13 | % 10.85/3.13 | Applying alpha-rule on (180) yields: % 10.85/3.13 | (181) findmin_pqp_res(all_0_5_5) = all_93_2_92 % 10.85/3.13 | (182) (all_93_0_90 = all_56_1_74 & triple(all_0_5_5, all_93_1_91, bad) = all_56_1_74 & update_slb(all_0_4_4, all_93_2_92) = all_93_1_91) | ( ~ (all_93_0_90 = 0) & lookup_slb(all_0_4_4, all_93_2_92) = all_93_1_91 & strictly_less_than(all_93_2_92, all_93_1_91) = all_93_0_90) | ( ~ (all_93_1_91 = 0) & contains_slb(all_0_4_4, all_93_2_92) = all_93_1_91) % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (54) with all_0_5_5, all_93_2_92, all_56_0_73 and discharging atoms findmin_pqp_res(all_0_5_5) = all_93_2_92, findmin_pqp_res(all_0_5_5) = all_56_0_73, yields: % 10.85/3.13 | (183) all_93_2_92 = all_56_0_73 % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (54) with all_0_5_5, all_88_2_89, all_93_2_92 and discharging atoms findmin_pqp_res(all_0_5_5) = all_93_2_92, findmin_pqp_res(all_0_5_5) = all_88_2_89, yields: % 10.85/3.13 | (184) all_93_2_92 = all_88_2_89 % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (54) with all_0_5_5, all_82_2_86, all_88_2_89 and discharging atoms findmin_pqp_res(all_0_5_5) = all_88_2_89, findmin_pqp_res(all_0_5_5) = all_82_2_86, yields: % 10.85/3.13 | (185) all_88_2_89 = all_82_2_86 % 10.85/3.13 | % 10.85/3.13 | Combining equations (184,183) yields a new equation: % 10.85/3.13 | (186) all_88_2_89 = all_56_0_73 % 10.85/3.13 | % 10.85/3.13 | Simplifying 186 yields: % 10.85/3.13 | (187) all_88_2_89 = all_56_0_73 % 10.85/3.13 | % 10.85/3.13 | Combining equations (185,187) yields a new equation: % 10.85/3.13 | (188) all_82_2_86 = all_56_0_73 % 10.85/3.13 | % 10.85/3.13 | Simplifying 188 yields: % 10.85/3.13 | (189) all_82_2_86 = all_56_0_73 % 10.85/3.13 | % 10.85/3.13 +-Applying beta-rule and splitting (168), into two cases. % 10.85/3.13 |-Branch one: % 10.85/3.13 | (190) all_82_0_84 = all_56_1_74 & triple(all_0_5_5, all_82_1_85, bad) = all_56_1_74 & update_slb(all_0_4_4, all_82_2_86) = all_82_1_85 % 10.85/3.13 | % 10.85/3.13 | Applying alpha-rule on (190) yields: % 10.85/3.13 | (191) all_82_0_84 = all_56_1_74 % 10.85/3.13 | (192) triple(all_0_5_5, all_82_1_85, bad) = all_56_1_74 % 10.85/3.13 | (193) update_slb(all_0_4_4, all_82_2_86) = all_82_1_85 % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (74) with all_0_0_0, all_56_1_74, all_56_0_73, bad, all_82_1_85, all_0_5_5 and discharging atoms triple(all_0_5_5, all_82_1_85, bad) = all_56_1_74, remove_cpq(all_56_1_74, all_56_0_73) = all_0_0_0, yields: % 10.85/3.13 | (194) ? [v0] : ((v0 = 0 & ok(all_56_1_74) = 0) | ( ~ (v0 = 0) & ok(all_0_0_0) = v0)) % 10.85/3.13 | % 10.85/3.13 | Instantiating formula (116) with all_56_1_74, all_82_1_85, all_0_5_5 and discharging atoms triple(all_0_5_5, all_82_1_85, bad) = all_56_1_74, yields: % 10.85/3.13 | (195) ? [v0] : ( ~ (v0 = 0) & ok(all_56_1_74) = v0) % 10.85/3.13 | % 10.85/3.13 | Instantiating (195) with all_111_0_93 yields: % 10.85/3.13 | (196) ~ (all_111_0_93 = 0) & ok(all_56_1_74) = all_111_0_93 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (196) yields: % 10.85/3.14 | (197) ~ (all_111_0_93 = 0) % 10.85/3.14 | (198) ok(all_56_1_74) = all_111_0_93 % 10.85/3.14 | % 10.85/3.14 | Instantiating (194) with all_115_0_100 yields: % 10.85/3.14 | (199) (all_115_0_100 = 0 & ok(all_56_1_74) = 0) | ( ~ (all_115_0_100 = 0) & ok(all_0_0_0) = all_115_0_100) % 10.85/3.14 | % 10.85/3.14 +-Applying beta-rule and splitting (199), into two cases. % 10.85/3.14 |-Branch one: % 10.85/3.14 | (200) all_115_0_100 = 0 & ok(all_56_1_74) = 0 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (200) yields: % 10.85/3.14 | (201) all_115_0_100 = 0 % 10.85/3.14 | (202) ok(all_56_1_74) = 0 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (77) with all_56_1_74, 0, all_111_0_93 and discharging atoms ok(all_56_1_74) = all_111_0_93, ok(all_56_1_74) = 0, yields: % 10.85/3.14 | (203) all_111_0_93 = 0 % 10.85/3.14 | % 10.85/3.14 | Equations (203) can reduce 197 to: % 10.85/3.14 | (130) $false % 10.85/3.14 | % 10.85/3.14 |-The branch is then unsatisfiable % 10.85/3.14 |-Branch two: % 10.85/3.14 | (205) ~ (all_115_0_100 = 0) & ok(all_0_0_0) = all_115_0_100 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (205) yields: % 10.85/3.14 | (206) ~ (all_115_0_100 = 0) % 10.85/3.14 | (207) ok(all_0_0_0) = all_115_0_100 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (77) with all_0_0_0, all_115_0_100, 0 and discharging atoms ok(all_0_0_0) = all_115_0_100, ok(all_0_0_0) = 0, yields: % 10.85/3.14 | (201) all_115_0_100 = 0 % 10.85/3.14 | % 10.85/3.14 | Equations (201) can reduce 206 to: % 10.85/3.14 | (130) $false % 10.85/3.14 | % 10.85/3.14 |-The branch is then unsatisfiable % 10.85/3.14 |-Branch two: % 10.85/3.14 | (210) all_82_1_85 = 0 & contains_slb(all_0_4_4, all_82_2_86) = 0 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (210) yields: % 10.85/3.14 | (211) all_82_1_85 = 0 % 10.85/3.14 | (212) contains_slb(all_0_4_4, all_82_2_86) = 0 % 10.85/3.14 | % 10.85/3.14 | From (189) and (212) follows: % 10.85/3.14 | (213) contains_slb(all_0_4_4, all_56_0_73) = 0 % 10.85/3.14 | % 10.85/3.14 +-Applying beta-rule and splitting (175), into two cases. % 10.85/3.14 |-Branch one: % 10.85/3.14 | (214) (all_88_0_87 = all_56_1_74 & triple(all_0_5_5, all_88_1_88, bad) = all_56_1_74 & update_slb(all_0_4_4, all_88_2_89) = all_88_1_88) | ( ~ (all_88_0_87 = 0) & lookup_slb(all_0_4_4, all_88_2_89) = all_88_1_88 & less_than(all_88_1_88, all_88_2_89) = all_88_0_87) % 10.85/3.14 | % 10.85/3.14 +-Applying beta-rule and splitting (214), into two cases. % 10.85/3.14 |-Branch one: % 10.85/3.14 | (215) all_88_0_87 = all_56_1_74 & triple(all_0_5_5, all_88_1_88, bad) = all_56_1_74 & update_slb(all_0_4_4, all_88_2_89) = all_88_1_88 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (215) yields: % 10.85/3.14 | (216) all_88_0_87 = all_56_1_74 % 10.85/3.14 | (217) triple(all_0_5_5, all_88_1_88, bad) = all_56_1_74 % 10.85/3.14 | (218) update_slb(all_0_4_4, all_88_2_89) = all_88_1_88 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (74) with all_0_0_0, all_56_1_74, all_56_0_73, bad, all_88_1_88, all_0_5_5 and discharging atoms triple(all_0_5_5, all_88_1_88, bad) = all_56_1_74, remove_cpq(all_56_1_74, all_56_0_73) = all_0_0_0, yields: % 10.85/3.14 | (194) ? [v0] : ((v0 = 0 & ok(all_56_1_74) = 0) | ( ~ (v0 = 0) & ok(all_0_0_0) = v0)) % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (116) with all_56_1_74, all_88_1_88, all_0_5_5 and discharging atoms triple(all_0_5_5, all_88_1_88, bad) = all_56_1_74, yields: % 10.85/3.14 | (195) ? [v0] : ( ~ (v0 = 0) & ok(all_56_1_74) = v0) % 10.85/3.14 | % 10.85/3.14 | Instantiating (195) with all_118_0_106 yields: % 10.85/3.14 | (221) ~ (all_118_0_106 = 0) & ok(all_56_1_74) = all_118_0_106 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (221) yields: % 10.85/3.14 | (222) ~ (all_118_0_106 = 0) % 10.85/3.14 | (223) ok(all_56_1_74) = all_118_0_106 % 10.85/3.14 | % 10.85/3.14 | Instantiating (194) with all_120_0_107 yields: % 10.85/3.14 | (224) (all_120_0_107 = 0 & ok(all_56_1_74) = 0) | ( ~ (all_120_0_107 = 0) & ok(all_0_0_0) = all_120_0_107) % 10.85/3.14 | % 10.85/3.14 +-Applying beta-rule and splitting (224), into two cases. % 10.85/3.14 |-Branch one: % 10.85/3.14 | (225) all_120_0_107 = 0 & ok(all_56_1_74) = 0 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (225) yields: % 10.85/3.14 | (226) all_120_0_107 = 0 % 10.85/3.14 | (202) ok(all_56_1_74) = 0 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (77) with all_56_1_74, 0, all_118_0_106 and discharging atoms ok(all_56_1_74) = all_118_0_106, ok(all_56_1_74) = 0, yields: % 10.85/3.14 | (228) all_118_0_106 = 0 % 10.85/3.14 | % 10.85/3.14 | Equations (228) can reduce 222 to: % 10.85/3.14 | (130) $false % 10.85/3.14 | % 10.85/3.14 |-The branch is then unsatisfiable % 10.85/3.14 |-Branch two: % 10.85/3.14 | (230) ~ (all_120_0_107 = 0) & ok(all_0_0_0) = all_120_0_107 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (230) yields: % 10.85/3.14 | (231) ~ (all_120_0_107 = 0) % 10.85/3.14 | (232) ok(all_0_0_0) = all_120_0_107 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (77) with all_0_0_0, all_120_0_107, 0 and discharging atoms ok(all_0_0_0) = all_120_0_107, ok(all_0_0_0) = 0, yields: % 10.85/3.14 | (226) all_120_0_107 = 0 % 10.85/3.14 | % 10.85/3.14 | Equations (226) can reduce 231 to: % 10.85/3.14 | (130) $false % 10.85/3.14 | % 10.85/3.14 |-The branch is then unsatisfiable % 10.85/3.14 |-Branch two: % 10.85/3.14 | (235) ~ (all_88_0_87 = 0) & lookup_slb(all_0_4_4, all_88_2_89) = all_88_1_88 & less_than(all_88_1_88, all_88_2_89) = all_88_0_87 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (235) yields: % 10.85/3.14 | (236) ~ (all_88_0_87 = 0) % 10.85/3.14 | (237) lookup_slb(all_0_4_4, all_88_2_89) = all_88_1_88 % 10.85/3.14 | (238) less_than(all_88_1_88, all_88_2_89) = all_88_0_87 % 10.85/3.14 | % 10.85/3.14 | From (187) and (237) follows: % 10.85/3.14 | (239) lookup_slb(all_0_4_4, all_56_0_73) = all_88_1_88 % 10.85/3.14 | % 10.85/3.14 | From (187) and (238) follows: % 10.85/3.14 | (240) less_than(all_88_1_88, all_56_0_73) = all_88_0_87 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (113) with all_88_0_87, all_88_1_88, all_56_0_73 and discharging atoms less_than(all_88_1_88, all_56_0_73) = all_88_0_87, yields: % 10.85/3.14 | (241) all_88_0_87 = 0 | less_than(all_56_0_73, all_88_1_88) = 0 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (12) with all_88_0_87, all_88_1_88, all_56_0_73 and discharging atoms less_than(all_88_1_88, all_56_0_73) = all_88_0_87, yields: % 10.85/3.14 | (242) all_88_0_87 = 0 | ? [v0] : ((v0 = 0 & strictly_less_than(all_56_0_73, all_88_1_88) = 0) | ( ~ (v0 = 0) & less_than(all_56_0_73, all_88_1_88) = v0)) % 10.85/3.14 | % 10.85/3.14 +-Applying beta-rule and splitting (182), into two cases. % 10.85/3.14 |-Branch one: % 10.85/3.14 | (243) (all_93_0_90 = all_56_1_74 & triple(all_0_5_5, all_93_1_91, bad) = all_56_1_74 & update_slb(all_0_4_4, all_93_2_92) = all_93_1_91) | ( ~ (all_93_0_90 = 0) & lookup_slb(all_0_4_4, all_93_2_92) = all_93_1_91 & strictly_less_than(all_93_2_92, all_93_1_91) = all_93_0_90) % 10.85/3.14 | % 10.85/3.14 +-Applying beta-rule and splitting (243), into two cases. % 10.85/3.14 |-Branch one: % 10.85/3.14 | (244) all_93_0_90 = all_56_1_74 & triple(all_0_5_5, all_93_1_91, bad) = all_56_1_74 & update_slb(all_0_4_4, all_93_2_92) = all_93_1_91 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (244) yields: % 10.85/3.14 | (245) all_93_0_90 = all_56_1_74 % 10.85/3.14 | (246) triple(all_0_5_5, all_93_1_91, bad) = all_56_1_74 % 10.85/3.14 | (247) update_slb(all_0_4_4, all_93_2_92) = all_93_1_91 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (74) with all_0_0_0, all_56_1_74, all_56_0_73, bad, all_93_1_91, all_0_5_5 and discharging atoms triple(all_0_5_5, all_93_1_91, bad) = all_56_1_74, remove_cpq(all_56_1_74, all_56_0_73) = all_0_0_0, yields: % 10.85/3.14 | (194) ? [v0] : ((v0 = 0 & ok(all_56_1_74) = 0) | ( ~ (v0 = 0) & ok(all_0_0_0) = v0)) % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (116) with all_56_1_74, all_93_1_91, all_0_5_5 and discharging atoms triple(all_0_5_5, all_93_1_91, bad) = all_56_1_74, yields: % 10.85/3.14 | (195) ? [v0] : ( ~ (v0 = 0) & ok(all_56_1_74) = v0) % 10.85/3.14 | % 10.85/3.14 | Instantiating (195) with all_148_0_122 yields: % 10.85/3.14 | (250) ~ (all_148_0_122 = 0) & ok(all_56_1_74) = all_148_0_122 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (250) yields: % 10.85/3.14 | (251) ~ (all_148_0_122 = 0) % 10.85/3.14 | (252) ok(all_56_1_74) = all_148_0_122 % 10.85/3.14 | % 10.85/3.14 | Instantiating (194) with all_150_0_123 yields: % 10.85/3.14 | (253) (all_150_0_123 = 0 & ok(all_56_1_74) = 0) | ( ~ (all_150_0_123 = 0) & ok(all_0_0_0) = all_150_0_123) % 10.85/3.14 | % 10.85/3.14 +-Applying beta-rule and splitting (253), into two cases. % 10.85/3.14 |-Branch one: % 10.85/3.14 | (254) all_150_0_123 = 0 & ok(all_56_1_74) = 0 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (254) yields: % 10.85/3.14 | (255) all_150_0_123 = 0 % 10.85/3.14 | (202) ok(all_56_1_74) = 0 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (77) with all_56_1_74, 0, all_148_0_122 and discharging atoms ok(all_56_1_74) = all_148_0_122, ok(all_56_1_74) = 0, yields: % 10.85/3.14 | (257) all_148_0_122 = 0 % 10.85/3.14 | % 10.85/3.14 | Equations (257) can reduce 251 to: % 10.85/3.14 | (130) $false % 10.85/3.14 | % 10.85/3.14 |-The branch is then unsatisfiable % 10.85/3.14 |-Branch two: % 10.85/3.14 | (259) ~ (all_150_0_123 = 0) & ok(all_0_0_0) = all_150_0_123 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (259) yields: % 10.85/3.14 | (260) ~ (all_150_0_123 = 0) % 10.85/3.14 | (261) ok(all_0_0_0) = all_150_0_123 % 10.85/3.14 | % 10.85/3.14 | Instantiating formula (77) with all_0_0_0, all_150_0_123, 0 and discharging atoms ok(all_0_0_0) = all_150_0_123, ok(all_0_0_0) = 0, yields: % 10.85/3.14 | (255) all_150_0_123 = 0 % 10.85/3.14 | % 10.85/3.14 | Equations (255) can reduce 260 to: % 10.85/3.14 | (130) $false % 10.85/3.14 | % 10.85/3.14 |-The branch is then unsatisfiable % 10.85/3.14 |-Branch two: % 10.85/3.14 | (264) ~ (all_93_0_90 = 0) & lookup_slb(all_0_4_4, all_93_2_92) = all_93_1_91 & strictly_less_than(all_93_2_92, all_93_1_91) = all_93_0_90 % 10.85/3.14 | % 10.85/3.14 | Applying alpha-rule on (264) yields: % 10.85/3.14 | (265) ~ (all_93_0_90 = 0) % 10.85/3.14 | (266) lookup_slb(all_0_4_4, all_93_2_92) = all_93_1_91 % 10.85/3.14 | (267) strictly_less_than(all_93_2_92, all_93_1_91) = all_93_0_90 % 10.85/3.14 | % 10.85/3.14 | From (183) and (266) follows: % 10.85/3.14 | (268) lookup_slb(all_0_4_4, all_56_0_73) = all_93_1_91 % 10.85/3.14 | % 10.85/3.14 | From (183) and (267) follows: % 10.85/3.15 | (269) strictly_less_than(all_56_0_73, all_93_1_91) = all_93_0_90 % 10.85/3.15 | % 10.85/3.15 +-Applying beta-rule and splitting (241), into two cases. % 10.85/3.15 |-Branch one: % 10.85/3.15 | (270) less_than(all_56_0_73, all_88_1_88) = 0 % 10.85/3.15 | % 10.85/3.15 +-Applying beta-rule and splitting (242), into two cases. % 10.85/3.15 |-Branch one: % 10.85/3.15 | (271) all_88_0_87 = 0 % 10.85/3.15 | % 10.85/3.15 | Equations (271) can reduce 236 to: % 10.85/3.15 | (130) $false % 10.85/3.15 | % 10.85/3.15 |-The branch is then unsatisfiable % 10.85/3.15 |-Branch two: % 10.85/3.15 | (236) ~ (all_88_0_87 = 0) % 10.85/3.15 | (274) ? [v0] : ((v0 = 0 & strictly_less_than(all_56_0_73, all_88_1_88) = 0) | ( ~ (v0 = 0) & less_than(all_56_0_73, all_88_1_88) = v0)) % 10.85/3.15 | % 10.85/3.15 | Instantiating (274) with all_130_0_137 yields: % 10.85/3.15 | (275) (all_130_0_137 = 0 & strictly_less_than(all_56_0_73, all_88_1_88) = 0) | ( ~ (all_130_0_137 = 0) & less_than(all_56_0_73, all_88_1_88) = all_130_0_137) % 10.85/3.15 | % 10.85/3.15 +-Applying beta-rule and splitting (275), into two cases. % 10.85/3.15 |-Branch one: % 10.85/3.15 | (276) all_130_0_137 = 0 & strictly_less_than(all_56_0_73, all_88_1_88) = 0 % 10.85/3.15 | % 10.85/3.15 | Applying alpha-rule on (276) yields: % 10.85/3.15 | (277) all_130_0_137 = 0 % 10.85/3.15 | (278) strictly_less_than(all_56_0_73, all_88_1_88) = 0 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (51) with all_0_4_4, all_56_0_73, all_93_1_91, all_88_1_88 and discharging atoms lookup_slb(all_0_4_4, all_56_0_73) = all_93_1_91, lookup_slb(all_0_4_4, all_56_0_73) = all_88_1_88, yields: % 10.85/3.15 | (279) all_93_1_91 = all_88_1_88 % 10.85/3.15 | % 10.85/3.15 | From (279) and (269) follows: % 10.85/3.15 | (280) strictly_less_than(all_56_0_73, all_88_1_88) = all_93_0_90 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (88) with all_56_0_73, all_88_1_88, all_93_0_90, 0 and discharging atoms strictly_less_than(all_56_0_73, all_88_1_88) = all_93_0_90, strictly_less_than(all_56_0_73, all_88_1_88) = 0, yields: % 10.85/3.15 | (281) all_93_0_90 = 0 % 10.85/3.15 | % 10.85/3.15 | Equations (281) can reduce 265 to: % 10.85/3.15 | (130) $false % 10.85/3.15 | % 10.85/3.15 |-The branch is then unsatisfiable % 10.85/3.15 |-Branch two: % 10.85/3.15 | (283) ~ (all_130_0_137 = 0) & less_than(all_56_0_73, all_88_1_88) = all_130_0_137 % 10.85/3.15 | % 10.85/3.15 | Applying alpha-rule on (283) yields: % 10.85/3.15 | (284) ~ (all_130_0_137 = 0) % 10.85/3.15 | (285) less_than(all_56_0_73, all_88_1_88) = all_130_0_137 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (115) with all_56_0_73, all_88_1_88, 0, all_130_0_137 and discharging atoms less_than(all_56_0_73, all_88_1_88) = all_130_0_137, less_than(all_56_0_73, all_88_1_88) = 0, yields: % 10.85/3.15 | (277) all_130_0_137 = 0 % 10.85/3.15 | % 10.85/3.15 | Equations (277) can reduce 284 to: % 10.85/3.15 | (130) $false % 10.85/3.15 | % 10.85/3.15 |-The branch is then unsatisfiable % 10.85/3.15 |-Branch two: % 10.85/3.15 | (288) ~ (less_than(all_56_0_73, all_88_1_88) = 0) % 10.85/3.15 | (271) all_88_0_87 = 0 % 10.85/3.15 | % 10.85/3.15 | Equations (271) can reduce 236 to: % 10.85/3.15 | (130) $false % 10.85/3.15 | % 10.85/3.15 |-The branch is then unsatisfiable % 10.85/3.15 |-Branch two: % 10.85/3.15 | (291) ~ (all_93_1_91 = 0) & contains_slb(all_0_4_4, all_93_2_92) = all_93_1_91 % 10.85/3.15 | % 10.85/3.15 | Applying alpha-rule on (291) yields: % 10.85/3.15 | (292) ~ (all_93_1_91 = 0) % 10.85/3.15 | (293) contains_slb(all_0_4_4, all_93_2_92) = all_93_1_91 % 10.85/3.15 | % 10.85/3.15 | From (183) and (293) follows: % 10.85/3.15 | (294) contains_slb(all_0_4_4, all_56_0_73) = all_93_1_91 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (107) with all_0_4_4, all_56_0_73, all_93_1_91, 0 and discharging atoms contains_slb(all_0_4_4, all_56_0_73) = all_93_1_91, contains_slb(all_0_4_4, all_56_0_73) = 0, yields: % 10.85/3.15 | (295) all_93_1_91 = 0 % 10.85/3.15 | % 10.85/3.15 | Equations (295) can reduce 292 to: % 10.85/3.15 | (130) $false % 10.85/3.15 | % 10.85/3.15 |-The branch is then unsatisfiable % 10.85/3.15 |-Branch two: % 10.85/3.15 | (297) ~ (all_88_1_88 = 0) & contains_slb(all_0_4_4, all_88_2_89) = all_88_1_88 % 10.85/3.15 | % 10.85/3.15 | Applying alpha-rule on (297) yields: % 10.85/3.15 | (298) ~ (all_88_1_88 = 0) % 10.85/3.15 | (299) contains_slb(all_0_4_4, all_88_2_89) = all_88_1_88 % 10.85/3.15 | % 10.85/3.15 | From (187) and (299) follows: % 10.85/3.15 | (300) contains_slb(all_0_4_4, all_56_0_73) = all_88_1_88 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (107) with all_0_4_4, all_56_0_73, all_88_1_88, 0 and discharging atoms contains_slb(all_0_4_4, all_56_0_73) = all_88_1_88, contains_slb(all_0_4_4, all_56_0_73) = 0, yields: % 10.85/3.15 | (301) all_88_1_88 = 0 % 10.85/3.15 | % 10.85/3.15 | Equations (301) can reduce 298 to: % 10.85/3.15 | (130) $false % 10.85/3.15 | % 10.85/3.15 |-The branch is then unsatisfiable % 10.85/3.15 |-Branch two: % 10.85/3.15 | (303) ~ (findmin_pqp_res(all_0_5_5) = all_56_0_73) % 10.85/3.15 | (139) all_0_4_4 = create_slb % 10.85/3.15 | % 10.85/3.15 | From (139) and (133) follows: % 10.85/3.15 | (140) triple(all_0_5_5, create_slb, bad) = all_0_2_2 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (11) with all_0_2_2, bad, all_0_5_5 and discharging atoms triple(all_0_5_5, create_slb, bad) = all_0_2_2, yields: % 10.85/3.15 | (141) findmin_cpq_res(all_0_2_2) = bottom % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (14) with all_0_2_2, bad, all_0_5_5 and discharging atoms triple(all_0_5_5, create_slb, bad) = all_0_2_2, yields: % 10.85/3.15 | (142) ? [v0] : (triple(all_0_5_5, create_slb, bad) = v0 & findmin_cpq_eff(all_0_2_2) = v0) % 10.85/3.15 | % 10.85/3.15 | Instantiating (142) with all_81_0_139 yields: % 10.85/3.15 | (308) triple(all_0_5_5, create_slb, bad) = all_81_0_139 & findmin_cpq_eff(all_0_2_2) = all_81_0_139 % 10.85/3.15 | % 10.85/3.15 | Applying alpha-rule on (308) yields: % 10.85/3.15 | (309) triple(all_0_5_5, create_slb, bad) = all_81_0_139 % 10.85/3.15 | (310) findmin_cpq_eff(all_0_2_2) = all_81_0_139 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (17) with all_0_2_2, bottom, all_56_0_73 and discharging atoms findmin_cpq_res(all_0_2_2) = all_56_0_73, findmin_cpq_res(all_0_2_2) = bottom, yields: % 10.85/3.15 | (146) all_56_0_73 = bottom % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (101) with all_0_5_5, create_slb, bad, all_81_0_139, all_0_2_2 and discharging atoms triple(all_0_5_5, create_slb, bad) = all_81_0_139, triple(all_0_5_5, create_slb, bad) = all_0_2_2, yields: % 10.85/3.15 | (312) all_81_0_139 = all_0_2_2 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (10) with all_0_2_2, all_81_0_139, all_56_1_74 and discharging atoms findmin_cpq_eff(all_0_2_2) = all_81_0_139, findmin_cpq_eff(all_0_2_2) = all_56_1_74, yields: % 10.85/3.15 | (313) all_81_0_139 = all_56_1_74 % 10.85/3.15 | % 10.85/3.15 | Combining equations (312,313) yields a new equation: % 10.85/3.15 | (149) all_56_1_74 = all_0_2_2 % 10.85/3.15 | % 10.85/3.15 | Combining equations (149,313) yields a new equation: % 10.85/3.15 | (312) all_81_0_139 = all_0_2_2 % 10.85/3.15 | % 10.85/3.15 | From (312) and (309) follows: % 10.85/3.15 | (140) triple(all_0_5_5, create_slb, bad) = all_0_2_2 % 10.85/3.15 | % 10.85/3.15 | From (149)(146) and (127) follows: % 10.85/3.15 | (152) remove_cpq(all_0_2_2, bottom) = all_0_0_0 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (74) with all_0_0_0, all_0_2_2, bottom, bad, create_slb, all_0_5_5 and discharging atoms triple(all_0_5_5, create_slb, bad) = all_0_2_2, remove_cpq(all_0_2_2, bottom) = all_0_0_0, yields: % 10.85/3.15 | (153) ? [v0] : ((v0 = 0 & ok(all_0_2_2) = 0) | ( ~ (v0 = 0) & ok(all_0_0_0) = v0)) % 10.85/3.15 | % 10.85/3.15 | Instantiating (153) with all_92_0_140 yields: % 10.85/3.15 | (319) (all_92_0_140 = 0 & ok(all_0_2_2) = 0) | ( ~ (all_92_0_140 = 0) & ok(all_0_0_0) = all_92_0_140) % 10.85/3.15 | % 10.85/3.15 +-Applying beta-rule and splitting (319), into two cases. % 10.85/3.15 |-Branch one: % 10.85/3.15 | (320) all_92_0_140 = 0 & ok(all_0_2_2) = 0 % 10.85/3.15 | % 10.85/3.15 | Applying alpha-rule on (320) yields: % 10.85/3.15 | (321) all_92_0_140 = 0 % 10.85/3.15 | (128) ok(all_0_2_2) = 0 % 10.85/3.15 | % 10.85/3.15 | Using (128) and (131) yields: % 10.85/3.15 | (158) $false % 10.85/3.15 | % 10.85/3.15 |-The branch is then unsatisfiable % 10.85/3.15 |-Branch two: % 10.85/3.15 | (324) ~ (all_92_0_140 = 0) & ok(all_0_0_0) = all_92_0_140 % 10.85/3.15 | % 10.85/3.15 | Applying alpha-rule on (324) yields: % 10.85/3.15 | (325) ~ (all_92_0_140 = 0) % 10.85/3.15 | (326) ok(all_0_0_0) = all_92_0_140 % 10.85/3.15 | % 10.85/3.15 | Instantiating formula (77) with all_0_0_0, all_92_0_140, 0 and discharging atoms ok(all_0_0_0) = all_92_0_140, ok(all_0_0_0) = 0, yields: % 10.85/3.15 | (321) all_92_0_140 = 0 % 10.85/3.15 | % 10.85/3.15 | Equations (321) can reduce 325 to: % 10.85/3.15 | (130) $false % 10.85/3.15 | % 10.85/3.15 |-The branch is then unsatisfiable % 10.85/3.15 % SZS output end Proof for theBenchmark % 10.85/3.15 % 10.85/3.15 2522ms %------------------------------------------------------------------------------