%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 17:51:09 EDT 2022 % Result : Theorem 4.49s 1.64s % Output : Proof 6.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n005.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Tue Jun 14 15:35:39 EDT 2022 % 0.13/0.35 % CPUTime : % 0.60/0.61 ____ _ % 0.60/0.61 ___ / __ \_____(_)___ ________ __________ % 0.60/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.61 % 0.60/0.61 A Theorem Prover for First-Order Logic % 0.65/0.62 (ePrincess v.1.0) % 0.65/0.62 % 0.65/0.62 (c) Philipp Rümmer, 2009-2015 % 0.65/0.62 (c) Peter Backeman, 2014-2015 % 0.65/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.65/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.65/0.62 Bug reports to peter@backeman.se % 0.65/0.62 % 0.65/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.65/0.62 % 0.65/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.03/1.04 Prover 0: Preprocessing ... % 3.75/1.46 Prover 0: Warning: ignoring some quantifiers % 3.76/1.49 Prover 0: Constructing countermodel ... % 4.49/1.64 Prover 0: proved (962ms) % 4.49/1.64 % 4.49/1.64 No countermodel exists, formula is valid % 4.49/1.64 % SZS status Theorem for theBenchmark % 4.49/1.64 % 4.49/1.64 Generating proof ... Warning: ignoring some quantifiers % 6.09/2.02 found it (size 33) % 6.09/2.02 % 6.09/2.02 % SZS output start Proof for theBenchmark % 6.09/2.02 Assumed formulas after preprocessing and simplification: % 6.09/2.02 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (i(v3) = v5 & findmin_cpq_res(v3) = v6 & triple(v0, v1, v2) = v3 & findmin_cpq_eff(v3) = v4 & phi(v4) & ~ pi_sharp_find_min(v5, v6) & ~ isnonempty_slb(create_slb) & ~ isnonempty_pq(create_pq) & ! [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) | ~ check_cpq(v14) | ~ strictly_less_than(v10, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v7, v13, v9) = v14) | ~ (pair(v10, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ~ less_than(v11, v10) | ? [v15] : (triple(v7, v8, v9) = v15 & ( ~ check_cpq(v15) | check_cpq(v14)) & ( ~ check_cpq(v14) | check_cpq(v15)))) & ! [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] : (i(v16) = v17 & i(v14) = v15 & triple(v7, v8, v9) = v16 & insert_pq(v17, v10) = v15)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (pair(v8, v10) = v12) | ~ (insert_slb(v7, v12) = v13) | ~ pair_in_list(v13, v9, v11) | pair_in_list(v7, v9, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (lookup_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ~ contains_slb(v7, v9) | lookup_slb(v7, v9) = v13) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (remove_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ~ contains_slb(v7, v9) | ? [v14] : (remove_slb(v7, v9) = v14 & insert_slb(v14, v11) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (remove_slb(v7, v9) = v12) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v12, v11) = v13) | ~ contains_slb(v7, v9) | ? [v14] : (remove_slb(v14, v9) = v13 & insert_slb(v7, v11) = v14)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (pair(v8, v10) = v12) | ~ (insert_slb(v7, v12) = v13) | ~ pair_in_list(v13, v9, v11) | pair_in_list(v7, v9, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (remove_pqp(v7, v10) = v11) | ~ (triple(v11, v12, v9) = v13) | ~ (remove_slb(v8, v10) = v12) | ~ contains_slb(v8, v10) | ? [v14] : ? [v15] : ? [v16] : (triple(v7, v8, v9) = v15 & remove_cpq(v15, v10) = v16 & lookup_slb(v8, v10) = v14 & (v16 = v13 | ~ less_than(v14, v10)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ~ strictly_less_than(v10, v9) | ? [v14] : ? [v15] : (update_slb(v7, v9) = v14 & pair(v8, v9) = v15 & insert_slb(v14, v15) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ~ less_than(v9, v10) | ? [v14] : (update_slb(v7, v9) = v14 & insert_slb(v14, v11) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v7, v9) = v12) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v12, v11) = v13) | ~ less_than(v9, v10) | ? [v14] : (update_slb(v14, v9) = v13 & insert_slb(v7, v11) = v14)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (pair(v8, v10) = v12) | ~ (insert_slb(v7, v12) = v13) | ~ pair_in_list(v7, v9, v11) | pair_in_list(v13, v9, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (lookup_slb(v11, v8) = v12) | ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v7 | ~ (remove_slb(v11, v8) = v12) | ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ~ contains_slb(v12, v9) | contains_slb(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = create_slb | ~ (findmin_pqp_res(v7) = v10) | ~ (triple(v7, v11, v9) = v12) | ~ (update_slb(v8, v10) = v11) | ~ contains_slb(v8, v10) | ? [v13] : ? [v14] : ? [v15] : (triple(v7, v8, v9) = v14 & findmin_cpq_eff(v14) = v15 & lookup_slb(v8, v10) = v13 & (v15 = v12 | ~ less_than(v13, v10)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ~ contains_slb(v8, v10) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (remove_pqp(v7, v10) = v14 & triple(v14, v15, v9) = v16 & lookup_slb(v8, v10) = v13 & remove_slb(v8, v10) = v15 & (v16 = v12 | ~ less_than(v13, v10)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ~ contains_slb(v8, v10) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (remove_pqp(v7, v10) = v14 & triple(v14, v15, bad) = v16 & lookup_slb(v8, v10) = v13 & remove_slb(v8, v10) = v15 & (v16 = v12 | ~ strictly_less_than(v10, v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | triple(v7, v8, bad) = v12 | contains_slb(v8, v10)) & ! [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] : ! [v12] : ( ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ~ contains_slb(v7, v9) | contains_slb(v12, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (remove_pq(v10, v9) = v11) | ~ (insert_pq(v7, v8) = v10) | ~ contains_pq(v7, v9) | ? [v12] : (remove_pq(v7, v9) = v12 & insert_pq(v12, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (remove_pq(v7, v9) = v10) | ~ (insert_pq(v10, v8) = v11) | ~ contains_pq(v7, v9) | ? [v12] : (remove_pq(v12, v9) = v11 & insert_pq(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] : ( ~ (triple(v7, v8, v9) = v11) | ~ contains_cpq(v11, v10) | contains_slb(v8, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v7, v8, v9) = v11) | ~ contains_slb(v8, v10) | contains_cpq(v11, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11) | pair_in_list(v11, v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11) | contains_slb(v11, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11) | isnonempty_slb(v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (insert_pq(v10, v9) = v11) | ~ (insert_pq(v7, v8) = v10) | ? [v12] : (insert_pq(v12, v8) = v11 & insert_pq(v7, v9) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (insert_pq(v10, v8) = v11) | ~ (insert_pq(v7, v9) = v10) | ? [v12] : (insert_pq(v12, v9) = v11 & insert_pq(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (remove_pq(v9, v8) = v10) | ~ (insert_pq(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (insert_pq(v7, v8) = v10) | ~ contains_pq(v10, v9) | contains_pq(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = bad | ~ (triple(v7, v8, v9) = v10) | ok(v10)) & ! [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 | ~ (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 | ~ (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 | ~ (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 | ~ (removemin_pq_res(v10, v9) = v8) | ~ (removemin_pq_res(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (removemin_pq_eff(v10, v9) = v8) | ~ (removemin_pq_eff(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (findmin_pq_res(v10, v9) = v8) | ~ (findmin_pq_res(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (findmin_pq_eff(v10, v9) = v8) | ~ (findmin_pq_eff(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (remove_pq(v10, v9) = v8) | ~ (remove_pq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (insert_pq(v10, v9) = v8) | ~ (insert_pq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (findmin_pqp_res(v7) = v11 & triple(v7, v14, v9) = v15 & findmin_cpq_eff(v10) = v13 & update_slb(v8, v11) = v14 & lookup_slb(v8, v11) = v12 & (v15 = v13 | ~ contains_slb(v8, v11) | ~ less_than(v12, v11)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (findmin_pqp_res(v7) = v11 & triple(v7, v14, bad) = v15 & findmin_cpq_eff(v10) = v13 & update_slb(v8, v11) = v14 & lookup_slb(v8, v11) = v12 & (v15 = v13 | ~ contains_slb(v8, v11) | ~ strictly_less_than(v11, v12)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (findmin_pqp_res(v7) = v11 & triple(v7, v13, bad) = v14 & findmin_cpq_eff(v10) = v12 & update_slb(v8, v11) = v13 & (v14 = v12 | contains_slb(v8, v11)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ? [v11] : (findmin_cpq_res(v10) = v11 & findmin_pqp_res(v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (findmin_cpq_res(v7) = v9) | ~ (findmin_cpq_eff(v7) = v8) | ~ (remove_cpq(v8, v9) = v10) | removemin_cpq_eff(v7) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (i(v10) = v12 & findmin_cpq_res(v10) = v13 & findmin_cpq_eff(v10) = v11 & ( ~ phi(v11) | issmallestelement_pq(v12, v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (i(v10) = v12 & findmin_cpq_res(v10) = v13 & findmin_cpq_eff(v10) = v11 & ( ~ phi(v11) | contains_pq(v12, v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (remove_cpq(v8, v9) = v10) | ~ succ_cpq(v7, v8) | succ_cpq(v7, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (insert_cpq(v8, v9) = v10) | ~ succ_cpq(v7, v8) | succ_cpq(v7, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (insert_pq(v7, v8) = v10) | ~ contains_pq(v7, v9) | contains_pq(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (removemin_pq_res(v7, v8) = v9) | ~ issmallestelement_pq(v7, v8) | ~ contains_pq(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (findmin_pq_res(v7, v8) = v9) | ~ issmallestelement_pq(v7, v8) | ~ contains_pq(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (findmin_pq_eff(v7, v8) = v9) | ~ issmallestelement_pq(v7, v8) | ~ contains_pq(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (i(v9) = v8) | ~ (i(v9) = v7)) & ! [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 | ~ (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] : ( ~ (i(v7) = v9) | ~ pi_remove(v7, v8) | pi_sharp_remove(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (i(v7) = v9) | ~ pi_sharp_remove(v9, v8) | pi_remove(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (i(v7) = v8) | ~ pi_sharp_find_min(v8, v9) | pi_removemin(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (i(v7) = v8) | ~ pi_sharp_find_min(v8, v9) | pi_find_min(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, v8, bad) = v9) | ~ ok(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, create_slb, v8) = v9) | i(v9) = create_pq) & ! [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)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, create_slb, v8) = v9) | ? [v10] : (triple(v7, create_slb, bad) = v10 & findmin_cpq_eff(v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (removemin_cpq_eff(v8) = v9) | ~ succ_cpq(v7, v8) | succ_cpq(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (findmin_cpq_eff(v8) = v9) | ~ succ_cpq(v7, v8) | succ_cpq(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (removemin_pq_eff(v7, v8) = v9) | ~ issmallestelement_pq(v7, v8) | ~ contains_pq(v7, v8) | remove_pq(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (remove_pq(v7, v8) = v9) | ~ issmallestelement_pq(v7, v8) | ~ contains_pq(v7, v8) | removemin_pq_eff(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (insert_pq(v7, v8) = v9) | contains_pq(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (insert_pq(v7, v8) = v9) | isnonempty_pq(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ issmallestelement_pq(v7, v8) | ~ contains_pq(v7, v9) | less_than(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ less_than(v8, v9) | ~ less_than(v7, v8) | less_than(v7, v9)) & ! [v7] : ! [v8] : (v8 = create_slb | ~ (update_slb(create_slb, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (i(v7) = v8) | ~ pi_removemin(v7) | ? [v9] : pi_sharp_find_min(v8, v9)) & ! [v7] : ! [v8] : ( ~ (i(v7) = v8) | ~ pi_find_min(v7) | ? [v9] : pi_sharp_find_min(v8, v9)) & ! [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] : ( ~ (removemin_cpq_eff(v7) = v8) | ? [v9] : ? [v10] : (findmin_cpq_res(v7) = v10 & findmin_cpq_eff(v7) = v9 & remove_cpq(v9, v10) = v8)) & ! [v7] : ! [v8] : ( ~ pi_sharp_removemin(v7, v8) | issmallestelement_pq(v7, v8)) & ! [v7] : ! [v8] : ( ~ pi_sharp_removemin(v7, v8) | contains_pq(v7, v8)) & ! [v7] : ! [v8] : ( ~ pi_sharp_find_min(v7, v8) | issmallestelement_pq(v7, v8)) & ! [v7] : ! [v8] : ( ~ pi_sharp_find_min(v7, v8) | contains_pq(v7, v8)) & ! [v7] : ! [v8] : ( ~ pi_sharp_remove(v7, v8) | contains_pq(v7, v8)) & ! [v7] : ! [v8] : ( ~ ok(v8) | ~ check_cpq(v8) | ~ succ_cpq(v7, v8) | phi(v7)) & ! [v7] : ! [v8] : ~ pair_in_list(create_slb, v7, v8) & ! [v7] : ! [v8] : ( ~ issmallestelement_pq(v7, v8) | ~ contains_pq(v7, v8) | pi_sharp_removemin(v7, v8)) & ! [v7] : ! [v8] : ( ~ issmallestelement_pq(v7, v8) | ~ contains_pq(v7, v8) | pi_sharp_find_min(v7, v8)) & ! [v7] : ! [v8] : ( ~ contains_pq(v7, v8) | pi_sharp_remove(v7, v8)) & ! [v7] : ! [v8] : ( ~ strictly_less_than(v7, v8) | ~ less_than(v8, v7)) & ! [v7] : ! [v8] : ( ~ strictly_less_than(v7, v8) | less_than(v7, v8)) & ! [v7] : ! [v8] : ( ~ less_than(v7, v8) | strictly_less_than(v7, v8) | less_than(v8, v7)) & ! [v7] : ( ~ phi(v7) | ? [v8] : (ok(v8) & check_cpq(v8) & succ_cpq(v7, v8))) & ! [v7] : ~ contains_slb(create_slb, v7) & ! [v7] : ~ contains_pq(create_pq, v7) & ? [v7] : ? [v8] : (issmallestelement_pq(v7, v8) | ? [v9] : (contains_pq(v7, v9) & ~ less_than(v8, v9))) & ? [v7] : ? [v8] : (less_than(v8, v7) | less_than(v7, v8)) & ? [v7] : succ_cpq(v7, v7) & ? [v7] : less_than(v7, v7) & ? [v7] : less_than(bottom, v7)) % 6.58/2.09 | 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: % 6.58/2.09 | (1) i(all_0_3_3) = all_0_1_1 & findmin_cpq_res(all_0_3_3) = all_0_0_0 & triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_3_3 & findmin_cpq_eff(all_0_3_3) = all_0_2_2 & phi(all_0_2_2) & ~ pi_sharp_find_min(all_0_1_1, all_0_0_0) & ~ isnonempty_slb(create_slb) & ~ isnonempty_pq(create_pq) & ! [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) | ~ check_cpq(v7) | ~ strictly_less_than(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ less_than(v4, v3) | ? [v8] : (triple(v0, v1, v2) = v8 & ( ~ check_cpq(v8) | check_cpq(v7)) & ( ~ check_cpq(v7) | check_cpq(v8)))) & ! [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] : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | lookup_slb(v0, v2) = v6) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ~ contains_slb(v1, v3) | ? [v7] : ? [v8] : ? [v9] : (triple(v0, v1, v2) = v8 & remove_cpq(v8, v3) = v9 & lookup_slb(v1, v3) = v7 & (v9 = v6 | ~ less_than(v7, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ strictly_less_than(v3, v2) | ? [v7] : ? [v8] : (update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v0, v2, v4) | pair_in_list(v6, v2, v4)) & ! [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] : (v2 = v1 | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v5, v2) | contains_slb(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : (triple(v0, v1, v2) = v7 & findmin_cpq_eff(v7) = v8 & lookup_slb(v1, v3) = v6 & (v8 = v5 | ~ less_than(v6, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, v2) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ less_than(v6, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, bad) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ strictly_less_than(v3, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | triple(v0, v1, bad) = v5 | contains_slb(v1, v3)) & ! [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] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | ? [v5] : (remove_pq(v0, v2) = v5 & insert_pq(v5, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v0, v2) = v3) | ~ (insert_pq(v3, v1) = v4) | ~ contains_pq(v0, v2) | ? [v5] : (remove_pq(v5, v2) = v4 & insert_pq(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] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : (insert_pq(v5, v1) = v4 & insert_pq(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v1) = v4) | ~ (insert_pq(v0, v2) = v3) | ? [v5] : (insert_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (remove_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v3, v2) | contains_pq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3)) & ! [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 | ~ (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 | ~ (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 | ~ (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 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) & ! [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, v2) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ less_than(v5, v4)))) & ! [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 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ strictly_less_than(v4, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v4 & triple(v0, v6, bad) = v7 & findmin_cpq_eff(v3) = v5 & update_slb(v1, v4) = v6 & (v7 = v5 | contains_slb(v1, v4)))) & ! [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] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (i(v3) = v5 & findmin_cpq_res(v3) = v6 & findmin_cpq_eff(v3) = v4 & ( ~ phi(v4) | issmallestelement_pq(v5, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (i(v3) = v5 & findmin_cpq_res(v3) = v6 & findmin_cpq_eff(v3) = v4 & ( ~ phi(v4) | contains_pq(v5, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | contains_pq(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [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 | ~ (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] : ( ~ (i(v0) = v2) | ~ pi_remove(v0, v1) | pi_sharp_remove(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_sharp_remove(v2, v1) | pi_remove(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_removemin(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_find_min(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq) & ! [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)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | remove_pq(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (remove_pq(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | removemin_pq_eff(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | contains_pq(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v2) | less_than(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2)) & ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_removemin(v0) | ? [v2] : pi_sharp_find_min(v1, v2)) & ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_find_min(v0) | ? [v2] : pi_sharp_find_min(v1, v2)) & ! [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] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | issmallestelement_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | contains_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | issmallestelement_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | contains_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_remove(v0, v1) | contains_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ ok(v1) | ~ check_cpq(v1) | ~ succ_cpq(v0, v1) | phi(v0)) & ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1) & ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_removemin(v0, v1)) & ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_find_min(v0, v1)) & ! [v0] : ! [v1] : ( ~ contains_pq(v0, v1) | pi_sharp_remove(v0, v1)) & ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0)) & ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1)) & ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0)) & ! [v0] : ( ~ phi(v0) | ? [v1] : (ok(v1) & check_cpq(v1) & succ_cpq(v0, v1))) & ! [v0] : ~ contains_slb(create_slb, v0) & ! [v0] : ~ contains_pq(create_pq, v0) & ? [v0] : ? [v1] : (issmallestelement_pq(v0, v1) | ? [v2] : (contains_pq(v0, v2) & ~ less_than(v1, v2))) & ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1)) & ? [v0] : succ_cpq(v0, v0) & ? [v0] : less_than(v0, v0) & ? [v0] : less_than(bottom, v0) % 6.58/2.11 | % 6.58/2.11 | Applying alpha-rule on (1) yields: % 6.58/2.11 | (2) ! [v0] : ~ contains_slb(create_slb, v0) % 6.58/2.11 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) % 6.58/2.11 | (4) ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | contains_pq(v0, v1)) % 6.58/2.12 | (5) findmin_cpq_eff(all_0_3_3) = all_0_2_2 % 6.58/2.12 | (6) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_find_min(v0) | ? [v2] : pi_sharp_find_min(v1, v2)) % 6.58/2.12 | (7) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1) % 6.58/2.12 | (8) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) % 6.58/2.12 | (9) ~ pi_sharp_find_min(all_0_1_1, all_0_0_0) % 6.58/2.12 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2)) % 6.77/2.12 | (11) phi(all_0_2_2) % 6.77/2.12 | (12) ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0)) % 6.77/2.12 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) % 6.77/2.12 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, v2) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ less_than(v6, v3)))) % 6.77/2.12 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2)) % 6.77/2.12 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : (insert_pq(v5, v1) = v4 & insert_pq(v0, v2) = v5)) % 6.77/2.12 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3)) % 6.77/2.12 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ strictly_less_than(v3, v2) | ? [v7] : ? [v8] : (update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6)) % 6.77/2.12 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4)) % 6.77/2.12 | (20) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) % 6.77/2.12 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 6.77/2.12 | (22) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) % 6.77/2.12 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) % 6.77/2.12 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v3, v2) | contains_pq(v0, v2)) % 6.77/2.12 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) % 6.77/2.12 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v0, v2, v4) | pair_in_list(v6, v2, v4)) % 6.77/2.12 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_find_min(v0)) % 6.77/2.12 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) % 6.77/2.12 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v2) | less_than(v1, v2)) % 6.77/2.12 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) % 6.77/2.12 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : (triple(v0, v1, v2) = v7 & findmin_cpq_eff(v7) = v8 & lookup_slb(v1, v3) = v6 & (v8 = v5 | ~ less_than(v6, v3)))) % 6.77/2.12 | (32) ? [v0] : succ_cpq(v0, v0) % 6.77/2.12 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq) % 6.77/2.13 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) % 6.77/2.13 | (35) ! [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)) % 6.77/2.13 | (36) ! [v0] : ~ contains_pq(create_pq, v0) % 6.77/2.13 | (37) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1)) % 6.77/2.13 | (38) ? [v0] : less_than(v0, v0) % 6.77/2.13 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v0, v2) = v3) | ~ (insert_pq(v3, v1) = v4) | ~ contains_pq(v0, v2) | ? [v5] : (remove_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5)) % 6.77/2.13 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) % 6.77/2.13 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0)) % 6.77/2.13 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v1) = v4) | ~ (insert_pq(v0, v2) = v3) | ? [v5] : (insert_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5)) % 6.77/2.13 | (43) i(all_0_3_3) = all_0_1_1 % 6.77/2.13 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) % 6.77/2.13 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) % 6.77/2.13 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) % 6.77/2.13 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | triple(v0, v1, bad) = v5 | contains_slb(v1, v3)) % 6.77/2.13 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1)) % 6.77/2.13 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | contains_pq(v3, v2)) % 6.77/2.13 | (50) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_removemin(v0) | ? [v2] : pi_sharp_find_min(v1, v2)) % 6.77/2.13 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) % 6.77/2.13 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2)) % 6.77/2.13 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) % 6.77/2.13 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | contains_pq(v2, v1)) % 6.77/2.13 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 6.77/2.13 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2)) % 6.77/2.13 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (remove_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2)) % 6.77/2.13 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4)) % 6.77/2.13 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ less_than(v4, v3) | ? [v8] : (triple(v0, v1, v2) = v8 & ( ~ check_cpq(v8) | check_cpq(v7)) & ( ~ check_cpq(v7) | check_cpq(v8)))) % 6.77/2.13 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2)) % 6.77/2.13 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0)) % 6.77/2.13 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6)) % 6.77/2.13 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | lookup_slb(v0, v2) = v6) % 6.77/2.13 | (64) ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1) % 6.77/2.13 | (65) ? [v0] : ? [v1] : (issmallestelement_pq(v0, v1) | ? [v2] : (contains_pq(v0, v2) & ~ less_than(v1, v2))) % 6.77/2.13 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 6.77/2.13 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_sharp_remove(v2, v1) | pi_remove(v0, v1)) % 6.77/2.13 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_remove(v0, v1) | pi_sharp_remove(v2, v1)) % 6.77/2.13 | (69) ! [v0] : ( ~ phi(v0) | ? [v1] : (ok(v1) & check_cpq(v1) & succ_cpq(v0, v1))) % 6.77/2.13 | (70) ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | contains_pq(v0, v1)) % 6.77/2.13 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0)) % 6.77/2.13 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) % 6.77/2.13 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v5, v2) | contains_slb(v0, v2)) % 6.77/2.13 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6)) % 6.86/2.13 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (remove_pq(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | removemin_pq_eff(v0, v1) = v2) % 6.86/2.13 | (76) findmin_cpq_res(all_0_3_3) = all_0_0_0 % 6.86/2.13 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2)) % 6.86/2.13 | (78) ! [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, v2) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ less_than(v5, v4)))) % 6.86/2.14 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ~ contains_slb(v1, v3) | ? [v7] : ? [v8] : ? [v9] : (triple(v0, v1, v2) = v8 & remove_cpq(v8, v3) = v9 & lookup_slb(v1, v3) = v7 & (v9 = v6 | ~ less_than(v7, v3)))) % 6.86/2.14 | (80) ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_find_min(v0, v1)) % 6.86/2.14 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 6.86/2.14 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (i(v3) = v5 & findmin_cpq_res(v3) = v6 & findmin_cpq_eff(v3) = v4 & ( ~ phi(v4) | contains_pq(v5, v6)))) % 6.86/2.14 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) % 6.86/2.14 | (84) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0)) % 6.86/2.14 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v4 & triple(v0, v6, bad) = v7 & findmin_cpq_eff(v3) = v5 & update_slb(v1, v4) = v6 & (v7 = v5 | contains_slb(v1, v4)))) % 6.86/2.14 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 6.86/2.14 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4)) % 6.86/2.14 | (88) triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_3_3 % 6.86/2.14 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7)) % 6.86/2.14 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3)) % 6.86/2.14 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3)) % 6.86/2.14 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ check_cpq(v7) | ~ strictly_less_than(v3, v4)) % 6.86/2.14 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 6.86/2.14 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | remove_pq(v0, v1) = v2) % 6.86/2.14 | (95) ! [v0] : ! [v1] : ( ~ ok(v1) | ~ check_cpq(v1) | ~ succ_cpq(v0, v1) | phi(v0)) % 6.86/2.14 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) % 6.86/2.14 | (97) ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_removemin(v0, v1)) % 6.86/2.14 | (98) ! [v0] : ! [v1] : ( ~ contains_pq(v0, v1) | pi_sharp_remove(v0, v1)) % 6.86/2.14 | (99) ! [v0] : ! [v1] : ( ~ pi_sharp_remove(v0, v1) | contains_pq(v0, v1)) % 6.86/2.14 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) % 6.86/2.14 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3) % 6.86/2.14 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4)) % 6.86/2.14 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 6.86/2.14 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) % 6.86/2.14 | (105) ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | issmallestelement_pq(v0, v1)) % 6.86/2.14 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_removemin(v0)) % 6.86/2.14 | (107) ~ isnonempty_pq(create_pq) % 6.86/2.14 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 6.86/2.14 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7)) % 6.86/2.14 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (i(v3) = v5 & findmin_cpq_res(v3) = v6 & findmin_cpq_eff(v3) = v4 & ( ~ phi(v4) | issmallestelement_pq(v5, v6)))) % 6.86/2.14 | (111) ! [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] : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = v8)) % 6.86/2.14 | (112) ? [v0] : less_than(bottom, v0) % 6.86/2.14 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | ? [v5] : (remove_pq(v0, v2) = v5 & insert_pq(v5, v1) = v4)) % 6.86/2.14 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0)) % 6.86/2.14 | (115) ! [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)) % 6.86/2.14 | (116) ~ isnonempty_slb(create_slb) % 6.86/2.14 | (117) ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1)) % 6.86/2.14 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) % 6.86/2.15 | (119) ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | issmallestelement_pq(v0, v1)) % 6.86/2.15 | (120) ! [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 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ strictly_less_than(v4, v5)))) % 6.86/2.15 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0)) % 6.86/2.15 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) % 6.86/2.15 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, bad) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ strictly_less_than(v3, v6)))) % 6.86/2.15 | % 6.86/2.15 | Instantiating formula (110) with 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_3_3, yields: % 6.86/2.15 | (124) ? [v0] : ? [v1] : ? [v2] : (i(all_0_3_3) = v1 & findmin_cpq_res(all_0_3_3) = v2 & findmin_cpq_eff(all_0_3_3) = v0 & ( ~ phi(v0) | issmallestelement_pq(v1, v2))) % 6.86/2.15 | % 6.86/2.15 | Instantiating formula (82) with 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_3_3, yields: % 6.86/2.15 | (125) ? [v0] : ? [v1] : ? [v2] : (i(all_0_3_3) = v1 & findmin_cpq_res(all_0_3_3) = v2 & findmin_cpq_eff(all_0_3_3) = v0 & ( ~ phi(v0) | contains_pq(v1, v2))) % 6.86/2.15 | % 6.86/2.15 | Instantiating (125) with all_19_0_15, all_19_1_16, all_19_2_17 yields: % 6.86/2.15 | (126) i(all_0_3_3) = all_19_1_16 & findmin_cpq_res(all_0_3_3) = all_19_0_15 & findmin_cpq_eff(all_0_3_3) = all_19_2_17 & ( ~ phi(all_19_2_17) | contains_pq(all_19_1_16, all_19_0_15)) % 6.86/2.15 | % 6.86/2.15 | Applying alpha-rule on (126) yields: % 6.86/2.15 | (127) i(all_0_3_3) = all_19_1_16 % 6.86/2.15 | (128) findmin_cpq_res(all_0_3_3) = all_19_0_15 % 6.86/2.15 | (129) findmin_cpq_eff(all_0_3_3) = all_19_2_17 % 6.86/2.15 | (130) ~ phi(all_19_2_17) | contains_pq(all_19_1_16, all_19_0_15) % 6.86/2.15 | % 6.86/2.15 | Instantiating (124) with all_21_0_18, all_21_1_19, all_21_2_20 yields: % 6.86/2.15 | (131) i(all_0_3_3) = all_21_1_19 & findmin_cpq_res(all_0_3_3) = all_21_0_18 & findmin_cpq_eff(all_0_3_3) = all_21_2_20 & ( ~ phi(all_21_2_20) | issmallestelement_pq(all_21_1_19, all_21_0_18)) % 6.86/2.15 | % 6.86/2.15 | Applying alpha-rule on (131) yields: % 6.86/2.15 | (132) i(all_0_3_3) = all_21_1_19 % 6.86/2.15 | (133) findmin_cpq_res(all_0_3_3) = all_21_0_18 % 6.86/2.15 | (134) findmin_cpq_eff(all_0_3_3) = all_21_2_20 % 6.86/2.15 | (135) ~ phi(all_21_2_20) | issmallestelement_pq(all_21_1_19, all_21_0_18) % 6.86/2.15 | % 6.86/2.15 | Instantiating formula (96) with all_0_3_3, all_21_1_19, all_0_1_1 and discharging atoms i(all_0_3_3) = all_21_1_19, i(all_0_3_3) = all_0_1_1, yields: % 6.86/2.15 | (136) all_21_1_19 = all_0_1_1 % 6.86/2.15 | % 6.86/2.15 | Instantiating formula (96) with all_0_3_3, all_19_1_16, all_21_1_19 and discharging atoms i(all_0_3_3) = all_21_1_19, i(all_0_3_3) = all_19_1_16, yields: % 6.86/2.15 | (137) all_21_1_19 = all_19_1_16 % 6.86/2.15 | % 6.86/2.15 | Instantiating formula (51) with all_0_3_3, all_21_0_18, all_0_0_0 and discharging atoms findmin_cpq_res(all_0_3_3) = all_21_0_18, findmin_cpq_res(all_0_3_3) = all_0_0_0, yields: % 6.86/2.15 | (138) all_21_0_18 = all_0_0_0 % 6.86/2.15 | % 6.86/2.15 | Instantiating formula (51) with all_0_3_3, all_19_0_15, all_21_0_18 and discharging atoms findmin_cpq_res(all_0_3_3) = all_21_0_18, findmin_cpq_res(all_0_3_3) = all_19_0_15, yields: % 6.86/2.15 | (139) all_21_0_18 = all_19_0_15 % 6.86/2.15 | % 6.86/2.15 | Instantiating formula (55) with all_0_3_3, all_21_2_20, all_0_2_2 and discharging atoms findmin_cpq_eff(all_0_3_3) = all_21_2_20, findmin_cpq_eff(all_0_3_3) = all_0_2_2, yields: % 6.86/2.15 | (140) all_21_2_20 = all_0_2_2 % 6.86/2.15 | % 6.86/2.15 | Instantiating formula (55) with all_0_3_3, all_19_2_17, all_21_2_20 and discharging atoms findmin_cpq_eff(all_0_3_3) = all_21_2_20, findmin_cpq_eff(all_0_3_3) = all_19_2_17, yields: % 6.86/2.15 | (141) all_21_2_20 = all_19_2_17 % 6.86/2.15 | % 6.86/2.15 | Combining equations (138,139) yields a new equation: % 6.86/2.15 | (142) all_19_0_15 = all_0_0_0 % 6.86/2.15 | % 6.86/2.15 | Combining equations (137,136) yields a new equation: % 6.86/2.15 | (143) all_19_1_16 = all_0_1_1 % 6.86/2.15 | % 6.86/2.15 | Simplifying 143 yields: % 6.86/2.15 | (144) all_19_1_16 = all_0_1_1 % 6.86/2.15 | % 6.86/2.15 | Combining equations (141,140) yields a new equation: % 6.86/2.15 | (145) all_19_2_17 = all_0_2_2 % 6.86/2.15 | % 6.86/2.15 | Simplifying 145 yields: % 6.86/2.15 | (146) all_19_2_17 = all_0_2_2 % 6.86/2.15 | % 6.86/2.15 | Combining equations (142,139) yields a new equation: % 6.86/2.15 | (138) all_21_0_18 = all_0_0_0 % 6.86/2.15 | % 6.86/2.15 +-Applying beta-rule and splitting (135), into two cases. % 6.86/2.15 |-Branch one: % 6.86/2.15 | (148) ~ phi(all_21_2_20) % 6.86/2.15 | % 6.86/2.15 | From (140) and (148) follows: % 6.86/2.15 | (149) ~ phi(all_0_2_2) % 6.86/2.15 | % 6.86/2.15 | Using (11) and (149) yields: % 6.86/2.15 | (150) $false % 6.86/2.15 | % 6.86/2.15 |-The branch is then unsatisfiable % 6.86/2.15 |-Branch two: % 6.86/2.15 | (151) phi(all_21_2_20) % 6.86/2.15 | (152) issmallestelement_pq(all_21_1_19, all_21_0_18) % 6.86/2.15 | % 6.86/2.15 | From (140) and (151) follows: % 6.86/2.15 | (11) phi(all_0_2_2) % 6.86/2.15 | % 6.86/2.15 | From (136)(138) and (152) follows: % 6.86/2.15 | (154) issmallestelement_pq(all_0_1_1, all_0_0_0) % 6.86/2.15 | % 6.86/2.15 +-Applying beta-rule and splitting (130), into two cases. % 6.86/2.15 |-Branch one: % 6.86/2.15 | (155) contains_pq(all_19_1_16, all_19_0_15) % 6.86/2.15 | % 6.86/2.15 | From (144)(142) and (155) follows: % 6.86/2.15 | (156) contains_pq(all_0_1_1, all_0_0_0) % 6.86/2.15 | % 6.86/2.15 | Instantiating formula (80) with all_0_0_0, all_0_1_1 and discharging atoms issmallestelement_pq(all_0_1_1, all_0_0_0), contains_pq(all_0_1_1, all_0_0_0), ~ pi_sharp_find_min(all_0_1_1, all_0_0_0), yields: % 6.86/2.15 | (150) $false % 6.86/2.15 | % 6.86/2.15 |-The branch is then unsatisfiable % 6.86/2.15 |-Branch two: % 6.86/2.15 | (158) ~ contains_pq(all_19_1_16, all_19_0_15) % 6.86/2.15 | (159) ~ phi(all_19_2_17) % 6.86/2.15 | % 6.86/2.15 | From (146) and (159) follows: % 6.86/2.15 | (149) ~ phi(all_0_2_2) % 6.86/2.15 | % 6.86/2.16 | Using (11) and (149) yields: % 6.86/2.16 | (150) $false % 6.86/2.16 | % 6.86/2.16 |-The branch is then unsatisfiable % 6.86/2.16 % SZS output end Proof for theBenchmark % 6.86/2.16 % 6.86/2.16 1523ms %------------------------------------------------------------------------------