%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV372+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 12.29s 3.48s % Output : Proof 16.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SWV372+1 : TPTP v8.1.0. Released v3.3.0. % 0.00/0.11 % Command : ePrincess-casc -timeout=%d %s % 0.10/0.30 % Computer : n032.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 600 % 0.10/0.30 % DateTime : Tue Jun 14 15:01:43 EDT 2022 % 0.10/0.31 % CPUTime : % 0.16/0.50 ____ _ % 0.16/0.50 ___ / __ \_____(_)___ ________ __________ % 0.16/0.50 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.16/0.50 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.16/0.50 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.16/0.50 % 0.16/0.50 A Theorem Prover for First-Order Logic % 0.16/0.50 (ePrincess v.1.0) % 0.16/0.50 % 0.16/0.50 (c) Philipp Rümmer, 2009-2015 % 0.16/0.50 (c) Peter Backeman, 2014-2015 % 0.16/0.50 (contributions by Angelo Brillout, Peter Baumgartner) % 0.16/0.50 Free software under GNU Lesser General Public License (LGPL). % 0.16/0.50 Bug reports to peter@backeman.se % 0.16/0.50 % 0.16/0.50 For more information, visit http://user.uu.se/~petba168/breu/ % 0.16/0.50 % 0.16/0.50 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.55 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.76/0.90 Prover 0: Preprocessing ... % 3.44/1.33 Prover 0: Warning: ignoring some quantifiers % 3.44/1.37 Prover 0: Constructing countermodel ... % 12.29/3.48 Prover 0: proved (2926ms) % 12.29/3.48 % 12.29/3.48 No countermodel exists, formula is valid % 12.29/3.48 % SZS status Theorem for theBenchmark % 12.29/3.48 % 12.29/3.48 Generating proof ... Warning: ignoring some quantifiers % 15.38/4.16 found it (size 134) % 15.38/4.16 % 15.38/4.16 % SZS output start Proof for theBenchmark % 15.38/4.16 Assumed formulas after preprocessing and simplification: % 15.38/4.16 | (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) & ~ isnonempty_slb(create_slb) & ~ contains_pq(v5, v6) & ~ 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_cpq(v11, v10) | ? [v12] : (i(v11) = v12 & contains_pq(v12, 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] : ! [v11] : ( ~ (triple(v8, v9, v10) = v11) | contains_cpq(v11, v7) | ? [v12] : (i(v11) = v12 & ~ contains_pq(v12, v7))) & ! [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) | ~ phi(v10) | ok(v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v7, v8, v9) = v10) | ? [v11] : ? [v12] : (findmin_cpq_res(v10) = v11 & findmin_cpq_eff(v10) = v12 & ( ~ ok(v12) | contains_cpq(v10, v11)))) & ! [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)) % 15.68/4.24 | 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: % 15.68/4.24 | (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) & ~ isnonempty_slb(create_slb) & ~ contains_pq(all_0_1_1, all_0_0_0) & ~ 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_cpq(v4, v3) | ? [v5] : (i(v4) = v5 & contains_pq(v5, 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] : ! [v4] : ( ~ (triple(v1, v2, v3) = v4) | contains_cpq(v4, v0) | ? [v5] : (i(v4) = v5 & ~ contains_pq(v5, v0))) & ! [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) | ~ phi(v3) | ok(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (findmin_cpq_res(v3) = v4 & findmin_cpq_eff(v3) = v5 & ( ~ ok(v5) | contains_cpq(v3, v4)))) & ! [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) % 15.68/4.27 | % 15.68/4.27 | Applying alpha-rule on (1) yields: % 15.68/4.27 | (2) ! [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)))) % 15.68/4.27 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3)) % 15.68/4.27 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3)) % 15.68/4.27 | (5) ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | contains_pq(v0, v1)) % 15.68/4.27 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq) % 15.68/4.27 | (7) ! [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)))) % 15.68/4.27 | (8) ! [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)) % 15.68/4.27 | (9) ! [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) % 15.68/4.27 | (10) ! [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)) % 15.68/4.27 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3) % 15.68/4.27 | (12) ! [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)))) % 15.68/4.27 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4)) % 15.68/4.27 | (14) ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0)) % 15.68/4.27 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) % 15.68/4.27 | (16) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) % 15.68/4.27 | (17) ! [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)) % 15.68/4.27 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 15.68/4.27 | (19) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v1, v2, v3) = v4) | contains_cpq(v4, v0) | ? [v5] : (i(v4) = v5 & ~ contains_pq(v5, v0))) % 15.68/4.27 | (20) ! [v0] : ~ contains_pq(create_pq, v0) % 15.68/4.27 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) % 15.68/4.27 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 15.68/4.28 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) % 15.68/4.28 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) % 15.68/4.28 | (25) ! [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)) % 15.68/4.28 | (26) ! [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)) % 15.68/4.28 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2)) % 15.68/4.28 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_find_min(v0)) % 15.68/4.28 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) % 15.68/4.28 | (30) ? [v0] : less_than(bottom, v0) % 15.68/4.28 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) % 15.68/4.28 | (32) ~ isnonempty_slb(create_slb) % 15.68/4.28 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (remove_pq(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | removemin_pq_eff(v0, v1) = v2) % 15.68/4.28 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) % 15.68/4.28 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v2) | less_than(v1, v2)) % 15.68/4.28 | (36) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) % 15.68/4.28 | (37) ! [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)))) % 15.68/4.28 | (38) triple(all_0_6_6, all_0_5_5, all_0_4_4) = all_0_3_3 % 16.17/4.28 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (remove_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2)) % 16.17/4.28 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) % 16.17/4.28 | (41) ! [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)))) % 16.17/4.28 | (42) ? [v0] : succ_cpq(v0, v0) % 16.17/4.28 | (43) ! [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)) % 16.17/4.28 | (44) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1)) % 16.17/4.28 | (45) ? [v0] : less_than(v0, v0) % 16.17/4.28 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | ? [v5] : (i(v4) = v5 & contains_pq(v5, v3))) % 16.17/4.28 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 16.17/4.28 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (findmin_cpq_res(v3) = v4 & findmin_cpq_eff(v3) = v5 & ( ~ ok(v5) | contains_cpq(v3, v4)))) % 16.17/4.29 | (49) ! [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)) % 16.17/4.29 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4)) % 16.17/4.29 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 16.17/4.29 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) % 16.17/4.29 | (53) ~ contains_pq(all_0_1_1, all_0_0_0) % 16.17/4.29 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) % 16.17/4.29 | (55) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_find_min(v0) | ? [v2] : pi_sharp_find_min(v1, v2)) % 16.17/4.29 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2)) % 16.17/4.29 | (57) i(all_0_3_3) = all_0_1_1 % 16.17/4.29 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_sharp_remove(v2, v1) | pi_remove(v0, v1)) % 16.17/4.29 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_remove(v0, v1) | pi_sharp_remove(v2, v1)) % 16.17/4.29 | (60) phi(all_0_2_2) % 16.17/4.29 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3)) % 16.17/4.29 | (62) ! [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)))) % 16.17/4.29 | (63) ? [v0] : ? [v1] : (issmallestelement_pq(v0, v1) | ? [v2] : (contains_pq(v0, v2) & ~ less_than(v1, v2))) % 16.17/4.29 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) % 16.17/4.29 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) % 16.17/4.29 | (66) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) % 16.17/4.29 | (67) ! [v0] : ( ~ phi(v0) | ? [v1] : (ok(v1) & check_cpq(v1) & succ_cpq(v0, v1))) % 16.17/4.29 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 16.17/4.29 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0)) % 16.17/4.29 | (70) ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | contains_pq(v0, v1)) % 16.17/4.29 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | remove_pq(v0, v1) = v2) % 16.17/4.29 | (72) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1) % 16.17/4.29 | (73) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) % 16.17/4.29 | (74) ! [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)) % 16.17/4.29 | (75) ! [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)) % 16.17/4.29 | (76) ! [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)) % 16.17/4.29 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v3, v2) | contains_pq(v0, v2)) % 16.17/4.29 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) % 16.17/4.30 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0)) % 16.17/4.30 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0)) % 16.17/4.30 | (81) ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_find_min(v0, v1)) % 16.17/4.30 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) % 16.17/4.30 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2)) % 16.17/4.30 | (84) ! [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)) % 16.17/4.30 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) % 16.17/4.30 | (86) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0)) % 16.17/4.30 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2)) % 16.17/4.30 | (88) ! [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)) % 16.17/4.30 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) % 16.17/4.30 | (90) findmin_cpq_res(all_0_3_3) = all_0_0_0 % 16.17/4.30 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 16.17/4.30 | (92) ! [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)) % 16.17/4.30 | (93) ! [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)) % 16.17/4.30 | (94) ! [v0] : ! [v1] : ( ~ ok(v1) | ~ check_cpq(v1) | ~ succ_cpq(v0, v1) | phi(v0)) % 16.17/4.30 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 16.17/4.30 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2)) % 16.25/4.30 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) % 16.25/4.30 | (98) ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_removemin(v0, v1)) % 16.25/4.30 | (99) ! [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)) % 16.25/4.30 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | contains_pq(v3, v2)) % 16.25/4.30 | (101) ! [v0] : ! [v1] : ( ~ contains_pq(v0, v1) | pi_sharp_remove(v0, v1)) % 16.25/4.30 | (102) ! [v0] : ! [v1] : ( ~ pi_sharp_remove(v0, v1) | contains_pq(v0, v1)) % 16.25/4.30 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0)) % 16.25/4.30 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1)) % 16.25/4.30 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | contains_pq(v2, v1)) % 16.25/4.30 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2)) % 16.25/4.30 | (107) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_removemin(v0) | ? [v2] : pi_sharp_find_min(v1, v2)) % 16.25/4.30 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ~ phi(v3) | ok(v3)) % 16.25/4.30 | (109) ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | issmallestelement_pq(v0, v1)) % 16.25/4.30 | (110) ! [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)) % 16.25/4.30 | (111) ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1) % 16.25/4.30 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_removemin(v0)) % 16.25/4.31 | (113) ! [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)) % 16.25/4.31 | (114) ~ isnonempty_pq(create_pq) % 16.25/4.31 | (115) ! [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)) % 16.25/4.31 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0)) % 16.25/4.31 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) % 16.25/4.31 | (118) ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1)) % 16.25/4.31 | (119) ! [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)))) % 16.25/4.31 | (120) ! [v0] : ~ contains_slb(create_slb, v0) % 16.25/4.31 | (121) ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | issmallestelement_pq(v0, v1)) % 16.25/4.31 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 16.25/4.31 | (123) ! [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)))) % 16.25/4.31 | (124) findmin_cpq_eff(all_0_3_3) = all_0_2_2 % 16.25/4.31 | (125) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) % 16.25/4.31 | % 16.25/4.31 | Instantiating (19) with all_11_0_14 yields: % 16.25/4.31 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | contains_cpq(v3, all_11_0_14) | ? [v4] : (i(v3) = v4 & ~ contains_pq(v4, all_11_0_14))) % 16.25/4.31 | % 16.25/4.31 | Instantiating formula (41) 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: % 16.25/4.31 | (127) all_0_5_5 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v3, all_0_4_4) = v4 & findmin_cpq_eff(all_0_3_3) = v2 & update_slb(all_0_5_5, v0) = v3 & lookup_slb(all_0_5_5, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_5_5, v0) | ~ less_than(v1, v0))) % 16.25/4.31 | % 16.25/4.31 | Instantiating formula (62) 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: % 16.25/4.31 | (128) all_0_5_5 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v3, bad) = v4 & findmin_cpq_eff(all_0_3_3) = v2 & update_slb(all_0_5_5, v0) = v3 & lookup_slb(all_0_5_5, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_5_5, v0) | ~ strictly_less_than(v0, v1))) % 16.25/4.31 | % 16.25/4.31 | Instantiating formula (123) 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: % 16.25/4.31 | (129) all_0_5_5 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v2, bad) = v3 & findmin_cpq_eff(all_0_3_3) = v1 & update_slb(all_0_5_5, v0) = v2 & (v3 = v1 | contains_slb(all_0_5_5, v0))) % 16.25/4.31 | % 16.25/4.31 | Instantiating formula (50) 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: % 16.25/4.31 | (130) all_0_5_5 = create_slb | ? [v0] : (findmin_cpq_res(all_0_3_3) = v0 & findmin_pqp_res(all_0_6_6) = v0) % 16.25/4.31 | % 16.25/4.31 | Instantiating formula (126) 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: % 16.25/4.31 | (131) contains_cpq(all_0_3_3, all_11_0_14) | ? [v0] : (i(all_0_3_3) = v0 & ~ contains_pq(v0, all_11_0_14)) % 16.25/4.31 | % 16.25/4.31 | Instantiating formula (48) 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: % 16.25/4.31 | (132) ? [v0] : ? [v1] : (findmin_cpq_res(all_0_3_3) = v0 & findmin_cpq_eff(all_0_3_3) = v1 & ( ~ ok(v1) | contains_cpq(all_0_3_3, v0))) % 16.25/4.31 | % 16.25/4.31 | Instantiating (132) with all_21_0_16, all_21_1_17 yields: % 16.25/4.31 | (133) findmin_cpq_res(all_0_3_3) = all_21_1_17 & findmin_cpq_eff(all_0_3_3) = all_21_0_16 & ( ~ ok(all_21_0_16) | contains_cpq(all_0_3_3, all_21_1_17)) % 16.25/4.31 | % 16.25/4.31 | Applying alpha-rule on (133) yields: % 16.25/4.31 | (134) findmin_cpq_res(all_0_3_3) = all_21_1_17 % 16.25/4.31 | (135) findmin_cpq_eff(all_0_3_3) = all_21_0_16 % 16.25/4.31 | (136) ~ ok(all_21_0_16) | contains_cpq(all_0_3_3, all_21_1_17) % 16.25/4.31 | % 16.25/4.31 | Instantiating formula (89) with all_0_3_3, all_21_1_17, all_0_0_0 and discharging atoms findmin_cpq_res(all_0_3_3) = all_21_1_17, findmin_cpq_res(all_0_3_3) = all_0_0_0, yields: % 16.25/4.31 | (137) all_21_1_17 = all_0_0_0 % 16.25/4.31 | % 16.25/4.31 | Instantiating formula (22) with all_0_3_3, all_21_0_16, all_0_2_2 and discharging atoms findmin_cpq_eff(all_0_3_3) = all_21_0_16, findmin_cpq_eff(all_0_3_3) = all_0_2_2, yields: % 16.25/4.31 | (138) all_21_0_16 = all_0_2_2 % 16.25/4.31 | % 16.25/4.31 | From (137) and (134) follows: % 16.25/4.32 | (90) findmin_cpq_res(all_0_3_3) = all_0_0_0 % 16.25/4.32 | % 16.25/4.32 | From (138) and (135) follows: % 16.25/4.32 | (124) findmin_cpq_eff(all_0_3_3) = all_0_2_2 % 16.25/4.32 | % 16.25/4.32 +-Applying beta-rule and splitting (130), into two cases. % 16.25/4.32 |-Branch one: % 16.25/4.32 | (141) all_0_5_5 = create_slb % 16.25/4.32 | % 16.25/4.32 | From (141) and (38) follows: % 16.25/4.32 | (142) triple(all_0_6_6, create_slb, all_0_4_4) = all_0_3_3 % 16.25/4.32 | % 16.25/4.32 | Instantiating formula (21) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms triple(all_0_6_6, create_slb, all_0_4_4) = all_0_3_3, yields: % 16.25/4.32 | (143) ? [v0] : (triple(all_0_6_6, create_slb, bad) = v0 & findmin_cpq_eff(all_0_3_3) = v0) % 16.25/4.32 | % 16.25/4.32 | Instantiating formula (48) with all_0_3_3, all_0_4_4, create_slb, all_0_6_6 and discharging atoms triple(all_0_6_6, create_slb, all_0_4_4) = all_0_3_3, yields: % 16.25/4.32 | (132) ? [v0] : ? [v1] : (findmin_cpq_res(all_0_3_3) = v0 & findmin_cpq_eff(all_0_3_3) = v1 & ( ~ ok(v1) | contains_cpq(all_0_3_3, v0))) % 16.25/4.32 | % 16.25/4.32 | Instantiating (132) with all_61_0_18, all_61_1_19 yields: % 16.25/4.32 | (145) findmin_cpq_res(all_0_3_3) = all_61_1_19 & findmin_cpq_eff(all_0_3_3) = all_61_0_18 & ( ~ ok(all_61_0_18) | contains_cpq(all_0_3_3, all_61_1_19)) % 16.25/4.32 | % 16.25/4.32 | Applying alpha-rule on (145) yields: % 16.25/4.32 | (146) findmin_cpq_res(all_0_3_3) = all_61_1_19 % 16.25/4.32 | (147) findmin_cpq_eff(all_0_3_3) = all_61_0_18 % 16.25/4.32 | (148) ~ ok(all_61_0_18) | contains_cpq(all_0_3_3, all_61_1_19) % 16.25/4.32 | % 16.25/4.32 | Instantiating (143) with all_63_0_20 yields: % 16.25/4.32 | (149) triple(all_0_6_6, create_slb, bad) = all_63_0_20 & findmin_cpq_eff(all_0_3_3) = all_63_0_20 % 16.25/4.32 | % 16.25/4.32 | Applying alpha-rule on (149) yields: % 16.25/4.32 | (150) triple(all_0_6_6, create_slb, bad) = all_63_0_20 % 16.25/4.32 | (151) findmin_cpq_eff(all_0_3_3) = all_63_0_20 % 16.25/4.32 | % 16.25/4.32 | Instantiating formula (22) with all_0_3_3, all_63_0_20, all_0_2_2 and discharging atoms findmin_cpq_eff(all_0_3_3) = all_63_0_20, findmin_cpq_eff(all_0_3_3) = all_0_2_2, yields: % 16.25/4.32 | (152) all_63_0_20 = all_0_2_2 % 16.25/4.32 | % 16.25/4.32 | Instantiating formula (22) with all_0_3_3, all_61_0_18, all_63_0_20 and discharging atoms findmin_cpq_eff(all_0_3_3) = all_63_0_20, findmin_cpq_eff(all_0_3_3) = all_61_0_18, yields: % 16.25/4.32 | (153) all_63_0_20 = all_61_0_18 % 16.25/4.32 | % 16.25/4.32 | Combining equations (152,153) yields a new equation: % 16.25/4.32 | (154) all_61_0_18 = all_0_2_2 % 16.25/4.32 | % 16.25/4.32 | Combining equations (154,153) yields a new equation: % 16.25/4.32 | (152) all_63_0_20 = all_0_2_2 % 16.25/4.32 | % 16.25/4.32 | From (152) and (150) follows: % 16.25/4.32 | (156) triple(all_0_6_6, create_slb, bad) = all_0_2_2 % 16.25/4.32 | % 16.25/4.32 | Instantiating formula (108) with all_0_2_2, bad, create_slb, all_0_6_6 and discharging atoms triple(all_0_6_6, create_slb, bad) = all_0_2_2, phi(all_0_2_2), yields: % 16.25/4.32 | (157) ok(all_0_2_2) % 16.25/4.32 | % 16.25/4.32 +-Applying beta-rule and splitting (136), into two cases. % 16.25/4.32 |-Branch one: % 16.25/4.32 | (158) ~ ok(all_21_0_16) % 16.25/4.32 | % 16.25/4.32 | From (138) and (158) follows: % 16.25/4.32 | (159) ~ ok(all_0_2_2) % 16.25/4.32 | % 16.25/4.32 | Using (157) and (159) yields: % 16.25/4.32 | (160) $false % 16.25/4.32 | % 16.25/4.32 |-The branch is then unsatisfiable % 16.25/4.32 |-Branch two: % 16.25/4.32 | (161) ok(all_21_0_16) % 16.25/4.32 | (162) contains_cpq(all_0_3_3, all_21_1_17) % 16.25/4.32 | % 16.25/4.32 | From (138) and (161) follows: % 16.25/4.32 | (157) ok(all_0_2_2) % 16.25/4.32 | % 16.25/4.32 | Instantiating formula (106) with all_0_2_2, create_slb, all_0_6_6 and discharging atoms triple(all_0_6_6, create_slb, bad) = all_0_2_2, ok(all_0_2_2), yields: % 16.25/4.32 | (160) $false % 16.25/4.32 | % 16.25/4.32 |-The branch is then unsatisfiable % 16.25/4.32 |-Branch two: % 16.25/4.32 | (165) ~ (all_0_5_5 = create_slb) % 16.25/4.32 | (166) ? [v0] : (findmin_cpq_res(all_0_3_3) = v0 & findmin_pqp_res(all_0_6_6) = v0) % 16.25/4.32 | % 16.25/4.32 | Instantiating (166) with all_55_0_24 yields: % 16.25/4.32 | (167) findmin_cpq_res(all_0_3_3) = all_55_0_24 & findmin_pqp_res(all_0_6_6) = all_55_0_24 % 16.25/4.32 | % 16.25/4.32 | Applying alpha-rule on (167) yields: % 16.25/4.32 | (168) findmin_cpq_res(all_0_3_3) = all_55_0_24 % 16.25/4.32 | (169) findmin_pqp_res(all_0_6_6) = all_55_0_24 % 16.25/4.32 | % 16.25/4.32 +-Applying beta-rule and splitting (129), into two cases. % 16.25/4.32 |-Branch one: % 16.25/4.32 | (141) all_0_5_5 = create_slb % 16.25/4.32 | % 16.25/4.32 | Equations (141) can reduce 165 to: % 16.25/4.32 | (171) $false % 16.25/4.32 | % 16.25/4.32 |-The branch is then unsatisfiable % 16.25/4.32 |-Branch two: % 16.25/4.32 | (165) ~ (all_0_5_5 = create_slb) % 16.25/4.32 | (173) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v2, bad) = v3 & findmin_cpq_eff(all_0_3_3) = v1 & update_slb(all_0_5_5, v0) = v2 & (v3 = v1 | contains_slb(all_0_5_5, v0))) % 16.25/4.32 | % 16.25/4.32 | Instantiating (173) with all_61_0_25, all_61_1_26, all_61_2_27, all_61_3_28 yields: % 16.25/4.32 | (174) findmin_pqp_res(all_0_6_6) = all_61_3_28 & triple(all_0_6_6, all_61_1_26, bad) = all_61_0_25 & findmin_cpq_eff(all_0_3_3) = all_61_2_27 & update_slb(all_0_5_5, all_61_3_28) = all_61_1_26 & (all_61_0_25 = all_61_2_27 | contains_slb(all_0_5_5, all_61_3_28)) % 16.25/4.32 | % 16.25/4.32 | Applying alpha-rule on (174) yields: % 16.25/4.32 | (175) findmin_cpq_eff(all_0_3_3) = all_61_2_27 % 16.25/4.32 | (176) all_61_0_25 = all_61_2_27 | contains_slb(all_0_5_5, all_61_3_28) % 16.25/4.32 | (177) triple(all_0_6_6, all_61_1_26, bad) = all_61_0_25 % 16.25/4.32 | (178) update_slb(all_0_5_5, all_61_3_28) = all_61_1_26 % 16.25/4.32 | (179) findmin_pqp_res(all_0_6_6) = all_61_3_28 % 16.25/4.32 | % 16.25/4.32 +-Applying beta-rule and splitting (127), into two cases. % 16.25/4.32 |-Branch one: % 16.25/4.32 | (141) all_0_5_5 = create_slb % 16.25/4.32 | % 16.25/4.32 | Equations (141) can reduce 165 to: % 16.25/4.32 | (171) $false % 16.25/4.32 | % 16.25/4.32 |-The branch is then unsatisfiable % 16.25/4.32 |-Branch two: % 16.25/4.32 | (165) ~ (all_0_5_5 = create_slb) % 16.25/4.32 | (183) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v3, all_0_4_4) = v4 & findmin_cpq_eff(all_0_3_3) = v2 & update_slb(all_0_5_5, v0) = v3 & lookup_slb(all_0_5_5, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_5_5, v0) | ~ less_than(v1, v0))) % 16.25/4.32 | % 16.25/4.33 | Instantiating (183) with all_66_0_29, all_66_1_30, all_66_2_31, all_66_3_32, all_66_4_33 yields: % 16.25/4.33 | (184) findmin_pqp_res(all_0_6_6) = all_66_4_33 & triple(all_0_6_6, all_66_1_30, all_0_4_4) = all_66_0_29 & findmin_cpq_eff(all_0_3_3) = all_66_2_31 & update_slb(all_0_5_5, all_66_4_33) = all_66_1_30 & lookup_slb(all_0_5_5, all_66_4_33) = all_66_3_32 & (all_66_0_29 = all_66_2_31 | ~ contains_slb(all_0_5_5, all_66_4_33) | ~ less_than(all_66_3_32, all_66_4_33)) % 16.25/4.33 | % 16.25/4.33 | Applying alpha-rule on (184) yields: % 16.25/4.33 | (185) update_slb(all_0_5_5, all_66_4_33) = all_66_1_30 % 16.25/4.33 | (186) triple(all_0_6_6, all_66_1_30, all_0_4_4) = all_66_0_29 % 16.25/4.33 | (187) findmin_cpq_eff(all_0_3_3) = all_66_2_31 % 16.25/4.33 | (188) lookup_slb(all_0_5_5, all_66_4_33) = all_66_3_32 % 16.25/4.33 | (189) findmin_pqp_res(all_0_6_6) = all_66_4_33 % 16.25/4.33 | (190) all_66_0_29 = all_66_2_31 | ~ contains_slb(all_0_5_5, all_66_4_33) | ~ less_than(all_66_3_32, all_66_4_33) % 16.25/4.33 | % 16.25/4.33 +-Applying beta-rule and splitting (128), into two cases. % 16.25/4.33 |-Branch one: % 16.25/4.33 | (141) all_0_5_5 = create_slb % 16.25/4.33 | % 16.25/4.33 | Equations (141) can reduce 165 to: % 16.25/4.33 | (171) $false % 16.25/4.33 | % 16.25/4.33 |-The branch is then unsatisfiable % 16.25/4.33 |-Branch two: % 16.25/4.33 | (165) ~ (all_0_5_5 = create_slb) % 16.25/4.33 | (194) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_6_6) = v0 & triple(all_0_6_6, v3, bad) = v4 & findmin_cpq_eff(all_0_3_3) = v2 & update_slb(all_0_5_5, v0) = v3 & lookup_slb(all_0_5_5, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_5_5, v0) | ~ strictly_less_than(v0, v1))) % 16.25/4.33 | % 16.25/4.33 | Instantiating (194) with all_71_0_34, all_71_1_35, all_71_2_36, all_71_3_37, all_71_4_38 yields: % 16.25/4.33 | (195) findmin_pqp_res(all_0_6_6) = all_71_4_38 & triple(all_0_6_6, all_71_1_35, bad) = all_71_0_34 & findmin_cpq_eff(all_0_3_3) = all_71_2_36 & update_slb(all_0_5_5, all_71_4_38) = all_71_1_35 & lookup_slb(all_0_5_5, all_71_4_38) = all_71_3_37 & (all_71_0_34 = all_71_2_36 | ~ contains_slb(all_0_5_5, all_71_4_38) | ~ strictly_less_than(all_71_4_38, all_71_3_37)) % 16.25/4.33 | % 16.25/4.33 | Applying alpha-rule on (195) yields: % 16.25/4.33 | (196) findmin_pqp_res(all_0_6_6) = all_71_4_38 % 16.25/4.33 | (197) triple(all_0_6_6, all_71_1_35, bad) = all_71_0_34 % 16.25/4.33 | (198) lookup_slb(all_0_5_5, all_71_4_38) = all_71_3_37 % 16.25/4.33 | (199) update_slb(all_0_5_5, all_71_4_38) = all_71_1_35 % 16.25/4.33 | (200) all_71_0_34 = all_71_2_36 | ~ contains_slb(all_0_5_5, all_71_4_38) | ~ strictly_less_than(all_71_4_38, all_71_3_37) % 16.25/4.33 | (201) findmin_cpq_eff(all_0_3_3) = all_71_2_36 % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (89) with all_0_3_3, all_55_0_24, all_0_0_0 and discharging atoms findmin_cpq_res(all_0_3_3) = all_55_0_24, findmin_cpq_res(all_0_3_3) = all_0_0_0, yields: % 16.25/4.33 | (202) all_55_0_24 = all_0_0_0 % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (68) with all_0_6_6, all_66_4_33, all_71_4_38 and discharging atoms findmin_pqp_res(all_0_6_6) = all_71_4_38, findmin_pqp_res(all_0_6_6) = all_66_4_33, yields: % 16.25/4.33 | (203) all_71_4_38 = all_66_4_33 % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (68) with all_0_6_6, all_61_3_28, all_71_4_38 and discharging atoms findmin_pqp_res(all_0_6_6) = all_71_4_38, findmin_pqp_res(all_0_6_6) = all_61_3_28, yields: % 16.25/4.33 | (204) all_71_4_38 = all_61_3_28 % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (68) with all_0_6_6, all_55_0_24, all_71_4_38 and discharging atoms findmin_pqp_res(all_0_6_6) = all_71_4_38, findmin_pqp_res(all_0_6_6) = all_55_0_24, yields: % 16.25/4.33 | (205) all_71_4_38 = all_55_0_24 % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (22) with all_0_3_3, all_71_2_36, all_0_2_2 and discharging atoms findmin_cpq_eff(all_0_3_3) = all_71_2_36, findmin_cpq_eff(all_0_3_3) = all_0_2_2, yields: % 16.25/4.33 | (206) all_71_2_36 = all_0_2_2 % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (22) with all_0_3_3, all_66_2_31, all_71_2_36 and discharging atoms findmin_cpq_eff(all_0_3_3) = all_71_2_36, findmin_cpq_eff(all_0_3_3) = all_66_2_31, yields: % 16.25/4.33 | (207) all_71_2_36 = all_66_2_31 % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (22) with all_0_3_3, all_61_2_27, all_66_2_31 and discharging atoms findmin_cpq_eff(all_0_3_3) = all_66_2_31, findmin_cpq_eff(all_0_3_3) = all_61_2_27, yields: % 16.25/4.33 | (208) all_66_2_31 = all_61_2_27 % 16.25/4.33 | % 16.25/4.33 | Combining equations (207,206) yields a new equation: % 16.25/4.33 | (209) all_66_2_31 = all_0_2_2 % 16.25/4.33 | % 16.25/4.33 | Simplifying 209 yields: % 16.25/4.33 | (210) all_66_2_31 = all_0_2_2 % 16.25/4.33 | % 16.25/4.33 | Combining equations (204,203) yields a new equation: % 16.25/4.33 | (211) all_66_4_33 = all_61_3_28 % 16.25/4.33 | % 16.25/4.33 | Combining equations (205,203) yields a new equation: % 16.25/4.33 | (212) all_66_4_33 = all_55_0_24 % 16.25/4.33 | % 16.25/4.33 | Combining equations (210,208) yields a new equation: % 16.25/4.33 | (213) all_61_2_27 = all_0_2_2 % 16.25/4.33 | % 16.25/4.33 | Combining equations (211,212) yields a new equation: % 16.25/4.33 | (214) all_61_3_28 = all_55_0_24 % 16.25/4.33 | % 16.25/4.33 | Simplifying 214 yields: % 16.25/4.33 | (215) all_61_3_28 = all_55_0_24 % 16.25/4.33 | % 16.25/4.33 | Combining equations (202,215) yields a new equation: % 16.25/4.33 | (216) all_61_3_28 = all_0_0_0 % 16.25/4.33 | % 16.25/4.33 | Combining equations (202,212) yields a new equation: % 16.25/4.33 | (217) all_66_4_33 = all_0_0_0 % 16.25/4.33 | % 16.25/4.33 | Combining equations (217,203) yields a new equation: % 16.25/4.33 | (218) all_71_4_38 = all_0_0_0 % 16.25/4.33 | % 16.25/4.33 | From (218) and (199) follows: % 16.25/4.33 | (219) update_slb(all_0_5_5, all_0_0_0) = all_71_1_35 % 16.25/4.33 | % 16.25/4.33 | From (216) and (178) follows: % 16.25/4.33 | (220) update_slb(all_0_5_5, all_0_0_0) = all_61_1_26 % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (122) with all_0_5_5, all_0_0_0, all_61_1_26, all_71_1_35 and discharging atoms update_slb(all_0_5_5, all_0_0_0) = all_71_1_35, update_slb(all_0_5_5, all_0_0_0) = all_61_1_26, yields: % 16.25/4.33 | (221) all_71_1_35 = all_61_1_26 % 16.25/4.33 | % 16.25/4.33 | From (221) and (197) follows: % 16.25/4.33 | (222) triple(all_0_6_6, all_61_1_26, bad) = all_71_0_34 % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (78) with all_0_6_6, all_61_1_26, bad, all_71_0_34, all_61_0_25 and discharging atoms triple(all_0_6_6, all_61_1_26, bad) = all_71_0_34, triple(all_0_6_6, all_61_1_26, bad) = all_61_0_25, yields: % 16.25/4.33 | (223) all_71_0_34 = all_61_0_25 % 16.25/4.33 | % 16.25/4.33 | From (223) and (222) follows: % 16.25/4.33 | (177) triple(all_0_6_6, all_61_1_26, bad) = all_61_0_25 % 16.25/4.33 | % 16.25/4.33 +-Applying beta-rule and splitting (131), into two cases. % 16.25/4.33 |-Branch one: % 16.25/4.33 | (225) contains_cpq(all_0_3_3, all_11_0_14) % 16.25/4.33 | % 16.25/4.33 | Instantiating formula (46) with all_0_3_3, all_11_0_14, 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, contains_cpq(all_0_3_3, all_11_0_14), yields: % 16.25/4.33 | (226) ? [v0] : (i(all_0_3_3) = v0 & contains_pq(v0, all_11_0_14)) % 16.25/4.33 | % 16.25/4.33 | Instantiating (226) with all_113_0_43 yields: % 16.25/4.33 | (227) i(all_0_3_3) = all_113_0_43 & contains_pq(all_113_0_43, all_11_0_14) % 16.25/4.33 | % 16.25/4.33 | Applying alpha-rule on (227) yields: % 16.25/4.33 | (228) i(all_0_3_3) = all_113_0_43 % 16.25/4.33 | (229) contains_pq(all_113_0_43, all_11_0_14) % 16.25/4.33 | % 16.40/4.33 | Instantiating formula (23) with all_0_3_3, all_113_0_43, all_0_1_1 and discharging atoms i(all_0_3_3) = all_113_0_43, i(all_0_3_3) = all_0_1_1, yields: % 16.40/4.33 | (230) all_113_0_43 = all_0_1_1 % 16.40/4.33 | % 16.40/4.33 | From (230) and (228) follows: % 16.40/4.33 | (57) i(all_0_3_3) = all_0_1_1 % 16.40/4.33 | % 16.40/4.33 +-Applying beta-rule and splitting (136), into two cases. % 16.40/4.33 |-Branch one: % 16.40/4.33 | (158) ~ ok(all_21_0_16) % 16.40/4.33 | % 16.40/4.33 | From (138) and (158) follows: % 16.40/4.33 | (159) ~ ok(all_0_2_2) % 16.40/4.33 | % 16.40/4.33 +-Applying beta-rule and splitting (176), into two cases. % 16.40/4.33 |-Branch one: % 16.40/4.33 | (234) contains_slb(all_0_5_5, all_61_3_28) % 16.40/4.33 | % 16.40/4.33 | From (216) and (234) follows: % 16.40/4.33 | (235) contains_slb(all_0_5_5, all_0_0_0) % 16.40/4.33 | % 16.40/4.33 | Instantiating formula (3) with all_0_3_3, all_0_0_0, 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, contains_slb(all_0_5_5, all_0_0_0), yields: % 16.40/4.33 | (236) contains_cpq(all_0_3_3, all_0_0_0) % 16.40/4.33 | % 16.40/4.33 | Instantiating formula (46) with all_0_3_3, all_0_0_0, 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, contains_cpq(all_0_3_3, all_0_0_0), yields: % 16.40/4.33 | (237) ? [v0] : (i(all_0_3_3) = v0 & contains_pq(v0, all_0_0_0)) % 16.40/4.33 | % 16.40/4.33 | Instantiating (237) with all_178_0_47 yields: % 16.40/4.33 | (238) i(all_0_3_3) = all_178_0_47 & contains_pq(all_178_0_47, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Applying alpha-rule on (238) yields: % 16.40/4.34 | (239) i(all_0_3_3) = all_178_0_47 % 16.40/4.34 | (240) contains_pq(all_178_0_47, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (23) with all_0_3_3, all_178_0_47, all_0_1_1 and discharging atoms i(all_0_3_3) = all_178_0_47, i(all_0_3_3) = all_0_1_1, yields: % 16.40/4.34 | (241) all_178_0_47 = all_0_1_1 % 16.40/4.34 | % 16.40/4.34 | From (241) and (240) follows: % 16.40/4.34 | (242) contains_pq(all_0_1_1, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Using (242) and (53) yields: % 16.40/4.34 | (160) $false % 16.40/4.34 | % 16.40/4.34 |-The branch is then unsatisfiable % 16.40/4.34 |-Branch two: % 16.40/4.34 | (244) ~ contains_slb(all_0_5_5, all_61_3_28) % 16.40/4.34 | (245) all_61_0_25 = all_61_2_27 % 16.40/4.34 | % 16.40/4.34 | Combining equations (213,245) yields a new equation: % 16.40/4.34 | (246) all_61_0_25 = all_0_2_2 % 16.40/4.34 | % 16.40/4.34 | From (246) and (177) follows: % 16.40/4.34 | (247) triple(all_0_6_6, all_61_1_26, bad) = all_0_2_2 % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (108) with all_0_2_2, bad, all_61_1_26, all_0_6_6 and discharging atoms triple(all_0_6_6, all_61_1_26, bad) = all_0_2_2, phi(all_0_2_2), ~ ok(all_0_2_2), yields: % 16.40/4.34 | (160) $false % 16.40/4.34 | % 16.40/4.34 |-The branch is then unsatisfiable % 16.40/4.34 |-Branch two: % 16.40/4.34 | (161) ok(all_21_0_16) % 16.40/4.34 | (162) contains_cpq(all_0_3_3, all_21_1_17) % 16.40/4.34 | % 16.40/4.34 | From (137) and (162) follows: % 16.40/4.34 | (236) contains_cpq(all_0_3_3, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (46) with all_0_3_3, all_0_0_0, 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, contains_cpq(all_0_3_3, all_0_0_0), yields: % 16.40/4.34 | (237) ? [v0] : (i(all_0_3_3) = v0 & contains_pq(v0, all_0_0_0)) % 16.40/4.34 | % 16.40/4.34 | Instantiating (237) with all_143_0_61 yields: % 16.40/4.34 | (253) i(all_0_3_3) = all_143_0_61 & contains_pq(all_143_0_61, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Applying alpha-rule on (253) yields: % 16.40/4.34 | (254) i(all_0_3_3) = all_143_0_61 % 16.40/4.34 | (255) contains_pq(all_143_0_61, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (23) with all_0_3_3, all_143_0_61, all_0_1_1 and discharging atoms i(all_0_3_3) = all_143_0_61, i(all_0_3_3) = all_0_1_1, yields: % 16.40/4.34 | (256) all_143_0_61 = all_0_1_1 % 16.40/4.34 | % 16.40/4.34 | From (256) and (255) follows: % 16.40/4.34 | (242) contains_pq(all_0_1_1, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Using (242) and (53) yields: % 16.40/4.34 | (160) $false % 16.40/4.34 | % 16.40/4.34 |-The branch is then unsatisfiable % 16.40/4.34 |-Branch two: % 16.40/4.34 | (259) ~ contains_cpq(all_0_3_3, all_11_0_14) % 16.40/4.34 | (260) ? [v0] : (i(all_0_3_3) = v0 & ~ contains_pq(v0, all_11_0_14)) % 16.40/4.34 | % 16.40/4.34 | Instantiating (260) with all_107_0_62 yields: % 16.40/4.34 | (261) i(all_0_3_3) = all_107_0_62 & ~ contains_pq(all_107_0_62, all_11_0_14) % 16.40/4.34 | % 16.40/4.34 | Applying alpha-rule on (261) yields: % 16.40/4.34 | (262) i(all_0_3_3) = all_107_0_62 % 16.40/4.34 | (263) ~ contains_pq(all_107_0_62, all_11_0_14) % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (23) with all_0_3_3, all_107_0_62, all_0_1_1 and discharging atoms i(all_0_3_3) = all_107_0_62, i(all_0_3_3) = all_0_1_1, yields: % 16.40/4.34 | (264) all_107_0_62 = all_0_1_1 % 16.40/4.34 | % 16.40/4.34 | From (264) and (262) follows: % 16.40/4.34 | (57) i(all_0_3_3) = all_0_1_1 % 16.40/4.34 | % 16.40/4.34 +-Applying beta-rule and splitting (136), into two cases. % 16.40/4.34 |-Branch one: % 16.40/4.34 | (158) ~ ok(all_21_0_16) % 16.40/4.34 | % 16.40/4.34 | From (138) and (158) follows: % 16.40/4.34 | (159) ~ ok(all_0_2_2) % 16.40/4.34 | % 16.40/4.34 +-Applying beta-rule and splitting (176), into two cases. % 16.40/4.34 |-Branch one: % 16.40/4.34 | (234) contains_slb(all_0_5_5, all_61_3_28) % 16.40/4.34 | % 16.40/4.34 | From (216) and (234) follows: % 16.40/4.34 | (235) contains_slb(all_0_5_5, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (3) with all_0_3_3, all_0_0_0, 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, contains_slb(all_0_5_5, all_0_0_0), yields: % 16.40/4.34 | (236) contains_cpq(all_0_3_3, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (46) with all_0_3_3, all_0_0_0, 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, contains_cpq(all_0_3_3, all_0_0_0), yields: % 16.40/4.34 | (237) ? [v0] : (i(all_0_3_3) = v0 & contains_pq(v0, all_0_0_0)) % 16.40/4.34 | % 16.40/4.34 | Instantiating (237) with all_162_0_66 yields: % 16.40/4.34 | (272) i(all_0_3_3) = all_162_0_66 & contains_pq(all_162_0_66, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Applying alpha-rule on (272) yields: % 16.40/4.34 | (273) i(all_0_3_3) = all_162_0_66 % 16.40/4.34 | (274) contains_pq(all_162_0_66, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (23) with all_0_3_3, all_162_0_66, all_0_1_1 and discharging atoms i(all_0_3_3) = all_162_0_66, i(all_0_3_3) = all_0_1_1, yields: % 16.40/4.34 | (275) all_162_0_66 = all_0_1_1 % 16.40/4.34 | % 16.40/4.34 | From (275) and (274) follows: % 16.40/4.34 | (242) contains_pq(all_0_1_1, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Using (242) and (53) yields: % 16.40/4.34 | (160) $false % 16.40/4.34 | % 16.40/4.34 |-The branch is then unsatisfiable % 16.40/4.34 |-Branch two: % 16.40/4.34 | (244) ~ contains_slb(all_0_5_5, all_61_3_28) % 16.40/4.34 | (245) all_61_0_25 = all_61_2_27 % 16.40/4.34 | % 16.40/4.34 | Combining equations (213,245) yields a new equation: % 16.40/4.34 | (246) all_61_0_25 = all_0_2_2 % 16.40/4.34 | % 16.40/4.34 | From (246) and (177) follows: % 16.40/4.34 | (247) triple(all_0_6_6, all_61_1_26, bad) = all_0_2_2 % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (108) with all_0_2_2, bad, all_61_1_26, all_0_6_6 and discharging atoms triple(all_0_6_6, all_61_1_26, bad) = all_0_2_2, phi(all_0_2_2), ~ ok(all_0_2_2), yields: % 16.40/4.34 | (160) $false % 16.40/4.34 | % 16.40/4.34 |-The branch is then unsatisfiable % 16.40/4.34 |-Branch two: % 16.40/4.34 | (161) ok(all_21_0_16) % 16.40/4.34 | (162) contains_cpq(all_0_3_3, all_21_1_17) % 16.40/4.34 | % 16.40/4.34 | From (137) and (162) follows: % 16.40/4.34 | (236) contains_cpq(all_0_3_3, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (46) with all_0_3_3, all_0_0_0, 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, contains_cpq(all_0_3_3, all_0_0_0), yields: % 16.40/4.34 | (237) ? [v0] : (i(all_0_3_3) = v0 & contains_pq(v0, all_0_0_0)) % 16.40/4.34 | % 16.40/4.34 | Instantiating (237) with all_132_0_80 yields: % 16.40/4.34 | (287) i(all_0_3_3) = all_132_0_80 & contains_pq(all_132_0_80, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Applying alpha-rule on (287) yields: % 16.40/4.34 | (288) i(all_0_3_3) = all_132_0_80 % 16.40/4.34 | (289) contains_pq(all_132_0_80, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Instantiating formula (23) with all_0_3_3, all_132_0_80, all_0_1_1 and discharging atoms i(all_0_3_3) = all_132_0_80, i(all_0_3_3) = all_0_1_1, yields: % 16.40/4.34 | (290) all_132_0_80 = all_0_1_1 % 16.40/4.34 | % 16.40/4.34 | From (290) and (289) follows: % 16.40/4.34 | (242) contains_pq(all_0_1_1, all_0_0_0) % 16.40/4.34 | % 16.40/4.34 | Using (242) and (53) yields: % 16.40/4.34 | (160) $false % 16.40/4.34 | % 16.40/4.34 |-The branch is then unsatisfiable % 16.40/4.34 % SZS output end Proof for theBenchmark % 16.40/4.34 % 16.40/4.34 3830ms %------------------------------------------------------------------------------