%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV384+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 17:51:12 EDT 2022 % Result : Theorem 4.43s 1.59s % Output : Proof 7.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWV384+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n024.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Tue Jun 14 17:05:03 EDT 2022 % 0.12/0.34 % CPUTime : % 0.49/0.59 ____ _ % 0.49/0.59 ___ / __ \_____(_)___ ________ __________ % 0.49/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.59 % 0.49/0.59 A Theorem Prover for First-Order Logic % 0.49/0.59 (ePrincess v.1.0) % 0.49/0.59 % 0.49/0.59 (c) Philipp Rümmer, 2009-2015 % 0.49/0.59 (c) Peter Backeman, 2014-2015 % 0.49/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.59 Bug reports to peter@backeman.se % 0.49/0.59 % 0.49/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.59 % 0.49/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.90/0.97 Prover 0: Preprocessing ... % 3.15/1.33 Prover 0: Warning: ignoring some quantifiers % 3.49/1.37 Prover 0: Constructing countermodel ... % 4.43/1.59 Prover 0: proved (955ms) % 4.43/1.59 % 4.43/1.59 No countermodel exists, formula is valid % 4.43/1.59 % SZS status Theorem for theBenchmark % 4.43/1.59 % 4.43/1.59 Generating proof ... Warning: ignoring some quantifiers % 6.73/2.07 found it (size 92) % 6.73/2.07 % 6.73/2.07 % SZS output start Proof for theBenchmark % 6.73/2.07 Assumed formulas after preprocessing and simplification: % 6.73/2.07 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (triple(v4, v5, v6) = v7 & triple(v0, v1, v2) = v3 & ok(v7) & check_cpq(v7) & succ_cpq(v3, v7) & ~ isnonempty_slb(create_slb) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (insert_pqp(v17, v20) = v21) | ~ (triple(v21, v23, v19) = v24) | ~ (pair(v20, bottom) = v22) | ~ (insert_slb(v18, v22) = v23) | ? [v25] : (triple(v17, v18, v19) = v25 & insert_cpq(v25, v20) = v24)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (triple(v17, v23, v19) = v24) | ~ (pair(v20, v21) = v22) | ~ (insert_slb(v18, v22) = v23) | ~ check_cpq(v24) | ~ strictly_less_than(v20, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (triple(v17, v23, v19) = v24) | ~ (pair(v20, v21) = v22) | ~ (insert_slb(v18, v22) = v23) | ~ less_than(v21, v20) | ? [v25] : (triple(v17, v18, v19) = v25 & ( ~ check_cpq(v25) | check_cpq(v24)) & ( ~ check_cpq(v24) | check_cpq(v25)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (pair(v18, v20) = v22) | ~ (insert_slb(v17, v22) = v23) | ~ pair_in_list(v23, v19, v21) | pair_in_list(v17, v19, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v19 = v18 | ~ (lookup_slb(v22, v19) = v23) | ~ (pair(v18, v20) = v21) | ~ (insert_slb(v17, v21) = v22) | ~ contains_slb(v17, v19) | lookup_slb(v17, v19) = v23) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v19 = v18 | ~ (remove_slb(v22, v19) = v23) | ~ (pair(v18, v20) = v21) | ~ (insert_slb(v17, v21) = v22) | ~ contains_slb(v17, v19) | ? [v24] : (remove_slb(v17, v19) = v24 & insert_slb(v24, v21) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v19 = v18 | ~ (remove_slb(v17, v19) = v22) | ~ (pair(v18, v20) = v21) | ~ (insert_slb(v22, v21) = v23) | ~ contains_slb(v17, v19) | ? [v24] : (remove_slb(v24, v19) = v23 & insert_slb(v17, v21) = v24)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v19 = v18 | ~ (pair(v18, v20) = v22) | ~ (insert_slb(v17, v22) = v23) | ~ pair_in_list(v23, v19, v21) | pair_in_list(v17, v19, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (remove_pqp(v17, v20) = v21) | ~ (triple(v21, v22, v19) = v23) | ~ (remove_slb(v18, v20) = v22) | ~ contains_slb(v18, v20) | ? [v24] : ? [v25] : ? [v26] : (triple(v17, v18, v19) = v25 & remove_cpq(v25, v20) = v26 & lookup_slb(v18, v20) = v24 & (v26 = v23 | ~ less_than(v24, v20)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (update_slb(v22, v19) = v23) | ~ (pair(v18, v20) = v21) | ~ (insert_slb(v17, v21) = v22) | ~ strictly_less_than(v20, v19) | ? [v24] : ? [v25] : (update_slb(v17, v19) = v24 & pair(v18, v19) = v25 & insert_slb(v24, v25) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (update_slb(v22, v19) = v23) | ~ (pair(v18, v20) = v21) | ~ (insert_slb(v17, v21) = v22) | ~ less_than(v19, v20) | ? [v24] : (update_slb(v17, v19) = v24 & insert_slb(v24, v21) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (update_slb(v17, v19) = v22) | ~ (pair(v18, v20) = v21) | ~ (insert_slb(v22, v21) = v23) | ~ less_than(v19, v20) | ? [v24] : (update_slb(v24, v19) = v23 & insert_slb(v17, v21) = v24)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (pair(v18, v20) = v22) | ~ (insert_slb(v17, v22) = v23) | ~ pair_in_list(v17, v19, v21) | pair_in_list(v23, v19, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v19 | ~ (lookup_slb(v21, v18) = v22) | ~ (pair(v18, v19) = v20) | ~ (insert_slb(v17, v20) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v17 | ~ (remove_slb(v21, v18) = v22) | ~ (pair(v18, v19) = v20) | ~ (insert_slb(v17, v20) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (pair(v18, v20) = v21) | ~ (insert_slb(v17, v21) = v22) | ~ contains_slb(v22, v19) | contains_slb(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v18 = create_slb | ~ (findmin_pqp_res(v17) = v20) | ~ (triple(v17, v21, v19) = v22) | ~ (update_slb(v18, v20) = v21) | ~ contains_slb(v18, v20) | ? [v23] : ? [v24] : ? [v25] : (triple(v17, v18, v19) = v24 & findmin_cpq_eff(v24) = v25 & lookup_slb(v18, v20) = v23 & (v25 = v22 | ~ less_than(v23, v20)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (triple(v17, v18, v19) = v21) | ~ (remove_cpq(v21, v20) = v22) | ~ contains_slb(v18, v20) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (remove_pqp(v17, v20) = v24 & triple(v24, v25, v19) = v26 & lookup_slb(v18, v20) = v23 & remove_slb(v18, v20) = v25 & (v26 = v22 | ~ less_than(v23, v20)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (triple(v17, v18, v19) = v21) | ~ (remove_cpq(v21, v20) = v22) | ~ contains_slb(v18, v20) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (remove_pqp(v17, v20) = v24 & triple(v24, v25, bad) = v26 & lookup_slb(v18, v20) = v23 & remove_slb(v18, v20) = v25 & (v26 = v22 | ~ strictly_less_than(v20, v23)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (triple(v17, v18, v19) = v21) | ~ (remove_cpq(v21, v20) = v22) | triple(v17, v18, bad) = v22 | contains_slb(v18, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (triple(v17, v18, v19) = v21) | ~ (insert_cpq(v21, v20) = v22) | ? [v23] : ? [v24] : ? [v25] : (insert_pqp(v17, v20) = v23 & triple(v23, v25, v19) = v22 & pair(v20, bottom) = v24 & insert_slb(v18, v24) = v25)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (pair(v18, v20) = v21) | ~ (insert_slb(v17, v21) = v22) | ~ contains_slb(v17, v19) | contains_slb(v22, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (triple(v21, v20, v19) = v18) | ~ (triple(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (triple(v17, v18, v19) = v21) | ~ contains_cpq(v21, v20) | contains_slb(v18, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (triple(v17, v18, v19) = v21) | ~ contains_slb(v18, v20) | contains_cpq(v21, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (pair(v18, v19) = v20) | ~ (insert_slb(v17, v20) = v21) | pair_in_list(v21, v18, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (pair(v18, v19) = v20) | ~ (insert_slb(v17, v20) = v21) | contains_slb(v21, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (pair(v18, v19) = v20) | ~ (insert_slb(v17, v20) = v21) | isnonempty_slb(v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = bad | ~ (triple(v17, v18, v19) = v20) | ok(v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (remove_pqp(v20, v19) = v18) | ~ (remove_pqp(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (insert_pqp(v20, v19) = v18) | ~ (insert_pqp(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (remove_cpq(v20, v19) = v18) | ~ (remove_cpq(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (insert_cpq(v20, v19) = v18) | ~ (insert_cpq(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (update_slb(v20, v19) = v18) | ~ (update_slb(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (lookup_slb(v20, v19) = v18) | ~ (lookup_slb(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (remove_slb(v20, v19) = v18) | ~ (remove_slb(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (pair(v20, v19) = v18) | ~ (pair(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (insert_slb(v20, v19) = v18) | ~ (insert_slb(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = create_slb | ~ (triple(v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (findmin_pqp_res(v17) = v21 & triple(v17, v24, v19) = v25 & findmin_cpq_eff(v20) = v23 & update_slb(v18, v21) = v24 & lookup_slb(v18, v21) = v22 & (v25 = v23 | ~ contains_slb(v18, v21) | ~ less_than(v22, v21)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = create_slb | ~ (triple(v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (findmin_pqp_res(v17) = v21 & triple(v17, v24, bad) = v25 & findmin_cpq_eff(v20) = v23 & update_slb(v18, v21) = v24 & lookup_slb(v18, v21) = v22 & (v25 = v23 | ~ contains_slb(v18, v21) | ~ strictly_less_than(v21, v22)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = create_slb | ~ (triple(v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (findmin_pqp_res(v17) = v21 & triple(v17, v23, bad) = v24 & findmin_cpq_eff(v20) = v22 & update_slb(v18, v21) = v23 & (v24 = v22 | contains_slb(v18, v21)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = create_slb | ~ (triple(v17, v18, v19) = v20) | ? [v21] : (findmin_cpq_res(v20) = v21 & findmin_pqp_res(v17) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (findmin_cpq_res(v17) = v19) | ~ (findmin_cpq_eff(v17) = v18) | ~ (remove_cpq(v18, v19) = v20) | removemin_cpq_eff(v17) = v20) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (triple(v17, v18, v19) = v20) | ok(v20) | ? [v21] : (im_succ_cpq(v20) = v21 & ( ~ ok(v21) | ~ check_cpq(v21)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (triple(v17, v18, v19) = v20) | check_cpq(v20) | ? [v21] : (im_succ_cpq(v20) = v21 & ( ~ ok(v21) | ~ check_cpq(v21)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (remove_cpq(v18, v19) = v20) | ~ succ_cpq(v17, v18) | succ_cpq(v17, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (insert_cpq(v18, v19) = v20) | ~ succ_cpq(v17, v18) | succ_cpq(v17, v20)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (im_succ_cpq(v19) = v18) | ~ (im_succ_cpq(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (removemin_cpq_res(v19) = v18) | ~ (removemin_cpq_res(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (findmin_cpq_res(v19) = v18) | ~ (findmin_cpq_res(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (findmin_pqp_res(v19) = v18) | ~ (findmin_pqp_res(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (removemin_cpq_eff(v19) = v18) | ~ (removemin_cpq_eff(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (findmin_cpq_eff(v19) = v18) | ~ (findmin_cpq_eff(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (triple(v17, v18, bad) = v19) | ~ ok(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (triple(v17, create_slb, v18) = v19) | findmin_cpq_res(v19) = bottom) & ! [v17] : ! [v18] : ! [v19] : ( ~ (triple(v17, create_slb, v18) = v19) | check_cpq(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (triple(v17, create_slb, v18) = v19) | ? [v20] : (triple(v17, create_slb, bad) = v20 & findmin_cpq_eff(v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (removemin_cpq_eff(v18) = v19) | ~ succ_cpq(v17, v18) | succ_cpq(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (findmin_cpq_eff(v18) = v19) | ~ succ_cpq(v17, v18) | succ_cpq(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ less_than(v18, v19) | ~ less_than(v17, v18) | less_than(v17, v19)) & ! [v17] : ! [v18] : (v18 = create_slb | ~ (update_slb(create_slb, v17) = v18)) & ! [v17] : ! [v18] : ( ~ (removemin_cpq_res(v17) = v18) | findmin_cpq_res(v17) = v18) & ! [v17] : ! [v18] : ( ~ (findmin_cpq_res(v17) = v18) | removemin_cpq_res(v17) = v18) & ! [v17] : ! [v18] : ( ~ (removemin_cpq_eff(v17) = v18) | ? [v19] : ? [v20] : (findmin_cpq_res(v17) = v20 & findmin_cpq_eff(v17) = v19 & remove_cpq(v19, v20) = v18)) & ! [v17] : ! [v18] : ~ pair_in_list(create_slb, v17, v18) & ! [v17] : ! [v18] : ( ~ strictly_less_than(v17, v18) | ~ less_than(v18, v17)) & ! [v17] : ! [v18] : ( ~ strictly_less_than(v17, v18) | less_than(v17, v18)) & ! [v17] : ! [v18] : ( ~ less_than(v17, v18) | strictly_less_than(v17, v18) | less_than(v18, v17)) & ! [v17] : ~ contains_slb(create_slb, v17) & ? [v17] : ? [v18] : (less_than(v18, v17) | less_than(v17, v18)) & ? [v17] : succ_cpq(v17, v17) & ? [v17] : less_than(v17, v17) & ? [v17] : less_than(bottom, v17) & ( ~ ok(v3) | ~ check_cpq(v3)) & ((im_succ_cpq(v15) = v16 & triple(v11, v12, v13) = v15 & triple(v8, v9, v10) = v14 & ok(v16) & check_cpq(v16) & succ_cpq(v14, v15) & ( ~ ok(v15) | ~ check_cpq(v15))) | ( ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (triple(v21, v22, v23) = v24) | ~ (triple(v17, v18, v19) = v20) | ~ ok(v24) | ~ check_cpq(v24) | ~ succ_cpq(v20, v24) | ok(v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (triple(v21, v22, v23) = v24) | ~ (triple(v17, v18, v19) = v20) | ~ ok(v24) | ~ check_cpq(v24) | ~ succ_cpq(v20, v24) | check_cpq(v20))))) % 6.98/2.12 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 yields: % 6.98/2.12 | (1) triple(all_0_12_12, all_0_11_11, all_0_10_10) = all_0_9_9 & triple(all_0_16_16, all_0_15_15, all_0_14_14) = all_0_13_13 & ok(all_0_9_9) & check_cpq(all_0_9_9) & succ_cpq(all_0_13_13, all_0_9_9) & ~ isnonempty_slb(create_slb) & ! [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] : (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] : (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] : (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 = 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) | ok(v3) | ? [v4] : (im_succ_cpq(v3) = v4 & ( ~ ok(v4) | ~ check_cpq(v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | check_cpq(v3) | ? [v4] : (im_succ_cpq(v3) = v4 & ( ~ ok(v4) | ~ check_cpq(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] : (v1 = v0 | ~ (im_succ_cpq(v2) = v1) | ~ (im_succ_cpq(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] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2)) & ! [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] : ( ~ 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] : ( ~ (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] : ~ pair_in_list(create_slb, 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] : ~ contains_slb(create_slb, v0) & ? [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) & ( ~ ok(all_0_13_13) | ~ check_cpq(all_0_13_13)) & ((im_succ_cpq(all_0_1_1) = all_0_0_0 & triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1 & triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_2_2 & ok(all_0_0_0) & check_cpq(all_0_0_0) & succ_cpq(all_0_2_2, all_0_1_1) & ( ~ ok(all_0_1_1) | ~ check_cpq(all_0_1_1))) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | ok(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | check_cpq(v3)))) % 6.98/2.15 | % 6.98/2.15 | Applying alpha-rule on (1) yields: % 6.98/2.15 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2)) % 6.98/2.15 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2)) % 6.98/2.15 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) % 6.98/2.15 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 6.98/2.15 | (6) ! [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)) % 6.98/2.15 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4)) % 6.98/2.15 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) % 6.98/2.15 | (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) % 6.98/2.15 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3) % 6.98/2.15 | (11) ! [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)))) % 6.98/2.15 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) % 6.98/2.15 | (13) ! [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)) % 6.98/2.15 | (14) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0)) % 6.98/2.15 | (15) triple(all_0_12_12, all_0_11_11, all_0_10_10) = all_0_9_9 % 6.98/2.15 | (16) ! [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)))) % 6.98/2.15 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 6.98/2.15 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) % 6.98/2.15 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 6.98/2.15 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2)) % 6.98/2.15 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) % 6.98/2.15 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) % 6.98/2.15 | (23) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) % 6.98/2.15 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) % 6.98/2.15 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) % 6.98/2.15 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) % 6.98/2.15 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) % 6.98/2.15 | (28) ! [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)))) % 6.98/2.15 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) % 6.98/2.15 | (30) ! [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)) % 6.98/2.16 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3)) % 6.98/2.16 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3)) % 6.98/2.16 | (33) ! [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)) % 6.98/2.16 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 6.98/2.16 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) % 6.98/2.16 | (36) ! [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)) % 6.98/2.16 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ok(v3) | ? [v4] : (im_succ_cpq(v3) = v4 & ( ~ ok(v4) | ~ check_cpq(v4)))) % 6.98/2.16 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1)) % 6.98/2.16 | (39) ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0)) % 6.98/2.16 | (40) ! [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)) % 6.98/2.16 | (41) ! [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)))) % 6.98/2.16 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2)) % 6.98/2.16 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 6.98/2.16 | (44) ! [v0] : ~ contains_slb(create_slb, v0) % 6.98/2.16 | (45) ok(all_0_9_9) % 6.98/2.16 | (46) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1)) % 6.98/2.16 | (47) ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1) % 6.98/2.16 | (48) ! [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)))) % 6.98/2.16 | (49) ! [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)) % 6.98/2.16 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4)) % 6.98/2.16 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) % 6.98/2.16 | (52) ! [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)) % 6.98/2.16 | (53) check_cpq(all_0_9_9) % 6.98/2.16 | (54) triple(all_0_16_16, all_0_15_15, all_0_14_14) = all_0_13_13 % 6.98/2.16 | (55) ! [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)))) % 6.98/2.16 | (56) ~ ok(all_0_13_13) | ~ check_cpq(all_0_13_13) % 6.98/2.16 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | check_cpq(v3) | ? [v4] : (im_succ_cpq(v3) = v4 & ( ~ ok(v4) | ~ check_cpq(v4)))) % 6.98/2.16 | (58) ? [v0] : succ_cpq(v0, v0) % 6.98/2.16 | (59) ? [v0] : less_than(v0, v0) % 6.98/2.16 | (60) ! [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)) % 6.98/2.16 | (61) ! [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)) % 6.98/2.17 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) % 6.98/2.17 | (63) ~ isnonempty_slb(create_slb) % 6.98/2.17 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) % 6.98/2.17 | (65) ? [v0] : less_than(bottom, v0) % 6.98/2.17 | (66) ! [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)))) % 6.98/2.17 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) % 6.98/2.17 | (68) ! [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)) % 6.98/2.17 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (im_succ_cpq(v2) = v1) | ~ (im_succ_cpq(v2) = v0)) % 6.98/2.17 | (70) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) % 6.98/2.17 | (71) ! [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)))) % 6.98/2.17 | (72) ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1)) % 6.98/2.17 | (73) succ_cpq(all_0_13_13, all_0_9_9) % 6.98/2.17 | (74) ! [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)) % 6.98/2.17 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2)) % 6.98/2.17 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3)) % 7.25/2.17 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 7.25/2.17 | (78) ! [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)) % 7.25/2.17 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) % 7.25/2.17 | (80) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1) % 7.25/2.17 | (81) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) % 7.25/2.17 | (82) (im_succ_cpq(all_0_1_1) = all_0_0_0 & triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1 & triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_2_2 & ok(all_0_0_0) & check_cpq(all_0_0_0) & succ_cpq(all_0_2_2, all_0_1_1) & ( ~ ok(all_0_1_1) | ~ check_cpq(all_0_1_1))) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | ok(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | check_cpq(v3))) % 7.25/2.17 | % 7.25/2.17 | Instantiating formula (76) with all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 and discharging atoms triple(all_0_16_16, all_0_15_15, all_0_14_14) = all_0_13_13, yields: % 7.25/2.17 | (83) all_0_14_14 = bad | ok(all_0_13_13) % 7.25/2.17 | % 7.25/2.17 | Instantiating formula (37) with all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 and discharging atoms triple(all_0_16_16, all_0_15_15, all_0_14_14) = all_0_13_13, yields: % 7.25/2.17 | (84) ok(all_0_13_13) | ? [v0] : (im_succ_cpq(all_0_13_13) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.17 | % 7.25/2.17 | Instantiating formula (57) with all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 and discharging atoms triple(all_0_16_16, all_0_15_15, all_0_14_14) = all_0_13_13, yields: % 7.25/2.17 | (85) check_cpq(all_0_13_13) | ? [v0] : (im_succ_cpq(all_0_13_13) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.17 | % 7.25/2.17 +-Applying beta-rule and splitting (56), into two cases. % 7.25/2.17 |-Branch one: % 7.25/2.17 | (86) ~ ok(all_0_13_13) % 7.25/2.18 | % 7.25/2.18 +-Applying beta-rule and splitting (83), into two cases. % 7.25/2.18 |-Branch one: % 7.25/2.18 | (87) ok(all_0_13_13) % 7.25/2.18 | % 7.25/2.18 | Using (87) and (86) yields: % 7.25/2.18 | (88) $false % 7.25/2.18 | % 7.25/2.18 |-The branch is then unsatisfiable % 7.25/2.18 |-Branch two: % 7.25/2.18 | (86) ~ ok(all_0_13_13) % 7.25/2.18 | (90) all_0_14_14 = bad % 7.25/2.18 | % 7.25/2.18 | From (90) and (54) follows: % 7.25/2.18 | (91) triple(all_0_16_16, all_0_15_15, bad) = all_0_13_13 % 7.25/2.18 | % 7.25/2.18 +-Applying beta-rule and splitting (84), into two cases. % 7.25/2.18 |-Branch one: % 7.25/2.18 | (87) ok(all_0_13_13) % 7.25/2.18 | % 7.25/2.18 | Using (87) and (86) yields: % 7.25/2.18 | (88) $false % 7.25/2.18 | % 7.25/2.18 |-The branch is then unsatisfiable % 7.25/2.18 |-Branch two: % 7.25/2.18 | (86) ~ ok(all_0_13_13) % 7.25/2.18 | (95) ? [v0] : (im_succ_cpq(all_0_13_13) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.18 | % 7.25/2.18 +-Applying beta-rule and splitting (82), into two cases. % 7.25/2.18 |-Branch one: % 7.25/2.18 | (96) im_succ_cpq(all_0_1_1) = all_0_0_0 & triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1 & triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_2_2 & ok(all_0_0_0) & check_cpq(all_0_0_0) & succ_cpq(all_0_2_2, all_0_1_1) & ( ~ ok(all_0_1_1) | ~ check_cpq(all_0_1_1)) % 7.25/2.18 | % 7.25/2.18 | Applying alpha-rule on (96) yields: % 7.25/2.18 | (97) triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_2_2 % 7.25/2.18 | (98) ok(all_0_0_0) % 7.25/2.18 | (99) succ_cpq(all_0_2_2, all_0_1_1) % 7.25/2.18 | (100) ~ ok(all_0_1_1) | ~ check_cpq(all_0_1_1) % 7.25/2.18 | (101) check_cpq(all_0_0_0) % 7.25/2.18 | (102) triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1 % 7.25/2.18 | (103) im_succ_cpq(all_0_1_1) = all_0_0_0 % 7.25/2.18 | % 7.25/2.18 | Instantiating formula (76) with all_0_1_1, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 7.25/2.18 | (104) all_0_3_3 = bad | ok(all_0_1_1) % 7.25/2.18 | % 7.25/2.18 | Instantiating formula (37) with all_0_1_1, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 7.25/2.18 | (105) ok(all_0_1_1) | ? [v0] : (im_succ_cpq(all_0_1_1) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.18 | % 7.25/2.18 | Instantiating formula (57) with all_0_1_1, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 7.25/2.18 | (106) check_cpq(all_0_1_1) | ? [v0] : (im_succ_cpq(all_0_1_1) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.18 | % 7.25/2.18 +-Applying beta-rule and splitting (106), into two cases. % 7.25/2.18 |-Branch one: % 7.25/2.18 | (107) check_cpq(all_0_1_1) % 7.25/2.18 | % 7.25/2.18 +-Applying beta-rule and splitting (100), into two cases. % 7.25/2.18 |-Branch one: % 7.25/2.18 | (108) ~ ok(all_0_1_1) % 7.25/2.18 | % 7.25/2.18 +-Applying beta-rule and splitting (104), into two cases. % 7.25/2.18 |-Branch one: % 7.25/2.18 | (109) ok(all_0_1_1) % 7.25/2.18 | % 7.25/2.18 | Using (109) and (108) yields: % 7.25/2.18 | (88) $false % 7.25/2.18 | % 7.25/2.18 |-The branch is then unsatisfiable % 7.25/2.18 |-Branch two: % 7.25/2.18 | (108) ~ ok(all_0_1_1) % 7.25/2.18 | (112) all_0_3_3 = bad % 7.25/2.18 | % 7.25/2.18 +-Applying beta-rule and splitting (105), into two cases. % 7.25/2.18 |-Branch one: % 7.25/2.18 | (109) ok(all_0_1_1) % 7.25/2.18 | % 7.25/2.18 | Using (109) and (108) yields: % 7.25/2.18 | (88) $false % 7.25/2.18 | % 7.25/2.18 |-The branch is then unsatisfiable % 7.25/2.18 |-Branch two: % 7.25/2.18 | (108) ~ ok(all_0_1_1) % 7.25/2.18 | (116) ? [v0] : (im_succ_cpq(all_0_1_1) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.18 | % 7.25/2.18 | Instantiating (116) with all_56_0_23 yields: % 7.25/2.18 | (117) im_succ_cpq(all_0_1_1) = all_56_0_23 & ( ~ ok(all_56_0_23) | ~ check_cpq(all_56_0_23)) % 7.25/2.18 | % 7.25/2.18 | Applying alpha-rule on (117) yields: % 7.25/2.18 | (118) im_succ_cpq(all_0_1_1) = all_56_0_23 % 7.25/2.18 | (119) ~ ok(all_56_0_23) | ~ check_cpq(all_56_0_23) % 7.25/2.18 | % 7.25/2.18 | Instantiating formula (69) with all_0_1_1, all_56_0_23, all_0_0_0 and discharging atoms im_succ_cpq(all_0_1_1) = all_56_0_23, im_succ_cpq(all_0_1_1) = all_0_0_0, yields: % 7.25/2.18 | (120) all_56_0_23 = all_0_0_0 % 7.25/2.18 | % 7.25/2.18 +-Applying beta-rule and splitting (119), into two cases. % 7.25/2.18 |-Branch one: % 7.25/2.18 | (121) ~ ok(all_56_0_23) % 7.25/2.18 | % 7.25/2.18 | From (120) and (121) follows: % 7.25/2.18 | (122) ~ ok(all_0_0_0) % 7.25/2.18 | % 7.25/2.18 | Using (98) and (122) yields: % 7.25/2.18 | (88) $false % 7.25/2.18 | % 7.25/2.18 |-The branch is then unsatisfiable % 7.25/2.18 |-Branch two: % 7.25/2.18 | (124) ok(all_56_0_23) % 7.25/2.18 | (125) ~ check_cpq(all_56_0_23) % 7.25/2.18 | % 7.25/2.18 | From (120) and (125) follows: % 7.25/2.18 | (126) ~ check_cpq(all_0_0_0) % 7.25/2.18 | % 7.25/2.18 | Using (101) and (126) yields: % 7.25/2.18 | (88) $false % 7.25/2.18 | % 7.25/2.18 |-The branch is then unsatisfiable % 7.25/2.18 |-Branch two: % 7.25/2.18 | (109) ok(all_0_1_1) % 7.25/2.18 | (129) ~ check_cpq(all_0_1_1) % 7.25/2.18 | % 7.25/2.18 | Using (107) and (129) yields: % 7.25/2.18 | (88) $false % 7.25/2.18 | % 7.25/2.18 |-The branch is then unsatisfiable % 7.25/2.18 |-Branch two: % 7.25/2.18 | (129) ~ check_cpq(all_0_1_1) % 7.25/2.18 | (116) ? [v0] : (im_succ_cpq(all_0_1_1) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.18 | % 7.25/2.19 | Instantiating (116) with all_44_0_24 yields: % 7.25/2.19 | (133) im_succ_cpq(all_0_1_1) = all_44_0_24 & ( ~ ok(all_44_0_24) | ~ check_cpq(all_44_0_24)) % 7.25/2.19 | % 7.25/2.19 | Applying alpha-rule on (133) yields: % 7.25/2.19 | (134) im_succ_cpq(all_0_1_1) = all_44_0_24 % 7.25/2.19 | (135) ~ ok(all_44_0_24) | ~ check_cpq(all_44_0_24) % 7.25/2.19 | % 7.25/2.19 | Instantiating formula (69) with all_0_1_1, all_44_0_24, all_0_0_0 and discharging atoms im_succ_cpq(all_0_1_1) = all_44_0_24, im_succ_cpq(all_0_1_1) = all_0_0_0, yields: % 7.25/2.19 | (136) all_44_0_24 = all_0_0_0 % 7.25/2.19 | % 7.25/2.19 +-Applying beta-rule and splitting (135), into two cases. % 7.25/2.19 |-Branch one: % 7.25/2.19 | (137) ~ ok(all_44_0_24) % 7.25/2.19 | % 7.25/2.19 | From (136) and (137) follows: % 7.25/2.19 | (122) ~ ok(all_0_0_0) % 7.25/2.19 | % 7.25/2.19 | Using (98) and (122) yields: % 7.25/2.19 | (88) $false % 7.25/2.19 | % 7.25/2.19 |-The branch is then unsatisfiable % 7.25/2.19 |-Branch two: % 7.25/2.19 | (140) ok(all_44_0_24) % 7.25/2.19 | (141) ~ check_cpq(all_44_0_24) % 7.25/2.19 | % 7.25/2.19 | From (136) and (141) follows: % 7.25/2.19 | (126) ~ check_cpq(all_0_0_0) % 7.25/2.19 | % 7.25/2.19 | Using (101) and (126) yields: % 7.25/2.19 | (88) $false % 7.25/2.19 | % 7.25/2.19 |-The branch is then unsatisfiable % 7.25/2.19 |-Branch two: % 7.25/2.19 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | ok(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | check_cpq(v3)) % 7.25/2.19 | % 7.25/2.19 | Applying alpha-rule on (144) yields: % 7.25/2.19 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | ok(v3)) % 7.25/2.19 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | check_cpq(v3)) % 7.25/2.19 | % 7.25/2.19 | Instantiating formula (145) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, bad, all_0_15_15, all_0_16_16 and discharging atoms triple(all_0_12_12, all_0_11_11, all_0_10_10) = all_0_9_9, triple(all_0_16_16, all_0_15_15, bad) = all_0_13_13, ok(all_0_9_9), check_cpq(all_0_9_9), succ_cpq(all_0_13_13, all_0_9_9), ~ ok(all_0_13_13), yields: % 7.25/2.19 | (88) $false % 7.25/2.19 | % 7.25/2.19 |-The branch is then unsatisfiable % 7.25/2.19 |-Branch two: % 7.25/2.19 | (87) ok(all_0_13_13) % 7.25/2.19 | (149) ~ check_cpq(all_0_13_13) % 7.25/2.19 | % 7.25/2.19 +-Applying beta-rule and splitting (85), into two cases. % 7.25/2.19 |-Branch one: % 7.25/2.19 | (150) check_cpq(all_0_13_13) % 7.25/2.19 | % 7.25/2.19 | Using (150) and (149) yields: % 7.25/2.19 | (88) $false % 7.25/2.19 | % 7.25/2.19 |-The branch is then unsatisfiable % 7.25/2.19 |-Branch two: % 7.25/2.19 | (149) ~ check_cpq(all_0_13_13) % 7.25/2.19 | (95) ? [v0] : (im_succ_cpq(all_0_13_13) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.19 | % 7.25/2.19 +-Applying beta-rule and splitting (82), into two cases. % 7.25/2.19 |-Branch one: % 7.25/2.19 | (96) im_succ_cpq(all_0_1_1) = all_0_0_0 & triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1 & triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_2_2 & ok(all_0_0_0) & check_cpq(all_0_0_0) & succ_cpq(all_0_2_2, all_0_1_1) & ( ~ ok(all_0_1_1) | ~ check_cpq(all_0_1_1)) % 7.25/2.19 | % 7.25/2.19 | Applying alpha-rule on (96) yields: % 7.25/2.19 | (97) triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_2_2 % 7.25/2.19 | (98) ok(all_0_0_0) % 7.25/2.19 | (99) succ_cpq(all_0_2_2, all_0_1_1) % 7.25/2.19 | (100) ~ ok(all_0_1_1) | ~ check_cpq(all_0_1_1) % 7.25/2.19 | (101) check_cpq(all_0_0_0) % 7.25/2.19 | (102) triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1 % 7.25/2.19 | (103) im_succ_cpq(all_0_1_1) = all_0_0_0 % 7.25/2.19 | % 7.25/2.19 | Instantiating formula (76) with all_0_1_1, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 7.25/2.19 | (104) all_0_3_3 = bad | ok(all_0_1_1) % 7.25/2.19 | % 7.25/2.19 | Instantiating formula (37) with all_0_1_1, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 7.25/2.19 | (105) ok(all_0_1_1) | ? [v0] : (im_succ_cpq(all_0_1_1) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.19 | % 7.25/2.19 | Instantiating formula (57) with all_0_1_1, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 7.25/2.19 | (106) check_cpq(all_0_1_1) | ? [v0] : (im_succ_cpq(all_0_1_1) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.19 | % 7.25/2.19 +-Applying beta-rule and splitting (106), into two cases. % 7.25/2.19 |-Branch one: % 7.25/2.19 | (107) check_cpq(all_0_1_1) % 7.25/2.19 | % 7.25/2.19 +-Applying beta-rule and splitting (100), into two cases. % 7.25/2.19 |-Branch one: % 7.25/2.19 | (108) ~ ok(all_0_1_1) % 7.25/2.19 | % 7.25/2.19 +-Applying beta-rule and splitting (104), into two cases. % 7.25/2.19 |-Branch one: % 7.25/2.19 | (109) ok(all_0_1_1) % 7.25/2.19 | % 7.25/2.19 | Using (109) and (108) yields: % 7.25/2.19 | (88) $false % 7.25/2.19 | % 7.25/2.19 |-The branch is then unsatisfiable % 7.25/2.19 |-Branch two: % 7.25/2.19 | (108) ~ ok(all_0_1_1) % 7.25/2.19 | (112) all_0_3_3 = bad % 7.25/2.19 | % 7.25/2.19 +-Applying beta-rule and splitting (105), into two cases. % 7.25/2.19 |-Branch one: % 7.25/2.19 | (109) ok(all_0_1_1) % 7.25/2.19 | % 7.25/2.19 | Using (109) and (108) yields: % 7.25/2.19 | (88) $false % 7.25/2.19 | % 7.25/2.19 |-The branch is then unsatisfiable % 7.25/2.19 |-Branch two: % 7.25/2.19 | (108) ~ ok(all_0_1_1) % 7.25/2.19 | (116) ? [v0] : (im_succ_cpq(all_0_1_1) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.19 | % 7.25/2.19 | Instantiating (116) with all_53_0_26 yields: % 7.25/2.19 | (175) im_succ_cpq(all_0_1_1) = all_53_0_26 & ( ~ ok(all_53_0_26) | ~ check_cpq(all_53_0_26)) % 7.25/2.19 | % 7.25/2.19 | Applying alpha-rule on (175) yields: % 7.25/2.19 | (176) im_succ_cpq(all_0_1_1) = all_53_0_26 % 7.25/2.19 | (177) ~ ok(all_53_0_26) | ~ check_cpq(all_53_0_26) % 7.25/2.19 | % 7.25/2.19 | Instantiating formula (69) with all_0_1_1, all_53_0_26, all_0_0_0 and discharging atoms im_succ_cpq(all_0_1_1) = all_53_0_26, im_succ_cpq(all_0_1_1) = all_0_0_0, yields: % 7.25/2.19 | (178) all_53_0_26 = all_0_0_0 % 7.25/2.19 | % 7.25/2.19 +-Applying beta-rule and splitting (177), into two cases. % 7.25/2.19 |-Branch one: % 7.25/2.19 | (179) ~ ok(all_53_0_26) % 7.25/2.19 | % 7.25/2.19 | From (178) and (179) follows: % 7.25/2.19 | (122) ~ ok(all_0_0_0) % 7.25/2.19 | % 7.25/2.19 | Using (98) and (122) yields: % 7.25/2.19 | (88) $false % 7.25/2.19 | % 7.25/2.19 |-The branch is then unsatisfiable % 7.25/2.19 |-Branch two: % 7.25/2.19 | (182) ok(all_53_0_26) % 7.25/2.19 | (183) ~ check_cpq(all_53_0_26) % 7.25/2.19 | % 7.25/2.19 | From (178) and (183) follows: % 7.25/2.19 | (126) ~ check_cpq(all_0_0_0) % 7.25/2.19 | % 7.25/2.19 | Using (101) and (126) yields: % 7.25/2.19 | (88) $false % 7.25/2.19 | % 7.25/2.19 |-The branch is then unsatisfiable % 7.25/2.19 |-Branch two: % 7.25/2.19 | (109) ok(all_0_1_1) % 7.25/2.19 | (129) ~ check_cpq(all_0_1_1) % 7.25/2.19 | % 7.25/2.19 | Using (107) and (129) yields: % 7.25/2.19 | (88) $false % 7.25/2.19 | % 7.25/2.19 |-The branch is then unsatisfiable % 7.25/2.19 |-Branch two: % 7.25/2.19 | (129) ~ check_cpq(all_0_1_1) % 7.25/2.19 | (116) ? [v0] : (im_succ_cpq(all_0_1_1) = v0 & ( ~ ok(v0) | ~ check_cpq(v0))) % 7.25/2.19 | % 7.25/2.19 | Instantiating (116) with all_41_0_27 yields: % 7.25/2.19 | (191) im_succ_cpq(all_0_1_1) = all_41_0_27 & ( ~ ok(all_41_0_27) | ~ check_cpq(all_41_0_27)) % 7.25/2.19 | % 7.25/2.19 | Applying alpha-rule on (191) yields: % 7.25/2.19 | (192) im_succ_cpq(all_0_1_1) = all_41_0_27 % 7.25/2.19 | (193) ~ ok(all_41_0_27) | ~ check_cpq(all_41_0_27) % 7.25/2.19 | % 7.25/2.19 | Instantiating formula (69) with all_0_1_1, all_41_0_27, all_0_0_0 and discharging atoms im_succ_cpq(all_0_1_1) = all_41_0_27, im_succ_cpq(all_0_1_1) = all_0_0_0, yields: % 7.25/2.19 | (194) all_41_0_27 = all_0_0_0 % 7.25/2.19 | % 7.25/2.19 +-Applying beta-rule and splitting (193), into two cases. % 7.25/2.19 |-Branch one: % 7.25/2.19 | (195) ~ ok(all_41_0_27) % 7.25/2.20 | % 7.25/2.20 | From (194) and (195) follows: % 7.25/2.20 | (122) ~ ok(all_0_0_0) % 7.25/2.20 | % 7.25/2.20 | Using (98) and (122) yields: % 7.25/2.20 | (88) $false % 7.25/2.20 | % 7.25/2.20 |-The branch is then unsatisfiable % 7.25/2.20 |-Branch two: % 7.25/2.20 | (198) ok(all_41_0_27) % 7.25/2.20 | (199) ~ check_cpq(all_41_0_27) % 7.25/2.20 | % 7.25/2.20 | From (194) and (199) follows: % 7.25/2.20 | (126) ~ check_cpq(all_0_0_0) % 7.25/2.20 | % 7.25/2.20 | Using (101) and (126) yields: % 7.25/2.20 | (88) $false % 7.25/2.20 | % 7.25/2.20 |-The branch is then unsatisfiable % 7.25/2.20 |-Branch two: % 7.25/2.20 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | ok(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | check_cpq(v3)) % 7.25/2.20 | % 7.25/2.20 | Applying alpha-rule on (144) yields: % 7.25/2.20 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | ok(v3)) % 7.25/2.20 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v4, v5, v6) = v7) | ~ (triple(v0, v1, v2) = v3) | ~ ok(v7) | ~ check_cpq(v7) | ~ succ_cpq(v3, v7) | check_cpq(v3)) % 7.25/2.20 | % 7.25/2.20 | Instantiating formula (146) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 and discharging atoms triple(all_0_12_12, all_0_11_11, all_0_10_10) = all_0_9_9, triple(all_0_16_16, all_0_15_15, all_0_14_14) = all_0_13_13, ok(all_0_9_9), check_cpq(all_0_9_9), succ_cpq(all_0_13_13, all_0_9_9), ~ check_cpq(all_0_13_13), yields: % 7.25/2.20 | (88) $false % 7.25/2.20 | % 7.25/2.20 |-The branch is then unsatisfiable % 7.25/2.20 % SZS output end Proof for theBenchmark % 7.25/2.20 % 7.25/2.20 1598ms %------------------------------------------------------------------------------