TSTP Solution File: SWV373+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV373+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 17:51:09 EDT 2022
% Result : Theorem 4.18s 1.55s
% Output : Proof 6.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV373+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 10:07:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.54/0.60 ____ _
% 0.54/0.60 ___ / __ \_____(_)___ ________ __________
% 0.54/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.60
% 0.54/0.60 A Theorem Prover for First-Order Logic
% 0.54/0.60 (ePrincess v.1.0)
% 0.54/0.60
% 0.54/0.60 (c) Philipp Rümmer, 2009-2015
% 0.54/0.60 (c) Peter Backeman, 2014-2015
% 0.54/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.60 Bug reports to peter@backeman.se
% 0.54/0.60
% 0.54/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.60
% 0.54/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.94/0.99 Prover 0: Preprocessing ...
% 3.16/1.33 Prover 0: Warning: ignoring some quantifiers
% 3.35/1.36 Prover 0: Constructing countermodel ...
% 4.18/1.55 Prover 0: proved (901ms)
% 4.18/1.55
% 4.18/1.55 No countermodel exists, formula is valid
% 4.18/1.55 % SZS status Theorem for theBenchmark
% 4.18/1.55
% 4.18/1.55 Generating proof ... Warning: ignoring some quantifiers
% 6.15/1.98 found it (size 57)
% 6.15/1.98
% 6.15/1.98 % SZS output start Proof for theBenchmark
% 6.15/1.98 Assumed formulas after preprocessing and simplification:
% 6.15/1.98 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (findmin_cpq_res(v3) = v4 & triple(v0, v1, v2) = v3 & findmin_cpq_eff(v3) = v5 & ok(v5) & ~ contains_cpq(v3, v4) & ~ isnonempty_slb(create_slb) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (insert_pqp(v6, v9) = v10) | ~ (triple(v10, v12, v8) = v13) | ~ (pair(v9, bottom) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : (triple(v6, v7, v8) = v14 & insert_cpq(v14, v9) = v13)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v6, v12, v8) = v13) | ~ (pair(v9, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ~ check_cpq(v13) | ~ strictly_less_than(v9, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v6, v12, v8) = v13) | ~ (pair(v9, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ~ less_than(v10, v9) | ? [v14] : (triple(v6, v7, v8) = v14 & ( ~ check_cpq(v14) | check_cpq(v13)) & ( ~ check_cpq(v13) | check_cpq(v14)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (pair(v7, v9) = v11) | ~ (insert_slb(v6, v11) = v12) | ~ pair_in_list(v12, v8, v10) | pair_in_list(v6, v8, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (lookup_slb(v11, v8) = v12) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ~ contains_slb(v6, v8) | lookup_slb(v6, v8) = v12) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (remove_slb(v11, v8) = v12) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ~ contains_slb(v6, v8) | ? [v13] : (remove_slb(v6, v8) = v13 & insert_slb(v13, v10) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (remove_slb(v6, v8) = v11) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v11, v10) = v12) | ~ contains_slb(v6, v8) | ? [v13] : (remove_slb(v13, v8) = v12 & insert_slb(v6, v10) = v13)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (pair(v7, v9) = v11) | ~ (insert_slb(v6, v11) = v12) | ~ pair_in_list(v12, v8, v10) | pair_in_list(v6, v8, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (remove_pqp(v6, v9) = v10) | ~ (triple(v10, v11, v8) = v12) | ~ (remove_slb(v7, v9) = v11) | ~ contains_slb(v7, v9) | ? [v13] : ? [v14] : ? [v15] : (triple(v6, v7, v8) = v14 & remove_cpq(v14, v9) = v15 & lookup_slb(v7, v9) = v13 & (v15 = v12 | ~ less_than(v13, v9)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (update_slb(v11, v8) = v12) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ~ strictly_less_than(v9, v8) | ? [v13] : ? [v14] : (update_slb(v6, v8) = v13 & pair(v7, v8) = v14 & insert_slb(v13, v14) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (update_slb(v11, v8) = v12) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ~ less_than(v8, v9) | ? [v13] : (update_slb(v6, v8) = v13 & insert_slb(v13, v10) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (update_slb(v6, v8) = v11) | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v11, v10) = v12) | ~ less_than(v8, v9) | ? [v13] : (update_slb(v13, v8) = v12 & insert_slb(v6, v10) = v13)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (pair(v7, v9) = v11) | ~ (insert_slb(v6, v11) = v12) | ~ pair_in_list(v6, v8, v10) | pair_in_list(v12, v8, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (lookup_slb(v10, v7) = v11) | ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v6 | ~ (remove_slb(v10, v7) = v11) | ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ~ contains_slb(v11, v8) | contains_slb(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = create_slb | ~ (findmin_pqp_res(v6) = v9) | ~ (triple(v6, v10, v8) = v11) | ~ (update_slb(v7, v9) = v10) | ~ contains_slb(v7, v9) | ? [v12] : ? [v13] : ? [v14] : (triple(v6, v7, v8) = v13 & findmin_cpq_eff(v13) = v14 & lookup_slb(v7, v9) = v12 & (v14 = v11 | ~ less_than(v12, v9)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v6, v7, v8) = v10) | ~ (remove_cpq(v10, v9) = v11) | ~ contains_slb(v7, v9) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (remove_pqp(v6, v9) = v13 & triple(v13, v14, v8) = v15 & lookup_slb(v7, v9) = v12 & remove_slb(v7, v9) = v14 & (v15 = v11 | ~ less_than(v12, v9)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v6, v7, v8) = v10) | ~ (remove_cpq(v10, v9) = v11) | ~ contains_slb(v7, v9) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (remove_pqp(v6, v9) = v13 & triple(v13, v14, bad) = v15 & lookup_slb(v7, v9) = v12 & remove_slb(v7, v9) = v14 & (v15 = v11 | ~ strictly_less_than(v9, v12)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v6, v7, v8) = v10) | ~ (remove_cpq(v10, v9) = v11) | triple(v6, v7, bad) = v11 | contains_slb(v7, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v6, v7, v8) = v10) | ~ (insert_cpq(v10, v9) = v11) | ? [v12] : ? [v13] : ? [v14] : (insert_pqp(v6, v9) = v12 & triple(v12, v14, v8) = v11 & pair(v9, bottom) = v13 & insert_slb(v7, v13) = v14)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (pair(v7, v9) = v10) | ~ (insert_slb(v6, v10) = v11) | ~ contains_slb(v6, v8) | contains_slb(v11, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (triple(v10, v9, v8) = v7) | ~ (triple(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v6, v7, v8) = v10) | ~ contains_cpq(v10, v9) | contains_slb(v7, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v6, v7, v8) = v10) | ~ contains_slb(v7, v9) | contains_cpq(v10, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10) | pair_in_list(v10, v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10) | contains_slb(v10, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (pair(v7, v8) = v9) | ~ (insert_slb(v6, v9) = v10) | isnonempty_slb(v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = bad | ~ (triple(v6, v7, v8) = v9) | ok(v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (remove_pqp(v9, v8) = v7) | ~ (remove_pqp(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (insert_pqp(v9, v8) = v7) | ~ (insert_pqp(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (remove_cpq(v9, v8) = v7) | ~ (remove_cpq(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (insert_cpq(v9, v8) = v7) | ~ (insert_cpq(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (update_slb(v9, v8) = v7) | ~ (update_slb(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (lookup_slb(v9, v8) = v7) | ~ (lookup_slb(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (remove_slb(v9, v8) = v7) | ~ (remove_slb(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (pair(v9, v8) = v7) | ~ (pair(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (insert_slb(v9, v8) = v7) | ~ (insert_slb(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = create_slb | ~ (triple(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (findmin_pqp_res(v6) = v10 & triple(v6, v13, v8) = v14 & findmin_cpq_eff(v9) = v12 & update_slb(v7, v10) = v13 & lookup_slb(v7, v10) = v11 & (v14 = v12 | ~ contains_slb(v7, v10) | ~ less_than(v11, v10)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = create_slb | ~ (triple(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (findmin_pqp_res(v6) = v10 & triple(v6, v13, bad) = v14 & findmin_cpq_eff(v9) = v12 & update_slb(v7, v10) = v13 & lookup_slb(v7, v10) = v11 & (v14 = v12 | ~ contains_slb(v7, v10) | ~ strictly_less_than(v10, v11)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = create_slb | ~ (triple(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (findmin_pqp_res(v6) = v10 & triple(v6, v12, bad) = v13 & findmin_cpq_eff(v9) = v11 & update_slb(v7, v10) = v12 & (v13 = v11 | contains_slb(v7, v10)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = create_slb | ~ (triple(v6, v7, v8) = v9) | ? [v10] : (findmin_cpq_res(v9) = v10 & findmin_pqp_res(v6) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (findmin_cpq_res(v6) = v8) | ~ (findmin_cpq_eff(v6) = v7) | ~ (remove_cpq(v7, v8) = v9) | removemin_cpq_eff(v6) = v9) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (findmin_pqp_res(v6) = v11 & findmin_cpq_eff(v9) = v10 & lookup_slb(v7, v11) = v12 & ( ~ ok(v10) | ( ~ (v7 = create_slb) & contains_slb(v7, v11) & less_than(v12, v11))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (remove_cpq(v7, v8) = v9) | ~ succ_cpq(v6, v7) | succ_cpq(v6, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (insert_cpq(v7, v8) = v9) | ~ succ_cpq(v6, v7) | succ_cpq(v6, v9)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (removemin_cpq_res(v8) = v7) | ~ (removemin_cpq_res(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (findmin_cpq_res(v8) = v7) | ~ (findmin_cpq_res(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (findmin_pqp_res(v8) = v7) | ~ (findmin_pqp_res(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (removemin_cpq_eff(v8) = v7) | ~ (removemin_cpq_eff(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (findmin_cpq_eff(v8) = v7) | ~ (findmin_cpq_eff(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (triple(v6, v7, bad) = v8) | ~ ok(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (triple(v6, create_slb, v7) = v8) | findmin_cpq_res(v8) = bottom) & ! [v6] : ! [v7] : ! [v8] : ( ~ (triple(v6, create_slb, v7) = v8) | check_cpq(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (triple(v6, create_slb, v7) = v8) | ? [v9] : (triple(v6, create_slb, bad) = v9 & findmin_cpq_eff(v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (removemin_cpq_eff(v7) = v8) | ~ succ_cpq(v6, v7) | succ_cpq(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (findmin_cpq_eff(v7) = v8) | ~ succ_cpq(v6, v7) | succ_cpq(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ less_than(v7, v8) | ~ less_than(v6, v7) | less_than(v6, v8)) & ! [v6] : ! [v7] : (v7 = create_slb | ~ (update_slb(create_slb, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (removemin_cpq_res(v6) = v7) | findmin_cpq_res(v6) = v7) & ! [v6] : ! [v7] : ( ~ (findmin_cpq_res(v6) = v7) | removemin_cpq_res(v6) = v7) & ! [v6] : ! [v7] : ( ~ (removemin_cpq_eff(v6) = v7) | ? [v8] : ? [v9] : (findmin_cpq_res(v6) = v9 & findmin_cpq_eff(v6) = v8 & remove_cpq(v8, v9) = v7)) & ! [v6] : ! [v7] : ~ pair_in_list(create_slb, v6, v7) & ! [v6] : ! [v7] : ( ~ strictly_less_than(v6, v7) | ~ less_than(v7, v6)) & ! [v6] : ! [v7] : ( ~ strictly_less_than(v6, v7) | less_than(v6, v7)) & ! [v6] : ! [v7] : ( ~ less_than(v6, v7) | strictly_less_than(v6, v7) | less_than(v7, v6)) & ! [v6] : ~ contains_slb(create_slb, v6) & ? [v6] : ? [v7] : (less_than(v7, v6) | less_than(v6, v7)) & ? [v6] : succ_cpq(v6, v6) & ? [v6] : less_than(v6, v6) & ? [v6] : less_than(bottom, v6))
% 6.15/2.03 | 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 yields:
% 6.15/2.03 | (1) findmin_cpq_res(all_0_2_2) = all_0_1_1 & triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2 & findmin_cpq_eff(all_0_2_2) = all_0_0_0 & ok(all_0_0_0) & ~ contains_cpq(all_0_2_2, all_0_1_1) & ~ 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) | ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(v0) = v5 & findmin_cpq_eff(v3) = v4 & lookup_slb(v1, v5) = v6 & ( ~ ok(v4) | ( ~ (v1 = create_slb) & contains_slb(v1, v5) & less_than(v6, v5))))) & ! [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 | ~ (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)
% 6.15/2.05 |
% 6.15/2.05 | Applying alpha-rule on (1) yields:
% 6.15/2.05 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2))
% 6.15/2.05 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2))
% 6.15/2.05 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2))
% 6.15/2.05 | (5) ! [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))
% 6.15/2.05 | (6) ! [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))
% 6.15/2.05 | (7) ! [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))
% 6.15/2.05 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3))
% 6.15/2.05 | (9) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0))
% 6.15/2.05 | (10) ! [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))
% 6.15/2.06 | (11) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1))
% 6.15/2.06 | (12) ! [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))))
% 6.15/2.06 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 6.15/2.06 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3))
% 6.15/2.06 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 6.15/2.06 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1))
% 6.15/2.06 | (17) triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2
% 6.15/2.06 | (18) ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1)
% 6.15/2.06 | (19) ~ isnonempty_slb(create_slb)
% 6.15/2.06 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 6.15/2.06 | (21) ! [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))
% 6.15/2.06 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 6.15/2.06 | (23) findmin_cpq_res(all_0_2_2) = all_0_1_1
% 6.15/2.06 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 6.15/2.06 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ strictly_less_than(v3, v2) | ? [v7] : ? [v8] : (update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6))
% 6.15/2.06 | (26) ! [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))
% 6.15/2.06 | (27) ok(all_0_0_0)
% 6.15/2.06 | (28) ! [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))))
% 6.15/2.06 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 6.15/2.06 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 6.15/2.06 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2))
% 6.15/2.06 | (32) ! [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))))
% 6.15/2.06 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3)
% 6.15/2.06 | (34) findmin_cpq_eff(all_0_2_2) = all_0_0_0
% 6.15/2.06 | (35) ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0))
% 6.53/2.06 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4))
% 6.53/2.06 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3))
% 6.53/2.06 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3))
% 6.53/2.06 | (39) ! [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))
% 6.53/2.06 | (40) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 6.53/2.06 | (41) ! [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))
% 6.53/2.06 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 6.53/2.06 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 6.53/2.06 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 6.53/2.07 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(v0) = v5 & findmin_cpq_eff(v3) = v4 & lookup_slb(v1, v5) = v6 & ( ~ ok(v4) | ( ~ (v1 = create_slb) & contains_slb(v1, v5) & less_than(v6, v5)))))
% 6.53/2.07 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2))
% 6.53/2.07 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 6.53/2.07 | (48) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1))
% 6.53/2.07 | (49) ! [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))
% 6.53/2.07 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 6.53/2.07 | (51) ! [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))))
% 6.53/2.07 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2))
% 6.53/2.07 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8))
% 6.53/2.07 | (54) ! [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))))
% 6.53/2.07 | (55) ! [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))))
% 6.53/2.07 | (56) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1)
% 6.53/2.07 | (57) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 6.53/2.07 | (58) ! [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))
% 6.53/2.07 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 6.53/2.07 | (60) ? [v0] : less_than(bottom, v0)
% 6.53/2.07 | (61) ? [v0] : succ_cpq(v0, v0)
% 6.53/2.07 | (62) ? [v0] : less_than(v0, v0)
% 6.53/2.07 | (63) ~ contains_cpq(all_0_2_2, all_0_1_1)
% 6.53/2.07 | (64) ! [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))))
% 6.53/2.07 | (65) ! [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))
% 6.53/2.07 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 6.53/2.07 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 6.53/2.07 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3))
% 6.53/2.07 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 6.53/2.07 | (70) ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1))
% 6.53/2.07 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 6.53/2.07 | (72) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 6.53/2.07 | (73) ! [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))))
% 6.53/2.07 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4))
% 6.53/2.07 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2))
% 6.53/2.07 | (76) ! [v0] : ~ contains_slb(create_slb, v0)
% 6.53/2.07 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 6.53/2.08 | (78) ! [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)
% 6.53/2.08 |
% 6.53/2.08 | Instantiating formula (54) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 6.53/2.08 | (79) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v3, all_0_3_3) = v4 & findmin_cpq_eff(all_0_2_2) = v2 & update_slb(all_0_4_4, v0) = v3 & lookup_slb(all_0_4_4, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_4_4, v0) | ~ less_than(v1, v0)))
% 6.53/2.08 |
% 6.53/2.08 | Instantiating formula (73) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 6.53/2.08 | (80) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v3, bad) = v4 & findmin_cpq_eff(all_0_2_2) = v2 & update_slb(all_0_4_4, v0) = v3 & lookup_slb(all_0_4_4, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_4_4, v0) | ~ strictly_less_than(v0, v1)))
% 6.53/2.08 |
% 6.53/2.08 | Instantiating formula (32) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 6.53/2.08 | (81) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v2, bad) = v3 & findmin_cpq_eff(all_0_2_2) = v1 & update_slb(all_0_4_4, v0) = v2 & (v3 = v1 | contains_slb(all_0_4_4, v0)))
% 6.53/2.08 |
% 6.53/2.08 | Instantiating formula (74) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 6.53/2.08 | (82) all_0_4_4 = create_slb | ? [v0] : (findmin_cpq_res(all_0_2_2) = v0 & findmin_pqp_res(all_0_5_5) = v0)
% 6.53/2.08 |
% 6.53/2.08 | Instantiating formula (45) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 6.53/2.08 | (83) ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v1 & findmin_cpq_eff(all_0_2_2) = v0 & lookup_slb(all_0_4_4, v1) = v2 & ( ~ ok(v0) | ( ~ (all_0_4_4 = create_slb) & contains_slb(all_0_4_4, v1) & less_than(v2, v1))))
% 6.53/2.08 |
% 6.53/2.08 | Instantiating (83) with all_16_0_11, all_16_1_12, all_16_2_13 yields:
% 6.53/2.08 | (84) findmin_pqp_res(all_0_5_5) = all_16_1_12 & findmin_cpq_eff(all_0_2_2) = all_16_2_13 & lookup_slb(all_0_4_4, all_16_1_12) = all_16_0_11 & ( ~ ok(all_16_2_13) | ( ~ (all_0_4_4 = create_slb) & contains_slb(all_0_4_4, all_16_1_12) & less_than(all_16_0_11, all_16_1_12)))
% 6.53/2.08 |
% 6.53/2.08 | Applying alpha-rule on (84) yields:
% 6.53/2.08 | (85) findmin_pqp_res(all_0_5_5) = all_16_1_12
% 6.53/2.08 | (86) findmin_cpq_eff(all_0_2_2) = all_16_2_13
% 6.53/2.08 | (87) lookup_slb(all_0_4_4, all_16_1_12) = all_16_0_11
% 6.53/2.08 | (88) ~ ok(all_16_2_13) | ( ~ (all_0_4_4 = create_slb) & contains_slb(all_0_4_4, all_16_1_12) & less_than(all_16_0_11, all_16_1_12))
% 6.53/2.08 |
% 6.53/2.08 | Instantiating formula (47) with all_0_2_2, all_16_2_13, all_0_0_0 and discharging atoms findmin_cpq_eff(all_0_2_2) = all_16_2_13, findmin_cpq_eff(all_0_2_2) = all_0_0_0, yields:
% 6.53/2.08 | (89) all_16_2_13 = all_0_0_0
% 6.53/2.08 |
% 6.53/2.08 +-Applying beta-rule and splitting (88), into two cases.
% 6.53/2.08 |-Branch one:
% 6.53/2.08 | (90) ~ ok(all_16_2_13)
% 6.53/2.08 |
% 6.53/2.08 | From (89) and (90) follows:
% 6.53/2.08 | (91) ~ ok(all_0_0_0)
% 6.53/2.08 |
% 6.53/2.08 | Using (27) and (91) yields:
% 6.53/2.08 | (92) $false
% 6.53/2.08 |
% 6.53/2.08 |-The branch is then unsatisfiable
% 6.53/2.08 |-Branch two:
% 6.53/2.08 | (93) ok(all_16_2_13)
% 6.53/2.08 | (94) ~ (all_0_4_4 = create_slb) & contains_slb(all_0_4_4, all_16_1_12) & less_than(all_16_0_11, all_16_1_12)
% 6.53/2.08 |
% 6.53/2.08 | Applying alpha-rule on (94) yields:
% 6.53/2.08 | (95) ~ (all_0_4_4 = create_slb)
% 6.53/2.08 | (96) contains_slb(all_0_4_4, all_16_1_12)
% 6.53/2.08 | (97) less_than(all_16_0_11, all_16_1_12)
% 6.53/2.08 |
% 6.53/2.08 +-Applying beta-rule and splitting (82), into two cases.
% 6.53/2.08 |-Branch one:
% 6.53/2.08 | (98) all_0_4_4 = create_slb
% 6.53/2.08 |
% 6.53/2.08 | Equations (98) can reduce 95 to:
% 6.53/2.08 | (99) $false
% 6.53/2.08 |
% 6.53/2.08 |-The branch is then unsatisfiable
% 6.53/2.08 |-Branch two:
% 6.53/2.08 | (95) ~ (all_0_4_4 = create_slb)
% 6.53/2.08 | (101) ? [v0] : (findmin_cpq_res(all_0_2_2) = v0 & findmin_pqp_res(all_0_5_5) = v0)
% 6.53/2.08 |
% 6.53/2.08 | Instantiating (101) with all_30_0_14 yields:
% 6.53/2.08 | (102) findmin_cpq_res(all_0_2_2) = all_30_0_14 & findmin_pqp_res(all_0_5_5) = all_30_0_14
% 6.53/2.08 |
% 6.53/2.08 | Applying alpha-rule on (102) yields:
% 6.53/2.08 | (103) findmin_cpq_res(all_0_2_2) = all_30_0_14
% 6.53/2.08 | (104) findmin_pqp_res(all_0_5_5) = all_30_0_14
% 6.53/2.08 |
% 6.53/2.08 +-Applying beta-rule and splitting (80), into two cases.
% 6.53/2.08 |-Branch one:
% 6.53/2.08 | (98) all_0_4_4 = create_slb
% 6.53/2.08 |
% 6.53/2.08 | Equations (98) can reduce 95 to:
% 6.53/2.08 | (99) $false
% 6.53/2.08 |
% 6.53/2.08 |-The branch is then unsatisfiable
% 6.53/2.08 |-Branch two:
% 6.53/2.08 | (95) ~ (all_0_4_4 = create_slb)
% 6.53/2.08 | (108) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v3, bad) = v4 & findmin_cpq_eff(all_0_2_2) = v2 & update_slb(all_0_4_4, v0) = v3 & lookup_slb(all_0_4_4, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_4_4, v0) | ~ strictly_less_than(v0, v1)))
% 6.53/2.09 |
% 6.53/2.09 | Instantiating (108) with all_35_0_15, all_35_1_16, all_35_2_17, all_35_3_18, all_35_4_19 yields:
% 6.53/2.09 | (109) findmin_pqp_res(all_0_5_5) = all_35_4_19 & triple(all_0_5_5, all_35_1_16, bad) = all_35_0_15 & findmin_cpq_eff(all_0_2_2) = all_35_2_17 & update_slb(all_0_4_4, all_35_4_19) = all_35_1_16 & lookup_slb(all_0_4_4, all_35_4_19) = all_35_3_18 & (all_35_0_15 = all_35_2_17 | ~ contains_slb(all_0_4_4, all_35_4_19) | ~ strictly_less_than(all_35_4_19, all_35_3_18))
% 6.53/2.09 |
% 6.53/2.09 | Applying alpha-rule on (109) yields:
% 6.53/2.09 | (110) findmin_cpq_eff(all_0_2_2) = all_35_2_17
% 6.53/2.09 | (111) all_35_0_15 = all_35_2_17 | ~ contains_slb(all_0_4_4, all_35_4_19) | ~ strictly_less_than(all_35_4_19, all_35_3_18)
% 6.53/2.09 | (112) findmin_pqp_res(all_0_5_5) = all_35_4_19
% 6.53/2.09 | (113) lookup_slb(all_0_4_4, all_35_4_19) = all_35_3_18
% 6.53/2.09 | (114) triple(all_0_5_5, all_35_1_16, bad) = all_35_0_15
% 6.53/2.09 | (115) update_slb(all_0_4_4, all_35_4_19) = all_35_1_16
% 6.53/2.09 |
% 6.53/2.09 +-Applying beta-rule and splitting (79), into two cases.
% 6.53/2.09 |-Branch one:
% 6.53/2.09 | (98) all_0_4_4 = create_slb
% 6.53/2.09 |
% 6.53/2.09 | Equations (98) can reduce 95 to:
% 6.53/2.09 | (99) $false
% 6.53/2.09 |
% 6.53/2.09 |-The branch is then unsatisfiable
% 6.53/2.09 |-Branch two:
% 6.53/2.09 | (95) ~ (all_0_4_4 = create_slb)
% 6.53/2.09 | (119) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v3, all_0_3_3) = v4 & findmin_cpq_eff(all_0_2_2) = v2 & update_slb(all_0_4_4, v0) = v3 & lookup_slb(all_0_4_4, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_4_4, v0) | ~ less_than(v1, v0)))
% 6.53/2.09 |
% 6.53/2.09 | Instantiating (119) with all_40_0_20, all_40_1_21, all_40_2_22, all_40_3_23, all_40_4_24 yields:
% 6.53/2.09 | (120) findmin_pqp_res(all_0_5_5) = all_40_4_24 & triple(all_0_5_5, all_40_1_21, all_0_3_3) = all_40_0_20 & findmin_cpq_eff(all_0_2_2) = all_40_2_22 & update_slb(all_0_4_4, all_40_4_24) = all_40_1_21 & lookup_slb(all_0_4_4, all_40_4_24) = all_40_3_23 & (all_40_0_20 = all_40_2_22 | ~ contains_slb(all_0_4_4, all_40_4_24) | ~ less_than(all_40_3_23, all_40_4_24))
% 6.53/2.09 |
% 6.53/2.09 | Applying alpha-rule on (120) yields:
% 6.53/2.09 | (121) findmin_pqp_res(all_0_5_5) = all_40_4_24
% 6.53/2.09 | (122) lookup_slb(all_0_4_4, all_40_4_24) = all_40_3_23
% 6.53/2.09 | (123) findmin_cpq_eff(all_0_2_2) = all_40_2_22
% 6.53/2.09 | (124) triple(all_0_5_5, all_40_1_21, all_0_3_3) = all_40_0_20
% 6.53/2.09 | (125) update_slb(all_0_4_4, all_40_4_24) = all_40_1_21
% 6.66/2.09 | (126) all_40_0_20 = all_40_2_22 | ~ contains_slb(all_0_4_4, all_40_4_24) | ~ less_than(all_40_3_23, all_40_4_24)
% 6.66/2.09 |
% 6.66/2.09 +-Applying beta-rule and splitting (81), into two cases.
% 6.66/2.09 |-Branch one:
% 6.66/2.09 | (98) all_0_4_4 = create_slb
% 6.66/2.09 |
% 6.66/2.09 | Equations (98) can reduce 95 to:
% 6.66/2.09 | (99) $false
% 6.66/2.09 |
% 6.66/2.09 |-The branch is then unsatisfiable
% 6.66/2.09 |-Branch two:
% 6.66/2.09 | (95) ~ (all_0_4_4 = create_slb)
% 6.66/2.09 | (130) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v2, bad) = v3 & findmin_cpq_eff(all_0_2_2) = v1 & update_slb(all_0_4_4, v0) = v2 & (v3 = v1 | contains_slb(all_0_4_4, v0)))
% 6.66/2.09 |
% 6.66/2.09 | Instantiating (130) with all_46_0_25, all_46_1_26, all_46_2_27, all_46_3_28 yields:
% 6.66/2.09 | (131) findmin_pqp_res(all_0_5_5) = all_46_3_28 & triple(all_0_5_5, all_46_1_26, bad) = all_46_0_25 & findmin_cpq_eff(all_0_2_2) = all_46_2_27 & update_slb(all_0_4_4, all_46_3_28) = all_46_1_26 & (all_46_0_25 = all_46_2_27 | contains_slb(all_0_4_4, all_46_3_28))
% 6.66/2.09 |
% 6.66/2.09 | Applying alpha-rule on (131) yields:
% 6.66/2.09 | (132) update_slb(all_0_4_4, all_46_3_28) = all_46_1_26
% 6.66/2.09 | (133) findmin_cpq_eff(all_0_2_2) = all_46_2_27
% 6.66/2.09 | (134) all_46_0_25 = all_46_2_27 | contains_slb(all_0_4_4, all_46_3_28)
% 6.66/2.09 | (135) triple(all_0_5_5, all_46_1_26, bad) = all_46_0_25
% 6.66/2.09 | (136) findmin_pqp_res(all_0_5_5) = all_46_3_28
% 6.66/2.09 |
% 6.66/2.09 | Instantiating formula (72) with all_0_2_2, all_30_0_14, all_0_1_1 and discharging atoms findmin_cpq_res(all_0_2_2) = all_30_0_14, findmin_cpq_res(all_0_2_2) = all_0_1_1, yields:
% 6.66/2.09 | (137) all_30_0_14 = all_0_1_1
% 6.66/2.09 |
% 6.66/2.09 | Instantiating formula (69) with all_0_5_5, all_40_4_24, all_16_1_12 and discharging atoms findmin_pqp_res(all_0_5_5) = all_40_4_24, findmin_pqp_res(all_0_5_5) = all_16_1_12, yields:
% 6.66/2.09 | (138) all_40_4_24 = all_16_1_12
% 6.66/2.09 |
% 6.66/2.09 | Instantiating formula (69) with all_0_5_5, all_40_4_24, all_46_3_28 and discharging atoms findmin_pqp_res(all_0_5_5) = all_46_3_28, findmin_pqp_res(all_0_5_5) = all_40_4_24, yields:
% 6.66/2.09 | (139) all_46_3_28 = all_40_4_24
% 6.66/2.09 |
% 6.66/2.09 | Instantiating formula (69) with all_0_5_5, all_35_4_19, all_46_3_28 and discharging atoms findmin_pqp_res(all_0_5_5) = all_46_3_28, findmin_pqp_res(all_0_5_5) = all_35_4_19, yields:
% 6.66/2.09 | (140) all_46_3_28 = all_35_4_19
% 6.66/2.09 |
% 6.66/2.09 | Instantiating formula (69) with all_0_5_5, all_30_0_14, all_40_4_24 and discharging atoms findmin_pqp_res(all_0_5_5) = all_40_4_24, findmin_pqp_res(all_0_5_5) = all_30_0_14, yields:
% 6.66/2.09 | (141) all_40_4_24 = all_30_0_14
% 6.66/2.09 |
% 6.66/2.09 | Combining equations (139,140) yields a new equation:
% 6.66/2.09 | (142) all_40_4_24 = all_35_4_19
% 6.66/2.09 |
% 6.66/2.09 | Simplifying 142 yields:
% 6.66/2.09 | (143) all_40_4_24 = all_35_4_19
% 6.66/2.09 |
% 6.66/2.09 | Combining equations (138,143) yields a new equation:
% 6.66/2.09 | (144) all_35_4_19 = all_16_1_12
% 6.66/2.09 |
% 6.66/2.09 | Combining equations (141,143) yields a new equation:
% 6.66/2.09 | (145) all_35_4_19 = all_30_0_14
% 6.66/2.09 |
% 6.66/2.09 | Combining equations (144,145) yields a new equation:
% 6.66/2.09 | (146) all_30_0_14 = all_16_1_12
% 6.66/2.09 |
% 6.66/2.09 | Combining equations (146,137) yields a new equation:
% 6.66/2.09 | (147) all_16_1_12 = all_0_1_1
% 6.66/2.09 |
% 6.66/2.09 | Simplifying 147 yields:
% 6.66/2.09 | (148) all_16_1_12 = all_0_1_1
% 6.66/2.09 |
% 6.66/2.09 | Combining equations (137,145) yields a new equation:
% 6.66/2.09 | (149) all_35_4_19 = all_0_1_1
% 6.66/2.09 |
% 6.66/2.09 | Combining equations (149,143) yields a new equation:
% 6.66/2.09 | (150) all_40_4_24 = all_0_1_1
% 6.66/2.09 |
% 6.66/2.09 | From (148) and (96) follows:
% 6.66/2.09 | (151) contains_slb(all_0_4_4, all_0_1_1)
% 6.66/2.09 |
% 6.66/2.09 +-Applying beta-rule and splitting (126), into two cases.
% 6.66/2.09 |-Branch one:
% 6.66/2.09 | (152) ~ contains_slb(all_0_4_4, all_40_4_24)
% 6.66/2.09 |
% 6.66/2.09 | From (150) and (152) follows:
% 6.66/2.09 | (153) ~ contains_slb(all_0_4_4, all_0_1_1)
% 6.66/2.09 |
% 6.66/2.09 | Using (151) and (153) yields:
% 6.66/2.09 | (92) $false
% 6.66/2.09 |
% 6.66/2.09 |-The branch is then unsatisfiable
% 6.66/2.09 |-Branch two:
% 6.66/2.09 | (155) contains_slb(all_0_4_4, all_40_4_24)
% 6.66/2.09 | (156) all_40_0_20 = all_40_2_22 | ~ less_than(all_40_3_23, all_40_4_24)
% 6.66/2.09 |
% 6.66/2.09 | From (150) and (155) follows:
% 6.66/2.09 | (151) contains_slb(all_0_4_4, all_0_1_1)
% 6.66/2.09 |
% 6.66/2.09 | Instantiating formula (37) with all_0_2_2, 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_2_2, contains_slb(all_0_4_4, all_0_1_1), ~ contains_cpq(all_0_2_2, all_0_1_1), yields:
% 6.66/2.09 | (92) $false
% 6.66/2.09 |
% 6.66/2.09 |-The branch is then unsatisfiable
% 6.66/2.09 % SZS output end Proof for theBenchmark
% 6.66/2.09
% 6.66/2.09 1480ms
%------------------------------------------------------------------------------