TSTP Solution File: SWV381+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV381+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 17:51:11 EDT 2022
% Result : Theorem 9.48s 2.82s
% Output : Proof 12.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV381+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 19:07:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.51/0.60 ____ _
% 0.51/0.60 ___ / __ \_____(_)___ ________ __________
% 0.51/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.60
% 0.51/0.60 A Theorem Prover for First-Order Logic
% 0.51/0.60 (ePrincess v.1.0)
% 0.51/0.60
% 0.51/0.60 (c) Philipp Rümmer, 2009-2015
% 0.51/0.60 (c) Peter Backeman, 2014-2015
% 0.51/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.60 Bug reports to peter@backeman.se
% 0.51/0.60
% 0.51/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.60
% 0.51/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.10/1.04 Prover 0: Preprocessing ...
% 3.63/1.45 Prover 0: Warning: ignoring some quantifiers
% 3.78/1.49 Prover 0: Constructing countermodel ...
% 5.33/1.89 Prover 0: gave up
% 5.33/1.89 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.70/1.95 Prover 1: Preprocessing ...
% 6.64/2.15 Prover 1: Constructing countermodel ...
% 8.04/2.46 Prover 1: gave up
% 8.04/2.46 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 8.04/2.50 Prover 2: Preprocessing ...
% 9.08/2.67 Prover 2: Warning: ignoring some quantifiers
% 9.08/2.68 Prover 2: Constructing countermodel ...
% 9.48/2.82 Prover 2: proved (363ms)
% 9.48/2.82
% 9.48/2.82 No countermodel exists, formula is valid
% 9.48/2.82 % SZS status Theorem for theBenchmark
% 9.48/2.82
% 9.48/2.82 Generating proof ... Warning: ignoring some quantifiers
% 11.96/3.35 found it (size 58)
% 11.96/3.35
% 11.96/3.35 % SZS output start Proof for theBenchmark
% 11.96/3.35 Assumed formulas after preprocessing and simplification:
% 11.96/3.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v1 = 0) & ~ (v0 = 0) & phi(v6) = 0 & i(v5) = v7 & findmin_cpq_res(v5) = v8 & triple(v2, v3, v4) = v5 & findmin_cpq_eff(v5) = v6 & isnonempty_slb(create_slb) = v1 & issmallestelement_pq(v7, v8) = v9 & isnonempty_pq(create_pq) = v0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (pair_in_list(v16, v12, v14) = v17) | ~ (pair(v11, v13) = v15) | ~ (insert_slb(v10, v15) = v16) | ? [v18] : ( ~ (v18 = 0) & pair_in_list(v10, v12, v14) = v18)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (insert_pqp(v10, v13) = v14) | ~ (triple(v14, v16, v12) = v17) | ~ (pair(v13, bottom) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : (triple(v10, v11, v12) = v18 & insert_cpq(v18, v13) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v10, v16, v12) = v17) | ~ (pair(v13, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : (i(v19) = v20 & i(v17) = v18 & triple(v10, v11, v12) = v19 & insert_pq(v20, v13) = v18)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v10, v16, v12) = v17) | ~ (pair(v13, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : (( ~ (v18 = 0) & less_than(v14, v13) = v18) | (((v20 = 0 & triple(v10, v11, v12) = v19 & check_cpq(v19) = 0) | ( ~ (v18 = 0) & check_cpq(v17) = v18)) & ((v18 = 0 & check_cpq(v17) = 0) | ( ~ (v20 = 0) & triple(v10, v11, v12) = v19 & check_cpq(v19) = v20))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v10, v16, v12) = v17) | ~ (pair(v13, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : (( ~ (v18 = 0) & check_cpq(v17) = v18) | ( ~ (v18 = 0) & strictly_less_than(v13, v14) = v18))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (i(v14) = v15) | ~ (triple(v10, v11, v12) = v14) | ~ (contains_pq(v15, v13) = v16) | ? [v17] : ( ~ (v17 = 0) & contains_cpq(v14, v13) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (contains_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ( ~ (v17 = 0) & contains_slb(v10, v12) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (pair_in_list(v16, v12, v14) = 0) | ~ (pair(v11, v13) = v15) | ~ (insert_slb(v10, v15) = v16) | pair_in_list(v10, v12, v14) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (lookup_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ((v17 = v16 & lookup_slb(v10, v12) = v16) | ( ~ (v17 = 0) & contains_slb(v10, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (remove_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ((v18 = v16 & remove_slb(v10, v12) = v17 & insert_slb(v17, v14) = v16) | ( ~ (v17 = 0) & contains_slb(v10, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (remove_slb(v10, v12) = v15) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v15, v14) = v16) | ? [v17] : ? [v18] : ((v18 = v16 & remove_slb(v17, v12) = v16 & insert_slb(v10, v14) = v17) | ( ~ (v17 = 0) & contains_slb(v10, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (pair_in_list(v16, v12, v14) = 0) | ~ (pair(v11, v13) = v15) | ~ (insert_slb(v10, v15) = v16) | pair_in_list(v10, v12, v14) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (remove_pqp(v10, v13) = v14) | ~ (triple(v14, v15, v12) = v16) | ~ (remove_slb(v11, v13) = v15) | ? [v17] : ? [v18] : ((v18 = v16 & triple(v10, v11, v12) = v17 & remove_cpq(v17, v13) = v16) | ( ~ (v18 = 0) & lookup_slb(v11, v13) = v17 & less_than(v17, v13) = v18) | ( ~ (v17 = 0) & contains_slb(v11, v13) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (update_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : ((v19 = v16 & update_slb(v10, v12) = v17 & pair(v11, v12) = v18 & insert_slb(v17, v18) = v16) | ( ~ (v17 = 0) & strictly_less_than(v13, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (update_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ((v18 = v16 & update_slb(v10, v12) = v17 & insert_slb(v17, v14) = v16) | ( ~ (v17 = 0) & less_than(v12, v13) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (update_slb(v10, v12) = v15) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v15, v14) = v16) | ? [v17] : ? [v18] : ((v18 = v16 & update_slb(v17, v12) = v16 & insert_slb(v10, v14) = v17) | ( ~ (v17 = 0) & less_than(v12, v13) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (contains_cpq(v14, v13) = v15) | ~ (triple(v10, v11, v12) = v14) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & i(v14) = v16 & contains_pq(v16, v13) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (contains_cpq(v14, v13) = v15) | ~ (triple(v10, v11, v12) = v14) | ? [v16] : ( ~ (v16 = 0) & contains_slb(v11, v13) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (pair_in_list(v14, v11, v12) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (contains_slb(v14, v11) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (contains_slb(v15, v12) = 0) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | contains_slb(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = create_slb | ~ (findmin_pqp_res(v10) = v13) | ~ (triple(v10, v14, v12) = v15) | ~ (update_slb(v11, v13) = v14) | ? [v16] : ? [v17] : ((v17 = v15 & triple(v10, v11, v12) = v16 & findmin_cpq_eff(v16) = v15) | ( ~ (v17 = 0) & lookup_slb(v11, v13) = v16 & less_than(v16, v13) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (i(v14) = v15) | ~ (triple(v10, v11, v12) = v14) | ~ (contains_pq(v15, v13) = 0) | contains_cpq(v14, v13) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (remove_cpq(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v15 & remove_pqp(v10, v13) = v16 & triple(v16, v17, v12) = v15 & remove_slb(v11, v13) = v17) | ( ~ (v17 = 0) & lookup_slb(v11, v13) = v16 & less_than(v16, v13) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (remove_cpq(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v15 & remove_pqp(v10, v13) = v16 & triple(v16, v17, bad) = v15 & remove_slb(v11, v13) = v17) | ( ~ (v17 = 0) & lookup_slb(v11, v13) = v16 & strictly_less_than(v13, v16) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (remove_cpq(v14, v13) = v15) | ? [v16] : ((v16 = v15 & triple(v10, v11, bad) = v15) | (v16 = 0 & contains_slb(v11, v13) = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (insert_cpq(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : (insert_pqp(v10, v13) = v16 & triple(v16, v18, v12) = v15 & pair(v13, bottom) = v17 & insert_slb(v11, v17) = v18)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (remove_cpq(v11, v12) = v13) | ~ (succ_cpq(v10, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & succ_cpq(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (insert_cpq(v11, v12) = v13) | ~ (succ_cpq(v10, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & succ_cpq(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (contains_pq(v13, v12) = v14) | ~ (insert_pq(v10, v11) = v13) | ? [v15] : ( ~ (v15 = 0) & contains_pq(v10, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (remove_pq(v13, v12) = v14) | ~ (insert_pq(v10, v11) = v13) | ? [v15] : ? [v16] : ((v16 = v14 & remove_pq(v10, v12) = v15 & insert_pq(v15, v11) = v14) | ( ~ (v15 = 0) & contains_pq(v10, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (remove_pq(v10, v12) = v13) | ~ (insert_pq(v13, v11) = v14) | ? [v15] : ? [v16] : ((v16 = v14 & remove_pq(v15, v12) = v14 & insert_pq(v10, v11) = v15) | ( ~ (v15 = 0) & contains_pq(v10, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (triple(v14, v13, v12) = v11) | ~ (triple(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (pair_in_list(v14, v13, v12) = v11) | ~ (pair_in_list(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = create_slb | ~ (findmin_cpq_res(v13) = v14) | ~ (triple(v10, v11, v12) = v13) | findmin_pqp_res(v10) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = create_slb | ~ (triple(v10, v11, v12) = v13) | ~ (findmin_cpq_eff(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (findmin_pqp_res(v10) = v15 & ((v17 = v14 & triple(v10, v16, v12) = v14 & update_slb(v11, v15) = v16) | ( ~ (v17 = 0) & lookup_slb(v11, v15) = v16 & less_than(v16, v15) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v15) = v16)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = create_slb | ~ (triple(v10, v11, v12) = v13) | ~ (findmin_cpq_eff(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (findmin_pqp_res(v10) = v15 & ((v17 = v14 & triple(v10, v16, bad) = v14 & update_slb(v11, v15) = v16) | (v16 = 0 & contains_slb(v11, v15) = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = create_slb | ~ (triple(v10, v11, v12) = v13) | ~ (findmin_cpq_eff(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (findmin_pqp_res(v10) = v15 & ((v17 = v14 & triple(v10, v16, bad) = v14 & update_slb(v11, v15) = v16) | ( ~ (v17 = 0) & lookup_slb(v11, v15) = v16 & strictly_less_than(v15, v16) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v15) = v16)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (contains_cpq(v14, v13) = 0) | ~ (triple(v10, v11, v12) = v14) | contains_slb(v11, v13) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (contains_cpq(v14, v13) = 0) | ~ (triple(v10, v11, v12) = v14) | ? [v15] : (i(v14) = v15 & contains_pq(v15, v13) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14) | lookup_slb(v14, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14) | remove_slb(v14, v11) = v10) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14) | isnonempty_slb(v14) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (insert_pq(v13, v12) = v14) | ~ (insert_pq(v10, v11) = v13) | ? [v15] : (insert_pq(v15, v11) = v14 & insert_pq(v10, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (insert_pq(v13, v11) = v14) | ~ (insert_pq(v10, v12) = v13) | ? [v15] : (insert_pq(v15, v12) = v14 & insert_pq(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (pi_sharp_remove(v12, v11) = v13) | ~ (i(v10) = v12) | ? [v14] : ( ~ (v14 = 0) & pi_remove(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (removemin_cpq_eff(v11) = v12) | ~ (succ_cpq(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & succ_cpq(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (findmin_cpq_eff(v11) = v12) | ~ (succ_cpq(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & succ_cpq(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (issmallestelement_pq(v10, v11) = 0) | ~ (less_than(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & contains_pq(v10, v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (contains_pq(v12, v11) = v13) | ~ (insert_pq(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (less_than(v11, v12) = 0) | ~ (less_than(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & less_than(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (less_than(v10, v12) = v13) | ~ (less_than(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & less_than(v11, v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (contains_pq(v13, v12) = 0) | ~ (insert_pq(v10, v11) = v13) | contains_pq(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = bad | ~ (triple(v10, v11, v12) = v13) | ok(v13) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (pi_sharp_removemin(v13, v12) = v11) | ~ (pi_sharp_removemin(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (pi_sharp_find_min(v13, v12) = v11) | ~ (pi_sharp_find_min(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (pi_remove(v13, v12) = v11) | ~ (pi_remove(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (pi_sharp_remove(v13, v12) = v11) | ~ (pi_sharp_remove(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (remove_pqp(v13, v12) = v11) | ~ (remove_pqp(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (insert_pqp(v13, v12) = v11) | ~ (insert_pqp(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (contains_cpq(v13, v12) = v11) | ~ (contains_cpq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (remove_cpq(v13, v12) = v11) | ~ (remove_cpq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (insert_cpq(v13, v12) = v11) | ~ (insert_cpq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (succ_cpq(v13, v12) = v11) | ~ (succ_cpq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (update_slb(v13, v12) = v11) | ~ (update_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (lookup_slb(v13, v12) = v11) | ~ (lookup_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (remove_slb(v13, v12) = v11) | ~ (remove_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (contains_slb(v13, v12) = v11) | ~ (contains_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (pair(v13, v12) = v11) | ~ (pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (insert_slb(v13, v12) = v11) | ~ (insert_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (removemin_pq_res(v13, v12) = v11) | ~ (removemin_pq_res(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (removemin_pq_eff(v13, v12) = v11) | ~ (removemin_pq_eff(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (findmin_pq_res(v13, v12) = v11) | ~ (findmin_pq_res(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (findmin_pq_eff(v13, v12) = v11) | ~ (findmin_pq_eff(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (remove_pq(v13, v12) = v11) | ~ (remove_pq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (issmallestelement_pq(v13, v12) = v11) | ~ (issmallestelement_pq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (contains_pq(v13, v12) = v11) | ~ (contains_pq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (insert_pq(v13, v12) = v11) | ~ (insert_pq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (strictly_less_than(v13, v12) = v11) | ~ (strictly_less_than(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (less_than(v13, v12) = v11) | ~ (less_than(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v10, v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v15 = 0) & phi(v14) = v15 & findmin_cpq_eff(v13) = v14) | (findmin_cpq_res(v13) = v14 & ! [v16] : ( ~ (contains_cpq(v13, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & strictly_less_than(v16, v14) = v17)) & ! [v16] : ( ~ (strictly_less_than(v16, v14) = 0) | ? [v17] : ( ~ (v17 = 0) & contains_cpq(v13, v16) = v17))))) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (removemin_pq_res(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & issmallestelement_pq(v10, v11) = v13) | ( ~ (v13 = 0) & contains_pq(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (findmin_pq_res(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & issmallestelement_pq(v10, v11) = v13) | ( ~ (v13 = 0) & contains_pq(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (findmin_pq_eff(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & issmallestelement_pq(v10, v11) = v13) | ( ~ (v13 = 0) & contains_pq(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (pi_sharp_removemin(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & issmallestelement_pq(v10, v11) = v13) | ( ~ (v13 = 0) & contains_pq(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (pi_sharp_find_min(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & issmallestelement_pq(v10, v11) = v13) | ( ~ (v13 = 0) & contains_pq(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (pi_remove(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & pi_sharp_remove(v13, v11) = v14 & i(v10) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (pi_sharp_remove(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & contains_pq(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (issmallestelement_pq(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & contains_pq(v10, v13) = 0 & less_than(v11, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (contains_pq(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & pi_sharp_remove(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (strictly_less_than(v10, v11) = v12) | ? [v13] : ((v13 = 0 & less_than(v11, v10) = 0) | ( ~ (v13 = 0) & less_than(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (less_than(v11, v10) = v12) | less_than(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (less_than(v11, v10) = v12) | ? [v13] : ((v13 = 0 & strictly_less_than(v10, v11) = 0) | ( ~ (v13 = 0) & less_than(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (less_than(v10, v11) = v12) | less_than(v11, v10) = 0) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (phi(v12) = v11) | ~ (phi(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (pi_removemin(v12) = v11) | ~ (pi_removemin(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (pi_find_min(v12) = v11) | ~ (pi_find_min(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (i(v12) = v11) | ~ (i(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (removemin_cpq_res(v12) = v11) | ~ (removemin_cpq_res(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (findmin_cpq_res(v12) = v11) | ~ (findmin_cpq_res(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (findmin_pqp_res(v12) = v11) | ~ (findmin_pqp_res(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ok(v12) = v11) | ~ (ok(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (check_cpq(v12) = v11) | ~ (check_cpq(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (removemin_cpq_eff(v12) = v11) | ~ (removemin_cpq_eff(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (findmin_cpq_eff(v12) = v11) | ~ (findmin_cpq_eff(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (isnonempty_slb(v12) = v11) | ~ (isnonempty_slb(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (isnonempty_pq(v12) = v11) | ~ (isnonempty_pq(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (phi(v10) = v11) | ~ (ok(v12) = 0) | ? [v13] : (( ~ (v13 = 0) & check_cpq(v12) = v13) | ( ~ (v13 = 0) & succ_cpq(v10, v12) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (phi(v10) = v11) | ~ (check_cpq(v12) = 0) | ? [v13] : (( ~ (v13 = 0) & ok(v12) = v13) | ( ~ (v13 = 0) & succ_cpq(v10, v12) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (phi(v10) = v11) | ~ (succ_cpq(v10, v12) = 0) | ? [v13] : (( ~ (v13 = 0) & ok(v12) = v13) | ( ~ (v13 = 0) & check_cpq(v12) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (pi_sharp_find_min(v11, v12) = 0) | ~ (i(v10) = v11) | pi_removemin(v10) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (pi_sharp_find_min(v11, v12) = 0) | ~ (i(v10) = v11) | pi_find_min(v10) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (pi_sharp_remove(v12, v11) = 0) | ~ (i(v10) = v12) | pi_remove(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v10, v11, bad) = v12) | ? [v13] : ( ~ (v13 = 0) & ok(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v10, create_slb, v11) = v12) | i(v12) = create_pq) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v10, create_slb, v11) = v12) | findmin_cpq_res(v12) = bottom) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v10, create_slb, v11) = v12) | check_cpq(v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v10, create_slb, v11) = v12) | ? [v13] : (triple(v10, create_slb, bad) = v13 & findmin_cpq_eff(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (removemin_pq_eff(v10, v11) = v12) | ? [v13] : ((v13 = v12 & remove_pq(v10, v11) = v12) | ( ~ (v13 = 0) & issmallestelement_pq(v10, v11) = v13) | ( ~ (v13 = 0) & contains_pq(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (remove_pq(v10, v11) = v12) | ? [v13] : ((v13 = v12 & removemin_pq_eff(v10, v11) = v12) | ( ~ (v13 = 0) & issmallestelement_pq(v10, v11) = v13) | ( ~ (v13 = 0) & contains_pq(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (issmallestelement_pq(v10, v11) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & contains_pq(v10, v11) = 0) | ( ~ (v13 = 0) & pi_sharp_removemin(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (issmallestelement_pq(v10, v11) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & contains_pq(v10, v11) = 0) | ( ~ (v13 = 0) & pi_sharp_find_min(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (issmallestelement_pq(v10, v11) = 0) | ~ (contains_pq(v10, v12) = 0) | less_than(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (contains_pq(v10, v11) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & issmallestelement_pq(v10, v11) = 0) | ( ~ (v13 = 0) & pi_sharp_removemin(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (contains_pq(v10, v11) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & issmallestelement_pq(v10, v11) = 0) | ( ~ (v13 = 0) & pi_sharp_find_min(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (insert_pq(v10, v11) = v12) | remove_pq(v12, v11) = v10) & ! [v10] : ! [v11] : ! [v12] : ( ~ (insert_pq(v10, v11) = v12) | isnonempty_pq(v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (less_than(v11, v12) = 0) | ~ (less_than(v10, v11) = 0) | less_than(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (less_than(v11, v10) = v12) | ? [v13] : ((v13 = 0 & ~ (v12 = 0) & less_than(v10, v11) = 0) | ( ~ (v13 = 0) & strictly_less_than(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (less_than(v10, v11) = v12) | ? [v13] : ((v12 = 0 & ~ (v13 = 0) & less_than(v11, v10) = v13) | ( ~ (v13 = 0) & strictly_less_than(v10, v11) = v13))) & ! [v10] : ! [v11] : (v11 = create_slb | ~ (update_slb(create_slb, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (pi_removemin(v10) = v11) | ? [v12] : (i(v10) = v12 & ! [v13] : ~ (pi_sharp_find_min(v12, v13) = 0))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (pi_find_min(v10) = v11) | ? [v12] : (i(v10) = v12 & ! [v13] : ~ (pi_sharp_find_min(v12, v13) = 0))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (succ_cpq(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (less_than(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (less_than(bottom, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (pi_sharp_removemin(v10, v11) = 0) | (issmallestelement_pq(v10, v11) = 0 & contains_pq(v10, v11) = 0)) & ! [v10] : ! [v11] : ( ~ (pi_sharp_find_min(v10, v11) = 0) | (issmallestelement_pq(v10, v11) = 0 & contains_pq(v10, v11) = 0)) & ! [v10] : ! [v11] : ( ~ (pi_remove(v10, v11) = 0) | ? [v12] : (pi_sharp_remove(v12, v11) = 0 & i(v10) = v12)) & ! [v10] : ! [v11] : ( ~ (pi_sharp_remove(v10, v11) = 0) | contains_pq(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (i(v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & pi_sharp_find_min(v11, v12) = 0) | ( ~ (v12 = 0) & pi_removemin(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (i(v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & pi_sharp_find_min(v11, v12) = 0) | ( ~ (v12 = 0) & pi_find_min(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (removemin_cpq_res(v10) = v11) | findmin_cpq_res(v10) = v11) & ! [v10] : ! [v11] : ( ~ (findmin_cpq_res(v10) = v11) | removemin_cpq_res(v10) = v11) & ! [v10] : ! [v11] : ( ~ (findmin_cpq_res(v10) = v11) | ? [v12] : ? [v13] : (removemin_cpq_eff(v10) = v12 & findmin_cpq_eff(v10) = v13 & remove_cpq(v13, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (removemin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : (findmin_cpq_res(v10) = v13 & findmin_cpq_eff(v10) = v12 & remove_cpq(v12, v13) = v11)) & ! [v10] : ! [v11] : ( ~ (findmin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : (findmin_cpq_res(v10) = v13 & removemin_cpq_eff(v10) = v12 & remove_cpq(v11, v13) = v12)) & ! [v10] : ! [v11] : ( ~ (succ_cpq(v10, v11) = 0) | ? [v12] : (removemin_cpq_eff(v11) = v12 & succ_cpq(v10, v12) = 0)) & ! [v10] : ! [v11] : ( ~ (succ_cpq(v10, v11) = 0) | ? [v12] : (findmin_cpq_eff(v11) = v12 & succ_cpq(v10, v12) = 0)) & ! [v10] : ! [v11] : ~ (pair_in_list(create_slb, v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (issmallestelement_pq(v10, v11) = 0) | ? [v12] : ? [v13] : ((v13 = v12 & removemin_pq_eff(v10, v11) = v12 & remove_pq(v10, v11) = v12) | ( ~ (v12 = 0) & contains_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (issmallestelement_pq(v10, v11) = 0) | ? [v12] : ((v12 = v11 & removemin_pq_res(v10, v11) = v11) | ( ~ (v12 = 0) & contains_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (issmallestelement_pq(v10, v11) = 0) | ? [v12] : ((v12 = v11 & findmin_pq_res(v10, v11) = v11) | ( ~ (v12 = 0) & contains_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (issmallestelement_pq(v10, v11) = 0) | ? [v12] : ((v12 = v10 & findmin_pq_eff(v10, v11) = v10) | ( ~ (v12 = 0) & contains_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (issmallestelement_pq(v10, v11) = 0) | ? [v12] : ((v12 = 0 & pi_sharp_removemin(v10, v11) = 0) | ( ~ (v12 = 0) & contains_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (issmallestelement_pq(v10, v11) = 0) | ? [v12] : ((v12 = 0 & pi_sharp_find_min(v10, v11) = 0) | ( ~ (v12 = 0) & contains_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (contains_pq(v10, v11) = 0) | pi_sharp_remove(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (contains_pq(v10, v11) = 0) | ? [v12] : ? [v13] : ((v13 = v12 & removemin_pq_eff(v10, v11) = v12 & remove_pq(v10, v11) = v12) | ( ~ (v12 = 0) & issmallestelement_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (contains_pq(v10, v11) = 0) | ? [v12] : ((v12 = v11 & removemin_pq_res(v10, v11) = v11) | ( ~ (v12 = 0) & issmallestelement_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (contains_pq(v10, v11) = 0) | ? [v12] : ((v12 = v11 & findmin_pq_res(v10, v11) = v11) | ( ~ (v12 = 0) & issmallestelement_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (contains_pq(v10, v11) = 0) | ? [v12] : ((v12 = v10 & findmin_pq_eff(v10, v11) = v10) | ( ~ (v12 = 0) & issmallestelement_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (contains_pq(v10, v11) = 0) | ? [v12] : ((v12 = 0 & pi_sharp_removemin(v10, v11) = 0) | ( ~ (v12 = 0) & issmallestelement_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (contains_pq(v10, v11) = 0) | ? [v12] : ((v12 = 0 & pi_sharp_find_min(v10, v11) = 0) | ( ~ (v12 = 0) & issmallestelement_pq(v10, v11) = v12))) & ! [v10] : ! [v11] : ( ~ (strictly_less_than(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & less_than(v11, v10) = v12 & less_than(v10, v11) = 0)) & ! [v10] : ! [v11] : ( ~ (less_than(v10, v11) = 0) | ? [v12] : ((v12 = 0 & strictly_less_than(v10, v11) = 0) | (v12 = 0 & less_than(v11, v10) = 0))) & ! [v10] : ( ~ (phi(v10) = 0) | ? [v11] : (ok(v11) = 0 & check_cpq(v11) = 0 & succ_cpq(v10, v11) = 0)) & ! [v10] : ( ~ (pi_removemin(v10) = 0) | ? [v11] : ? [v12] : (pi_sharp_find_min(v11, v12) = 0 & i(v10) = v11)) & ! [v10] : ( ~ (pi_find_min(v10) = 0) | ? [v11] : ? [v12] : (pi_sharp_find_min(v11, v12) = 0 & i(v10) = v11)) & ! [v10] : ~ (contains_slb(create_slb, v10) = 0) & ! [v10] : ~ (contains_pq(create_pq, v10) = 0) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : triple(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : ? [v13] : pair_in_list(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : pi_sharp_removemin(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : pi_sharp_find_min(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : pi_remove(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : pi_sharp_remove(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : remove_pqp(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : insert_pqp(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : contains_cpq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : remove_cpq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : insert_cpq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : succ_cpq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : update_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : lookup_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : remove_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : contains_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : insert_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : removemin_pq_res(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : removemin_pq_eff(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : findmin_pq_res(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : findmin_pq_eff(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : remove_pq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : issmallestelement_pq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : contains_pq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : insert_pq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : strictly_less_than(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : less_than(v11, v10) = v12 & ? [v10] : ? [v11] : phi(v10) = v11 & ? [v10] : ? [v11] : pi_removemin(v10) = v11 & ? [v10] : ? [v11] : pi_find_min(v10) = v11 & ? [v10] : ? [v11] : i(v10) = v11 & ? [v10] : ? [v11] : removemin_cpq_res(v10) = v11 & ? [v10] : ? [v11] : findmin_cpq_res(v10) = v11 & ? [v10] : ? [v11] : findmin_pqp_res(v10) = v11 & ? [v10] : ? [v11] : ok(v10) = v11 & ? [v10] : ? [v11] : check_cpq(v10) = v11 & ? [v10] : ? [v11] : removemin_cpq_eff(v10) = v11 & ? [v10] : ? [v11] : findmin_cpq_eff(v10) = v11 & ? [v10] : ? [v11] : isnonempty_slb(v10) = v11 & ? [v10] : ? [v11] : isnonempty_pq(v10) = v11)
% 12.20/3.43 | 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 yields:
% 12.20/3.43 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_9_9 = 0) & phi(all_0_3_3) = 0 & i(all_0_4_4) = all_0_2_2 & findmin_cpq_res(all_0_4_4) = all_0_1_1 & triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_4_4 & findmin_cpq_eff(all_0_4_4) = all_0_3_3 & isnonempty_slb(create_slb) = all_0_8_8 & issmallestelement_pq(all_0_2_2, all_0_1_1) = all_0_0_0 & isnonempty_pq(create_pq) = all_0_9_9 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & pair_in_list(v0, v2, v4) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (insert_pqp(v0, v3) = v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : (( ~ (v8 = 0) & less_than(v4, v3) = v8) | (((v10 = 0 & triple(v0, v1, v2) = v9 & check_cpq(v9) = 0) | ( ~ (v8 = 0) & check_cpq(v7) = v8)) & ((v8 = 0 & check_cpq(v7) = 0) | ( ~ (v10 = 0) & triple(v0, v1, v2) = v9 & check_cpq(v9) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (( ~ (v8 = 0) & check_cpq(v7) = v8) | ( ~ (v8 = 0) & strictly_less_than(v3, v4) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~ (contains_pq(v5, v3) = v6) | ? [v7] : ( ~ (v7 = 0) & contains_cpq(v4, v3) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ((v7 = v6 & lookup_slb(v0, v2) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & triple(v0, v1, v2) = v7 & remove_cpq(v7, v3) = v6) | ( ~ (v8 = 0) & lookup_slb(v1, v3) = v7 & less_than(v7, v3) = v8) | ( ~ (v7 = 0) & contains_slb(v1, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6) | ( ~ (v7 = 0) & strictly_less_than(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & less_than(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & less_than(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & i(v4) = v6 & contains_pq(v6, v3) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | contains_slb(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ((v7 = v5 & triple(v0, v1, v2) = v6 & findmin_cpq_eff(v6) = v5) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~ (contains_pq(v5, v3) = 0) | contains_cpq(v4, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, v2) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, bad) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & strictly_less_than(v3, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = v5 & triple(v0, v1, bad) = v5) | (v6 = 0 & contains_slb(v1, v3) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (remove_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (insert_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (contains_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & contains_pq(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & remove_pq(v0, v2) = v5 & insert_pq(v5, v1) = v4) | ( ~ (v5 = 0) & contains_pq(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v0, v2) = v3) | ~ (insert_pq(v3, v1) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & remove_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5) | ( ~ (v5 = 0) & contains_pq(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, v2) = v3) | findmin_pqp_res(v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, v2) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & less_than(v6, v5) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | (v6 = 0 & contains_slb(v1, v5) = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & strictly_less_than(v5, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | ? [v5] : (i(v4) = v5 & contains_pq(v5, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | lookup_slb(v4, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | remove_slb(v4, v1) = v0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : (insert_pq(v5, v1) = v4 & insert_pq(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v1) = v4) | ~ (insert_pq(v0, v2) = v3) | ? [v5] : (insert_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pi_sharp_remove(v2, v1) = v3) | ~ (i(v0) = v2) | ? [v4] : ( ~ (v4 = 0) & pi_remove(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (issmallestelement_pq(v0, v1) = 0) | ~ (less_than(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & contains_pq(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (contains_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & less_than(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (contains_pq(v3, v2) = 0) | ~ (insert_pq(v0, v1) = v3) | contains_pq(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~ (pi_sharp_find_min(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~ (issmallestelement_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & phi(v4) = v5 & findmin_cpq_eff(v3) = v4) | (findmin_cpq_res(v3) = v4 & ! [v6] : ( ~ (contains_cpq(v3, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & strictly_less_than(v6, v4) = v7)) & ! [v6] : ( ~ (strictly_less_than(v6, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & contains_cpq(v3, v6) = v7))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_removemin(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_find_min(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_remove(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & pi_sharp_remove(v3, v1) = v4 & i(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_remove(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & contains_pq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (issmallestelement_pq(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & contains_pq(v0, v3) = 0 & less_than(v1, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (contains_pq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & pi_sharp_remove(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ((v3 = 0 & less_than(v1, v0) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | less_than(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & strictly_less_than(v0, v1) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pi_removemin(v2) = v1) | ~ (pi_removemin(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~ (pi_find_min(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (phi(v0) = v1) | ~ (ok(v2) = 0) | ? [v3] : (( ~ (v3 = 0) & check_cpq(v2) = v3) | ( ~ (v3 = 0) & succ_cpq(v0, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (phi(v0) = v1) | ~ (check_cpq(v2) = 0) | ? [v3] : (( ~ (v3 = 0) & ok(v2) = v3) | ( ~ (v3 = 0) & succ_cpq(v0, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (phi(v0) = v1) | ~ (succ_cpq(v0, v2) = 0) | ? [v3] : (( ~ (v3 = 0) & ok(v2) = v3) | ( ~ (v3 = 0) & check_cpq(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (pi_sharp_find_min(v1, v2) = 0) | ~ (i(v0) = v1) | pi_removemin(v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (pi_sharp_find_min(v1, v2) = 0) | ~ (i(v0) = v1) | pi_find_min(v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (pi_sharp_remove(v2, v1) = 0) | ~ (i(v0) = v2) | pi_remove(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ? [v3] : ((v3 = v2 & remove_pq(v0, v1) = v2) | ( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (remove_pq(v0, v1) = v2) | ? [v3] : ((v3 = v2 & removemin_pq_eff(v0, v1) = v2) | ( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (issmallestelement_pq(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & contains_pq(v0, v1) = 0) | ( ~ (v3 = 0) & pi_sharp_removemin(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (issmallestelement_pq(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & contains_pq(v0, v1) = 0) | ( ~ (v3 = 0) & pi_sharp_find_min(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ~ (contains_pq(v0, v2) = 0) | less_than(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (contains_pq(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & issmallestelement_pq(v0, v1) = 0) | ( ~ (v3 = 0) & pi_sharp_removemin(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (contains_pq(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & issmallestelement_pq(v0, v1) = 0) | ( ~ (v3 = 0) & pi_sharp_find_min(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | remove_pq(v2, v1) = v0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v1) = 0) | less_than(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ~ (v2 = 0) & less_than(v0, v1) = 0) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v0, v1) = v2) | ? [v3] : ((v2 = 0 & ~ (v3 = 0) & less_than(v1, v0) = v3) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pi_removemin(v0) = v1) | ? [v2] : (i(v0) = v2 & ! [v3] : ~ (pi_sharp_find_min(v2, v3) = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pi_find_min(v0) = v1) | ? [v2] : (i(v0) = v2 & ! [v3] : ~ (pi_sharp_find_min(v2, v3) = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (pi_sharp_removemin(v0, v1) = 0) | (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (pi_sharp_find_min(v0, v1) = 0) | (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (pi_remove(v0, v1) = 0) | ? [v2] : (pi_sharp_remove(v2, v1) = 0 & i(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (pi_sharp_remove(v0, v1) = 0) | contains_pq(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & pi_sharp_find_min(v1, v2) = 0) | ( ~ (v2 = 0) & pi_removemin(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & pi_sharp_find_min(v1, v2) = 0) | ( ~ (v2 = 0) & pi_find_min(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | ? [v2] : ? [v3] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (findmin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2)) & ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (removemin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (findmin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0)) & ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = v2 & removemin_pq_eff(v0, v1) = v2 & remove_pq(v0, v1) = v2) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = v1 & removemin_pq_res(v0, v1) = v1) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = v1 & findmin_pq_res(v0, v1) = v1) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = v0 & findmin_pq_eff(v0, v1) = v0) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = 0 & pi_sharp_removemin(v0, v1) = 0) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = 0 & pi_sharp_find_min(v0, v1) = 0) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | pi_sharp_remove(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = v2 & removemin_pq_eff(v0, v1) = v2 & remove_pq(v0, v1) = v2) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = v1 & removemin_pq_res(v0, v1) = v1) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = v1 & findmin_pq_res(v0, v1) = v1) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = v0 & findmin_pq_eff(v0, v1) = v0) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = 0 & pi_sharp_removemin(v0, v1) = 0) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = 0 & pi_sharp_find_min(v0, v1) = 0) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (less_than(v0, v1) = 0) | ? [v2] : ((v2 = 0 & strictly_less_than(v0, v1) = 0) | (v2 = 0 & less_than(v1, v0) = 0))) & ! [v0] : ( ~ (phi(v0) = 0) | ? [v1] : (ok(v1) = 0 & check_cpq(v1) = 0 & succ_cpq(v0, v1) = 0)) & ! [v0] : ( ~ (pi_removemin(v0) = 0) | ? [v1] : ? [v2] : (pi_sharp_find_min(v1, v2) = 0 & i(v0) = v1)) & ! [v0] : ( ~ (pi_find_min(v0) = 0) | ? [v1] : ? [v2] : (pi_sharp_find_min(v1, v2) = 0 & i(v0) = v1)) & ! [v0] : ~ (contains_slb(create_slb, v0) = 0) & ! [v0] : ~ (contains_pq(create_pq, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : triple(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : pi_sharp_removemin(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : pi_sharp_find_min(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : pi_remove(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : pi_sharp_remove(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : remove_pqp(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_pqp(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : contains_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : remove_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : succ_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : update_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : lookup_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : remove_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : contains_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : removemin_pq_res(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : removemin_pq_eff(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : findmin_pq_res(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : findmin_pq_eff(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : remove_pq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : issmallestelement_pq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : contains_pq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_pq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : strictly_less_than(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : less_than(v1, v0) = v2 & ? [v0] : ? [v1] : phi(v0) = v1 & ? [v0] : ? [v1] : pi_removemin(v0) = v1 & ? [v0] : ? [v1] : pi_find_min(v0) = v1 & ? [v0] : ? [v1] : i(v0) = v1 & ? [v0] : ? [v1] : removemin_cpq_res(v0) = v1 & ? [v0] : ? [v1] : findmin_cpq_res(v0) = v1 & ? [v0] : ? [v1] : findmin_pqp_res(v0) = v1 & ? [v0] : ? [v1] : ok(v0) = v1 & ? [v0] : ? [v1] : check_cpq(v0) = v1 & ? [v0] : ? [v1] : removemin_cpq_eff(v0) = v1 & ? [v0] : ? [v1] : findmin_cpq_eff(v0) = v1 & ? [v0] : ? [v1] : isnonempty_slb(v0) = v1 & ? [v0] : ? [v1] : isnonempty_pq(v0) = v1
% 12.61/3.46 |
% 12.61/3.46 | Applying alpha-rule on (1) yields:
% 12.61/3.46 | (2) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & pi_sharp_find_min(v1, v2) = 0) | ( ~ (v2 = 0) & pi_removemin(v0) = v2)))
% 12.61/3.46 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (contains_pq(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & issmallestelement_pq(v0, v1) = 0) | ( ~ (v3 = 0) & pi_sharp_find_min(v0, v1) = v3)))
% 12.61/3.46 | (4) ? [v0] : ? [v1] : isnonempty_slb(v0) = v1
% 12.61/3.46 | (5) findmin_cpq_eff(all_0_4_4) = all_0_3_3
% 12.61/3.46 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 12.61/3.46 | (7) ? [v0] : ? [v1] : ? [v2] : lookup_slb(v1, v0) = v2
% 12.61/3.46 | (8) ? [v0] : ? [v1] : phi(v0) = v1
% 12.61/3.46 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0)
% 12.61/3.46 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | (v6 = 0 & contains_slb(v1, v5) = 0))))
% 12.61/3.46 | (11) ? [v0] : ? [v1] : ? [v2] : ? [v3] : triple(v2, v1, v0) = v3
% 12.61/3.46 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : (( ~ (v8 = 0) & less_than(v4, v3) = v8) | (((v10 = 0 & triple(v0, v1, v2) = v9 & check_cpq(v9) = 0) | ( ~ (v8 = 0) & check_cpq(v7) = v8)) & ((v8 = 0 & check_cpq(v7) = 0) | ( ~ (v10 = 0) & triple(v0, v1, v2) = v9 & check_cpq(v9) = v10)))))
% 12.61/3.46 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0))
% 12.61/3.46 | (14) ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | pi_sharp_remove(v0, v1) = 0)
% 12.61/3.46 | (15) ! [v0] : ! [v1] : ( ~ (pi_sharp_remove(v0, v1) = 0) | contains_pq(v0, v1) = 0)
% 12.61/3.46 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (pi_sharp_remove(v2, v1) = 0) | ~ (i(v0) = v2) | pi_remove(v0, v1) = 0)
% 12.61/3.46 | (17) ? [v0] : ? [v1] : ? [v2] : succ_cpq(v1, v0) = v2
% 12.61/3.46 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 12.61/3.46 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ~ (v2 = 0) & less_than(v0, v1) = 0) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3)))
% 12.61/3.46 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, bad) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & strictly_less_than(v3, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)))
% 12.61/3.46 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (remove_pq(v0, v1) = v2) | ? [v3] : ((v3 = v2 & removemin_pq_eff(v0, v1) = v2) | ( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3)))
% 12.61/3.46 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) = v0))
% 12.61/3.46 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0)
% 12.61/3.46 | (24) ? [v0] : ? [v1] : ? [v2] : contains_cpq(v1, v0) = v2
% 12.61/3.46 | (25) ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3
% 12.61/3.46 | (26) ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = v1 & removemin_pq_res(v0, v1) = v1) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2)))
% 12.61/3.46 | (27) ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = v1 & removemin_pq_res(v0, v1) = v1) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2)))
% 12.61/3.46 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 12.61/3.46 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 12.61/3.46 | (30) ? [v0] : ? [v1] : ? [v2] : contains_slb(v1, v0) = v2
% 12.61/3.46 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 12.61/3.46 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & pair_in_list(v0, v2, v4) = v8))
% 12.61/3.46 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0))
% 12.61/3.46 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pi_removemin(v2) = v1) | ~ (pi_removemin(v2) = v0))
% 12.61/3.46 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 12.61/3.46 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ~ (contains_pq(v0, v2) = 0) | less_than(v1, v2) = 0)
% 12.61/3.46 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pi_sharp_remove(v2, v1) = v3) | ~ (i(v0) = v2) | ? [v4] : ( ~ (v4 = 0) & pi_remove(v0, v1) = v4))
% 12.61/3.46 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~ (contains_pq(v5, v3) = 0) | contains_cpq(v4, v3) = 0)
% 12.61/3.46 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0))
% 12.61/3.46 | (40) ! [v0] : ~ (contains_slb(create_slb, v0) = 0)
% 12.61/3.46 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 12.61/3.46 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_find_min(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3)))
% 12.61/3.46 | (43) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1))
% 12.61/3.46 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0))
% 12.61/3.46 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (issmallestelement_pq(v0, v1) = 0) | ~ (less_than(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & contains_pq(v0, v2) = v4))
% 12.61/3.46 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 12.61/3.46 | (47) isnonempty_slb(create_slb) = all_0_8_8
% 12.61/3.46 | (48) ? [v0] : ? [v1] : ? [v2] : insert_pqp(v1, v0) = v2
% 12.61/3.47 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))
% 12.61/3.47 | (50) ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1))
% 12.61/3.47 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v0, v2) = v3) | ~ (insert_pq(v3, v1) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & remove_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5) | ( ~ (v5 = 0) & contains_pq(v0, v2) = v5)))
% 12.61/3.47 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (phi(v0) = v1) | ~ (succ_cpq(v0, v2) = 0) | ? [v3] : (( ~ (v3 = 0) & ok(v2) = v3) | ( ~ (v3 = 0) & check_cpq(v2) = v3)))
% 12.61/3.47 | (53) phi(all_0_3_3) = 0
% 12.61/3.47 | (54) ? [v0] : ? [v1] : ? [v2] : findmin_pq_eff(v1, v0) = v2
% 12.61/3.47 | (55) ? [v0] : ? [v1] : ? [v2] : insert_pq(v1, v0) = v2
% 12.61/3.47 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 12.61/3.47 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 12.61/3.47 | (58) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1))
% 12.61/3.47 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0))
% 12.61/3.47 | (60) triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_4_4
% 12.61/3.47 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3)))
% 12.61/3.47 | (62) ! [v0] : ~ (contains_pq(create_pq, v0) = 0)
% 12.61/3.47 | (63) ? [v0] : ? [v1] : ? [v2] : findmin_pq_res(v1, v0) = v2
% 12.61/3.47 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3))
% 12.61/3.47 | (65) ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = v0 & findmin_pq_eff(v0, v1) = v0) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2)))
% 12.61/3.47 | (66) ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = v0 & findmin_pq_eff(v0, v1) = v0) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2)))
% 12.61/3.47 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v0, v1) = v2) | ? [v3] : ((v2 = 0 & ~ (v3 = 0) & less_than(v1, v0) = v3) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3)))
% 12.61/3.47 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0))
% 12.61/3.47 | (69) ! [v0] : ! [v1] : ( ~ (findmin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2))
% 12.61/3.47 | (70) ? [v0] : ? [v1] : i(v0) = v1
% 12.61/3.47 | (71) ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = 0 & pi_sharp_removemin(v0, v1) = 0) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2)))
% 12.61/3.47 | (72) ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = 0 & pi_sharp_removemin(v0, v1) = 0) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2)))
% 12.61/3.47 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)))
% 12.61/3.47 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (issmallestelement_pq(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & contains_pq(v0, v1) = 0) | ( ~ (v3 = 0) & pi_sharp_find_min(v0, v1) = v3)))
% 12.61/3.47 | (75) ? [v0] : ? [v1] : isnonempty_pq(v0) = v1
% 12.61/3.47 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 12.61/3.47 | (77) ? [v0] : ? [v1] : pi_removemin(v0) = v1
% 12.61/3.47 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)))
% 12.61/3.47 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v1) = v4) | ~ (insert_pq(v0, v2) = v3) | ? [v5] : (insert_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5))
% 12.61/3.47 | (80) ~ (all_0_9_9 = 0)
% 12.61/3.47 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (phi(v0) = v1) | ~ (check_cpq(v2) = 0) | ? [v3] : (( ~ (v3 = 0) & ok(v2) = v3) | ( ~ (v3 = 0) & succ_cpq(v0, v2) = v3)))
% 12.61/3.47 | (82) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (contains_pq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & pi_sharp_remove(v0, v1) = v3))
% 12.61/3.47 | (83) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_remove(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & contains_pq(v0, v1) = v3))
% 12.61/3.47 | (84) ? [v0] : ? [v1] : removemin_cpq_eff(v0) = v1
% 12.61/3.47 | (85) ! [v0] : ! [v1] : ( ~ (less_than(v0, v1) = 0) | ? [v2] : ((v2 = 0 & strictly_less_than(v0, v1) = 0) | (v2 = 0 & less_than(v1, v0) = 0)))
% 12.61/3.47 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, v2) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & less_than(v6, v5) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6))))
% 12.61/3.47 | (87) ? [v0] : ? [v1] : ? [v2] : removemin_pq_eff(v1, v0) = v2
% 12.61/3.47 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 12.61/3.47 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | contains_slb(v0, v2) = 0)
% 12.61/3.47 | (90) ? [v0] : ? [v1] : pi_find_min(v0) = v1
% 12.61/3.47 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (contains_pq(v3, v2) = 0) | ~ (insert_pq(v0, v1) = v3) | contains_pq(v0, v2) = 0)
% 12.61/3.47 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & less_than(v2, v3) = v7)))
% 12.61/3.47 | (93) ? [v0] : ? [v1] : ? [v2] : insert_cpq(v1, v0) = v2
% 12.61/3.47 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0))
% 12.61/3.47 | (95) ! [v0] : ( ~ (phi(v0) = 0) | ? [v1] : (ok(v1) = 0 & check_cpq(v1) = 0 & succ_cpq(v0, v1) = 0))
% 12.61/3.47 | (96) ? [v0] : ? [v1] : ? [v2] : issmallestelement_pq(v1, v0) = v2
% 12.61/3.47 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & triple(v0, v1, v2) = v7 & remove_cpq(v7, v3) = v6) | ( ~ (v8 = 0) & lookup_slb(v1, v3) = v7 & less_than(v7, v3) = v8) | ( ~ (v7 = 0) & contains_slb(v1, v3) = v7)))
% 12.61/3.47 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0))
% 12.61/3.47 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 12.61/3.48 | (100) isnonempty_pq(create_pq) = all_0_9_9
% 12.61/3.48 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6) | ( ~ (v7 = 0) & strictly_less_than(v3, v2) = v7)))
% 12.61/3.48 | (102) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1)
% 12.61/3.48 | (103) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 12.61/3.48 | (104) ? [v0] : ? [v1] : ? [v2] : pi_remove(v1, v0) = v2
% 12.61/3.48 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0))
% 12.61/3.48 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = v5 & triple(v0, v1, bad) = v5) | (v6 = 0 & contains_slb(v1, v3) = 0)))
% 12.61/3.48 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 12.61/3.48 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | lookup_slb(v4, v1) = v2)
% 12.61/3.48 | (109) ? [v0] : ? [v1] : ? [v2] : strictly_less_than(v1, v0) = v2
% 12.61/3.48 | (110) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_removemin(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3)))
% 12.61/3.48 | (111) ? [v0] : ? [v1] : removemin_cpq_res(v0) = v1
% 12.61/3.48 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2) = 0)
% 12.61/3.48 | (113) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 12.61/3.48 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0))
% 12.61/3.48 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ((v7 = v5 & triple(v0, v1, v2) = v6 & findmin_cpq_eff(v6) = v5) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)))
% 12.61/3.48 | (116) ! [v0] : ! [v1] : ( ~ (pi_sharp_removemin(v0, v1) = 0) | (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0))
% 12.73/3.48 | (117) ? [v0] : ? [v1] : ? [v2] : remove_pq(v1, v0) = v2
% 12.73/3.48 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0))
% 12.73/3.48 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v1) = 0) | less_than(v0, v2) = 0)
% 12.73/3.48 | (120) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 12.73/3.48 | (121) ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (findmin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0))
% 12.73/3.48 | (122) ? [v0] : ? [v1] : findmin_pqp_res(v0) = v1
% 12.73/3.48 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, v2) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)))
% 12.73/3.48 | (124) ? [v0] : ? [v1] : ok(v0) = v1
% 12.73/3.48 | (125) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 12.73/3.48 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4))
% 12.73/3.48 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0))
% 12.73/3.48 | (128) ! [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))
% 12.73/3.48 | (129) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3)))
% 12.73/3.48 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 12.73/3.48 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq)
% 12.73/3.48 | (132) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3)))
% 12.73/3.48 | (133) ! [v0] : ! [v1] : ( ~ (pi_sharp_find_min(v0, v1) = 0) | (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0))
% 12.73/3.48 | (134) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ((v3 = 0 & less_than(v1, v0) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3)))
% 12.73/3.48 | (135) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0))
% 12.73/3.48 | (136) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (phi(v0) = v1) | ~ (ok(v2) = 0) | ? [v3] : (( ~ (v3 = 0) & check_cpq(v2) = v3) | ( ~ (v3 = 0) & succ_cpq(v0, v2) = v3)))
% 12.73/3.48 | (137) ? [v0] : ? [v1] : ? [v2] : pi_sharp_find_min(v1, v0) = v2
% 12.73/3.48 | (138) ! [v0] : ! [v1] : ( ~ (pi_remove(v0, v1) = 0) | ? [v2] : (pi_sharp_remove(v2, v1) = 0 & i(v0) = v2))
% 12.73/3.48 | (139) ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = v1 & findmin_pq_res(v0, v1) = v1) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2)))
% 12.73/3.48 | (140) ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = v1 & findmin_pq_res(v0, v1) = v1) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2)))
% 12.73/3.48 | (141) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 12.73/3.48 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0)
% 12.73/3.48 | (143) ? [v0] : ? [v1] : ? [v2] : remove_slb(v1, v0) = v2
% 12.73/3.48 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0))
% 12.73/3.48 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & i(v4) = v6 & contains_pq(v6, v3) = v7))
% 12.73/3.48 | (146) ? [v0] : ? [v1] : ? [v2] : contains_pq(v1, v0) = v2
% 12.73/3.48 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 12.73/3.48 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0)
% 12.73/3.48 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 12.73/3.48 | (150) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1))
% 12.73/3.48 | (151) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0)
% 12.73/3.48 | (152) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | less_than(v0, v1) = 0)
% 12.73/3.48 | (153) ? [v0] : ? [v1] : ? [v2] : less_than(v1, v0) = v2
% 12.73/3.48 | (154) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0)
% 12.73/3.48 | (155) ! [v0] : ( ~ (pi_removemin(v0) = 0) | ? [v1] : ? [v2] : (pi_sharp_find_min(v1, v2) = 0 & i(v0) = v1))
% 12.73/3.49 | (156) ? [v0] : ? [v1] : findmin_cpq_res(v0) = v1
% 12.73/3.49 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (contains_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & contains_pq(v0, v2) = v5))
% 12.73/3.49 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 12.73/3.49 | (159) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~ (pi_find_min(v2) = v0))
% 12.73/3.49 | (160) ? [v0] : ? [v1] : ? [v2] : removemin_pq_res(v1, v0) = v2
% 12.73/3.49 | (161) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | remove_pq(v2, v1) = v0)
% 12.73/3.49 | (162) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & pi_sharp_find_min(v1, v2) = 0) | ( ~ (v2 = 0) & pi_find_min(v0) = v2)))
% 12.73/3.49 | (163) ! [v0] : ! [v1] : (v1 = 0 | ~ (pi_find_min(v0) = v1) | ? [v2] : (i(v0) = v2 & ! [v3] : ~ (pi_sharp_find_min(v2, v3) = 0)))
% 12.73/3.49 | (164) ! [v0] : ! [v1] : (v1 = 0 | ~ (pi_removemin(v0) = v1) | ? [v2] : (i(v0) = v2 & ! [v3] : ~ (pi_sharp_find_min(v2, v3) = 0)))
% 12.73/3.49 | (165) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0))
% 12.73/3.49 | (166) ? [v0] : ? [v1] : ? [v2] : remove_pqp(v1, v0) = v2
% 12.73/3.49 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 12.73/3.49 | (168) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0)
% 12.73/3.49 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ((v7 = v6 & lookup_slb(v0, v2) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)))
% 12.73/3.49 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = v8))
% 12.73/3.49 | (171) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 12.73/3.49 | (172) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (( ~ (v8 = 0) & check_cpq(v7) = v8) | ( ~ (v8 = 0) & strictly_less_than(v3, v4) = v8)))
% 12.73/3.49 | (173) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 12.73/3.49 | (174) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ? [v3] : ((v3 = v2 & remove_pq(v0, v1) = v2) | ( ~ (v3 = 0) & issmallestelement_pq(v0, v1) = v3) | ( ~ (v3 = 0) & contains_pq(v0, v1) = v3)))
% 12.73/3.49 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : (insert_pq(v5, v1) = v4 & insert_pq(v0, v2) = v5))
% 12.73/3.49 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & less_than(v2, v3) = v7)))
% 12.73/3.49 | (177) ! [v0] : ! [v1] : ! [v2] : ( ~ (pi_sharp_find_min(v1, v2) = 0) | ~ (i(v0) = v1) | pi_find_min(v0) = 0)
% 12.73/3.49 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))
% 12.73/3.49 | (179) ! [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))
% 12.73/3.49 | (180) ? [v0] : ? [v1] : check_cpq(v0) = v1
% 12.73/3.49 | (181) ? [v0] : ? [v1] : ? [v2] : insert_slb(v1, v0) = v2
% 12.73/3.49 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 12.73/3.49 | (183) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | remove_slb(v4, v1) = v0)
% 12.73/3.49 | (184) issmallestelement_pq(all_0_2_2, all_0_1_1) = all_0_0_0
% 12.73/3.49 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & strictly_less_than(v5, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6))))
% 12.73/3.49 | (186) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_remove(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & pi_sharp_remove(v3, v1) = v4 & i(v0) = v3))
% 12.73/3.49 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, v2) = v3) | findmin_pqp_res(v0) = v4)
% 12.73/3.49 | (188) ! [v0] : ( ~ (pi_find_min(v0) = 0) | ? [v1] : ? [v2] : (pi_sharp_find_min(v1, v2) = 0 & i(v0) = v1))
% 12.73/3.49 | (189) ! [v0] : ! [v1] : ! [v2] : ( ~ (pi_sharp_find_min(v1, v2) = 0) | ~ (i(v0) = v1) | pi_removemin(v0) = 0)
% 12.73/3.49 | (190) ? [v0] : ? [v1] : ? [v2] : pi_sharp_remove(v1, v0) = v2
% 12.73/3.49 | (191) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & phi(v4) = v5 & findmin_cpq_eff(v3) = v4) | (findmin_cpq_res(v3) = v4 & ! [v6] : ( ~ (contains_cpq(v3, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & strictly_less_than(v6, v4) = v7)) & ! [v6] : ( ~ (strictly_less_than(v6, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & contains_cpq(v3, v6) = v7)))))
% 12.73/3.49 | (192) ? [v0] : ? [v1] : ? [v2] : pi_sharp_removemin(v1, v0) = v2
% 12.73/3.49 | (193) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & strictly_less_than(v0, v1) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3)))
% 12.73/3.49 | (194) ! [v0] : ! [v1] : ! [v2] : ( ~ (contains_pq(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & issmallestelement_pq(v0, v1) = 0) | ( ~ (v3 = 0) & pi_sharp_removemin(v0, v1) = v3)))
% 12.73/3.49 | (195) ? [v0] : ? [v1] : ? [v2] : update_slb(v1, v0) = v2
% 12.73/3.49 | (196) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0)
% 12.73/3.49 | (197) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & remove_pq(v0, v2) = v5 & insert_pq(v5, v1) = v4) | ( ~ (v5 = 0) & contains_pq(v0, v2) = v5)))
% 12.73/3.49 | (198) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | ? [v2] : ? [v3] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2))
% 12.73/3.49 | (199) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (contains_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2))
% 12.73/3.49 | (200) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~ (pi_sharp_find_min(v3, v2) = v0))
% 12.73/3.49 | (201) ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ((v2 = 0 & pi_sharp_find_min(v0, v1) = 0) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2)))
% 12.73/3.49 | (202) ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ((v2 = 0 & pi_sharp_find_min(v0, v1) = 0) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2)))
% 12.73/3.49 | (203) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & less_than(v0, v1) = v4))
% 12.73/3.49 | (204) ? [v0] : ? [v1] : ? [v2] : pair(v1, v0) = v2
% 12.73/3.49 | (205) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (issmallestelement_pq(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & contains_pq(v0, v3) = 0 & less_than(v1, v3) = v4))
% 12.73/3.49 | (206) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (insert_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5))
% 12.73/3.50 | (207) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0))
% 12.73/3.50 | (208) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0))
% 12.73/3.50 | (209) ? [v0] : ? [v1] : findmin_cpq_eff(v0) = v1
% 12.73/3.50 | (210) ! [v0] : ! [v1] : ( ~ (contains_pq(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = v2 & removemin_pq_eff(v0, v1) = v2 & remove_pq(v0, v1) = v2) | ( ~ (v2 = 0) & issmallestelement_pq(v0, v1) = v2)))
% 12.73/3.50 | (211) ! [v0] : ! [v1] : ( ~ (issmallestelement_pq(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = v2 & removemin_pq_eff(v0, v1) = v2 & remove_pq(v0, v1) = v2) | ( ~ (v2 = 0) & contains_pq(v0, v1) = v2)))
% 12.73/3.50 | (212) ~ (all_0_8_8 = 0)
% 12.73/3.50 | (213) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 12.73/3.50 | (214) i(all_0_4_4) = all_0_2_2
% 12.73/3.50 | (215) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (remove_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5))
% 12.73/3.50 | (216) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | ? [v5] : (i(v4) = v5 & contains_pq(v5, v3) = 0))
% 12.73/3.50 | (217) findmin_cpq_res(all_0_4_4) = all_0_1_1
% 12.73/3.50 | (218) ? [v0] : ? [v1] : ? [v2] : remove_cpq(v1, v0) = v2
% 12.73/3.50 | (219) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~ (issmallestelement_pq(v3, v2) = v0))
% 12.73/3.50 | (220) ! [v0] : ! [v1] : ! [v2] : ( ~ (issmallestelement_pq(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & contains_pq(v0, v1) = 0) | ( ~ (v3 = 0) & pi_sharp_removemin(v0, v1) = v3)))
% 12.73/3.50 | (221) ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (removemin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0))
% 12.73/3.50 | (222) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~ (contains_pq(v5, v3) = v6) | ? [v7] : ( ~ (v7 = 0) & contains_cpq(v4, v3) = v7))
% 12.73/3.50 | (223) ~ (all_0_0_0 = 0)
% 12.73/3.50 |
% 12.73/3.50 | Instantiating formula (198) with all_0_1_1, all_0_4_4 and discharging atoms findmin_cpq_res(all_0_4_4) = all_0_1_1, yields:
% 12.73/3.50 | (224) ? [v0] : ? [v1] : (removemin_cpq_eff(all_0_4_4) = v0 & findmin_cpq_eff(all_0_4_4) = v1 & remove_cpq(v1, all_0_1_1) = v0)
% 12.73/3.50 |
% 12.73/3.50 | Instantiating formula (191) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 12.73/3.50 | (225) ? [v0] : ? [v1] : (( ~ (v1 = 0) & phi(v0) = v1 & findmin_cpq_eff(all_0_4_4) = v0) | (findmin_cpq_res(all_0_4_4) = v0 & ! [v2] : ( ~ (contains_cpq(all_0_4_4, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & strictly_less_than(v2, v0) = v3)) & ! [v2] : ( ~ (strictly_less_than(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & contains_cpq(all_0_4_4, v2) = v3))))
% 12.73/3.50 |
% 12.73/3.50 | Instantiating formula (69) with all_0_3_3, all_0_4_4 and discharging atoms findmin_cpq_eff(all_0_4_4) = all_0_3_3, yields:
% 12.73/3.50 | (226) ? [v0] : ? [v1] : (findmin_cpq_res(all_0_4_4) = v1 & removemin_cpq_eff(all_0_4_4) = v0 & remove_cpq(all_0_3_3, v1) = v0)
% 12.73/3.50 |
% 12.73/3.50 | Instantiating formula (205) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms issmallestelement_pq(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 12.73/3.50 | (227) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & contains_pq(all_0_2_2, v0) = 0 & less_than(all_0_1_1, v0) = v1)
% 12.73/3.50 |
% 12.73/3.50 | Instantiating (226) with all_96_0_127, all_96_1_128 yields:
% 12.73/3.50 | (228) findmin_cpq_res(all_0_4_4) = all_96_0_127 & removemin_cpq_eff(all_0_4_4) = all_96_1_128 & remove_cpq(all_0_3_3, all_96_0_127) = all_96_1_128
% 12.73/3.50 |
% 12.73/3.50 | Applying alpha-rule on (228) yields:
% 12.73/3.50 | (229) findmin_cpq_res(all_0_4_4) = all_96_0_127
% 12.73/3.50 | (230) removemin_cpq_eff(all_0_4_4) = all_96_1_128
% 12.73/3.50 | (231) remove_cpq(all_0_3_3, all_96_0_127) = all_96_1_128
% 12.73/3.50 |
% 12.73/3.50 | Instantiating (225) with all_98_0_129, all_98_1_130 yields:
% 12.73/3.50 | (232) ( ~ (all_98_0_129 = 0) & phi(all_98_1_130) = all_98_0_129 & findmin_cpq_eff(all_0_4_4) = all_98_1_130) | (findmin_cpq_res(all_0_4_4) = all_98_1_130 & ! [v0] : ( ~ (contains_cpq(all_0_4_4, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & strictly_less_than(v0, all_98_1_130) = v1)) & ! [v0] : ( ~ (strictly_less_than(v0, all_98_1_130) = 0) | ? [v1] : ( ~ (v1 = 0) & contains_cpq(all_0_4_4, v0) = v1)))
% 12.73/3.50 |
% 12.73/3.50 | Instantiating (224) with all_99_0_131, all_99_1_132 yields:
% 12.73/3.50 | (233) removemin_cpq_eff(all_0_4_4) = all_99_1_132 & findmin_cpq_eff(all_0_4_4) = all_99_0_131 & remove_cpq(all_99_0_131, all_0_1_1) = all_99_1_132
% 12.73/3.50 |
% 12.73/3.50 | Applying alpha-rule on (233) yields:
% 12.73/3.50 | (234) removemin_cpq_eff(all_0_4_4) = all_99_1_132
% 12.73/3.50 | (235) findmin_cpq_eff(all_0_4_4) = all_99_0_131
% 12.73/3.50 | (236) remove_cpq(all_99_0_131, all_0_1_1) = all_99_1_132
% 12.73/3.50 |
% 12.73/3.50 +-Applying beta-rule and splitting (227), into two cases.
% 12.73/3.50 |-Branch one:
% 12.73/3.50 | (237) all_0_0_0 = 0
% 12.73/3.50 |
% 12.73/3.50 | Equations (237) can reduce 223 to:
% 12.73/3.50 | (238) $false
% 12.73/3.50 |
% 12.73/3.50 |-The branch is then unsatisfiable
% 12.73/3.50 |-Branch two:
% 12.73/3.50 | (223) ~ (all_0_0_0 = 0)
% 12.73/3.50 | (240) ? [v0] : ? [v1] : ( ~ (v1 = 0) & contains_pq(all_0_2_2, v0) = 0 & less_than(all_0_1_1, v0) = v1)
% 12.73/3.50 |
% 12.73/3.50 | Instantiating (240) with all_109_0_135, all_109_1_136 yields:
% 12.73/3.50 | (241) ~ (all_109_0_135 = 0) & contains_pq(all_0_2_2, all_109_1_136) = 0 & less_than(all_0_1_1, all_109_1_136) = all_109_0_135
% 12.73/3.50 |
% 12.73/3.50 | Applying alpha-rule on (241) yields:
% 12.73/3.50 | (242) ~ (all_109_0_135 = 0)
% 12.73/3.50 | (243) contains_pq(all_0_2_2, all_109_1_136) = 0
% 12.73/3.50 | (244) less_than(all_0_1_1, all_109_1_136) = all_109_0_135
% 12.73/3.50 |
% 12.73/3.50 | Instantiating formula (113) with all_0_4_4, all_96_0_127, all_0_1_1 and discharging atoms findmin_cpq_res(all_0_4_4) = all_96_0_127, findmin_cpq_res(all_0_4_4) = all_0_1_1, yields:
% 12.73/3.50 | (245) all_96_0_127 = all_0_1_1
% 12.73/3.50 |
% 12.73/3.50 | Instantiating formula (120) with all_0_4_4, all_99_0_131, all_0_3_3 and discharging atoms findmin_cpq_eff(all_0_4_4) = all_99_0_131, findmin_cpq_eff(all_0_4_4) = all_0_3_3, yields:
% 12.73/3.50 | (246) all_99_0_131 = all_0_3_3
% 12.73/3.50 |
% 12.73/3.50 | From (245) and (229) follows:
% 12.73/3.50 | (217) findmin_cpq_res(all_0_4_4) = all_0_1_1
% 12.73/3.50 |
% 12.73/3.50 | From (246) and (235) follows:
% 12.73/3.50 | (5) findmin_cpq_eff(all_0_4_4) = all_0_3_3
% 12.73/3.50 |
% 12.73/3.50 +-Applying beta-rule and splitting (232), into two cases.
% 12.73/3.50 |-Branch one:
% 12.73/3.50 | (249) ~ (all_98_0_129 = 0) & phi(all_98_1_130) = all_98_0_129 & findmin_cpq_eff(all_0_4_4) = all_98_1_130
% 12.73/3.50 |
% 12.73/3.50 | Applying alpha-rule on (249) yields:
% 12.73/3.50 | (250) ~ (all_98_0_129 = 0)
% 12.73/3.50 | (251) phi(all_98_1_130) = all_98_0_129
% 12.73/3.50 | (252) findmin_cpq_eff(all_0_4_4) = all_98_1_130
% 12.73/3.50 |
% 12.73/3.50 | Instantiating formula (120) with all_0_4_4, all_98_1_130, all_0_3_3 and discharging atoms findmin_cpq_eff(all_0_4_4) = all_98_1_130, findmin_cpq_eff(all_0_4_4) = all_0_3_3, yields:
% 12.73/3.51 | (253) all_98_1_130 = all_0_3_3
% 12.73/3.51 |
% 12.73/3.51 | From (253) and (251) follows:
% 12.73/3.51 | (254) phi(all_0_3_3) = all_98_0_129
% 12.73/3.51 |
% 12.73/3.51 | Instantiating formula (135) with all_0_3_3, all_98_0_129, 0 and discharging atoms phi(all_0_3_3) = all_98_0_129, phi(all_0_3_3) = 0, yields:
% 12.73/3.51 | (255) all_98_0_129 = 0
% 12.73/3.51 |
% 12.73/3.51 | Equations (255) can reduce 250 to:
% 12.73/3.51 | (238) $false
% 12.73/3.51 |
% 12.73/3.51 |-The branch is then unsatisfiable
% 12.73/3.51 |-Branch two:
% 12.73/3.51 | (257) findmin_cpq_res(all_0_4_4) = all_98_1_130 & ! [v0] : ( ~ (contains_cpq(all_0_4_4, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & strictly_less_than(v0, all_98_1_130) = v1)) & ! [v0] : ( ~ (strictly_less_than(v0, all_98_1_130) = 0) | ? [v1] : ( ~ (v1 = 0) & contains_cpq(all_0_4_4, v0) = v1))
% 12.73/3.51 |
% 12.73/3.51 | Applying alpha-rule on (257) yields:
% 12.73/3.51 | (258) findmin_cpq_res(all_0_4_4) = all_98_1_130
% 12.73/3.51 | (259) ! [v0] : ( ~ (contains_cpq(all_0_4_4, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & strictly_less_than(v0, all_98_1_130) = v1))
% 12.73/3.51 | (260) ! [v0] : ( ~ (strictly_less_than(v0, all_98_1_130) = 0) | ? [v1] : ( ~ (v1 = 0) & contains_cpq(all_0_4_4, v0) = v1))
% 12.73/3.51 |
% 12.73/3.51 | Instantiating formula (113) with all_0_4_4, all_98_1_130, all_0_1_1 and discharging atoms findmin_cpq_res(all_0_4_4) = all_98_1_130, findmin_cpq_res(all_0_4_4) = all_0_1_1, yields:
% 12.73/3.51 | (261) all_98_1_130 = all_0_1_1
% 12.73/3.51 |
% 12.73/3.51 | Instantiating formula (38) with all_0_2_2, all_0_4_4, all_109_1_136, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms i(all_0_4_4) = all_0_2_2, triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_4_4, contains_pq(all_0_2_2, all_109_1_136) = 0, yields:
% 12.73/3.51 | (262) contains_cpq(all_0_4_4, all_109_1_136) = 0
% 12.73/3.51 |
% 12.73/3.51 | Instantiating formula (152) with all_109_0_135, all_0_1_1, all_109_1_136 and discharging atoms less_than(all_0_1_1, all_109_1_136) = all_109_0_135, yields:
% 12.73/3.51 | (263) all_109_0_135 = 0 | less_than(all_109_1_136, all_0_1_1) = 0
% 12.73/3.51 |
% 12.73/3.51 | Instantiating formula (193) with all_109_0_135, all_0_1_1, all_109_1_136 and discharging atoms less_than(all_0_1_1, all_109_1_136) = all_109_0_135, yields:
% 12.73/3.51 | (264) all_109_0_135 = 0 | ? [v0] : ((v0 = 0 & strictly_less_than(all_109_1_136, all_0_1_1) = 0) | ( ~ (v0 = 0) & less_than(all_109_1_136, all_0_1_1) = v0))
% 12.73/3.51 |
% 12.73/3.51 +-Applying beta-rule and splitting (263), into two cases.
% 12.73/3.51 |-Branch one:
% 12.73/3.51 | (265) less_than(all_109_1_136, all_0_1_1) = 0
% 12.73/3.51 |
% 12.73/3.51 +-Applying beta-rule and splitting (264), into two cases.
% 12.73/3.51 |-Branch one:
% 12.73/3.51 | (266) all_109_0_135 = 0
% 12.73/3.51 |
% 12.73/3.51 | Equations (266) can reduce 242 to:
% 12.73/3.51 | (238) $false
% 12.73/3.51 |
% 12.73/3.51 |-The branch is then unsatisfiable
% 12.73/3.51 |-Branch two:
% 12.73/3.51 | (242) ~ (all_109_0_135 = 0)
% 12.73/3.51 | (269) ? [v0] : ((v0 = 0 & strictly_less_than(all_109_1_136, all_0_1_1) = 0) | ( ~ (v0 = 0) & less_than(all_109_1_136, all_0_1_1) = v0))
% 12.73/3.51 |
% 12.73/3.51 | Instantiating (269) with all_164_0_151 yields:
% 12.73/3.51 | (270) (all_164_0_151 = 0 & strictly_less_than(all_109_1_136, all_0_1_1) = 0) | ( ~ (all_164_0_151 = 0) & less_than(all_109_1_136, all_0_1_1) = all_164_0_151)
% 12.73/3.51 |
% 12.73/3.51 +-Applying beta-rule and splitting (270), into two cases.
% 12.73/3.51 |-Branch one:
% 12.73/3.51 | (271) all_164_0_151 = 0 & strictly_less_than(all_109_1_136, all_0_1_1) = 0
% 12.73/3.51 |
% 12.73/3.51 | Applying alpha-rule on (271) yields:
% 12.73/3.51 | (272) all_164_0_151 = 0
% 12.73/3.51 | (273) strictly_less_than(all_109_1_136, all_0_1_1) = 0
% 12.73/3.51 |
% 12.73/3.51 | Instantiating formula (259) with all_109_1_136 and discharging atoms contains_cpq(all_0_4_4, all_109_1_136) = 0, yields:
% 12.73/3.51 | (274) ? [v0] : ( ~ (v0 = 0) & strictly_less_than(all_109_1_136, all_98_1_130) = v0)
% 12.73/3.51 |
% 12.73/3.51 | Instantiating formula (260) with all_109_1_136 yields:
% 12.73/3.51 | (275) ~ (strictly_less_than(all_109_1_136, all_98_1_130) = 0) | ? [v0] : ( ~ (v0 = 0) & contains_cpq(all_0_4_4, all_109_1_136) = v0)
% 12.73/3.51 |
% 12.73/3.51 | Instantiating (274) with all_196_0_161 yields:
% 12.73/3.51 | (276) ~ (all_196_0_161 = 0) & strictly_less_than(all_109_1_136, all_98_1_130) = all_196_0_161
% 12.73/3.51 |
% 12.73/3.51 | Applying alpha-rule on (276) yields:
% 12.73/3.51 | (277) ~ (all_196_0_161 = 0)
% 12.73/3.51 | (278) strictly_less_than(all_109_1_136, all_98_1_130) = all_196_0_161
% 12.73/3.51 |
% 12.73/3.51 | From (261) and (278) follows:
% 12.73/3.51 | (279) strictly_less_than(all_109_1_136, all_0_1_1) = all_196_0_161
% 12.73/3.51 |
% 12.73/3.51 +-Applying beta-rule and splitting (275), into two cases.
% 12.73/3.51 |-Branch one:
% 12.73/3.51 | (280) ~ (strictly_less_than(all_109_1_136, all_98_1_130) = 0)
% 12.73/3.51 |
% 12.73/3.51 | From (261) and (280) follows:
% 12.73/3.51 | (281) ~ (strictly_less_than(all_109_1_136, all_0_1_1) = 0)
% 12.73/3.51 |
% 12.73/3.51 | Using (273) and (281) yields:
% 12.73/3.51 | (282) $false
% 12.73/3.51 |
% 12.73/3.51 |-The branch is then unsatisfiable
% 12.73/3.51 |-Branch two:
% 12.73/3.51 | (283) strictly_less_than(all_109_1_136, all_98_1_130) = 0
% 12.73/3.51 | (284) ? [v0] : ( ~ (v0 = 0) & contains_cpq(all_0_4_4, all_109_1_136) = v0)
% 12.73/3.51 |
% 12.73/3.51 | From (261) and (283) follows:
% 12.73/3.51 | (273) strictly_less_than(all_109_1_136, all_0_1_1) = 0
% 12.73/3.51 |
% 12.73/3.51 | Instantiating formula (105) with all_109_1_136, all_0_1_1, all_196_0_161, 0 and discharging atoms strictly_less_than(all_109_1_136, all_0_1_1) = all_196_0_161, strictly_less_than(all_109_1_136, all_0_1_1) = 0, yields:
% 12.73/3.51 | (286) all_196_0_161 = 0
% 12.73/3.51 |
% 12.73/3.51 | Equations (286) can reduce 277 to:
% 12.73/3.51 | (238) $false
% 12.73/3.51 |
% 12.73/3.51 |-The branch is then unsatisfiable
% 12.73/3.51 |-Branch two:
% 12.73/3.51 | (288) ~ (all_164_0_151 = 0) & less_than(all_109_1_136, all_0_1_1) = all_164_0_151
% 12.73/3.51 |
% 12.73/3.51 | Applying alpha-rule on (288) yields:
% 12.73/3.51 | (289) ~ (all_164_0_151 = 0)
% 12.73/3.51 | (290) less_than(all_109_1_136, all_0_1_1) = all_164_0_151
% 12.73/3.51 |
% 12.73/3.51 | Instantiating formula (88) with all_109_1_136, all_0_1_1, 0, all_164_0_151 and discharging atoms less_than(all_109_1_136, all_0_1_1) = all_164_0_151, less_than(all_109_1_136, all_0_1_1) = 0, yields:
% 12.73/3.51 | (272) all_164_0_151 = 0
% 12.73/3.51 |
% 12.73/3.51 | Equations (272) can reduce 289 to:
% 12.73/3.51 | (238) $false
% 12.73/3.51 |
% 12.73/3.51 |-The branch is then unsatisfiable
% 12.73/3.51 |-Branch two:
% 12.73/3.51 | (293) ~ (less_than(all_109_1_136, all_0_1_1) = 0)
% 12.73/3.51 | (266) all_109_0_135 = 0
% 12.73/3.51 |
% 12.73/3.51 | Equations (266) can reduce 242 to:
% 12.73/3.51 | (238) $false
% 12.73/3.51 |
% 12.73/3.51 |-The branch is then unsatisfiable
% 12.73/3.51 % SZS output end Proof for theBenchmark
% 12.73/3.51
% 12.73/3.51 2902ms
%------------------------------------------------------------------------------