TSTP Solution File: SWV415+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV415+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 17:51:18 EDT 2022
% Result : Theorem 4.62s 1.73s
% Output : Proof 6.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV415+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 15 22:05:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.59/0.58 ___ / __ \_____(_)___ ________ __________
% 0.59/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.58
% 0.59/0.58 A Theorem Prover for First-Order Logic
% 0.59/0.58 (ePrincess v.1.0)
% 0.59/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/1.02 Prover 0: Preprocessing ...
% 3.80/1.48 Prover 0: Warning: ignoring some quantifiers
% 3.89/1.52 Prover 0: Constructing countermodel ...
% 4.62/1.73 Prover 0: proved (1099ms)
% 4.62/1.73
% 4.62/1.73 No countermodel exists, formula is valid
% 4.62/1.73 % SZS status Theorem for theBenchmark
% 4.62/1.73
% 4.62/1.73 Generating proof ... Warning: ignoring some quantifiers
% 6.46/2.09 found it (size 21)
% 6.46/2.09
% 6.46/2.09 % SZS output start Proof for theBenchmark
% 6.46/2.09 Assumed formulas after preprocessing and simplification:
% 6.46/2.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v6) & i(v5) = v6 & i(v4) = v7 & triple(v0, v1, v2) = v4 & insert_cpq(v4, v3) = v5 & insert_pq(v7, v3) = v8 & ~ isnonempty_slb(create_slb) & ~ isnonempty_pq(create_pq) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (insert_pqp(v9, v12) = v13) | ~ (triple(v13, v15, v11) = v16) | ~ (pair(v12, bottom) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : (triple(v9, v10, v11) = v17 & insert_cpq(v17, v12) = v16)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (triple(v9, v15, v11) = v16) | ~ (pair(v12, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ~ check_cpq(v16) | ~ strictly_less_than(v12, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (triple(v9, v15, v11) = v16) | ~ (pair(v12, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ~ less_than(v13, v12) | ? [v17] : (triple(v9, v10, v11) = v17 & ( ~ check_cpq(v17) | check_cpq(v16)) & ( ~ check_cpq(v16) | check_cpq(v17)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (triple(v9, v15, v11) = v16) | ~ (pair(v12, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : (i(v18) = v19 & i(v16) = v17 & triple(v9, v10, v11) = v18 & insert_pq(v19, v12) = v17)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (pair(v10, v12) = v14) | ~ (insert_slb(v9, v14) = v15) | ~ pair_in_list(v15, v11, v13) | pair_in_list(v9, v11, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = v10 | ~ (lookup_slb(v14, v11) = v15) | ~ (pair(v10, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ~ contains_slb(v9, v11) | lookup_slb(v9, v11) = v15) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = v10 | ~ (remove_slb(v14, v11) = v15) | ~ (pair(v10, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ~ contains_slb(v9, v11) | ? [v16] : (remove_slb(v9, v11) = v16 & insert_slb(v16, v13) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = v10 | ~ (remove_slb(v9, v11) = v14) | ~ (pair(v10, v12) = v13) | ~ (insert_slb(v14, v13) = v15) | ~ contains_slb(v9, v11) | ? [v16] : (remove_slb(v16, v11) = v15 & insert_slb(v9, v13) = v16)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = v10 | ~ (pair(v10, v12) = v14) | ~ (insert_slb(v9, v14) = v15) | ~ pair_in_list(v15, v11, v13) | pair_in_list(v9, v11, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (remove_pqp(v9, v12) = v13) | ~ (triple(v13, v14, v11) = v15) | ~ (remove_slb(v10, v12) = v14) | ~ contains_slb(v10, v12) | ? [v16] : ? [v17] : ? [v18] : (triple(v9, v10, v11) = v17 & remove_cpq(v17, v12) = v18 & lookup_slb(v10, v12) = v16 & (v18 = v15 | ~ less_than(v16, v12)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v13) = v15) | ~ (triple(v9, v11, v12) = v14) | ? [v16] : (i(v15) = v16 & i(v14) = v16)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (update_slb(v14, v11) = v15) | ~ (pair(v10, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ~ strictly_less_than(v12, v11) | ? [v16] : ? [v17] : (update_slb(v9, v11) = v16 & pair(v10, v11) = v17 & insert_slb(v16, v17) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (update_slb(v14, v11) = v15) | ~ (pair(v10, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ~ less_than(v11, v12) | ? [v16] : (update_slb(v9, v11) = v16 & insert_slb(v16, v13) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (update_slb(v9, v11) = v14) | ~ (pair(v10, v12) = v13) | ~ (insert_slb(v14, v13) = v15) | ~ less_than(v11, v12) | ? [v16] : (update_slb(v16, v11) = v15 & insert_slb(v9, v13) = v16)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (pair(v10, v12) = v14) | ~ (insert_slb(v9, v14) = v15) | ~ pair_in_list(v9, v11, v13) | pair_in_list(v15, v11, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (lookup_slb(v13, v10) = v14) | ~ (pair(v10, v11) = v12) | ~ (insert_slb(v9, v12) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v9 | ~ (remove_slb(v13, v10) = v14) | ~ (pair(v10, v11) = v12) | ~ (insert_slb(v9, v12) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (pair(v10, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ~ contains_slb(v14, v11) | contains_slb(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = create_slb | ~ (findmin_pqp_res(v9) = v12) | ~ (triple(v9, v13, v11) = v14) | ~ (update_slb(v10, v12) = v13) | ~ contains_slb(v10, v12) | ? [v15] : ? [v16] : ? [v17] : (triple(v9, v10, v11) = v16 & findmin_cpq_eff(v16) = v17 & lookup_slb(v10, v12) = v15 & (v17 = v14 | ~ less_than(v15, v12)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v9, v10, v11) = v13) | ~ (remove_cpq(v13, v12) = v14) | ~ contains_slb(v10, v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (remove_pqp(v9, v12) = v16 & triple(v16, v17, v11) = v18 & lookup_slb(v10, v12) = v15 & remove_slb(v10, v12) = v17 & (v18 = v14 | ~ less_than(v15, v12)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v9, v10, v11) = v13) | ~ (remove_cpq(v13, v12) = v14) | ~ contains_slb(v10, v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (remove_pqp(v9, v12) = v16 & triple(v16, v17, bad) = v18 & lookup_slb(v10, v12) = v15 & remove_slb(v10, v12) = v17 & (v18 = v14 | ~ strictly_less_than(v12, v15)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v9, v10, v11) = v13) | ~ (remove_cpq(v13, v12) = v14) | triple(v9, v10, bad) = v14 | contains_slb(v10, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v9, v10, v11) = v13) | ~ (insert_cpq(v13, v12) = v14) | ? [v15] : ? [v16] : ? [v17] : (insert_pqp(v9, v12) = v15 & triple(v15, v17, v11) = v14 & pair(v12, bottom) = v16 & insert_slb(v10, v16) = v17)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (pair(v10, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ~ contains_slb(v9, v11) | contains_slb(v14, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (remove_pq(v12, v11) = v13) | ~ (insert_pq(v9, v10) = v12) | ~ contains_pq(v9, v11) | ? [v14] : (remove_pq(v9, v11) = v14 & insert_pq(v14, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (remove_pq(v9, v11) = v12) | ~ (insert_pq(v12, v10) = v13) | ~ contains_pq(v9, v11) | ? [v14] : (remove_pq(v14, v11) = v13 & insert_pq(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (triple(v13, v12, v11) = v10) | ~ (triple(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v9, v10, v11) = v13) | ~ contains_cpq(v13, v12) | contains_slb(v10, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v9, v10, v11) = v13) | ~ contains_slb(v10, v12) | contains_cpq(v13, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (pair(v10, v11) = v12) | ~ (insert_slb(v9, v12) = v13) | pair_in_list(v13, v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (pair(v10, v11) = v12) | ~ (insert_slb(v9, v12) = v13) | contains_slb(v13, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (pair(v10, v11) = v12) | ~ (insert_slb(v9, v12) = v13) | isnonempty_slb(v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (insert_pq(v12, v11) = v13) | ~ (insert_pq(v9, v10) = v12) | ? [v14] : (insert_pq(v14, v10) = v13 & insert_pq(v9, v11) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (insert_pq(v12, v10) = v13) | ~ (insert_pq(v9, v11) = v12) | ? [v14] : (insert_pq(v14, v11) = v13 & insert_pq(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (remove_pq(v11, v10) = v12) | ~ (insert_pq(v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (insert_pq(v9, v10) = v12) | ~ contains_pq(v12, v11) | contains_pq(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = bad | ~ (triple(v9, v10, v11) = v12) | ok(v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (remove_pqp(v12, v11) = v10) | ~ (remove_pqp(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (insert_pqp(v12, v11) = v10) | ~ (insert_pqp(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (remove_cpq(v12, v11) = v10) | ~ (remove_cpq(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (insert_cpq(v12, v11) = v10) | ~ (insert_cpq(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (update_slb(v12, v11) = v10) | ~ (update_slb(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (lookup_slb(v12, v11) = v10) | ~ (lookup_slb(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (remove_slb(v12, v11) = v10) | ~ (remove_slb(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (pair(v12, v11) = v10) | ~ (pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (insert_slb(v12, v11) = v10) | ~ (insert_slb(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (removemin_pq_res(v12, v11) = v10) | ~ (removemin_pq_res(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (removemin_pq_eff(v12, v11) = v10) | ~ (removemin_pq_eff(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (findmin_pq_res(v12, v11) = v10) | ~ (findmin_pq_res(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (findmin_pq_eff(v12, v11) = v10) | ~ (findmin_pq_eff(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (remove_pq(v12, v11) = v10) | ~ (remove_pq(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (insert_pq(v12, v11) = v10) | ~ (insert_pq(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = create_slb | ~ (triple(v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (findmin_pqp_res(v9) = v13 & triple(v9, v16, v11) = v17 & findmin_cpq_eff(v12) = v15 & update_slb(v10, v13) = v16 & lookup_slb(v10, v13) = v14 & (v17 = v15 | ~ contains_slb(v10, v13) | ~ less_than(v14, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = create_slb | ~ (triple(v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (findmin_pqp_res(v9) = v13 & triple(v9, v16, bad) = v17 & findmin_cpq_eff(v12) = v15 & update_slb(v10, v13) = v16 & lookup_slb(v10, v13) = v14 & (v17 = v15 | ~ contains_slb(v10, v13) | ~ strictly_less_than(v13, v14)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = create_slb | ~ (triple(v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (findmin_pqp_res(v9) = v13 & triple(v9, v15, bad) = v16 & findmin_cpq_eff(v12) = v14 & update_slb(v10, v13) = v15 & (v16 = v14 | contains_slb(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = create_slb | ~ (triple(v9, v10, v11) = v12) | ? [v13] : (findmin_cpq_res(v12) = v13 & findmin_pqp_res(v9) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (findmin_cpq_res(v9) = v11) | ~ (findmin_cpq_eff(v9) = v10) | ~ (remove_cpq(v10, v11) = v12) | removemin_cpq_eff(v9) = v12) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (remove_cpq(v10, v11) = v12) | ~ succ_cpq(v9, v10) | succ_cpq(v9, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (insert_cpq(v10, v11) = v12) | ~ succ_cpq(v9, v10) | succ_cpq(v9, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (insert_pq(v9, v10) = v12) | ~ contains_pq(v9, v11) | contains_pq(v12, v11)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (removemin_pq_res(v9, v10) = v11) | ~ issmallestelement_pq(v9, v10) | ~ contains_pq(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (findmin_pq_res(v9, v10) = v11) | ~ issmallestelement_pq(v9, v10) | ~ contains_pq(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (findmin_pq_eff(v9, v10) = v11) | ~ issmallestelement_pq(v9, v10) | ~ contains_pq(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (i(v11) = v10) | ~ (i(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (removemin_cpq_res(v11) = v10) | ~ (removemin_cpq_res(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (findmin_cpq_res(v11) = v10) | ~ (findmin_cpq_res(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (findmin_pqp_res(v11) = v10) | ~ (findmin_pqp_res(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (removemin_cpq_eff(v11) = v10) | ~ (removemin_cpq_eff(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (findmin_cpq_eff(v11) = v10) | ~ (findmin_cpq_eff(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (i(v9) = v11) | ~ pi_remove(v9, v10) | pi_sharp_remove(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (i(v9) = v11) | ~ pi_sharp_remove(v11, v10) | pi_remove(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (i(v9) = v10) | ~ pi_sharp_find_min(v10, v11) | pi_removemin(v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (i(v9) = v10) | ~ pi_sharp_find_min(v10, v11) | pi_find_min(v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v9, v10, bad) = v11) | ~ ok(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v9, create_slb, v10) = v11) | i(v11) = create_pq) & ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v9, create_slb, v10) = v11) | findmin_cpq_res(v11) = bottom) & ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v9, create_slb, v10) = v11) | check_cpq(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (triple(v9, create_slb, v10) = v11) | ? [v12] : (triple(v9, create_slb, bad) = v12 & findmin_cpq_eff(v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (removemin_cpq_eff(v10) = v11) | ~ succ_cpq(v9, v10) | succ_cpq(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (findmin_cpq_eff(v10) = v11) | ~ succ_cpq(v9, v10) | succ_cpq(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (removemin_pq_eff(v9, v10) = v11) | ~ issmallestelement_pq(v9, v10) | ~ contains_pq(v9, v10) | remove_pq(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (remove_pq(v9, v10) = v11) | ~ issmallestelement_pq(v9, v10) | ~ contains_pq(v9, v10) | removemin_pq_eff(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (insert_pq(v9, v10) = v11) | contains_pq(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (insert_pq(v9, v10) = v11) | isnonempty_pq(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ issmallestelement_pq(v9, v10) | ~ contains_pq(v9, v11) | less_than(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ less_than(v10, v11) | ~ less_than(v9, v10) | less_than(v9, v11)) & ! [v9] : ! [v10] : (v10 = create_slb | ~ (update_slb(create_slb, v9) = v10)) & ! [v9] : ! [v10] : ( ~ (i(v9) = v10) | ~ pi_removemin(v9) | ? [v11] : pi_sharp_find_min(v10, v11)) & ! [v9] : ! [v10] : ( ~ (i(v9) = v10) | ~ pi_find_min(v9) | ? [v11] : pi_sharp_find_min(v10, v11)) & ! [v9] : ! [v10] : ( ~ (removemin_cpq_res(v9) = v10) | findmin_cpq_res(v9) = v10) & ! [v9] : ! [v10] : ( ~ (findmin_cpq_res(v9) = v10) | removemin_cpq_res(v9) = v10) & ! [v9] : ! [v10] : ( ~ (removemin_cpq_eff(v9) = v10) | ? [v11] : ? [v12] : (findmin_cpq_res(v9) = v12 & findmin_cpq_eff(v9) = v11 & remove_cpq(v11, v12) = v10)) & ! [v9] : ! [v10] : ( ~ pi_sharp_removemin(v9, v10) | issmallestelement_pq(v9, v10)) & ! [v9] : ! [v10] : ( ~ pi_sharp_removemin(v9, v10) | contains_pq(v9, v10)) & ! [v9] : ! [v10] : ( ~ pi_sharp_find_min(v9, v10) | issmallestelement_pq(v9, v10)) & ! [v9] : ! [v10] : ( ~ pi_sharp_find_min(v9, v10) | contains_pq(v9, v10)) & ! [v9] : ! [v10] : ( ~ pi_sharp_remove(v9, v10) | contains_pq(v9, v10)) & ! [v9] : ! [v10] : ( ~ ok(v10) | ~ check_cpq(v10) | ~ succ_cpq(v9, v10) | phi(v9)) & ! [v9] : ! [v10] : ~ pair_in_list(create_slb, v9, v10) & ! [v9] : ! [v10] : ( ~ issmallestelement_pq(v9, v10) | ~ contains_pq(v9, v10) | pi_sharp_removemin(v9, v10)) & ! [v9] : ! [v10] : ( ~ issmallestelement_pq(v9, v10) | ~ contains_pq(v9, v10) | pi_sharp_find_min(v9, v10)) & ! [v9] : ! [v10] : ( ~ contains_pq(v9, v10) | pi_sharp_remove(v9, v10)) & ! [v9] : ! [v10] : ( ~ strictly_less_than(v9, v10) | ~ less_than(v10, v9)) & ! [v9] : ! [v10] : ( ~ strictly_less_than(v9, v10) | less_than(v9, v10)) & ! [v9] : ! [v10] : ( ~ less_than(v9, v10) | strictly_less_than(v9, v10) | less_than(v10, v9)) & ! [v9] : ( ~ phi(v9) | ? [v10] : (ok(v10) & check_cpq(v10) & succ_cpq(v9, v10))) & ! [v9] : ~ contains_slb(create_slb, v9) & ! [v9] : ~ contains_pq(create_pq, v9) & ? [v9] : ? [v10] : (issmallestelement_pq(v9, v10) | ? [v11] : (contains_pq(v9, v11) & ~ less_than(v10, v11))) & ? [v9] : ? [v10] : (less_than(v10, v9) | less_than(v9, v10)) & ? [v9] : succ_cpq(v9, v9) & ? [v9] : less_than(v9, v9) & ? [v9] : less_than(bottom, v9))
% 6.52/2.16 | 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 yields:
% 6.52/2.16 | (1) ~ (all_0_0_0 = all_0_2_2) & i(all_0_3_3) = all_0_2_2 & i(all_0_4_4) = all_0_1_1 & triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4 & insert_cpq(all_0_4_4, all_0_5_5) = all_0_3_3 & insert_pq(all_0_1_1, all_0_5_5) = all_0_0_0 & ~ isnonempty_slb(create_slb) & ~ isnonempty_pq(create_pq) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (insert_pqp(v0, v3) = v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ check_cpq(v7) | ~ strictly_less_than(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ less_than(v4, v3) | ? [v8] : (triple(v0, v1, v2) = v8 & ( ~ check_cpq(v8) | check_cpq(v7)) & ( ~ check_cpq(v7) | check_cpq(v8)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | lookup_slb(v0, v2) = v6) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ~ contains_slb(v1, v3) | ? [v7] : ? [v8] : ? [v9] : (triple(v0, v1, v2) = v8 & remove_cpq(v8, v3) = v9 & lookup_slb(v1, v3) = v7 & (v9 = v6 | ~ less_than(v7, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (triple(v1, v2, v4) = v6) | ~ (triple(v0, v2, v3) = v5) | ? [v7] : (i(v6) = v7 & i(v5) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ strictly_less_than(v3, v2) | ? [v7] : ? [v8] : (update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v0, v2, v4) | pair_in_list(v6, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v5, v2) | contains_slb(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : (triple(v0, v1, v2) = v7 & findmin_cpq_eff(v7) = v8 & lookup_slb(v1, v3) = v6 & (v8 = v5 | ~ less_than(v6, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, v2) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ less_than(v6, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, bad) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ strictly_less_than(v3, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | triple(v0, v1, bad) = v5 | contains_slb(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | ? [v5] : (remove_pq(v0, v2) = v5 & insert_pq(v5, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v0, v2) = v3) | ~ (insert_pq(v3, v1) = v4) | ~ contains_pq(v0, v2) | ? [v5] : (remove_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : (insert_pq(v5, v1) = v4 & insert_pq(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v1) = v4) | ~ (insert_pq(v0, v2) = v3) | ? [v5] : (insert_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (remove_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v3, v2) | contains_pq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, v2) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ less_than(v5, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, bad) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ strictly_less_than(v4, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v4 & triple(v0, v6, bad) = v7 & findmin_cpq_eff(v3) = v5 & update_slb(v1, v4) = v6 & (v7 = v5 | contains_slb(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | contains_pq(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_remove(v0, v1) | pi_sharp_remove(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_sharp_remove(v2, v1) | pi_remove(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_removemin(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_find_min(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | remove_pq(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (remove_pq(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | removemin_pq_eff(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | contains_pq(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v2) | less_than(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2)) & ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_removemin(v0) | ? [v2] : pi_sharp_find_min(v1, v2)) & ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_find_min(v0) | ? [v2] : pi_sharp_find_min(v1, v2)) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | issmallestelement_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | contains_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | issmallestelement_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | contains_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ pi_sharp_remove(v0, v1) | contains_pq(v0, v1)) & ! [v0] : ! [v1] : ( ~ ok(v1) | ~ check_cpq(v1) | ~ succ_cpq(v0, v1) | phi(v0)) & ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1) & ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_removemin(v0, v1)) & ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_find_min(v0, v1)) & ! [v0] : ! [v1] : ( ~ contains_pq(v0, v1) | pi_sharp_remove(v0, v1)) & ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0)) & ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1)) & ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0)) & ! [v0] : ( ~ phi(v0) | ? [v1] : (ok(v1) & check_cpq(v1) & succ_cpq(v0, v1))) & ! [v0] : ~ contains_slb(create_slb, v0) & ! [v0] : ~ contains_pq(create_pq, v0) & ? [v0] : ? [v1] : (issmallestelement_pq(v0, v1) | ? [v2] : (contains_pq(v0, v2) & ~ less_than(v1, v2))) & ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1)) & ? [v0] : succ_cpq(v0, v0) & ? [v0] : less_than(v0, v0) & ? [v0] : less_than(bottom, v0)
% 6.52/2.19 |
% 6.52/2.19 | Applying alpha-rule on (1) yields:
% 6.52/2.19 | (2) ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | contains_pq(v0, v1))
% 6.52/2.19 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (insert_pqp(v0, v3) = v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7))
% 6.52/2.19 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_find_min(v0))
% 6.52/2.19 | (5) ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0))
% 6.52/2.19 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8))
% 6.52/2.19 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 6.52/2.19 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4))
% 6.52/2.19 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | contains_pq(v3, v2))
% 6.52/2.19 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6))
% 6.52/2.19 | (11) i(all_0_3_3) = all_0_2_2
% 6.52/2.19 | (12) i(all_0_4_4) = all_0_1_1
% 6.52/2.19 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 6.52/2.19 | (14) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1))
% 6.52/2.19 | (15) ! [v0] : ~ contains_pq(create_pq, v0)
% 6.52/2.19 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 6.52/2.19 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 6.52/2.19 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, bad) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ strictly_less_than(v3, v6))))
% 6.52/2.19 | (19) ~ (all_0_0_0 = all_0_2_2)
% 6.52/2.19 | (20) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1)
% 6.52/2.20 | (21) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 6.52/2.20 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1))
% 6.52/2.20 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0))
% 6.52/2.20 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ strictly_less_than(v3, v2) | ? [v7] : ? [v8] : (update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6))
% 6.52/2.20 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2))
% 6.52/2.20 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2))
% 6.52/2.20 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v0, v2, v4) | pair_in_list(v6, v2, v4))
% 6.52/2.20 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v2) | less_than(v1, v2))
% 6.52/2.20 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 6.52/2.20 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6))
% 6.52/2.20 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v0, v2) = v3) | ~ (insert_pq(v3, v1) = v4) | ~ contains_pq(v0, v2) | ? [v5] : (remove_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5))
% 6.52/2.20 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = v8))
% 6.52/2.20 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 6.52/2.20 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 6.52/2.20 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | lookup_slb(v0, v2) = v6)
% 6.52/2.20 | (36) ? [v0] : succ_cpq(v0, v0)
% 6.52/2.20 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (remove_pq(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | removemin_pq_eff(v0, v1) = v2)
% 6.52/2.20 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 6.52/2.20 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_sharp_remove(v2, v1) | pi_remove(v0, v1))
% 6.52/2.20 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_remove(v0, v1) | pi_sharp_remove(v2, v1))
% 6.52/2.20 | (41) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1))
% 6.52/2.20 | (42) ? [v0] : less_than(v0, v0)
% 6.52/2.20 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 6.52/2.20 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | contains_pq(v2, v1))
% 6.52/2.20 | (45) ~ isnonempty_pq(create_pq)
% 6.52/2.20 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0))
% 6.52/2.20 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : (insert_pq(v5, v1) = v4 & insert_pq(v0, v2) = v5))
% 6.52/2.20 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | remove_pq(v0, v1) = v2)
% 6.52/2.20 | (49) ! [v0] : ~ contains_slb(create_slb, v0)
% 6.52/2.20 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1))
% 6.52/2.20 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7))
% 6.52/2.20 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v5, v2) | contains_slb(v0, v2))
% 6.52/2.20 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, bad) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ strictly_less_than(v4, v5))))
% 6.52/2.20 | (54) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_removemin(v0) | ? [v2] : pi_sharp_find_min(v1, v2))
% 6.52/2.20 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v3, v2) | contains_pq(v0, v2))
% 6.52/2.20 | (56) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_find_min(v0) | ? [v2] : pi_sharp_find_min(v1, v2))
% 6.52/2.20 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0))
% 6.52/2.21 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3))
% 6.52/2.21 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2))
% 6.52/2.21 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2))
% 6.52/2.21 | (61) insert_cpq(all_0_4_4, all_0_5_5) = all_0_3_3
% 6.52/2.21 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1))
% 6.52/2.21 | (63) ? [v0] : ? [v1] : (issmallestelement_pq(v0, v1) | ? [v2] : (contains_pq(v0, v2) & ~ less_than(v1, v2)))
% 6.52/2.21 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (remove_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2))
% 6.52/2.21 | (65) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1))
% 6.52/2.21 | (66) ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1)
% 6.52/2.21 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4))
% 6.52/2.21 | (68) ! [v0] : ( ~ phi(v0) | ? [v1] : (ok(v1) & check_cpq(v1) & succ_cpq(v0, v1)))
% 6.52/2.21 | (69) ~ isnonempty_slb(create_slb)
% 6.52/2.21 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3)
% 6.52/2.21 | (71) ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | contains_pq(v0, v1))
% 6.52/2.21 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v4 & triple(v0, v6, bad) = v7 & findmin_cpq_eff(v3) = v5 & update_slb(v1, v4) = v6 & (v7 = v5 | contains_slb(v1, v4))))
% 6.52/2.21 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3))
% 6.52/2.21 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4))
% 6.52/2.21 | (75) insert_pq(all_0_1_1, all_0_5_5) = all_0_0_0
% 6.52/2.21 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (triple(v1, v2, v4) = v6) | ~ (triple(v0, v2, v3) = v5) | ? [v7] : (i(v6) = v7 & i(v5) = v7))
% 6.52/2.21 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2))
% 6.52/2.21 | (78) ? [v0] : less_than(bottom, v0)
% 6.52/2.21 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ less_than(v4, v3) | ? [v8] : (triple(v0, v1, v2) = v8 & ( ~ check_cpq(v8) | check_cpq(v7)) & ( ~ check_cpq(v7) | check_cpq(v8))))
% 6.52/2.21 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 6.52/2.21 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_removemin(v0))
% 6.52/2.21 | (82) ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_find_min(v0, v1))
% 6.52/2.21 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2))
% 6.52/2.21 | (84) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 6.52/2.21 | (85) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0))
% 6.52/2.21 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | triple(v0, v1, bad) = v5 | contains_slb(v1, v3))
% 6.52/2.21 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 6.52/2.21 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ~ contains_slb(v1, v3) | ? [v7] : ? [v8] : ? [v9] : (triple(v0, v1, v2) = v8 & remove_cpq(v8, v3) = v9 & lookup_slb(v1, v3) = v7 & (v9 = v6 | ~ less_than(v7, v3))))
% 6.52/2.21 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2))
% 6.52/2.21 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 6.52/2.21 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3))
% 6.52/2.21 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3))
% 6.52/2.21 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, v2) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ less_than(v5, v4))))
% 6.52/2.21 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0))
% 6.52/2.21 | (95) ! [v0] : ! [v1] : ( ~ ok(v1) | ~ check_cpq(v1) | ~ succ_cpq(v0, v1) | phi(v0))
% 6.52/2.21 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 6.52/2.21 | (97) ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_removemin(v0, v1))
% 6.52/2.22 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7))
% 6.52/2.22 | (99) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0))
% 6.52/2.22 | (100) ! [v0] : ! [v1] : ( ~ contains_pq(v0, v1) | pi_sharp_remove(v0, v1))
% 6.52/2.22 | (101) ! [v0] : ! [v1] : ( ~ pi_sharp_remove(v0, v1) | contains_pq(v0, v1))
% 6.52/2.22 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3))
% 6.52/2.22 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 6.52/2.22 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4))
% 6.52/2.22 | (105) ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | issmallestelement_pq(v0, v1))
% 6.52/2.22 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 6.52/2.22 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 6.52/2.22 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0))
% 6.52/2.22 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2))
% 6.52/2.22 | (110) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 6.52/2.22 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0))
% 6.52/2.22 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ check_cpq(v7) | ~ strictly_less_than(v3, v4))
% 6.52/2.22 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, v2) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ less_than(v6, v3))))
% 6.52/2.22 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq)
% 6.52/2.22 | (115) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 6.52/2.22 | (116) ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1))
% 6.52/2.22 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 6.52/2.22 | (118) ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | issmallestelement_pq(v0, v1))
% 6.52/2.22 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v1) = v4) | ~ (insert_pq(v0, v2) = v3) | ? [v5] : (insert_pq(v5, v2) = v4 & insert_pq(v0, v1) = v5))
% 6.94/2.22 | (120) triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4
% 6.94/2.22 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : (triple(v0, v1, v2) = v7 & findmin_cpq_eff(v7) = v8 & lookup_slb(v1, v3) = v6 & (v8 = v5 | ~ less_than(v6, v3))))
% 6.94/2.22 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | ? [v5] : (remove_pq(v0, v2) = v5 & insert_pq(v5, v1) = v4))
% 6.94/2.22 |
% 6.94/2.22 | Instantiating formula (6) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4, insert_cpq(all_0_4_4, all_0_5_5) = all_0_3_3, yields:
% 6.94/2.22 | (123) ? [v0] : ? [v1] : ? [v2] : (insert_pqp(all_0_8_8, all_0_5_5) = v0 & triple(v0, v2, all_0_6_6) = all_0_3_3 & pair(all_0_5_5, bottom) = v1 & insert_slb(all_0_7_7, v1) = v2)
% 6.94/2.22 |
% 6.94/2.22 | Instantiating (123) with all_17_0_16, all_17_1_17, all_17_2_18 yields:
% 6.94/2.22 | (124) insert_pqp(all_0_8_8, all_0_5_5) = all_17_2_18 & triple(all_17_2_18, all_17_0_16, all_0_6_6) = all_0_3_3 & pair(all_0_5_5, bottom) = all_17_1_17 & insert_slb(all_0_7_7, all_17_1_17) = all_17_0_16
% 6.94/2.22 |
% 6.94/2.22 | Applying alpha-rule on (124) yields:
% 6.94/2.22 | (125) insert_pqp(all_0_8_8, all_0_5_5) = all_17_2_18
% 6.94/2.22 | (126) triple(all_17_2_18, all_17_0_16, all_0_6_6) = all_0_3_3
% 6.94/2.22 | (127) pair(all_0_5_5, bottom) = all_17_1_17
% 6.94/2.22 | (128) insert_slb(all_0_7_7, all_17_1_17) = all_17_0_16
% 6.94/2.22 |
% 6.94/2.22 | Instantiating formula (32) with all_0_3_3, all_17_0_16, all_17_1_17, bottom, all_0_5_5, all_0_6_6, all_0_7_7, all_17_2_18 and discharging atoms triple(all_17_2_18, all_17_0_16, all_0_6_6) = all_0_3_3, pair(all_0_5_5, bottom) = all_17_1_17, insert_slb(all_0_7_7, all_17_1_17) = all_17_0_16, yields:
% 6.94/2.22 | (129) ? [v0] : ? [v1] : ? [v2] : (i(v1) = v2 & i(all_0_3_3) = v0 & triple(all_17_2_18, all_0_7_7, all_0_6_6) = v1 & insert_pq(v2, all_0_5_5) = v0)
% 6.94/2.22 |
% 6.94/2.22 | Instantiating (129) with all_25_0_19, all_25_1_20, all_25_2_21 yields:
% 6.94/2.22 | (130) i(all_25_1_20) = all_25_0_19 & i(all_0_3_3) = all_25_2_21 & triple(all_17_2_18, all_0_7_7, all_0_6_6) = all_25_1_20 & insert_pq(all_25_0_19, all_0_5_5) = all_25_2_21
% 6.94/2.22 |
% 6.94/2.22 | Applying alpha-rule on (130) yields:
% 6.94/2.22 | (131) i(all_25_1_20) = all_25_0_19
% 6.94/2.22 | (132) i(all_0_3_3) = all_25_2_21
% 6.94/2.22 | (133) triple(all_17_2_18, all_0_7_7, all_0_6_6) = all_25_1_20
% 6.94/2.22 | (134) insert_pq(all_25_0_19, all_0_5_5) = all_25_2_21
% 6.94/2.22 |
% 6.94/2.22 | Instantiating formula (99) with all_0_3_3, all_25_2_21, all_0_2_2 and discharging atoms i(all_0_3_3) = all_25_2_21, i(all_0_3_3) = all_0_2_2, yields:
% 6.94/2.22 | (135) all_25_2_21 = all_0_2_2
% 6.94/2.22 |
% 6.94/2.22 | From (135) and (134) follows:
% 6.94/2.22 | (136) insert_pq(all_25_0_19, all_0_5_5) = all_0_2_2
% 6.94/2.23 |
% 6.94/2.23 | Instantiating formula (76) with all_25_1_20, all_0_4_4, all_0_6_6, all_0_6_6, all_0_7_7, all_17_2_18, all_0_8_8 and discharging atoms triple(all_17_2_18, all_0_7_7, all_0_6_6) = all_25_1_20, triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4, yields:
% 6.94/2.23 | (137) ? [v0] : (i(all_25_1_20) = v0 & i(all_0_4_4) = v0)
% 6.94/2.23 |
% 6.94/2.23 | Instantiating (137) with all_37_0_22 yields:
% 6.94/2.23 | (138) i(all_25_1_20) = all_37_0_22 & i(all_0_4_4) = all_37_0_22
% 6.94/2.23 |
% 6.94/2.23 | Applying alpha-rule on (138) yields:
% 6.94/2.23 | (139) i(all_25_1_20) = all_37_0_22
% 6.94/2.23 | (140) i(all_0_4_4) = all_37_0_22
% 6.94/2.23 |
% 6.94/2.23 | Instantiating formula (99) with all_25_1_20, all_37_0_22, all_25_0_19 and discharging atoms i(all_25_1_20) = all_37_0_22, i(all_25_1_20) = all_25_0_19, yields:
% 6.94/2.23 | (141) all_37_0_22 = all_25_0_19
% 6.94/2.23 |
% 6.94/2.23 | Instantiating formula (99) with all_0_4_4, all_37_0_22, all_0_1_1 and discharging atoms i(all_0_4_4) = all_37_0_22, i(all_0_4_4) = all_0_1_1, yields:
% 6.94/2.23 | (142) all_37_0_22 = all_0_1_1
% 6.94/2.23 |
% 6.94/2.23 | Combining equations (141,142) yields a new equation:
% 6.94/2.23 | (143) all_25_0_19 = all_0_1_1
% 6.94/2.23 |
% 6.94/2.23 | Simplifying 143 yields:
% 6.94/2.23 | (144) all_25_0_19 = all_0_1_1
% 6.94/2.23 |
% 6.94/2.23 | From (144) and (136) follows:
% 6.94/2.23 | (145) insert_pq(all_0_1_1, all_0_5_5) = all_0_2_2
% 6.94/2.23 |
% 6.94/2.23 | Instantiating formula (57) with all_0_1_1, all_0_5_5, all_0_2_2, all_0_0_0 and discharging atoms insert_pq(all_0_1_1, all_0_5_5) = all_0_0_0, insert_pq(all_0_1_1, all_0_5_5) = all_0_2_2, yields:
% 6.94/2.23 | (146) all_0_0_0 = all_0_2_2
% 6.94/2.23 |
% 6.94/2.23 | Equations (146) can reduce 19 to:
% 6.94/2.23 | (147) $false
% 6.94/2.23 |
% 6.94/2.23 |-The branch is then unsatisfiable
% 6.94/2.23 % SZS output end Proof for theBenchmark
% 6.94/2.23
% 6.94/2.23 1635ms
%------------------------------------------------------------------------------