TSTP Solution File: SWV415+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV415+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 5.31s 1.89s
% Output : Proof 8.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV415+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n014.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 07:39:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.58 ____ _
% 0.57/0.58 ___ / __ \_____(_)___ ________ __________
% 0.57/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.58
% 0.57/0.58 A Theorem Prover for First-Order Logic
% 0.57/0.58 (ePrincess v.1.0)
% 0.57/0.58
% 0.57/0.58 (c) Philipp Rümmer, 2009-2015
% 0.57/0.58 (c) Peter Backeman, 2014-2015
% 0.57/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.58 Bug reports to peter@backeman.se
% 0.57/0.58
% 0.57/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.58
% 0.57/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.63/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.79/1.00 Prover 0: Preprocessing ...
% 3.50/1.42 Prover 0: Warning: ignoring some quantifiers
% 3.50/1.46 Prover 0: Constructing countermodel ...
% 5.31/1.89 Prover 0: proved (1256ms)
% 5.31/1.89
% 5.31/1.89 No countermodel exists, formula is valid
% 5.31/1.89 % SZS status Theorem for theBenchmark
% 5.31/1.89
% 5.31/1.89 Generating proof ... Warning: ignoring some quantifiers
% 7.58/2.40 found it (size 52)
% 7.58/2.40
% 7.58/2.40 % SZS output start Proof for theBenchmark
% 7.58/2.40 Assumed formulas after preprocessing and simplification:
% 7.58/2.40 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ( ~ (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) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ! [v29] : ( ~ (insert_pqp(v22, v25) = v26) | ~ (triple(v26, v28, v24) = v29) | ~ (pair(v25, bottom) = v27) | ~ (insert_slb(v23, v27) = v28) | ? [v30] : (triple(v22, v23, v24) = v30 & insert_cpq(v30, v25) = v29)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ! [v29] : ( ~ (triple(v22, v28, v24) = v29) | ~ (pair(v25, v26) = v27) | ~ (insert_slb(v23, v27) = v28) | ~ check_cpq(v29) | ~ strictly_less_than(v25, v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ! [v29] : ( ~ (triple(v22, v28, v24) = v29) | ~ (pair(v25, v26) = v27) | ~ (insert_slb(v23, v27) = v28) | ~ less_than(v26, v25) | ? [v30] : (triple(v22, v23, v24) = v30 & ( ~ check_cpq(v30) | check_cpq(v29)) & ( ~ check_cpq(v29) | check_cpq(v30)))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ! [v29] : ( ~ (triple(v22, v28, v24) = v29) | ~ (pair(v25, v26) = v27) | ~ (insert_slb(v23, v27) = v28) | ? [v30] : ? [v31] : ? [v32] : (i(v31) = v32 & i(v29) = v30 & triple(v22, v23, v24) = v31 & insert_pq(v32, v25) = v30)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : (v26 = v25 | ~ (pair(v23, v25) = v27) | ~ (insert_slb(v22, v27) = v28) | ~ pair_in_list(v28, v24, v26) | pair_in_list(v22, v24, v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : (v24 = v23 | ~ (lookup_slb(v27, v24) = v28) | ~ (pair(v23, v25) = v26) | ~ (insert_slb(v22, v26) = v27) | ~ contains_slb(v22, v24) | lookup_slb(v22, v24) = v28) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : (v24 = v23 | ~ (remove_slb(v27, v24) = v28) | ~ (pair(v23, v25) = v26) | ~ (insert_slb(v22, v26) = v27) | ~ contains_slb(v22, v24) | ? [v29] : (remove_slb(v22, v24) = v29 & insert_slb(v29, v26) = v28)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : (v24 = v23 | ~ (remove_slb(v22, v24) = v27) | ~ (pair(v23, v25) = v26) | ~ (insert_slb(v27, v26) = v28) | ~ contains_slb(v22, v24) | ? [v29] : (remove_slb(v29, v24) = v28 & insert_slb(v22, v26) = v29)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : (v24 = v23 | ~ (pair(v23, v25) = v27) | ~ (insert_slb(v22, v27) = v28) | ~ pair_in_list(v28, v24, v26) | pair_in_list(v22, v24, v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ( ~ (remove_pqp(v22, v25) = v26) | ~ (triple(v26, v27, v24) = v28) | ~ (remove_slb(v23, v25) = v27) | ~ contains_slb(v23, v25) | ? [v29] : ? [v30] : ? [v31] : (triple(v22, v23, v24) = v30 & remove_cpq(v30, v25) = v31 & lookup_slb(v23, v25) = v29 & (v31 = v28 | ~ less_than(v29, v25)))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ( ~ (update_slb(v27, v24) = v28) | ~ (pair(v23, v25) = v26) | ~ (insert_slb(v22, v26) = v27) | ~ strictly_less_than(v25, v24) | ? [v29] : ? [v30] : (update_slb(v22, v24) = v29 & pair(v23, v24) = v30 & insert_slb(v29, v30) = v28)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ( ~ (update_slb(v27, v24) = v28) | ~ (pair(v23, v25) = v26) | ~ (insert_slb(v22, v26) = v27) | ~ less_than(v24, v25) | ? [v29] : (update_slb(v22, v24) = v29 & insert_slb(v29, v26) = v28)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ( ~ (update_slb(v22, v24) = v27) | ~ (pair(v23, v25) = v26) | ~ (insert_slb(v27, v26) = v28) | ~ less_than(v24, v25) | ? [v29] : (update_slb(v29, v24) = v28 & insert_slb(v22, v26) = v29)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ( ~ (pair(v23, v25) = v27) | ~ (insert_slb(v22, v27) = v28) | ~ pair_in_list(v22, v24, v26) | pair_in_list(v28, v24, v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v27 = v24 | ~ (lookup_slb(v26, v23) = v27) | ~ (pair(v23, v24) = v25) | ~ (insert_slb(v22, v25) = v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v27 = v22 | ~ (remove_slb(v26, v23) = v27) | ~ (pair(v23, v24) = v25) | ~ (insert_slb(v22, v25) = v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v24 = v23 | ~ (pair(v23, v25) = v26) | ~ (insert_slb(v22, v26) = v27) | ~ contains_slb(v27, v24) | contains_slb(v22, v24)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v23 = create_slb | ~ (findmin_pqp_res(v22) = v25) | ~ (triple(v22, v26, v24) = v27) | ~ (update_slb(v23, v25) = v26) | ~ contains_slb(v23, v25) | ? [v28] : ? [v29] : ? [v30] : (triple(v22, v23, v24) = v29 & findmin_cpq_eff(v29) = v30 & lookup_slb(v23, v25) = v28 & (v30 = v27 | ~ less_than(v28, v25)))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (triple(v22, v23, v24) = v26) | ~ (remove_cpq(v26, v25) = v27) | ~ contains_slb(v23, v25) | ? [v28] : ? [v29] : ? [v30] : ? [v31] : (remove_pqp(v22, v25) = v29 & triple(v29, v30, v24) = v31 & lookup_slb(v23, v25) = v28 & remove_slb(v23, v25) = v30 & (v31 = v27 | ~ less_than(v28, v25)))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (triple(v22, v23, v24) = v26) | ~ (remove_cpq(v26, v25) = v27) | ~ contains_slb(v23, v25) | ? [v28] : ? [v29] : ? [v30] : ? [v31] : (remove_pqp(v22, v25) = v29 & triple(v29, v30, bad) = v31 & lookup_slb(v23, v25) = v28 & remove_slb(v23, v25) = v30 & (v31 = v27 | ~ strictly_less_than(v25, v28)))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (triple(v22, v23, v24) = v26) | ~ (remove_cpq(v26, v25) = v27) | triple(v22, v23, bad) = v27 | contains_slb(v23, v25)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (triple(v22, v23, v24) = v26) | ~ (insert_cpq(v26, v25) = v27) | ? [v28] : ? [v29] : ? [v30] : (insert_pqp(v22, v25) = v28 & triple(v28, v30, v24) = v27 & pair(v25, bottom) = v29 & insert_slb(v23, v29) = v30)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (pair(v23, v25) = v26) | ~ (insert_slb(v22, v26) = v27) | ~ contains_slb(v22, v24) | contains_slb(v27, v24)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v24 = v23 | ~ (remove_pq(v25, v24) = v26) | ~ (insert_pq(v22, v23) = v25) | ~ contains_pq(v22, v24) | ? [v27] : (remove_pq(v22, v24) = v27 & insert_pq(v27, v23) = v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v24 = v23 | ~ (remove_pq(v22, v24) = v25) | ~ (insert_pq(v25, v23) = v26) | ~ contains_pq(v22, v24) | ? [v27] : (remove_pq(v27, v24) = v26 & insert_pq(v22, v23) = v27)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v23 = v22 | ~ (triple(v26, v25, v24) = v23) | ~ (triple(v26, v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (triple(v22, v23, v24) = v26) | ~ contains_cpq(v26, v25) | contains_slb(v23, v25)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (triple(v22, v23, v24) = v26) | ~ contains_slb(v23, v25) | contains_cpq(v26, v25)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (pair(v23, v24) = v25) | ~ (insert_slb(v22, v25) = v26) | pair_in_list(v26, v23, v24)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (pair(v23, v24) = v25) | ~ (insert_slb(v22, v25) = v26) | contains_slb(v26, v23)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (pair(v23, v24) = v25) | ~ (insert_slb(v22, v25) = v26) | isnonempty_slb(v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (insert_pq(v25, v24) = v26) | ~ (insert_pq(v22, v23) = v25) | ? [v27] : (insert_pq(v27, v23) = v26 & insert_pq(v22, v24) = v27)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (insert_pq(v25, v23) = v26) | ~ (insert_pq(v22, v24) = v25) | ? [v27] : (insert_pq(v27, v24) = v26 & insert_pq(v22, v23) = v27)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = v22 | ~ (remove_pq(v24, v23) = v25) | ~ (insert_pq(v22, v23) = v24)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v24 = v23 | ~ (insert_pq(v22, v23) = v25) | ~ contains_pq(v25, v24) | contains_pq(v22, v24)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v24 = bad | ~ (triple(v22, v23, v24) = v25) | ok(v25)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (remove_pqp(v25, v24) = v23) | ~ (remove_pqp(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (insert_pqp(v25, v24) = v23) | ~ (insert_pqp(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (remove_cpq(v25, v24) = v23) | ~ (remove_cpq(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (insert_cpq(v25, v24) = v23) | ~ (insert_cpq(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (update_slb(v25, v24) = v23) | ~ (update_slb(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (lookup_slb(v25, v24) = v23) | ~ (lookup_slb(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (remove_slb(v25, v24) = v23) | ~ (remove_slb(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (pair(v25, v24) = v23) | ~ (pair(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (insert_slb(v25, v24) = v23) | ~ (insert_slb(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (removemin_pq_res(v25, v24) = v23) | ~ (removemin_pq_res(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (removemin_pq_eff(v25, v24) = v23) | ~ (removemin_pq_eff(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (findmin_pq_res(v25, v24) = v23) | ~ (findmin_pq_res(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (findmin_pq_eff(v25, v24) = v23) | ~ (findmin_pq_eff(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (remove_pq(v25, v24) = v23) | ~ (remove_pq(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (insert_pq(v25, v24) = v23) | ~ (insert_pq(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = create_slb | ~ (triple(v22, v23, v24) = v25) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (findmin_pqp_res(v22) = v26 & triple(v22, v29, v24) = v30 & findmin_cpq_eff(v25) = v28 & update_slb(v23, v26) = v29 & lookup_slb(v23, v26) = v27 & (v30 = v28 | ~ contains_slb(v23, v26) | ~ less_than(v27, v26)))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = create_slb | ~ (triple(v22, v23, v24) = v25) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (findmin_pqp_res(v22) = v26 & triple(v22, v29, bad) = v30 & findmin_cpq_eff(v25) = v28 & update_slb(v23, v26) = v29 & lookup_slb(v23, v26) = v27 & (v30 = v28 | ~ contains_slb(v23, v26) | ~ strictly_less_than(v26, v27)))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = create_slb | ~ (triple(v22, v23, v24) = v25) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : (findmin_pqp_res(v22) = v26 & triple(v22, v28, bad) = v29 & findmin_cpq_eff(v25) = v27 & update_slb(v23, v26) = v28 & (v29 = v27 | contains_slb(v23, v26)))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = create_slb | ~ (triple(v22, v23, v24) = v25) | ? [v26] : (findmin_cpq_res(v25) = v26 & findmin_pqp_res(v22) = v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (findmin_cpq_res(v22) = v24) | ~ (findmin_cpq_eff(v22) = v23) | ~ (remove_cpq(v23, v24) = v25) | removemin_cpq_eff(v22) = v25) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (remove_cpq(v23, v24) = v25) | ~ succ_cpq(v22, v23) | succ_cpq(v22, v25)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (insert_cpq(v23, v24) = v25) | ~ succ_cpq(v22, v23) | succ_cpq(v22, v25)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (insert_pq(v22, v23) = v25) | ~ contains_pq(v22, v24) | contains_pq(v25, v24)) & ! [v22] : ! [v23] : ! [v24] : (v24 = v23 | ~ (removemin_pq_res(v22, v23) = v24) | ~ issmallestelement_pq(v22, v23) | ~ contains_pq(v22, v23)) & ! [v22] : ! [v23] : ! [v24] : (v24 = v23 | ~ (findmin_pq_res(v22, v23) = v24) | ~ issmallestelement_pq(v22, v23) | ~ contains_pq(v22, v23)) & ! [v22] : ! [v23] : ! [v24] : (v24 = v22 | ~ (findmin_pq_eff(v22, v23) = v24) | ~ issmallestelement_pq(v22, v23) | ~ contains_pq(v22, v23)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (i(v24) = v23) | ~ (i(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (removemin_cpq_res(v24) = v23) | ~ (removemin_cpq_res(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (findmin_cpq_res(v24) = v23) | ~ (findmin_cpq_res(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (findmin_pqp_res(v24) = v23) | ~ (findmin_pqp_res(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (removemin_cpq_eff(v24) = v23) | ~ (removemin_cpq_eff(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (findmin_cpq_eff(v24) = v23) | ~ (findmin_cpq_eff(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (i(v22) = v24) | ~ pi_remove(v22, v23) | pi_sharp_remove(v24, v23)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (i(v22) = v24) | ~ pi_sharp_remove(v24, v23) | pi_remove(v22, v23)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (i(v22) = v23) | ~ pi_sharp_find_min(v23, v24) | pi_removemin(v22)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (i(v22) = v23) | ~ pi_sharp_find_min(v23, v24) | pi_find_min(v22)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (triple(v22, v23, bad) = v24) | ~ ok(v24)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (triple(v22, create_slb, v23) = v24) | i(v24) = create_pq) & ! [v22] : ! [v23] : ! [v24] : ( ~ (triple(v22, create_slb, v23) = v24) | findmin_cpq_res(v24) = bottom) & ! [v22] : ! [v23] : ! [v24] : ( ~ (triple(v22, create_slb, v23) = v24) | check_cpq(v24)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (triple(v22, create_slb, v23) = v24) | ? [v25] : (triple(v22, create_slb, bad) = v25 & findmin_cpq_eff(v24) = v25)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (removemin_cpq_eff(v23) = v24) | ~ succ_cpq(v22, v23) | succ_cpq(v22, v24)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (findmin_cpq_eff(v23) = v24) | ~ succ_cpq(v22, v23) | succ_cpq(v22, v24)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (removemin_pq_eff(v22, v23) = v24) | ~ issmallestelement_pq(v22, v23) | ~ contains_pq(v22, v23) | remove_pq(v22, v23) = v24) & ! [v22] : ! [v23] : ! [v24] : ( ~ (remove_pq(v22, v23) = v24) | ~ issmallestelement_pq(v22, v23) | ~ contains_pq(v22, v23) | removemin_pq_eff(v22, v23) = v24) & ! [v22] : ! [v23] : ! [v24] : ( ~ (insert_pq(v22, v23) = v24) | contains_pq(v24, v23)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (insert_pq(v22, v23) = v24) | isnonempty_pq(v24)) & ! [v22] : ! [v23] : ! [v24] : ( ~ issmallestelement_pq(v22, v23) | ~ contains_pq(v22, v24) | less_than(v23, v24)) & ! [v22] : ! [v23] : ! [v24] : ( ~ less_than(v23, v24) | ~ less_than(v22, v23) | less_than(v22, v24)) & ! [v22] : ! [v23] : (v23 = create_slb | ~ (update_slb(create_slb, v22) = v23)) & ! [v22] : ! [v23] : ( ~ (i(v22) = v23) | ~ pi_removemin(v22) | ? [v24] : pi_sharp_find_min(v23, v24)) & ! [v22] : ! [v23] : ( ~ (i(v22) = v23) | ~ pi_find_min(v22) | ? [v24] : pi_sharp_find_min(v23, v24)) & ! [v22] : ! [v23] : ( ~ (removemin_cpq_res(v22) = v23) | findmin_cpq_res(v22) = v23) & ! [v22] : ! [v23] : ( ~ (findmin_cpq_res(v22) = v23) | removemin_cpq_res(v22) = v23) & ! [v22] : ! [v23] : ( ~ (removemin_cpq_eff(v22) = v23) | ? [v24] : ? [v25] : (findmin_cpq_res(v22) = v25 & findmin_cpq_eff(v22) = v24 & remove_cpq(v24, v25) = v23)) & ! [v22] : ! [v23] : ( ~ pi_sharp_removemin(v22, v23) | issmallestelement_pq(v22, v23)) & ! [v22] : ! [v23] : ( ~ pi_sharp_removemin(v22, v23) | contains_pq(v22, v23)) & ! [v22] : ! [v23] : ( ~ pi_sharp_find_min(v22, v23) | issmallestelement_pq(v22, v23)) & ! [v22] : ! [v23] : ( ~ pi_sharp_find_min(v22, v23) | contains_pq(v22, v23)) & ! [v22] : ! [v23] : ( ~ pi_sharp_remove(v22, v23) | contains_pq(v22, v23)) & ! [v22] : ! [v23] : ( ~ ok(v23) | ~ check_cpq(v23) | ~ succ_cpq(v22, v23) | phi(v22)) & ! [v22] : ! [v23] : ~ pair_in_list(create_slb, v22, v23) & ! [v22] : ! [v23] : ( ~ issmallestelement_pq(v22, v23) | ~ contains_pq(v22, v23) | pi_sharp_removemin(v22, v23)) & ! [v22] : ! [v23] : ( ~ issmallestelement_pq(v22, v23) | ~ contains_pq(v22, v23) | pi_sharp_find_min(v22, v23)) & ! [v22] : ! [v23] : ( ~ contains_pq(v22, v23) | pi_sharp_remove(v22, v23)) & ! [v22] : ! [v23] : ( ~ strictly_less_than(v22, v23) | ~ less_than(v23, v22)) & ! [v22] : ! [v23] : ( ~ strictly_less_than(v22, v23) | less_than(v22, v23)) & ! [v22] : ! [v23] : ( ~ less_than(v22, v23) | strictly_less_than(v22, v23) | less_than(v23, v22)) & ! [v22] : ( ~ phi(v22) | ? [v23] : (ok(v23) & check_cpq(v23) & succ_cpq(v22, v23))) & ! [v22] : ~ contains_slb(create_slb, v22) & ! [v22] : ~ contains_pq(create_pq, v22) & ? [v22] : ? [v23] : (issmallestelement_pq(v22, v23) | ? [v24] : (contains_pq(v22, v24) & ~ less_than(v23, v24))) & ? [v22] : ? [v23] : (less_than(v23, v22) | less_than(v22, v23)) & ? [v22] : succ_cpq(v22, v22) & ? [v22] : less_than(v22, v22) & ? [v22] : less_than(bottom, v22) & ( ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ( ~ (triple(v23, v24, v26) = v28) | ~ (triple(v22, v24, v25) = v27) | ? [v29] : (i(v28) = v29 & i(v27) = v29)) | ( ~ (v21 = v19) & i(v20) = v21 & i(v18) = v19 & triple(v11, v17, v13) = v20 & triple(v10, v17, v12) = v18 & pair(v14, v15) = v16 & insert_slb(v9, v16) = v17 & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (triple(v23, v9, v25) = v27) | ~ (triple(v22, v9, v24) = v26) | ? [v28] : (i(v27) = v28 & i(v26) = v28))) | ( ~ (v16 = v14) & i(v15) = v16 & i(v13) = v14 & triple(v10, create_slb, v12) = v15 & triple(v9, create_slb, v11) = v13)))
% 7.99/2.46 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21 yields:
% 7.99/2.46 | (1) ~ (all_0_13_13 = all_0_15_15) & i(all_0_16_16) = all_0_15_15 & i(all_0_17_17) = all_0_14_14 & triple(all_0_21_21, all_0_20_20, all_0_19_19) = all_0_17_17 & insert_cpq(all_0_17_17, all_0_18_18) = all_0_16_16 & insert_pq(all_0_14_14, all_0_18_18) = all_0_13_13 & ~ 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] : ( ~ (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) & ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (triple(v1, v2, v4) = v6) | ~ (triple(v0, v2, v3) = v5) | ? [v7] : (i(v6) = v7 & i(v5) = v7)) | ( ~ (all_0_0_0 = all_0_2_2) & i(all_0_1_1) = all_0_0_0 & i(all_0_3_3) = all_0_2_2 & triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1 & triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3 & pair(all_0_7_7, all_0_6_6) = all_0_5_5 & insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v1, all_0_12_12, v3) = v5) | ~ (triple(v0, all_0_12_12, v2) = v4) | ? [v6] : (i(v5) = v6 & i(v4) = v6))) | ( ~ (all_0_5_5 = all_0_7_7) & i(all_0_6_6) = all_0_5_5 & i(all_0_8_8) = all_0_7_7 & triple(all_0_11_11, create_slb, all_0_9_9) = all_0_6_6 & triple(all_0_12_12, create_slb, all_0_10_10) = all_0_8_8))
% 7.99/2.48 |
% 7.99/2.48 | Applying alpha-rule on (1) yields:
% 7.99/2.48 | (2) ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | contains_pq(v0, v1))
% 7.99/2.48 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0))
% 7.99/2.48 | (4) ! [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))
% 7.99/2.48 | (5) insert_pq(all_0_14_14, all_0_18_18) = all_0_13_13
% 7.99/2.48 | (6) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_find_min(v0) | ? [v2] : pi_sharp_find_min(v1, v2))
% 7.99/2.48 | (7) ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0))
% 7.99/2.48 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2))
% 7.99/2.48 | (9) ~ isnonempty_pq(create_pq)
% 7.99/2.48 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0))
% 7.99/2.48 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1))
% 7.99/2.48 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0))
% 7.99/2.48 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1))
% 7.99/2.48 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq)
% 7.99/2.48 | (15) ? [v0] : less_than(bottom, v0)
% 7.99/2.48 | (16) ! [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))
% 7.99/2.48 | (17) ! [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)
% 7.99/2.48 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 7.99/2.48 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2))
% 7.99/2.48 | (20) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1)
% 7.99/2.49 | (21) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 7.99/2.49 | (22) ! [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))))
% 7.99/2.49 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_sharp_remove(v2, v1) | pi_remove(v0, v1))
% 7.99/2.49 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v2) | ~ pi_remove(v0, v1) | pi_sharp_remove(v2, v1))
% 7.99/2.49 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0))
% 7.99/2.49 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2))
% 7.99/2.49 | (27) ! [v0] : ~ contains_slb(create_slb, v0)
% 7.99/2.49 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v2) | less_than(v1, v2))
% 7.99/2.49 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 7.99/2.49 | (30) ! [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))
% 7.99/2.49 | (31) ! [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))
% 7.99/2.49 | (32) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1))
% 7.99/2.49 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (remove_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2))
% 7.99/2.49 | (34) ! [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))
% 7.99/2.49 | (35) ? [v0] : succ_cpq(v0, v0)
% 7.99/2.49 | (36) ~ isnonempty_slb(create_slb)
% 7.99/2.49 | (37) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1))
% 7.99/2.49 | (38) ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1)
% 7.99/2.49 | (39) ? [v0] : less_than(v0, v0)
% 7.99/2.49 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v0, v2, v4) | pair_in_list(v6, v2, v4))
% 7.99/2.49 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 7.99/2.49 | (42) ! [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))
% 7.99/2.49 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | contains_pq(v2, v1))
% 7.99/2.49 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4))
% 7.99/2.49 | (45) i(all_0_17_17) = all_0_14_14
% 7.99/2.49 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4))
% 7.99/2.49 | (47) ! [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))
% 7.99/2.49 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : (triple(v0, v1, v2) = v7 & findmin_cpq_eff(v7) = v8 & lookup_slb(v1, v3) = v6 & (v8 = v5 | ~ less_than(v6, v3))))
% 7.99/2.49 | (49) ! [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))
% 7.99/2.49 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (triple(v1, v2, v4) = v6) | ~ (triple(v0, v2, v3) = v5) | ? [v7] : (i(v6) = v7 & i(v5) = v7)) | ( ~ (all_0_0_0 = all_0_2_2) & i(all_0_1_1) = all_0_0_0 & i(all_0_3_3) = all_0_2_2 & triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1 & triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3 & pair(all_0_7_7, all_0_6_6) = all_0_5_5 & insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v1, all_0_12_12, v3) = v5) | ~ (triple(v0, all_0_12_12, v2) = v4) | ? [v6] : (i(v5) = v6 & i(v4) = v6))) | ( ~ (all_0_5_5 = all_0_7_7) & i(all_0_6_6) = all_0_5_5 & i(all_0_8_8) = all_0_7_7 & triple(all_0_11_11, create_slb, all_0_9_9) = all_0_6_6 & triple(all_0_12_12, create_slb, all_0_10_10) = all_0_8_8)
% 7.99/2.49 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (remove_pq(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | removemin_pq_eff(v0, v1) = v2)
% 7.99/2.49 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2))
% 7.99/2.49 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3))
% 7.99/2.49 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v0, v2) | contains_pq(v3, v2))
% 7.99/2.49 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3))
% 7.99/2.49 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3))
% 7.99/2.49 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2))
% 7.99/2.49 | (58) ! [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))))
% 8.41/2.49 | (59) triple(all_0_21_21, all_0_20_20, all_0_19_19) = all_0_17_17
% 8.41/2.49 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3)
% 8.41/2.50 | (61) ? [v0] : ? [v1] : (issmallestelement_pq(v0, v1) | ? [v2] : (contains_pq(v0, v2) & ~ less_than(v1, v2)))
% 8.41/2.50 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0))
% 8.41/2.50 | (63) ! [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))
% 8.41/2.50 | (64) ! [v0] : ( ~ phi(v0) | ? [v1] : (ok(v1) & check_cpq(v1) & succ_cpq(v0, v1)))
% 8.41/2.50 | (65) ~ (all_0_13_13 = all_0_15_15)
% 8.41/2.50 | (66) ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | contains_pq(v0, v1))
% 8.41/2.50 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3))
% 8.41/2.50 | (68) ! [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))))
% 8.41/2.50 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2))
% 8.41/2.50 | (70) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 8.41/2.50 | (71) i(all_0_16_16) = all_0_15_15
% 8.41/2.50 | (72) ! [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))
% 8.41/2.50 | (73) ! [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))
% 8.41/2.50 | (74) ! [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))))
% 8.41/2.50 | (75) insert_cpq(all_0_17_17, all_0_18_18) = all_0_16_16
% 8.41/2.50 | (76) ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_find_min(v0, v1))
% 8.41/2.50 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 8.41/2.50 | (78) ! [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))
% 8.41/2.50 | (79) ! [v0] : ~ contains_pq(create_pq, v0)
% 8.41/2.50 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 8.41/2.50 | (81) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0))
% 8.41/2.50 | (82) ! [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))
% 8.41/2.50 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 8.41/2.50 | (84) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1))
% 8.41/2.50 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 8.41/2.50 | (86) ! [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))))
% 8.41/2.50 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 8.41/2.50 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 8.41/2.50 | (89) ! [v0] : ! [v1] : ( ~ (i(v0) = v1) | ~ pi_removemin(v0) | ? [v2] : pi_sharp_find_min(v1, v2))
% 8.41/2.50 | (90) ! [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))))
% 8.41/2.50 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 8.41/2.50 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 8.41/2.50 | (93) ! [v0] : ! [v1] : ( ~ ok(v1) | ~ check_cpq(v1) | ~ succ_cpq(v0, v1) | phi(v0))
% 8.41/2.50 | (94) ! [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))
% 8.41/2.50 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 8.41/2.50 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2))
% 8.41/2.50 | (97) ! [v0] : ! [v1] : ( ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | pi_sharp_removemin(v0, v1))
% 8.41/2.50 | (98) ! [v0] : ! [v1] : ( ~ contains_pq(v0, v1) | pi_sharp_remove(v0, v1))
% 8.41/2.50 | (99) ! [v0] : ! [v1] : ( ~ pi_sharp_remove(v0, v1) | contains_pq(v0, v1))
% 8.41/2.50 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_removemin(v0))
% 8.41/2.50 | (101) ! [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))
% 8.41/2.51 | (102) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | remove_pq(v0, v1) = v2)
% 8.41/2.51 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (insert_pq(v0, v1) = v3) | ~ contains_pq(v3, v2) | contains_pq(v0, v2))
% 8.41/2.51 | (104) ! [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))
% 8.41/2.51 | (105) ! [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))))
% 8.41/2.51 | (106) ! [v0] : ! [v1] : ( ~ pi_sharp_find_min(v0, v1) | issmallestelement_pq(v0, v1))
% 8.41/2.51 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (i(v0) = v1) | ~ pi_sharp_find_min(v1, v2) | pi_find_min(v0))
% 8.41/2.51 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3))
% 8.41/2.51 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 8.41/2.51 | (110) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 8.41/2.51 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 8.41/2.51 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0))
% 8.41/2.51 | (113) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ~ issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1))
% 8.41/2.51 | (114) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 8.41/2.51 | (115) ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1))
% 8.41/2.51 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2))
% 8.41/2.51 | (117) ! [v0] : ! [v1] : ( ~ pi_sharp_removemin(v0, v1) | issmallestelement_pq(v0, v1))
% 8.41/2.51 | (118) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 8.41/2.51 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0))
% 8.41/2.51 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 8.41/2.51 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 8.41/2.51 | (122) ! [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))
% 8.41/2.51 |
% 8.41/2.51 | Instantiating formula (49) with all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21 and discharging atoms triple(all_0_21_21, all_0_20_20, all_0_19_19) = all_0_17_17, insert_cpq(all_0_17_17, all_0_18_18) = all_0_16_16, yields:
% 8.41/2.51 | (123) ? [v0] : ? [v1] : ? [v2] : (insert_pqp(all_0_21_21, all_0_18_18) = v0 & triple(v0, v2, all_0_19_19) = all_0_16_16 & pair(all_0_18_18, bottom) = v1 & insert_slb(all_0_20_20, v1) = v2)
% 8.41/2.51 |
% 8.41/2.51 | Instantiating (123) with all_17_0_29, all_17_1_30, all_17_2_31 yields:
% 8.41/2.51 | (124) insert_pqp(all_0_21_21, all_0_18_18) = all_17_2_31 & triple(all_17_2_31, all_17_0_29, all_0_19_19) = all_0_16_16 & pair(all_0_18_18, bottom) = all_17_1_30 & insert_slb(all_0_20_20, all_17_1_30) = all_17_0_29
% 8.41/2.51 |
% 8.41/2.51 | Applying alpha-rule on (124) yields:
% 8.41/2.51 | (125) insert_pqp(all_0_21_21, all_0_18_18) = all_17_2_31
% 8.41/2.51 | (126) triple(all_17_2_31, all_17_0_29, all_0_19_19) = all_0_16_16
% 8.41/2.51 | (127) pair(all_0_18_18, bottom) = all_17_1_30
% 8.41/2.51 | (128) insert_slb(all_0_20_20, all_17_1_30) = all_17_0_29
% 8.41/2.51 |
% 8.41/2.51 | Instantiating formula (47) with all_0_16_16, all_17_0_29, all_17_1_30, bottom, all_0_18_18, all_0_19_19, all_0_20_20, all_17_2_31 and discharging atoms triple(all_17_2_31, all_17_0_29, all_0_19_19) = all_0_16_16, pair(all_0_18_18, bottom) = all_17_1_30, insert_slb(all_0_20_20, all_17_1_30) = all_17_0_29, yields:
% 8.41/2.51 | (129) ? [v0] : ? [v1] : ? [v2] : (i(v1) = v2 & i(all_0_16_16) = v0 & triple(all_17_2_31, all_0_20_20, all_0_19_19) = v1 & insert_pq(v2, all_0_18_18) = v0)
% 8.41/2.51 |
% 8.41/2.51 | Instantiating (129) with all_25_0_32, all_25_1_33, all_25_2_34 yields:
% 8.41/2.51 | (130) i(all_25_1_33) = all_25_0_32 & i(all_0_16_16) = all_25_2_34 & triple(all_17_2_31, all_0_20_20, all_0_19_19) = all_25_1_33 & insert_pq(all_25_0_32, all_0_18_18) = all_25_2_34
% 8.41/2.51 |
% 8.41/2.51 | Applying alpha-rule on (130) yields:
% 8.41/2.51 | (131) i(all_25_1_33) = all_25_0_32
% 8.41/2.51 | (132) i(all_0_16_16) = all_25_2_34
% 8.41/2.51 | (133) triple(all_17_2_31, all_0_20_20, all_0_19_19) = all_25_1_33
% 8.41/2.51 | (134) insert_pq(all_25_0_32, all_0_18_18) = all_25_2_34
% 8.41/2.51 |
% 8.41/2.51 | Instantiating formula (3) with all_0_16_16, all_25_2_34, all_0_15_15 and discharging atoms i(all_0_16_16) = all_25_2_34, i(all_0_16_16) = all_0_15_15, yields:
% 8.41/2.51 | (135) all_25_2_34 = all_0_15_15
% 8.41/2.51 |
% 8.41/2.51 | From (135) and (134) follows:
% 8.41/2.51 | (136) insert_pq(all_25_0_32, all_0_18_18) = all_0_15_15
% 8.41/2.51 |
% 8.41/2.51 +-Applying beta-rule and splitting (50), into two cases.
% 8.41/2.51 |-Branch one:
% 8.41/2.51 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (triple(v1, v2, v4) = v6) | ~ (triple(v0, v2, v3) = v5) | ? [v7] : (i(v6) = v7 & i(v5) = v7)) | ( ~ (all_0_0_0 = all_0_2_2) & i(all_0_1_1) = all_0_0_0 & i(all_0_3_3) = all_0_2_2 & triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1 & triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3 & pair(all_0_7_7, all_0_6_6) = all_0_5_5 & insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v1, all_0_12_12, v3) = v5) | ~ (triple(v0, all_0_12_12, v2) = v4) | ? [v6] : (i(v5) = v6 & i(v4) = v6)))
% 8.41/2.52 |
% 8.41/2.52 +-Applying beta-rule and splitting (137), into two cases.
% 8.41/2.52 |-Branch one:
% 8.41/2.52 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (triple(v1, v2, v4) = v6) | ~ (triple(v0, v2, v3) = v5) | ? [v7] : (i(v6) = v7 & i(v5) = v7))
% 8.41/2.52 |
% 8.41/2.52 | Instantiating formula (138) with all_0_17_17, all_25_1_33, all_0_19_19, all_0_19_19, all_0_20_20, all_0_21_21, all_17_2_31 and discharging atoms triple(all_17_2_31, all_0_20_20, all_0_19_19) = all_25_1_33, triple(all_0_21_21, all_0_20_20, all_0_19_19) = all_0_17_17, yields:
% 8.41/2.52 | (139) ? [v0] : (i(all_25_1_33) = v0 & i(all_0_17_17) = v0)
% 8.41/2.52 |
% 8.41/2.52 | Instantiating (139) with all_63_0_35 yields:
% 8.41/2.52 | (140) i(all_25_1_33) = all_63_0_35 & i(all_0_17_17) = all_63_0_35
% 8.41/2.52 |
% 8.41/2.52 | Applying alpha-rule on (140) yields:
% 8.41/2.52 | (141) i(all_25_1_33) = all_63_0_35
% 8.41/2.52 | (142) i(all_0_17_17) = all_63_0_35
% 8.41/2.52 |
% 8.41/2.52 | Instantiating formula (3) with all_25_1_33, all_63_0_35, all_25_0_32 and discharging atoms i(all_25_1_33) = all_63_0_35, i(all_25_1_33) = all_25_0_32, yields:
% 8.41/2.52 | (143) all_63_0_35 = all_25_0_32
% 8.41/2.52 |
% 8.41/2.52 | Instantiating formula (3) with all_0_17_17, all_63_0_35, all_0_14_14 and discharging atoms i(all_0_17_17) = all_63_0_35, i(all_0_17_17) = all_0_14_14, yields:
% 8.41/2.52 | (144) all_63_0_35 = all_0_14_14
% 8.41/2.52 |
% 8.41/2.52 | Combining equations (143,144) yields a new equation:
% 8.41/2.52 | (145) all_25_0_32 = all_0_14_14
% 8.41/2.52 |
% 8.41/2.52 | Simplifying 145 yields:
% 8.41/2.52 | (146) all_25_0_32 = all_0_14_14
% 8.41/2.52 |
% 8.41/2.52 | From (146) and (136) follows:
% 8.41/2.52 | (147) insert_pq(all_0_14_14, all_0_18_18) = all_0_15_15
% 8.41/2.52 |
% 8.41/2.52 | Instantiating formula (62) with all_0_14_14, all_0_18_18, all_0_15_15, all_0_13_13 and discharging atoms insert_pq(all_0_14_14, all_0_18_18) = all_0_13_13, insert_pq(all_0_14_14, all_0_18_18) = all_0_15_15, yields:
% 8.41/2.52 | (148) all_0_13_13 = all_0_15_15
% 8.41/2.52 |
% 8.41/2.52 | Equations (148) can reduce 65 to:
% 8.41/2.52 | (149) $false
% 8.41/2.52 |
% 8.41/2.52 |-The branch is then unsatisfiable
% 8.41/2.52 |-Branch two:
% 8.41/2.52 | (150) ~ (all_0_0_0 = all_0_2_2) & i(all_0_1_1) = all_0_0_0 & i(all_0_3_3) = all_0_2_2 & triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1 & triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3 & pair(all_0_7_7, all_0_6_6) = all_0_5_5 & insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v1, all_0_12_12, v3) = v5) | ~ (triple(v0, all_0_12_12, v2) = v4) | ? [v6] : (i(v5) = v6 & i(v4) = v6))
% 8.41/2.52 |
% 8.41/2.52 | Applying alpha-rule on (150) yields:
% 8.41/2.52 | (151) triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1
% 8.41/2.52 | (152) pair(all_0_7_7, all_0_6_6) = all_0_5_5
% 8.41/2.52 | (153) i(all_0_3_3) = all_0_2_2
% 8.41/2.52 | (154) i(all_0_1_1) = all_0_0_0
% 8.41/2.52 | (155) insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4
% 8.41/2.52 | (156) ~ (all_0_0_0 = all_0_2_2)
% 8.41/2.52 | (157) triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3
% 8.41/2.52 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v1, all_0_12_12, v3) = v5) | ~ (triple(v0, all_0_12_12, v2) = v4) | ? [v6] : (i(v5) = v6 & i(v4) = v6))
% 8.41/2.52 |
% 8.41/2.52 | Instantiating formula (47) with all_0_1_1, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_12_12, all_0_10_10 and discharging atoms triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1, pair(all_0_7_7, all_0_6_6) = all_0_5_5, insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4, yields:
% 8.41/2.52 | (159) ? [v0] : ? [v1] : ? [v2] : (i(v1) = v2 & i(all_0_1_1) = v0 & triple(all_0_10_10, all_0_12_12, all_0_8_8) = v1 & insert_pq(v2, all_0_7_7) = v0)
% 8.41/2.52 |
% 8.41/2.52 | Instantiating formula (47) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_9_9, all_0_12_12, all_0_11_11 and discharging atoms triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3, pair(all_0_7_7, all_0_6_6) = all_0_5_5, insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4, yields:
% 8.41/2.52 | (160) ? [v0] : ? [v1] : ? [v2] : (i(v1) = v2 & i(all_0_3_3) = v0 & triple(all_0_11_11, all_0_12_12, all_0_9_9) = v1 & insert_pq(v2, all_0_7_7) = v0)
% 8.41/2.52 |
% 8.41/2.52 | Instantiating (160) with all_70_0_36, all_70_1_37, all_70_2_38 yields:
% 8.41/2.52 | (161) i(all_70_1_37) = all_70_0_36 & i(all_0_3_3) = all_70_2_38 & triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_70_1_37 & insert_pq(all_70_0_36, all_0_7_7) = all_70_2_38
% 8.41/2.52 |
% 8.41/2.52 | Applying alpha-rule on (161) yields:
% 8.41/2.52 | (162) i(all_70_1_37) = all_70_0_36
% 8.41/2.52 | (163) i(all_0_3_3) = all_70_2_38
% 8.41/2.52 | (164) triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_70_1_37
% 8.41/2.52 | (165) insert_pq(all_70_0_36, all_0_7_7) = all_70_2_38
% 8.41/2.52 |
% 8.41/2.52 | Instantiating (159) with all_72_0_39, all_72_1_40, all_72_2_41 yields:
% 8.41/2.52 | (166) i(all_72_1_40) = all_72_0_39 & i(all_0_1_1) = all_72_2_41 & triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_72_1_40 & insert_pq(all_72_0_39, all_0_7_7) = all_72_2_41
% 8.41/2.52 |
% 8.41/2.52 | Applying alpha-rule on (166) yields:
% 8.41/2.52 | (167) i(all_72_1_40) = all_72_0_39
% 8.41/2.52 | (168) i(all_0_1_1) = all_72_2_41
% 8.41/2.52 | (169) triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_72_1_40
% 8.41/2.52 | (170) insert_pq(all_72_0_39, all_0_7_7) = all_72_2_41
% 8.41/2.52 |
% 8.41/2.52 | Instantiating formula (3) with all_0_1_1, all_72_2_41, all_0_0_0 and discharging atoms i(all_0_1_1) = all_72_2_41, i(all_0_1_1) = all_0_0_0, yields:
% 8.41/2.52 | (171) all_72_2_41 = all_0_0_0
% 8.41/2.52 |
% 8.41/2.52 | Instantiating formula (3) with all_0_3_3, all_70_2_38, all_0_2_2 and discharging atoms i(all_0_3_3) = all_70_2_38, i(all_0_3_3) = all_0_2_2, yields:
% 8.41/2.52 | (172) all_70_2_38 = all_0_2_2
% 8.41/2.52 |
% 8.41/2.52 | From (171) and (170) follows:
% 8.41/2.52 | (173) insert_pq(all_72_0_39, all_0_7_7) = all_0_0_0
% 8.41/2.52 |
% 8.41/2.52 | From (172) and (165) follows:
% 8.41/2.52 | (174) insert_pq(all_70_0_36, all_0_7_7) = all_0_2_2
% 8.41/2.52 |
% 8.41/2.52 | Instantiating formula (158) with all_70_1_37, all_72_1_40, all_0_9_9, all_0_8_8, all_0_11_11, all_0_10_10 and discharging atoms triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_72_1_40, triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_70_1_37, yields:
% 8.41/2.53 | (175) ? [v0] : (i(all_72_1_40) = v0 & i(all_70_1_37) = v0)
% 8.41/2.53 |
% 8.41/2.53 | Instantiating (175) with all_84_0_42 yields:
% 8.41/2.53 | (176) i(all_72_1_40) = all_84_0_42 & i(all_70_1_37) = all_84_0_42
% 8.41/2.53 |
% 8.41/2.53 | Applying alpha-rule on (176) yields:
% 8.41/2.53 | (177) i(all_72_1_40) = all_84_0_42
% 8.41/2.53 | (178) i(all_70_1_37) = all_84_0_42
% 8.41/2.53 |
% 8.41/2.53 | Instantiating formula (3) with all_72_1_40, all_84_0_42, all_72_0_39 and discharging atoms i(all_72_1_40) = all_84_0_42, i(all_72_1_40) = all_72_0_39, yields:
% 8.41/2.53 | (179) all_84_0_42 = all_72_0_39
% 8.41/2.53 |
% 8.41/2.53 | Instantiating formula (3) with all_70_1_37, all_84_0_42, all_70_0_36 and discharging atoms i(all_70_1_37) = all_84_0_42, i(all_70_1_37) = all_70_0_36, yields:
% 8.41/2.53 | (180) all_84_0_42 = all_70_0_36
% 8.41/2.53 |
% 8.41/2.53 | Combining equations (179,180) yields a new equation:
% 8.41/2.53 | (181) all_72_0_39 = all_70_0_36
% 8.41/2.53 |
% 8.41/2.53 | Simplifying 181 yields:
% 8.41/2.53 | (182) all_72_0_39 = all_70_0_36
% 8.41/2.53 |
% 8.41/2.53 | From (182) and (173) follows:
% 8.41/2.53 | (183) insert_pq(all_70_0_36, all_0_7_7) = all_0_0_0
% 8.41/2.53 |
% 8.41/2.53 | Instantiating formula (62) with all_70_0_36, all_0_7_7, all_0_0_0, all_0_2_2 and discharging atoms insert_pq(all_70_0_36, all_0_7_7) = all_0_0_0, insert_pq(all_70_0_36, all_0_7_7) = all_0_2_2, yields:
% 8.41/2.53 | (184) all_0_0_0 = all_0_2_2
% 8.41/2.53 |
% 8.41/2.53 | Equations (184) can reduce 156 to:
% 8.41/2.53 | (149) $false
% 8.41/2.53 |
% 8.41/2.53 |-The branch is then unsatisfiable
% 8.41/2.53 |-Branch two:
% 8.41/2.53 | (186) ~ (all_0_5_5 = all_0_7_7) & i(all_0_6_6) = all_0_5_5 & i(all_0_8_8) = all_0_7_7 & triple(all_0_11_11, create_slb, all_0_9_9) = all_0_6_6 & triple(all_0_12_12, create_slb, all_0_10_10) = all_0_8_8
% 8.41/2.53 |
% 8.41/2.53 | Applying alpha-rule on (186) yields:
% 8.41/2.53 | (187) ~ (all_0_5_5 = all_0_7_7)
% 8.41/2.53 | (188) i(all_0_8_8) = all_0_7_7
% 8.41/2.53 | (189) triple(all_0_11_11, create_slb, all_0_9_9) = all_0_6_6
% 8.41/2.53 | (190) i(all_0_6_6) = all_0_5_5
% 8.41/2.53 | (191) triple(all_0_12_12, create_slb, all_0_10_10) = all_0_8_8
% 8.41/2.53 |
% 8.41/2.53 | Instantiating formula (14) with all_0_6_6, all_0_9_9, all_0_11_11 and discharging atoms triple(all_0_11_11, create_slb, all_0_9_9) = all_0_6_6, yields:
% 8.41/2.53 | (192) i(all_0_6_6) = create_pq
% 8.41/2.53 |
% 8.41/2.53 | Instantiating formula (14) with all_0_8_8, all_0_10_10, all_0_12_12 and discharging atoms triple(all_0_12_12, create_slb, all_0_10_10) = all_0_8_8, yields:
% 8.41/2.53 | (193) i(all_0_8_8) = create_pq
% 8.41/2.53 |
% 8.41/2.53 | Instantiating formula (3) with all_0_6_6, create_pq, all_0_5_5 and discharging atoms i(all_0_6_6) = all_0_5_5, i(all_0_6_6) = create_pq, yields:
% 8.41/2.53 | (194) all_0_5_5 = create_pq
% 8.41/2.53 |
% 8.41/2.53 | Instantiating formula (3) with all_0_8_8, create_pq, all_0_7_7 and discharging atoms i(all_0_8_8) = all_0_7_7, i(all_0_8_8) = create_pq, yields:
% 8.41/2.53 | (195) all_0_7_7 = create_pq
% 8.41/2.53 |
% 8.41/2.53 | Equations (194,195) can reduce 187 to:
% 8.41/2.53 | (149) $false
% 8.41/2.53 |
% 8.41/2.53 |-The branch is then unsatisfiable
% 8.41/2.53 % SZS output end Proof for theBenchmark
% 8.41/2.53
% 8.41/2.53 1938ms
%------------------------------------------------------------------------------