TSTP Solution File: SWV374+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV374+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 17:51:10 EDT 2022
% Result : Theorem 6.80s 2.19s
% Output : Proof 10.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV374+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 18:17:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.59 ____ _
% 0.18/0.59 ___ / __ \_____(_)___ ________ __________
% 0.18/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic
% 0.18/0.59 (ePrincess v.1.0)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2015
% 0.18/0.59 (c) Peter Backeman, 2014-2015
% 0.18/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.59 Bug reports to peter@backeman.se
% 0.18/0.59
% 0.18/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/0.98 Prover 0: Preprocessing ...
% 2.83/1.32 Prover 0: Warning: ignoring some quantifiers
% 3.19/1.35 Prover 0: Constructing countermodel ...
% 5.78/1.93 Prover 0: gave up
% 5.78/1.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.03/1.98 Prover 1: Preprocessing ...
% 6.53/2.10 Prover 1: Constructing countermodel ...
% 6.80/2.19 Prover 1: proved (257ms)
% 6.80/2.19
% 6.80/2.19 No countermodel exists, formula is valid
% 6.80/2.19 % SZS status Theorem for theBenchmark
% 6.80/2.19
% 6.80/2.19 Generating proof ... found it (size 173)
% 9.45/2.79
% 9.45/2.79 % SZS output start Proof for theBenchmark
% 9.45/2.79 Assumed formulas after preprocessing and simplification:
% 9.45/2.79 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v0 = 0) & findmin_pqp_res(v1) = v6 & ok(v5) = 0 & triple(v1, v2, v3) = v4 & findmin_cpq_eff(v4) = v5 & lookup_slb(v2, v6) = v8 & contains_slb(v2, v6) = v7 & isnonempty_slb(create_slb) = v0 & less_than(v8, v6) = v9 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (pair_in_list(v16, v12, v14) = v17) | ~ (pair(v11, v13) = v15) | ~ (insert_slb(v10, v15) = v16) | ? [v18] : ( ~ (v18 = 0) & pair_in_list(v10, v12, v14) = v18)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (insert_pqp(v10, v13) = v14) | ~ (triple(v14, v16, v12) = v17) | ~ (pair(v13, bottom) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : (triple(v10, v11, v12) = v18 & insert_cpq(v18, v13) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v10, v16, v12) = v17) | ~ (pair(v13, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (triple(v10, v11, v12) = v20 & check_cpq(v20) = v21 & check_cpq(v17) = v19 & less_than(v14, v13) = v18 & ( ~ (v18 = 0) | (( ~ (v21 = 0) | v19 = 0) & ( ~ (v19 = 0) | v21 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v10, v16, v12) = v17) | ~ (pair(v13, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : ? [v19] : (check_cpq(v17) = v19 & strictly_less_than(v13, v14) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (contains_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ( ~ (v17 = 0) & contains_slb(v10, v12) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (pair_in_list(v16, v12, v14) = 0) | ~ (pair(v11, v13) = v15) | ~ (insert_slb(v10, v15) = v16) | pair_in_list(v10, v12, v14) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (lookup_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : (lookup_slb(v10, v12) = v18 & contains_slb(v10, v12) = v17 & ( ~ (v17 = 0) | v18 = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (remove_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : (remove_slb(v10, v12) = v18 & contains_slb(v10, v12) = v17 & insert_slb(v18, v14) = v19 & ( ~ (v17 = 0) | v19 = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (pair_in_list(v16, v12, v14) = 0) | ~ (pair(v11, v13) = v15) | ~ (insert_slb(v10, v15) = v16) | pair_in_list(v10, v12, v14) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (remove_pqp(v10, v13) = v14) | ~ (triple(v14, v15, v12) = v16) | ~ (remove_slb(v11, v13) = v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (triple(v10, v11, v12) = v20 & remove_cpq(v20, v13) = v21 & lookup_slb(v11, v13) = v18 & contains_slb(v11, v13) = v17 & less_than(v18, v13) = v19 & ( ~ (v19 = 0) | ~ (v17 = 0) | v21 = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (update_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (update_slb(v10, v12) = v18 & pair(v11, v12) = v19 & insert_slb(v18, v19) = v20 & strictly_less_than(v13, v12) = v17 & ( ~ (v17 = 0) | v20 = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (update_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : (update_slb(v10, v12) = v18 & insert_slb(v18, v14) = v19 & less_than(v12, v13) = v17 & ( ~ (v17 = 0) | v19 = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (lookup_slb(v14, v11) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v10 | ~ (remove_slb(v14, v11) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (contains_cpq(v14, v13) = v15) | ~ (triple(v10, v11, v12) = v14) | ? [v16] : ( ~ (v16 = 0) & contains_slb(v11, v13) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (pair_in_list(v14, v11, v12) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (contains_slb(v14, v11) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (contains_slb(v15, v12) = 0) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | contains_slb(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = create_slb | ~ (findmin_pqp_res(v10) = v13) | ~ (triple(v10, v14, v12) = v15) | ~ (update_slb(v11, v13) = v14) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (triple(v10, v11, v12) = v19 & findmin_cpq_eff(v19) = v20 & lookup_slb(v11, v13) = v17 & contains_slb(v11, v13) = v16 & less_than(v17, v13) = v18 & ( ~ (v18 = 0) | ~ (v16 = 0) | v20 = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (remove_cpq(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (remove_pqp(v10, v13) = v19 & triple(v19, v20, bad) = v21 & lookup_slb(v11, v13) = v17 & remove_slb(v11, v13) = v20 & contains_slb(v11, v13) = v16 & strictly_less_than(v13, v17) = v18 & ( ~ (v18 = 0) | ~ (v16 = 0) | v21 = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (remove_cpq(v14, v13) = v15) | ? [v16] : ? [v17] : (triple(v10, v11, bad) = v17 & contains_slb(v11, v13) = v16 & (v17 = v15 | v16 = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (remove_cpq(v11, v12) = v13) | ~ (succ_cpq(v10, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & succ_cpq(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (insert_cpq(v11, v12) = v13) | ~ (succ_cpq(v10, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & succ_cpq(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (triple(v14, v13, v12) = v11) | ~ (triple(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (pair_in_list(v14, v13, v12) = v11) | ~ (pair_in_list(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (contains_cpq(v14, v13) = 0) | ~ (triple(v10, v11, v12) = v14) | contains_slb(v11, v13) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14) | isnonempty_slb(v14) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (removemin_cpq_eff(v11) = v12) | ~ (succ_cpq(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & succ_cpq(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (findmin_cpq_eff(v11) = v12) | ~ (succ_cpq(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & succ_cpq(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (less_than(v10, v12) = v13) | ~ (less_than(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & less_than(v11, v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = bad | ~ (triple(v10, v11, v12) = v13) | ok(v13) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (remove_pqp(v13, v12) = v11) | ~ (remove_pqp(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (insert_pqp(v13, v12) = v11) | ~ (insert_pqp(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (contains_cpq(v13, v12) = v11) | ~ (contains_cpq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (remove_cpq(v13, v12) = v11) | ~ (remove_cpq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (insert_cpq(v13, v12) = v11) | ~ (insert_cpq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (succ_cpq(v13, v12) = v11) | ~ (succ_cpq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (update_slb(v13, v12) = v11) | ~ (update_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (lookup_slb(v13, v12) = v11) | ~ (lookup_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (remove_slb(v13, v12) = v11) | ~ (remove_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (contains_slb(v13, v12) = v11) | ~ (contains_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (pair(v13, v12) = v11) | ~ (pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (insert_slb(v13, v12) = v11) | ~ (insert_slb(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (strictly_less_than(v13, v12) = v11) | ~ (strictly_less_than(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (less_than(v13, v12) = v11) | ~ (less_than(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = create_slb | ~ (triple(v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (findmin_pqp_res(v10) = v14 & triple(v10, v19, bad) = v20 & findmin_cpq_eff(v13) = v18 & update_slb(v11, v14) = v19 & lookup_slb(v11, v14) = v16 & contains_slb(v11, v14) = v15 & strictly_less_than(v14, v16) = v17 & ( ~ (v17 = 0) | ~ (v15 = 0) | v20 = v18))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = create_slb | ~ (triple(v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (findmin_pqp_res(v10) = v14 & triple(v10, v17, bad) = v18 & findmin_cpq_eff(v13) = v16 & update_slb(v11, v14) = v17 & contains_slb(v11, v14) = v15 & (v18 = v16 | v15 = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = create_slb | ~ (triple(v10, v11, v12) = v13) | ? [v14] : (findmin_cpq_res(v13) = v14 & findmin_pqp_res(v10) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (findmin_cpq_res(v10) = v12) | ~ (findmin_cpq_eff(v10) = v11) | ~ (remove_cpq(v11, v12) = v13) | removemin_cpq_eff(v10) = v13) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (strictly_less_than(v10, v11) = v12) | ? [v13] : ? [v14] : (less_than(v11, v10) = v14 & less_than(v10, v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (less_than(v10, v11) = v12) | less_than(v11, v10) = 0) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (removemin_cpq_res(v12) = v11) | ~ (removemin_cpq_res(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (findmin_cpq_res(v12) = v11) | ~ (findmin_cpq_res(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (findmin_pqp_res(v12) = v11) | ~ (findmin_pqp_res(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ok(v12) = v11) | ~ (ok(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (check_cpq(v12) = v11) | ~ (check_cpq(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (removemin_cpq_eff(v12) = v11) | ~ (removemin_cpq_eff(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (findmin_cpq_eff(v12) = v11) | ~ (findmin_cpq_eff(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (isnonempty_slb(v12) = v11) | ~ (isnonempty_slb(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v10, v11, bad) = v12) | ? [v13] : ( ~ (v13 = 0) & ok(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v10, create_slb, v11) = v12) | findmin_cpq_res(v12) = bottom) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v10, create_slb, v11) = v12) | check_cpq(v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v10, create_slb, v11) = v12) | ? [v13] : (triple(v10, create_slb, bad) = v13 & findmin_cpq_eff(v12) = v13)) & ! [v10] : ! [v11] : (v11 = create_slb | ~ (update_slb(create_slb, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (succ_cpq(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (less_than(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (less_than(bottom, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (removemin_cpq_res(v10) = v11) | findmin_cpq_res(v10) = v11) & ! [v10] : ! [v11] : ~ (pair_in_list(create_slb, v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (strictly_less_than(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & less_than(v11, v10) = v12 & less_than(v10, v11) = 0)) & ! [v10] : ~ (contains_slb(create_slb, v10) = 0) & ( ~ (v9 = 0) | ~ (v7 = 0) | v2 = create_slb))
% 9.85/2.86 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 9.85/2.86 | (1) ~ (all_0_9_9 = 0) & findmin_pqp_res(all_0_8_8) = all_0_3_3 & ok(all_0_4_4) = 0 & triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_5_5 & findmin_cpq_eff(all_0_5_5) = all_0_4_4 & lookup_slb(all_0_7_7, all_0_3_3) = all_0_1_1 & contains_slb(all_0_7_7, all_0_3_3) = all_0_2_2 & isnonempty_slb(create_slb) = all_0_9_9 & less_than(all_0_1_1, all_0_3_3) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & pair_in_list(v0, v2, v4) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (insert_pqp(v0, v3) = v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 & check_cpq(v7) = v9 & less_than(v4, v3) = v8 & ( ~ (v8 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : (check_cpq(v7) = v9 & strictly_less_than(v3, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : (lookup_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & ( ~ (v7 = 0) | v8 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (remove_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & insert_slb(v8, v4) = v9 & ( ~ (v7 = 0) | v9 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v11 & lookup_slb(v1, v3) = v8 & contains_slb(v1, v3) = v7 & less_than(v8, v3) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (update_slb(v0, v2) = v8 & pair(v1, v2) = v9 & insert_slb(v8, v9) = v10 & strictly_less_than(v3, v2) = v7 & ( ~ (v7 = 0) | v10 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (update_slb(v0, v2) = v8 & insert_slb(v8, v4) = v9 & less_than(v2, v3) = v7 & ( ~ (v7 = 0) | v9 = v6))) & ! [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] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | contains_slb(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v11 & lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & strictly_less_than(v3, v7) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v11 = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 & (v7 = v5 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (remove_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (insert_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (findmin_pqp_res(v0) = v4 & triple(v0, v9, bad) = v10 & findmin_cpq_eff(v3) = v8 & update_slb(v1, v4) = v9 & lookup_slb(v1, v4) = v6 & contains_slb(v1, v4) = v5 & strictly_less_than(v4, v6) = v7 & ( ~ (v7 = 0) | ~ (v5 = 0) | v10 = v8))) & ! [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 & contains_slb(v1, v4) = v5 & (v8 = v6 | v5 = 0))) & ! [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] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ? [v4] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) & ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0] : ~ (contains_slb(create_slb, v0) = 0) & ( ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0) | all_0_7_7 = create_slb)
% 9.85/2.88 |
% 9.85/2.88 | Applying alpha-rule on (1) yields:
% 9.85/2.88 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))
% 9.85/2.88 | (3) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 9.85/2.88 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1))
% 9.85/2.88 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (insert_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5))
% 9.85/2.88 | (6) lookup_slb(all_0_7_7, all_0_3_3) = all_0_1_1
% 9.85/2.88 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 9.85/2.88 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 9.85/2.88 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0)
% 9.85/2.88 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 9.85/2.88 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 9.85/2.88 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0))
% 9.85/2.88 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 9.85/2.88 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v11 & lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & strictly_less_than(v3, v7) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v11 = v5)))
% 9.85/2.88 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1))
% 9.85/2.88 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0)
% 9.85/2.88 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 9.85/2.89 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 9.85/2.89 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 9.85/2.89 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1))
% 9.85/2.89 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))
% 9.85/2.89 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0))
% 9.85/2.89 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 9.85/2.89 | (24) ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0) | all_0_7_7 = create_slb
% 9.85/2.89 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 9.85/2.89 | (26) ! [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))
% 9.85/2.89 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5)))
% 9.85/2.89 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (remove_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & insert_slb(v8, v4) = v9 & ( ~ (v7 = 0) | v9 = v6)))
% 9.85/2.89 | (29) ! [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 & contains_slb(v1, v4) = v5 & (v8 = v6 | v5 = 0)))
% 10.23/2.89 | (30) isnonempty_slb(create_slb) = all_0_9_9
% 10.23/2.89 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4))
% 10.23/2.89 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0)
% 10.23/2.89 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 10.23/2.89 | (34) ~ (all_0_9_9 = 0)
% 10.23/2.89 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0)
% 10.23/2.89 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ? [v4] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 10.23/2.89 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 10.23/2.89 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0)
% 10.23/2.89 | (39) less_than(all_0_1_1, all_0_3_3) = all_0_0_0
% 10.23/2.89 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 10.23/2.89 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (update_slb(v0, v2) = v8 & insert_slb(v8, v4) = v9 & less_than(v2, v3) = v7 & ( ~ (v7 = 0) | v9 = v6)))
% 10.23/2.89 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0))
% 10.23/2.89 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 10.23/2.89 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 10.23/2.90 | (45) triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_5_5
% 10.23/2.90 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v11 & lookup_slb(v1, v3) = v8 & contains_slb(v1, v3) = v7 & less_than(v8, v3) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = v6)))
% 10.23/2.90 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 10.23/2.90 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (remove_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5))
% 10.23/2.90 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 10.23/2.90 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 10.23/2.90 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 10.23/2.90 | (52) ok(all_0_4_4) = 0
% 10.23/2.90 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 10.23/2.90 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : (lookup_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & ( ~ (v7 = 0) | v8 = v6)))
% 10.23/2.90 | (55) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0))
% 10.23/2.90 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : (check_cpq(v7) = v9 & strictly_less_than(v3, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))
% 10.23/2.90 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0))
% 10.23/2.90 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 10.23/2.90 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 & (v7 = v5 | v6 = 0)))
% 10.23/2.90 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (update_slb(v0, v2) = v8 & pair(v1, v2) = v9 & insert_slb(v8, v9) = v10 & strictly_less_than(v3, v2) = v7 & ( ~ (v7 = 0) | v10 = v6)))
% 10.23/2.90 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 10.23/2.90 | (62) findmin_pqp_res(all_0_8_8) = all_0_3_3
% 10.23/2.90 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 10.23/2.90 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 10.23/2.90 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0)
% 10.23/2.90 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 10.23/2.90 | (67) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 10.23/2.90 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & pair_in_list(v0, v2, v4) = v8))
% 10.23/2.90 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (findmin_pqp_res(v0) = v4 & triple(v0, v9, bad) = v10 & findmin_cpq_eff(v3) = v8 & update_slb(v1, v4) = v9 & lookup_slb(v1, v4) = v6 & contains_slb(v1, v4) = v5 & strictly_less_than(v4, v6) = v7 & ( ~ (v7 = 0) | ~ (v5 = 0) | v10 = v8)))
% 10.23/2.91 | (70) contains_slb(all_0_7_7, all_0_3_3) = all_0_2_2
% 10.23/2.91 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | contains_slb(v0, v2) = 0)
% 10.23/2.91 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3)
% 10.23/2.91 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3))
% 10.23/2.91 | (74) ! [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] : ? [v11] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 & check_cpq(v7) = v9 & less_than(v4, v3) = v8 & ( ~ (v8 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0)))))
% 10.23/2.91 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 10.23/2.91 | (76) findmin_cpq_eff(all_0_5_5) = all_0_4_4
% 10.23/2.91 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 10.23/2.91 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0)
% 10.23/2.91 | (79) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0)
% 10.23/2.91 | (80) ! [v0] : ~ (contains_slb(create_slb, v0) = 0)
% 10.23/2.91 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 10.23/2.91 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4))
% 10.23/2.91 |
% 10.23/2.91 | Instantiating formula (63) with all_0_5_5, all_0_6_6, all_0_8_8 yields:
% 10.23/2.91 | (83) ~ (triple(all_0_8_8, create_slb, all_0_6_6) = all_0_5_5) | findmin_cpq_res(all_0_5_5) = bottom
% 10.23/2.91 |
% 10.23/2.91 | Instantiating formula (38) with all_0_5_5, all_0_6_6, all_0_8_8 yields:
% 10.23/2.91 | (84) ~ (triple(all_0_8_8, create_slb, all_0_6_6) = all_0_5_5) | check_cpq(all_0_5_5) = 0
% 10.23/2.91 |
% 10.23/2.91 | Instantiating formula (23) with all_0_5_5, all_0_6_6, all_0_8_8 yields:
% 10.23/2.91 | (85) ~ (triple(all_0_8_8, create_slb, all_0_6_6) = all_0_5_5) | ? [v0] : (triple(all_0_8_8, create_slb, bad) = v0 & findmin_cpq_eff(all_0_5_5) = v0)
% 10.23/2.91 |
% 10.23/2.91 | Instantiating formula (69) with 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_5_5, yields:
% 10.23/2.91 | (86) all_0_7_7 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(all_0_8_8) = v0 & triple(all_0_8_8, v5, bad) = v6 & findmin_cpq_eff(all_0_5_5) = v4 & update_slb(all_0_7_7, v0) = v5 & lookup_slb(all_0_7_7, v0) = v2 & contains_slb(all_0_7_7, v0) = v1 & strictly_less_than(v0, v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0) | v6 = v4))
% 10.23/2.91 |
% 10.23/2.91 | Instantiating formula (29) with 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_5_5, yields:
% 10.23/2.91 | (87) all_0_7_7 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_8_8) = v0 & triple(all_0_8_8, v3, bad) = v4 & findmin_cpq_eff(all_0_5_5) = v2 & update_slb(all_0_7_7, v0) = v3 & contains_slb(all_0_7_7, v0) = v1 & (v4 = v2 | v1 = 0))
% 10.23/2.91 |
% 10.23/2.91 | Instantiating formula (82) with 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_5_5, yields:
% 10.23/2.91 | (88) all_0_7_7 = create_slb | ? [v0] : (findmin_cpq_res(all_0_5_5) = v0 & findmin_pqp_res(all_0_8_8) = v0)
% 10.23/2.91 |
% 10.23/2.91 | Instantiating formula (16) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms less_than(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 10.23/2.91 | (89) all_0_0_0 = 0 | less_than(all_0_3_3, all_0_1_1) = 0
% 10.23/2.91 |
% 10.23/2.91 +-Applying beta-rule and splitting (84), into two cases.
% 10.23/2.91 |-Branch one:
% 10.23/2.91 | (90) ~ (triple(all_0_8_8, create_slb, all_0_6_6) = all_0_5_5)
% 10.23/2.91 |
% 10.23/2.92 | Using (45) and (90) yields:
% 10.23/2.92 | (91) ~ (all_0_7_7 = create_slb)
% 10.23/2.92 |
% 10.23/2.92 +-Applying beta-rule and splitting (88), into two cases.
% 10.23/2.92 |-Branch one:
% 10.23/2.92 | (92) all_0_7_7 = create_slb
% 10.23/2.92 |
% 10.23/2.92 | Equations (92) can reduce 91 to:
% 10.23/2.92 | (93) $false
% 10.23/2.92 |
% 10.23/2.92 |-The branch is then unsatisfiable
% 10.23/2.92 |-Branch two:
% 10.23/2.92 | (91) ~ (all_0_7_7 = create_slb)
% 10.23/2.92 | (95) ? [v0] : (findmin_cpq_res(all_0_5_5) = v0 & findmin_pqp_res(all_0_8_8) = v0)
% 10.23/2.92 |
% 10.23/2.92 | Instantiating (95) with all_18_0_10 yields:
% 10.23/2.92 | (96) findmin_cpq_res(all_0_5_5) = all_18_0_10 & findmin_pqp_res(all_0_8_8) = all_18_0_10
% 10.23/2.92 |
% 10.23/2.92 | Applying alpha-rule on (96) yields:
% 10.23/2.92 | (97) findmin_cpq_res(all_0_5_5) = all_18_0_10
% 10.23/2.92 | (98) findmin_pqp_res(all_0_8_8) = all_18_0_10
% 10.23/2.92 |
% 10.23/2.92 +-Applying beta-rule and splitting (87), into two cases.
% 10.23/2.92 |-Branch one:
% 10.23/2.92 | (92) all_0_7_7 = create_slb
% 10.23/2.92 |
% 10.23/2.92 | Equations (92) can reduce 91 to:
% 10.23/2.92 | (93) $false
% 10.23/2.92 |
% 10.23/2.92 |-The branch is then unsatisfiable
% 10.23/2.92 |-Branch two:
% 10.23/2.92 | (91) ~ (all_0_7_7 = create_slb)
% 10.23/2.92 | (102) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_8_8) = v0 & triple(all_0_8_8, v3, bad) = v4 & findmin_cpq_eff(all_0_5_5) = v2 & update_slb(all_0_7_7, v0) = v3 & contains_slb(all_0_7_7, v0) = v1 & (v4 = v2 | v1 = 0))
% 10.23/2.92 |
% 10.23/2.92 | Instantiating (102) with all_24_0_11, all_24_1_12, all_24_2_13, all_24_3_14, all_24_4_15 yields:
% 10.23/2.92 | (103) findmin_pqp_res(all_0_8_8) = all_24_4_15 & triple(all_0_8_8, all_24_1_12, bad) = all_24_0_11 & findmin_cpq_eff(all_0_5_5) = all_24_2_13 & update_slb(all_0_7_7, all_24_4_15) = all_24_1_12 & contains_slb(all_0_7_7, all_24_4_15) = all_24_3_14 & (all_24_0_11 = all_24_2_13 | all_24_3_14 = 0)
% 10.23/2.92 |
% 10.23/2.92 | Applying alpha-rule on (103) yields:
% 10.23/2.92 | (104) update_slb(all_0_7_7, all_24_4_15) = all_24_1_12
% 10.23/2.92 | (105) findmin_cpq_eff(all_0_5_5) = all_24_2_13
% 10.23/2.92 | (106) contains_slb(all_0_7_7, all_24_4_15) = all_24_3_14
% 10.23/2.92 | (107) all_24_0_11 = all_24_2_13 | all_24_3_14 = 0
% 10.23/2.92 | (108) findmin_pqp_res(all_0_8_8) = all_24_4_15
% 10.23/2.92 | (109) triple(all_0_8_8, all_24_1_12, bad) = all_24_0_11
% 10.23/2.92 |
% 10.23/2.92 +-Applying beta-rule and splitting (86), into two cases.
% 10.23/2.92 |-Branch one:
% 10.23/2.92 | (92) all_0_7_7 = create_slb
% 10.23/2.92 |
% 10.23/2.92 | Equations (92) can reduce 91 to:
% 10.23/2.92 | (93) $false
% 10.23/2.92 |
% 10.23/2.92 |-The branch is then unsatisfiable
% 10.23/2.92 |-Branch two:
% 10.23/2.92 | (91) ~ (all_0_7_7 = create_slb)
% 10.23/2.92 | (113) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(all_0_8_8) = v0 & triple(all_0_8_8, v5, bad) = v6 & findmin_cpq_eff(all_0_5_5) = v4 & update_slb(all_0_7_7, v0) = v5 & lookup_slb(all_0_7_7, v0) = v2 & contains_slb(all_0_7_7, v0) = v1 & strictly_less_than(v0, v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0) | v6 = v4))
% 10.23/2.92 |
% 10.23/2.92 | Instantiating (113) with all_29_0_16, all_29_1_17, all_29_2_18, all_29_3_19, all_29_4_20, all_29_5_21, all_29_6_22 yields:
% 10.23/2.92 | (114) findmin_pqp_res(all_0_8_8) = all_29_6_22 & triple(all_0_8_8, all_29_1_17, bad) = all_29_0_16 & findmin_cpq_eff(all_0_5_5) = all_29_2_18 & update_slb(all_0_7_7, all_29_6_22) = all_29_1_17 & lookup_slb(all_0_7_7, all_29_6_22) = all_29_4_20 & contains_slb(all_0_7_7, all_29_6_22) = all_29_5_21 & strictly_less_than(all_29_6_22, all_29_4_20) = all_29_3_19 & ( ~ (all_29_3_19 = 0) | ~ (all_29_5_21 = 0) | all_29_0_16 = all_29_2_18)
% 10.23/2.92 |
% 10.23/2.92 | Applying alpha-rule on (114) yields:
% 10.23/2.92 | (115) findmin_pqp_res(all_0_8_8) = all_29_6_22
% 10.23/2.92 | (116) findmin_cpq_eff(all_0_5_5) = all_29_2_18
% 10.23/2.92 | (117) contains_slb(all_0_7_7, all_29_6_22) = all_29_5_21
% 10.23/2.92 | (118) ~ (all_29_3_19 = 0) | ~ (all_29_5_21 = 0) | all_29_0_16 = all_29_2_18
% 10.23/2.92 | (119) update_slb(all_0_7_7, all_29_6_22) = all_29_1_17
% 10.23/2.92 | (120) lookup_slb(all_0_7_7, all_29_6_22) = all_29_4_20
% 10.23/2.92 | (121) strictly_less_than(all_29_6_22, all_29_4_20) = all_29_3_19
% 10.23/2.92 | (122) triple(all_0_8_8, all_29_1_17, bad) = all_29_0_16
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (61) with all_0_8_8, all_24_4_15, all_0_3_3 and discharging atoms findmin_pqp_res(all_0_8_8) = all_24_4_15, findmin_pqp_res(all_0_8_8) = all_0_3_3, yields:
% 10.23/2.92 | (123) all_24_4_15 = all_0_3_3
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (61) with all_0_8_8, all_24_4_15, all_29_6_22 and discharging atoms findmin_pqp_res(all_0_8_8) = all_29_6_22, findmin_pqp_res(all_0_8_8) = all_24_4_15, yields:
% 10.23/2.92 | (124) all_29_6_22 = all_24_4_15
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (61) with all_0_8_8, all_18_0_10, all_29_6_22 and discharging atoms findmin_pqp_res(all_0_8_8) = all_29_6_22, findmin_pqp_res(all_0_8_8) = all_18_0_10, yields:
% 10.23/2.92 | (125) all_29_6_22 = all_18_0_10
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (49) with all_0_8_8, all_24_1_12, bad, all_24_0_11, all_29_0_16 and discharging atoms triple(all_0_8_8, all_24_1_12, bad) = all_24_0_11, yields:
% 10.23/2.92 | (126) all_29_0_16 = all_24_0_11 | ~ (triple(all_0_8_8, all_24_1_12, bad) = all_29_0_16)
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (58) with all_0_5_5, all_29_2_18, all_0_4_4 and discharging atoms findmin_cpq_eff(all_0_5_5) = all_29_2_18, findmin_cpq_eff(all_0_5_5) = all_0_4_4, yields:
% 10.23/2.92 | (127) all_29_2_18 = all_0_4_4
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (58) with all_0_5_5, all_24_2_13, all_29_2_18 and discharging atoms findmin_cpq_eff(all_0_5_5) = all_29_2_18, findmin_cpq_eff(all_0_5_5) = all_24_2_13, yields:
% 10.23/2.92 | (128) all_29_2_18 = all_24_2_13
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (81) with all_0_7_7, all_24_4_15, all_24_1_12, all_29_1_17 and discharging atoms update_slb(all_0_7_7, all_24_4_15) = all_24_1_12, yields:
% 10.23/2.92 | (129) all_29_1_17 = all_24_1_12 | ~ (update_slb(all_0_7_7, all_24_4_15) = all_29_1_17)
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (11) with all_0_7_7, all_0_3_3, all_29_4_20, all_0_1_1 and discharging atoms lookup_slb(all_0_7_7, all_0_3_3) = all_0_1_1, yields:
% 10.23/2.92 | (130) all_29_4_20 = all_0_1_1 | ~ (lookup_slb(all_0_7_7, all_0_3_3) = all_29_4_20)
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (33) with all_0_7_7, all_0_3_3, all_24_3_14, all_0_2_2 and discharging atoms contains_slb(all_0_7_7, all_0_3_3) = all_0_2_2, yields:
% 10.23/2.92 | (131) all_24_3_14 = all_0_2_2 | ~ (contains_slb(all_0_7_7, all_0_3_3) = all_24_3_14)
% 10.23/2.92 |
% 10.23/2.92 | Instantiating formula (33) with all_0_7_7, all_24_4_15, all_24_3_14, all_29_5_21 and discharging atoms contains_slb(all_0_7_7, all_24_4_15) = all_24_3_14, yields:
% 10.23/2.92 | (132) all_29_5_21 = all_24_3_14 | ~ (contains_slb(all_0_7_7, all_24_4_15) = all_29_5_21)
% 10.23/2.92 |
% 10.23/2.92 | Combining equations (127,128) yields a new equation:
% 10.23/2.92 | (133) all_24_2_13 = all_0_4_4
% 10.23/2.92 |
% 10.23/2.92 | Combining equations (124,125) yields a new equation:
% 10.23/2.92 | (134) all_24_4_15 = all_18_0_10
% 10.23/2.92 |
% 10.23/2.92 | Simplifying 134 yields:
% 10.23/2.92 | (135) all_24_4_15 = all_18_0_10
% 10.23/2.92 |
% 10.23/2.92 | Combining equations (123,135) yields a new equation:
% 10.23/2.92 | (136) all_18_0_10 = all_0_3_3
% 10.23/2.92 |
% 10.23/2.92 | Combining equations (136,135) yields a new equation:
% 10.23/2.92 | (123) all_24_4_15 = all_0_3_3
% 10.23/2.92 |
% 10.23/2.92 | Combining equations (136,125) yields a new equation:
% 10.23/2.92 | (138) all_29_6_22 = all_0_3_3
% 10.23/2.92 |
% 10.23/2.92 | Combining equations (133,128) yields a new equation:
% 10.23/2.92 | (127) all_29_2_18 = all_0_4_4
% 10.23/2.92 |
% 10.23/2.92 | From (136) and (98) follows:
% 10.23/2.93 | (62) findmin_pqp_res(all_0_8_8) = all_0_3_3
% 10.23/2.93 |
% 10.23/2.93 | From (138) and (119) follows:
% 10.23/2.93 | (141) update_slb(all_0_7_7, all_0_3_3) = all_29_1_17
% 10.23/2.93 |
% 10.23/2.93 | From (138) and (120) follows:
% 10.23/2.93 | (142) lookup_slb(all_0_7_7, all_0_3_3) = all_29_4_20
% 10.23/2.93 |
% 10.23/2.93 | From (138) and (117) follows:
% 10.23/2.93 | (143) contains_slb(all_0_7_7, all_0_3_3) = all_29_5_21
% 10.23/2.93 |
% 10.23/2.93 | From (138) and (121) follows:
% 10.23/2.93 | (144) strictly_less_than(all_0_3_3, all_29_4_20) = all_29_3_19
% 10.23/2.93 |
% 10.23/2.93 +-Applying beta-rule and splitting (130), into two cases.
% 10.23/2.93 |-Branch one:
% 10.23/2.93 | (145) ~ (lookup_slb(all_0_7_7, all_0_3_3) = all_29_4_20)
% 10.23/2.93 |
% 10.23/2.93 | Using (142) and (145) yields:
% 10.23/2.93 | (146) $false
% 10.23/2.93 |
% 10.23/2.93 |-The branch is then unsatisfiable
% 10.23/2.93 |-Branch two:
% 10.23/2.93 | (142) lookup_slb(all_0_7_7, all_0_3_3) = all_29_4_20
% 10.23/2.93 | (148) all_29_4_20 = all_0_1_1
% 10.23/2.93 |
% 10.23/2.93 | From (148) and (142) follows:
% 10.23/2.93 | (6) lookup_slb(all_0_7_7, all_0_3_3) = all_0_1_1
% 10.23/2.93 |
% 10.23/2.93 | From (148) and (144) follows:
% 10.23/2.93 | (150) strictly_less_than(all_0_3_3, all_0_1_1) = all_29_3_19
% 10.23/2.93 |
% 10.23/2.93 +-Applying beta-rule and splitting (132), into two cases.
% 10.23/2.93 |-Branch one:
% 10.23/2.93 | (151) ~ (contains_slb(all_0_7_7, all_24_4_15) = all_29_5_21)
% 10.23/2.93 |
% 10.23/2.93 | From (123) and (151) follows:
% 10.23/2.93 | (152) ~ (contains_slb(all_0_7_7, all_0_3_3) = all_29_5_21)
% 10.23/2.93 |
% 10.23/2.93 | Using (143) and (152) yields:
% 10.23/2.93 | (146) $false
% 10.23/2.93 |
% 10.23/2.93 |-The branch is then unsatisfiable
% 10.23/2.93 |-Branch two:
% 10.23/2.93 | (154) contains_slb(all_0_7_7, all_24_4_15) = all_29_5_21
% 10.23/2.93 | (155) all_29_5_21 = all_24_3_14
% 10.23/2.93 |
% 10.23/2.93 | From (155) and (143) follows:
% 10.23/2.93 | (156) contains_slb(all_0_7_7, all_0_3_3) = all_24_3_14
% 10.23/2.93 |
% 10.23/2.93 +-Applying beta-rule and splitting (129), into two cases.
% 10.23/2.93 |-Branch one:
% 10.23/2.93 | (157) ~ (update_slb(all_0_7_7, all_24_4_15) = all_29_1_17)
% 10.23/2.93 |
% 10.23/2.93 | From (123) and (157) follows:
% 10.23/2.93 | (158) ~ (update_slb(all_0_7_7, all_0_3_3) = all_29_1_17)
% 10.23/2.93 |
% 10.23/2.93 | Using (141) and (158) yields:
% 10.23/2.93 | (146) $false
% 10.23/2.93 |
% 10.23/2.93 |-The branch is then unsatisfiable
% 10.23/2.93 |-Branch two:
% 10.23/2.93 | (160) update_slb(all_0_7_7, all_24_4_15) = all_29_1_17
% 10.23/2.93 | (161) all_29_1_17 = all_24_1_12
% 10.23/2.93 |
% 10.23/2.93 | From (161) and (122) follows:
% 10.23/2.93 | (162) triple(all_0_8_8, all_24_1_12, bad) = all_29_0_16
% 10.23/2.93 |
% 10.23/2.93 | From (161) and (141) follows:
% 10.23/2.93 | (163) update_slb(all_0_7_7, all_0_3_3) = all_24_1_12
% 10.23/2.93 |
% 10.23/2.93 +-Applying beta-rule and splitting (126), into two cases.
% 10.23/2.93 |-Branch one:
% 10.23/2.93 | (164) ~ (triple(all_0_8_8, all_24_1_12, bad) = all_29_0_16)
% 10.23/2.93 |
% 10.23/2.93 | Using (162) and (164) yields:
% 10.23/2.93 | (146) $false
% 10.23/2.93 |
% 10.23/2.93 |-The branch is then unsatisfiable
% 10.23/2.93 |-Branch two:
% 10.23/2.93 | (162) triple(all_0_8_8, all_24_1_12, bad) = all_29_0_16
% 10.23/2.93 | (167) all_29_0_16 = all_24_0_11
% 10.23/2.93 |
% 10.23/2.93 | From (167) and (162) follows:
% 10.23/2.93 | (109) triple(all_0_8_8, all_24_1_12, bad) = all_24_0_11
% 10.23/2.93 |
% 10.23/2.93 +-Applying beta-rule and splitting (131), into two cases.
% 10.23/2.93 |-Branch one:
% 10.23/2.93 | (169) ~ (contains_slb(all_0_7_7, all_0_3_3) = all_24_3_14)
% 10.23/2.93 |
% 10.23/2.93 | Using (156) and (169) yields:
% 10.23/2.93 | (146) $false
% 10.23/2.93 |
% 10.23/2.93 |-The branch is then unsatisfiable
% 10.23/2.93 |-Branch two:
% 10.23/2.93 | (156) contains_slb(all_0_7_7, all_0_3_3) = all_24_3_14
% 10.23/2.93 | (172) all_24_3_14 = all_0_2_2
% 10.23/2.93 |
% 10.23/2.93 | Combining equations (172,155) yields a new equation:
% 10.23/2.93 | (173) all_29_5_21 = all_0_2_2
% 10.23/2.93 |
% 10.23/2.93 | Instantiating formula (73) with all_24_0_11, all_24_1_12, all_0_8_8 and discharging atoms triple(all_0_8_8, all_24_1_12, bad) = all_24_0_11, yields:
% 10.23/2.93 | (174) ? [v0] : ( ~ (v0 = 0) & ok(all_24_0_11) = v0)
% 10.23/2.93 |
% 10.23/2.93 | Instantiating formula (27) with all_24_0_11, all_24_1_12, all_0_3_3, bad, all_0_7_7, all_0_8_8 and discharging atoms findmin_pqp_res(all_0_8_8) = all_0_3_3, triple(all_0_8_8, all_24_1_12, bad) = all_24_0_11, update_slb(all_0_7_7, all_0_3_3) = all_24_1_12, yields:
% 10.23/2.93 | (175) all_0_7_7 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (triple(all_0_8_8, all_0_7_7, bad) = v3 & findmin_cpq_eff(v3) = v4 & lookup_slb(all_0_7_7, all_0_3_3) = v1 & contains_slb(all_0_7_7, all_0_3_3) = v0 & less_than(v1, all_0_3_3) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = all_24_0_11))
% 10.23/2.93 |
% 10.23/2.93 | Instantiating formula (36) with all_29_3_19, all_0_1_1, all_0_3_3 and discharging atoms strictly_less_than(all_0_3_3, all_0_1_1) = all_29_3_19, yields:
% 10.23/2.93 | (176) all_29_3_19 = 0 | ? [v0] : ? [v1] : (less_than(all_0_1_1, all_0_3_3) = v1 & less_than(all_0_3_3, all_0_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 10.23/2.93 |
% 10.23/2.93 | Instantiating (174) with all_60_0_23 yields:
% 10.23/2.93 | (177) ~ (all_60_0_23 = 0) & ok(all_24_0_11) = all_60_0_23
% 10.23/2.93 |
% 10.23/2.93 | Applying alpha-rule on (177) yields:
% 10.23/2.93 | (178) ~ (all_60_0_23 = 0)
% 10.23/2.93 | (179) ok(all_24_0_11) = all_60_0_23
% 10.23/2.93 |
% 10.23/2.93 +-Applying beta-rule and splitting (175), into two cases.
% 10.23/2.93 |-Branch one:
% 10.23/2.93 | (92) all_0_7_7 = create_slb
% 10.23/2.93 |
% 10.23/2.93 | Equations (92) can reduce 91 to:
% 10.23/2.93 | (93) $false
% 10.23/2.93 |
% 10.23/2.93 |-The branch is then unsatisfiable
% 10.23/2.93 |-Branch two:
% 10.23/2.93 | (91) ~ (all_0_7_7 = create_slb)
% 10.23/2.93 | (183) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (triple(all_0_8_8, all_0_7_7, bad) = v3 & findmin_cpq_eff(v3) = v4 & lookup_slb(all_0_7_7, all_0_3_3) = v1 & contains_slb(all_0_7_7, all_0_3_3) = v0 & less_than(v1, all_0_3_3) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = all_24_0_11))
% 10.23/2.93 |
% 10.23/2.93 | Instantiating (183) with all_66_0_24, all_66_1_25, all_66_2_26, all_66_3_27, all_66_4_28 yields:
% 10.23/2.93 | (184) triple(all_0_8_8, all_0_7_7, bad) = all_66_1_25 & findmin_cpq_eff(all_66_1_25) = all_66_0_24 & lookup_slb(all_0_7_7, all_0_3_3) = all_66_3_27 & contains_slb(all_0_7_7, all_0_3_3) = all_66_4_28 & less_than(all_66_3_27, all_0_3_3) = all_66_2_26 & ( ~ (all_66_2_26 = 0) | ~ (all_66_4_28 = 0) | all_66_0_24 = all_24_0_11)
% 10.23/2.93 |
% 10.23/2.93 | Applying alpha-rule on (184) yields:
% 10.23/2.93 | (185) lookup_slb(all_0_7_7, all_0_3_3) = all_66_3_27
% 10.23/2.93 | (186) triple(all_0_8_8, all_0_7_7, bad) = all_66_1_25
% 10.23/2.93 | (187) ~ (all_66_2_26 = 0) | ~ (all_66_4_28 = 0) | all_66_0_24 = all_24_0_11
% 10.23/2.93 | (188) contains_slb(all_0_7_7, all_0_3_3) = all_66_4_28
% 10.23/2.93 | (189) findmin_cpq_eff(all_66_1_25) = all_66_0_24
% 10.23/2.93 | (190) less_than(all_66_3_27, all_0_3_3) = all_66_2_26
% 10.23/2.93 |
% 10.23/2.93 | Instantiating formula (19) with all_0_4_4, all_60_0_23, 0 and discharging atoms ok(all_0_4_4) = 0, yields:
% 10.23/2.93 | (191) all_60_0_23 = 0 | ~ (ok(all_0_4_4) = all_60_0_23)
% 10.23/2.93 |
% 10.23/2.93 | Instantiating formula (11) with all_0_7_7, all_0_3_3, all_66_3_27, all_0_1_1 and discharging atoms lookup_slb(all_0_7_7, all_0_3_3) = all_66_3_27, lookup_slb(all_0_7_7, all_0_3_3) = all_0_1_1, yields:
% 10.23/2.93 | (192) all_66_3_27 = all_0_1_1
% 10.23/2.93 |
% 10.23/2.93 | Instantiating formula (37) with all_0_1_1, all_0_3_3, all_66_2_26, all_0_0_0 and discharging atoms less_than(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 10.23/2.93 | (193) all_66_2_26 = all_0_0_0 | ~ (less_than(all_0_1_1, all_0_3_3) = all_66_2_26)
% 10.23/2.93 |
% 10.23/2.93 | From (192) and (190) follows:
% 10.23/2.93 | (194) less_than(all_0_1_1, all_0_3_3) = all_66_2_26
% 10.23/2.93 |
% 10.23/2.93 +-Applying beta-rule and splitting (193), into two cases.
% 10.23/2.93 |-Branch one:
% 10.23/2.93 | (195) ~ (less_than(all_0_1_1, all_0_3_3) = all_66_2_26)
% 10.23/2.93 |
% 10.23/2.93 | Using (194) and (195) yields:
% 10.23/2.93 | (146) $false
% 10.23/2.93 |
% 10.23/2.93 |-The branch is then unsatisfiable
% 10.23/2.93 |-Branch two:
% 10.23/2.93 | (194) less_than(all_0_1_1, all_0_3_3) = all_66_2_26
% 10.23/2.93 | (198) all_66_2_26 = all_0_0_0
% 10.23/2.93 |
% 10.23/2.93 | From (198) and (194) follows:
% 10.23/2.93 | (39) less_than(all_0_1_1, all_0_3_3) = all_0_0_0
% 10.23/2.93 |
% 10.23/2.93 | Instantiating formula (69) with all_66_1_25, bad, all_0_7_7, all_0_8_8 and discharging atoms triple(all_0_8_8, all_0_7_7, bad) = all_66_1_25, yields:
% 10.23/2.93 | (200) all_0_7_7 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(all_0_8_8) = v0 & triple(all_0_8_8, v5, bad) = v6 & findmin_cpq_eff(all_66_1_25) = v4 & update_slb(all_0_7_7, v0) = v5 & lookup_slb(all_0_7_7, v0) = v2 & contains_slb(all_0_7_7, v0) = v1 & strictly_less_than(v0, v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0) | v6 = v4))
% 10.23/2.93 |
% 10.23/2.93 | Instantiating formula (29) with all_66_1_25, bad, all_0_7_7, all_0_8_8 and discharging atoms triple(all_0_8_8, all_0_7_7, bad) = all_66_1_25, yields:
% 10.23/2.94 | (201) all_0_7_7 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_8_8) = v0 & triple(all_0_8_8, v3, bad) = v4 & findmin_cpq_eff(all_66_1_25) = v2 & update_slb(all_0_7_7, v0) = v3 & contains_slb(all_0_7_7, v0) = v1 & (v4 = v2 | v1 = 0))
% 10.23/2.94 |
% 10.23/2.94 | Instantiating formula (82) with all_66_1_25, bad, all_0_7_7, all_0_8_8 and discharging atoms triple(all_0_8_8, all_0_7_7, bad) = all_66_1_25, yields:
% 10.23/2.94 | (202) all_0_7_7 = create_slb | ? [v0] : (findmin_cpq_res(all_66_1_25) = v0 & findmin_pqp_res(all_0_8_8) = v0)
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (202), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (92) all_0_7_7 = create_slb
% 10.23/2.94 |
% 10.23/2.94 | Equations (92) can reduce 91 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (91) ~ (all_0_7_7 = create_slb)
% 10.23/2.94 | (206) ? [v0] : (findmin_cpq_res(all_66_1_25) = v0 & findmin_pqp_res(all_0_8_8) = v0)
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (200), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (92) all_0_7_7 = create_slb
% 10.23/2.94 |
% 10.23/2.94 | Equations (92) can reduce 91 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (91) ~ (all_0_7_7 = create_slb)
% 10.23/2.94 | (210) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(all_0_8_8) = v0 & triple(all_0_8_8, v5, bad) = v6 & findmin_cpq_eff(all_66_1_25) = v4 & update_slb(all_0_7_7, v0) = v5 & lookup_slb(all_0_7_7, v0) = v2 & contains_slb(all_0_7_7, v0) = v1 & strictly_less_than(v0, v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0) | v6 = v4))
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (201), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (92) all_0_7_7 = create_slb
% 10.23/2.94 |
% 10.23/2.94 | Equations (92) can reduce 91 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (91) ~ (all_0_7_7 = create_slb)
% 10.23/2.94 | (214) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_8_8) = v0 & triple(all_0_8_8, v3, bad) = v4 & findmin_cpq_eff(all_66_1_25) = v2 & update_slb(all_0_7_7, v0) = v3 & contains_slb(all_0_7_7, v0) = v1 & (v4 = v2 | v1 = 0))
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (24), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (215) ~ (all_0_0_0 = 0)
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (89), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (216) less_than(all_0_3_3, all_0_1_1) = 0
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (176), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (217) all_29_3_19 = 0
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (107), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (218) all_24_3_14 = 0
% 10.23/2.94 |
% 10.23/2.94 | Combining equations (218,172) yields a new equation:
% 10.23/2.94 | (219) all_0_2_2 = 0
% 10.23/2.94 |
% 10.23/2.94 | Combining equations (219,173) yields a new equation:
% 10.23/2.94 | (220) all_29_5_21 = 0
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (118), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (221) ~ (all_29_3_19 = 0)
% 10.23/2.94 |
% 10.23/2.94 | Equations (217) can reduce 221 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (217) all_29_3_19 = 0
% 10.23/2.94 | (224) ~ (all_29_5_21 = 0) | all_29_0_16 = all_29_2_18
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (224), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (225) ~ (all_29_5_21 = 0)
% 10.23/2.94 |
% 10.23/2.94 | Equations (220) can reduce 225 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (220) all_29_5_21 = 0
% 10.23/2.94 | (228) all_29_0_16 = all_29_2_18
% 10.23/2.94 |
% 10.23/2.94 | Combining equations (167,228) yields a new equation:
% 10.23/2.94 | (229) all_29_2_18 = all_24_0_11
% 10.23/2.94 |
% 10.23/2.94 | Combining equations (229,127) yields a new equation:
% 10.23/2.94 | (230) all_24_0_11 = all_0_4_4
% 10.23/2.94 |
% 10.23/2.94 | Simplifying 230 yields:
% 10.23/2.94 | (231) all_24_0_11 = all_0_4_4
% 10.23/2.94 |
% 10.23/2.94 | From (231) and (179) follows:
% 10.23/2.94 | (232) ok(all_0_4_4) = all_60_0_23
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (191), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (233) ~ (ok(all_0_4_4) = all_60_0_23)
% 10.23/2.94 |
% 10.23/2.94 | Using (232) and (233) yields:
% 10.23/2.94 | (146) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (232) ok(all_0_4_4) = all_60_0_23
% 10.23/2.94 | (236) all_60_0_23 = 0
% 10.23/2.94 |
% 10.23/2.94 | Equations (236) can reduce 178 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (238) ~ (all_24_3_14 = 0)
% 10.23/2.94 | (239) all_24_0_11 = all_24_2_13
% 10.23/2.94 |
% 10.23/2.94 | Combining equations (133,239) yields a new equation:
% 10.23/2.94 | (231) all_24_0_11 = all_0_4_4
% 10.23/2.94 |
% 10.23/2.94 | From (231) and (179) follows:
% 10.23/2.94 | (232) ok(all_0_4_4) = all_60_0_23
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (191), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (233) ~ (ok(all_0_4_4) = all_60_0_23)
% 10.23/2.94 |
% 10.23/2.94 | Using (232) and (233) yields:
% 10.23/2.94 | (146) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (232) ok(all_0_4_4) = all_60_0_23
% 10.23/2.94 | (236) all_60_0_23 = 0
% 10.23/2.94 |
% 10.23/2.94 | Equations (236) can reduce 178 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (221) ~ (all_29_3_19 = 0)
% 10.23/2.94 | (248) ? [v0] : ? [v1] : (less_than(all_0_1_1, all_0_3_3) = v1 & less_than(all_0_3_3, all_0_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 10.23/2.94 |
% 10.23/2.94 | Instantiating (248) with all_171_0_43, all_171_1_44 yields:
% 10.23/2.94 | (249) less_than(all_0_1_1, all_0_3_3) = all_171_0_43 & less_than(all_0_3_3, all_0_1_1) = all_171_1_44 & ( ~ (all_171_1_44 = 0) | all_171_0_43 = 0)
% 10.23/2.94 |
% 10.23/2.94 | Applying alpha-rule on (249) yields:
% 10.23/2.94 | (250) less_than(all_0_1_1, all_0_3_3) = all_171_0_43
% 10.23/2.94 | (251) less_than(all_0_3_3, all_0_1_1) = all_171_1_44
% 10.23/2.94 | (252) ~ (all_171_1_44 = 0) | all_171_0_43 = 0
% 10.23/2.94 |
% 10.23/2.94 | Instantiating formula (37) with all_0_1_1, all_0_3_3, all_171_0_43, all_0_0_0 and discharging atoms less_than(all_0_1_1, all_0_3_3) = all_171_0_43, less_than(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 10.23/2.94 | (253) all_171_0_43 = all_0_0_0
% 10.23/2.94 |
% 10.23/2.94 | Instantiating formula (37) with all_0_3_3, all_0_1_1, 0, all_171_1_44 and discharging atoms less_than(all_0_3_3, all_0_1_1) = all_171_1_44, less_than(all_0_3_3, all_0_1_1) = 0, yields:
% 10.23/2.94 | (254) all_171_1_44 = 0
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (252), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (255) ~ (all_171_1_44 = 0)
% 10.23/2.94 |
% 10.23/2.94 | Equations (254) can reduce 255 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (254) all_171_1_44 = 0
% 10.23/2.94 | (258) all_171_0_43 = 0
% 10.23/2.94 |
% 10.23/2.94 | Combining equations (258,253) yields a new equation:
% 10.23/2.94 | (259) all_0_0_0 = 0
% 10.23/2.94 |
% 10.23/2.94 | Equations (259) can reduce 215 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (261) ~ (less_than(all_0_3_3, all_0_1_1) = 0)
% 10.23/2.94 | (259) all_0_0_0 = 0
% 10.23/2.94 |
% 10.23/2.94 | Equations (259) can reduce 215 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (259) all_0_0_0 = 0
% 10.23/2.94 | (265) ~ (all_0_2_2 = 0) | all_0_7_7 = create_slb
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (265), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (266) ~ (all_0_2_2 = 0)
% 10.23/2.94 |
% 10.23/2.94 +-Applying beta-rule and splitting (107), into two cases.
% 10.23/2.94 |-Branch one:
% 10.23/2.94 | (218) all_24_3_14 = 0
% 10.23/2.94 |
% 10.23/2.94 | Combining equations (172,218) yields a new equation:
% 10.23/2.94 | (268) all_0_2_2 = 0
% 10.23/2.94 |
% 10.23/2.94 | Simplifying 268 yields:
% 10.23/2.94 | (219) all_0_2_2 = 0
% 10.23/2.94 |
% 10.23/2.94 | Equations (219) can reduce 266 to:
% 10.23/2.94 | (93) $false
% 10.23/2.94 |
% 10.23/2.94 |-The branch is then unsatisfiable
% 10.23/2.94 |-Branch two:
% 10.23/2.94 | (238) ~ (all_24_3_14 = 0)
% 10.23/2.94 | (239) all_24_0_11 = all_24_2_13
% 10.23/2.94 |
% 10.23/2.95 | Combining equations (133,239) yields a new equation:
% 10.23/2.95 | (231) all_24_0_11 = all_0_4_4
% 10.23/2.95 |
% 10.23/2.95 | From (231) and (179) follows:
% 10.23/2.95 | (232) ok(all_0_4_4) = all_60_0_23
% 10.23/2.95 |
% 10.23/2.95 +-Applying beta-rule and splitting (191), into two cases.
% 10.23/2.95 |-Branch one:
% 10.23/2.95 | (233) ~ (ok(all_0_4_4) = all_60_0_23)
% 10.23/2.95 |
% 10.23/2.95 | Using (232) and (233) yields:
% 10.23/2.95 | (146) $false
% 10.23/2.95 |
% 10.23/2.95 |-The branch is then unsatisfiable
% 10.23/2.95 |-Branch two:
% 10.23/2.95 | (232) ok(all_0_4_4) = all_60_0_23
% 10.23/2.95 | (236) all_60_0_23 = 0
% 10.23/2.95 |
% 10.23/2.95 | Equations (236) can reduce 178 to:
% 10.23/2.95 | (93) $false
% 10.23/2.95 |
% 10.23/2.95 |-The branch is then unsatisfiable
% 10.23/2.95 |-Branch two:
% 10.23/2.95 | (219) all_0_2_2 = 0
% 10.23/2.95 | (92) all_0_7_7 = create_slb
% 10.23/2.95 |
% 10.23/2.95 | Equations (92) can reduce 91 to:
% 10.23/2.95 | (93) $false
% 10.23/2.95 |
% 10.23/2.95 |-The branch is then unsatisfiable
% 10.23/2.95 |-Branch two:
% 10.23/2.95 | (283) triple(all_0_8_8, create_slb, all_0_6_6) = all_0_5_5
% 10.23/2.95 | (284) check_cpq(all_0_5_5) = 0
% 10.23/2.95 |
% 10.23/2.95 +-Applying beta-rule and splitting (83), into two cases.
% 10.23/2.95 |-Branch one:
% 10.23/2.95 | (90) ~ (triple(all_0_8_8, create_slb, all_0_6_6) = all_0_5_5)
% 10.23/2.95 |
% 10.23/2.95 | Using (283) and (90) yields:
% 10.23/2.95 | (146) $false
% 10.23/2.95 |
% 10.23/2.95 |-The branch is then unsatisfiable
% 10.23/2.95 |-Branch two:
% 10.23/2.95 | (283) triple(all_0_8_8, create_slb, all_0_6_6) = all_0_5_5
% 10.23/2.95 | (288) findmin_cpq_res(all_0_5_5) = bottom
% 10.23/2.95 |
% 10.23/2.95 +-Applying beta-rule and splitting (85), into two cases.
% 10.23/2.95 |-Branch one:
% 10.23/2.95 | (90) ~ (triple(all_0_8_8, create_slb, all_0_6_6) = all_0_5_5)
% 10.23/2.95 |
% 10.23/2.95 | Using (283) and (90) yields:
% 10.23/2.95 | (146) $false
% 10.23/2.95 |
% 10.23/2.95 |-The branch is then unsatisfiable
% 10.23/2.95 |-Branch two:
% 10.23/2.95 | (283) triple(all_0_8_8, create_slb, all_0_6_6) = all_0_5_5
% 10.23/2.95 | (292) ? [v0] : (triple(all_0_8_8, create_slb, bad) = v0 & findmin_cpq_eff(all_0_5_5) = v0)
% 10.23/2.95 |
% 10.23/2.95 | Instantiating (292) with all_18_0_45 yields:
% 10.23/2.95 | (293) triple(all_0_8_8, create_slb, bad) = all_18_0_45 & findmin_cpq_eff(all_0_5_5) = all_18_0_45
% 10.23/2.95 |
% 10.23/2.95 | Applying alpha-rule on (293) yields:
% 10.23/2.95 | (294) triple(all_0_8_8, create_slb, bad) = all_18_0_45
% 10.23/2.95 | (295) findmin_cpq_eff(all_0_5_5) = all_18_0_45
% 10.23/2.95 |
% 10.23/2.95 | Instantiating formula (58) with all_0_5_5, all_18_0_45, all_0_4_4 and discharging atoms findmin_cpq_eff(all_0_5_5) = all_18_0_45, findmin_cpq_eff(all_0_5_5) = all_0_4_4, yields:
% 10.23/2.95 | (296) all_18_0_45 = all_0_4_4
% 10.23/2.95 |
% 10.23/2.95 | From (296) and (294) follows:
% 10.23/2.95 | (297) triple(all_0_8_8, create_slb, bad) = all_0_4_4
% 10.23/2.95 |
% 10.23/2.95 | Instantiating formula (73) with all_0_4_4, create_slb, all_0_8_8 and discharging atoms triple(all_0_8_8, create_slb, bad) = all_0_4_4, yields:
% 10.23/2.95 | (298) ? [v0] : ( ~ (v0 = 0) & ok(all_0_4_4) = v0)
% 10.23/2.95 |
% 10.23/2.95 | Instantiating (298) with all_30_0_46 yields:
% 10.23/2.95 | (299) ~ (all_30_0_46 = 0) & ok(all_0_4_4) = all_30_0_46
% 10.23/2.95 |
% 10.23/2.95 | Applying alpha-rule on (299) yields:
% 10.23/2.95 | (300) ~ (all_30_0_46 = 0)
% 10.23/2.95 | (301) ok(all_0_4_4) = all_30_0_46
% 10.23/2.95 |
% 10.23/2.95 | Instantiating formula (19) with all_0_4_4, all_30_0_46, 0 and discharging atoms ok(all_0_4_4) = all_30_0_46, ok(all_0_4_4) = 0, yields:
% 10.23/2.95 | (302) all_30_0_46 = 0
% 10.23/2.95 |
% 10.23/2.95 | Equations (302) can reduce 300 to:
% 10.23/2.95 | (93) $false
% 10.23/2.95 |
% 10.23/2.95 |-The branch is then unsatisfiable
% 10.23/2.95 % SZS output end Proof for theBenchmark
% 10.23/2.95
% 10.23/2.95 2352ms
%------------------------------------------------------------------------------