TSTP Solution File: SWV379+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV379+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 17:51:11 EDT 2022
% Result : Theorem 6.56s 2.13s
% Output : Proof 10.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV379+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 03:43:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.60/0.63 ____ _
% 0.60/0.63 ___ / __ \_____(_)___ ________ __________
% 0.60/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.63
% 0.60/0.63 A Theorem Prover for First-Order Logic
% 0.65/0.63 (ePrincess v.1.0)
% 0.65/0.63
% 0.65/0.63 (c) Philipp Rümmer, 2009-2015
% 0.65/0.63 (c) Peter Backeman, 2014-2015
% 0.65/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.65/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.65/0.63 Bug reports to peter@backeman.se
% 0.65/0.63
% 0.65/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.65/0.63
% 0.65/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.89/1.06 Prover 0: Preprocessing ...
% 3.03/1.39 Prover 0: Warning: ignoring some quantifiers
% 3.29/1.42 Prover 0: Constructing countermodel ...
% 5.25/1.90 Prover 0: gave up
% 5.25/1.90 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.60/1.94 Prover 1: Preprocessing ...
% 5.92/2.05 Prover 1: Constructing countermodel ...
% 6.56/2.13 Prover 1: proved (229ms)
% 6.56/2.13
% 6.56/2.13 No countermodel exists, formula is valid
% 6.56/2.13 % SZS status Theorem for theBenchmark
% 6.56/2.13
% 6.56/2.13 Generating proof ... found it (size 160)
% 9.26/2.77
% 9.26/2.77 % SZS output start Proof for theBenchmark
% 9.26/2.77 Assumed formulas after preprocessing and simplification:
% 9.26/2.77 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v0 = 0) & ok(v6) = 0 & ok(v4) = v5 & triple(v1, v2, v3) = v4 & findmin_cpq_eff(v4) = v6 & isnonempty_slb(create_slb) = v0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (pair_in_list(v13, v9, v11) = v14) | ~ (pair(v8, v10) = v12) | ~ (insert_slb(v7, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & pair_in_list(v7, v9, v11) = v15)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (insert_pqp(v7, v10) = v11) | ~ (triple(v11, v13, v9) = v14) | ~ (pair(v10, bottom) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : (triple(v7, v8, v9) = v15 & insert_cpq(v15, v10) = v14)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v7, v13, v9) = v14) | ~ (pair(v10, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (triple(v7, v8, v9) = v17 & check_cpq(v17) = v18 & check_cpq(v14) = v16 & less_than(v11, v10) = v15 & ( ~ (v15 = 0) | (( ~ (v18 = 0) | v16 = 0) & ( ~ (v16 = 0) | v18 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v7, v13, v9) = v14) | ~ (pair(v10, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : ? [v16] : (check_cpq(v14) = v16 & strictly_less_than(v10, v11) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (contains_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & contains_slb(v7, v9) = v14)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (pair_in_list(v13, v9, v11) = 0) | ~ (pair(v8, v10) = v12) | ~ (insert_slb(v7, v12) = v13) | pair_in_list(v7, v9, v11) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (lookup_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ? [v15] : (lookup_slb(v7, v9) = v15 & contains_slb(v7, v9) = v14 & ( ~ (v14 = 0) | v15 = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (remove_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : (remove_slb(v7, v9) = v15 & contains_slb(v7, v9) = v14 & insert_slb(v15, v11) = v16 & ( ~ (v14 = 0) | v16 = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (pair_in_list(v13, v9, v11) = 0) | ~ (pair(v8, v10) = v12) | ~ (insert_slb(v7, v12) = v13) | pair_in_list(v7, v9, v11) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (remove_pqp(v7, v10) = v11) | ~ (triple(v11, v12, v9) = v13) | ~ (remove_slb(v8, v10) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (triple(v7, v8, v9) = v17 & remove_cpq(v17, v10) = v18 & lookup_slb(v8, v10) = v15 & contains_slb(v8, v10) = v14 & less_than(v15, v10) = v16 & ( ~ (v16 = 0) | ~ (v14 = 0) | v18 = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (update_slb(v7, v9) = v15 & pair(v8, v9) = v16 & insert_slb(v15, v16) = v17 & strictly_less_than(v10, v9) = v14 & ( ~ (v14 = 0) | v17 = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : (update_slb(v7, v9) = v15 & insert_slb(v15, v11) = v16 & less_than(v9, v10) = v14 & ( ~ (v14 = 0) | v16 = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (lookup_slb(v11, v8) = v12) | ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v7 | ~ (remove_slb(v11, v8) = v12) | ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (contains_cpq(v11, v10) = v12) | ~ (triple(v7, v8, v9) = v11) | ? [v13] : ( ~ (v13 = 0) & contains_slb(v8, v10) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (pair_in_list(v11, v8, v9) = v12) | ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (contains_slb(v11, v8) = v12) | ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (contains_slb(v12, v9) = 0) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | contains_slb(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = create_slb | ~ (findmin_pqp_res(v7) = v10) | ~ (triple(v7, v11, v9) = v12) | ~ (update_slb(v8, v10) = v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (triple(v7, v8, v9) = v16 & findmin_cpq_eff(v16) = v17 & lookup_slb(v8, v10) = v14 & contains_slb(v8, v10) = v13 & less_than(v14, v10) = v15 & ( ~ (v15 = 0) | ~ (v13 = 0) | v17 = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (remove_pqp(v7, v10) = v16 & triple(v16, v17, bad) = v18 & lookup_slb(v8, v10) = v14 & remove_slb(v8, v10) = v17 & contains_slb(v8, v10) = v13 & strictly_less_than(v10, v14) = v15 & ( ~ (v15 = 0) | ~ (v13 = 0) | v18 = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ? [v14] : (triple(v7, v8, bad) = v14 & contains_slb(v8, v10) = v13 & (v14 = v12 | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (remove_cpq(v8, v9) = v10) | ~ (succ_cpq(v7, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & succ_cpq(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (insert_cpq(v8, v9) = v10) | ~ (succ_cpq(v7, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & succ_cpq(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (triple(v11, v10, v9) = v8) | ~ (triple(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (pair_in_list(v11, v10, v9) = v8) | ~ (pair_in_list(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (contains_cpq(v11, v10) = 0) | ~ (triple(v7, v8, v9) = v11) | contains_slb(v8, v10) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11) | isnonempty_slb(v11) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (removemin_cpq_eff(v8) = v9) | ~ (succ_cpq(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & succ_cpq(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (findmin_cpq_eff(v8) = v9) | ~ (succ_cpq(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & succ_cpq(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (less_than(v7, v9) = v10) | ~ (less_than(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & less_than(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = bad | ~ (triple(v7, v8, v9) = v10) | ok(v10) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (remove_pqp(v10, v9) = v8) | ~ (remove_pqp(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (insert_pqp(v10, v9) = v8) | ~ (insert_pqp(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (contains_cpq(v10, v9) = v8) | ~ (contains_cpq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (remove_cpq(v10, v9) = v8) | ~ (remove_cpq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (insert_cpq(v10, v9) = v8) | ~ (insert_cpq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (succ_cpq(v10, v9) = v8) | ~ (succ_cpq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (update_slb(v10, v9) = v8) | ~ (update_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (lookup_slb(v10, v9) = v8) | ~ (lookup_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (remove_slb(v10, v9) = v8) | ~ (remove_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (contains_slb(v10, v9) = v8) | ~ (contains_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (pair(v10, v9) = v8) | ~ (pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (insert_slb(v10, v9) = v8) | ~ (insert_slb(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (strictly_less_than(v10, v9) = v8) | ~ (strictly_less_than(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (less_than(v10, v9) = v8) | ~ (less_than(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (findmin_pqp_res(v7) = v11 & triple(v7, v16, bad) = v17 & findmin_cpq_eff(v10) = v15 & update_slb(v8, v11) = v16 & lookup_slb(v8, v11) = v13 & contains_slb(v8, v11) = v12 & strictly_less_than(v11, v13) = v14 & ( ~ (v14 = 0) | ~ (v12 = 0) | v17 = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (findmin_pqp_res(v7) = v11 & triple(v7, v14, bad) = v15 & findmin_cpq_eff(v10) = v13 & update_slb(v8, v11) = v14 & contains_slb(v8, v11) = v12 & (v15 = v13 | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ? [v11] : (findmin_cpq_res(v10) = v11 & findmin_pqp_res(v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (findmin_cpq_res(v7) = v9) | ~ (findmin_cpq_eff(v7) = v8) | ~ (remove_cpq(v8, v9) = v10) | removemin_cpq_eff(v7) = v10) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (strictly_less_than(v7, v8) = v9) | ? [v10] : ? [v11] : (less_than(v8, v7) = v11 & less_than(v7, v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(v7, v8) = v9) | less_than(v8, v7) = 0) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (removemin_cpq_res(v9) = v8) | ~ (removemin_cpq_res(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (findmin_cpq_res(v9) = v8) | ~ (findmin_cpq_res(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (findmin_pqp_res(v9) = v8) | ~ (findmin_pqp_res(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (ok(v9) = v8) | ~ (ok(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (check_cpq(v9) = v8) | ~ (check_cpq(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (removemin_cpq_eff(v9) = v8) | ~ (removemin_cpq_eff(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (findmin_cpq_eff(v9) = v8) | ~ (findmin_cpq_eff(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (isnonempty_slb(v9) = v8) | ~ (isnonempty_slb(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, v8, bad) = v9) | ? [v10] : ( ~ (v10 = 0) & ok(v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, create_slb, v8) = v9) | findmin_cpq_res(v9) = bottom) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, create_slb, v8) = v9) | check_cpq(v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (triple(v7, create_slb, v8) = v9) | ? [v10] : (triple(v7, create_slb, bad) = v10 & findmin_cpq_eff(v9) = v10)) & ! [v7] : ! [v8] : (v8 = create_slb | ~ (update_slb(create_slb, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (succ_cpq(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (less_than(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (less_than(bottom, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (removemin_cpq_res(v7) = v8) | findmin_cpq_res(v7) = v8) & ! [v7] : ! [v8] : ~ (pair_in_list(create_slb, v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (strictly_less_than(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & less_than(v8, v7) = v9 & less_than(v7, v8) = 0)) & ! [v7] : ~ (contains_slb(create_slb, v7) = 0))
% 9.70/2.83 | 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 yields:
% 9.70/2.83 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_6_6 = 0) & ok(all_0_0_0) = 0 & ok(all_0_2_2) = all_0_1_1 & triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2 & findmin_cpq_eff(all_0_2_2) = all_0_0_0 & isnonempty_slb(create_slb) = all_0_6_6 & ! [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)
% 9.70/2.85 |
% 9.70/2.85 | Applying alpha-rule on (1) yields:
% 9.70/2.85 | (2) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0)
% 9.70/2.85 | (3) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 9.70/2.85 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 9.70/2.85 | (5) ! [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)))
% 9.70/2.85 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 9.70/2.85 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 9.70/2.85 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4))
% 9.70/2.85 | (9) triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2
% 9.70/2.85 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 9.70/2.85 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 9.70/2.85 | (12) ! [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)))
% 9.70/2.85 | (13) isnonempty_slb(create_slb) = all_0_6_6
% 9.70/2.85 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0)
% 9.70/2.85 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 9.70/2.85 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 9.70/2.85 | (17) ! [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))
% 9.70/2.85 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 9.70/2.85 | (19) ! [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))
% 9.70/2.86 | (20) ! [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)))
% 9.70/2.86 | (21) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0))
% 9.70/2.86 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 9.70/2.86 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3))
% 9.70/2.86 | (24) ! [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)))
% 9.70/2.86 | (25) ! [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)))
% 9.70/2.86 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0))
% 9.70/2.86 | (27) ok(all_0_0_0) = 0
% 9.70/2.86 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0)
% 9.70/2.86 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 9.70/2.86 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4))
% 9.70/2.86 | (31) ! [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))
% 9.70/2.86 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 9.70/2.86 | (33) ~ (all_0_1_1 = 0)
% 9.70/2.86 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 9.70/2.86 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 9.70/2.86 | (36) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1))
% 9.70/2.86 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 9.70/2.86 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 9.70/2.86 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 9.70/2.86 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 9.70/2.86 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 9.70/2.86 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 9.70/2.86 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0)
% 9.70/2.86 | (44) ! [v0] : ~ (contains_slb(create_slb, v0) = 0)
% 9.70/2.86 | (45) ! [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)))
% 9.70/2.86 | (46) ! [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))
% 9.70/2.86 | (47) ! [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)))
% 9.70/2.87 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 9.70/2.87 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3)
% 9.70/2.87 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 9.70/2.87 | (51) ! [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)))
% 9.70/2.87 | (52) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 9.70/2.87 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1))
% 9.70/2.87 | (54) ok(all_0_2_2) = all_0_1_1
% 9.70/2.87 | (55) ! [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)))
% 9.70/2.87 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0))
% 9.70/2.87 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 9.70/2.87 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 9.70/2.87 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0))
% 9.70/2.87 | (60) findmin_cpq_eff(all_0_2_2) = all_0_0_0
% 9.70/2.87 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 9.70/2.87 | (62) ! [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)))
% 9.70/2.87 | (63) ! [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)))
% 9.70/2.87 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 9.70/2.87 | (65) ! [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)
% 9.70/2.87 | (66) ! [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))))
% 9.70/2.87 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0)
% 9.70/2.87 | (68) ! [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))
% 9.70/2.87 | (69) ! [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)
% 9.70/2.88 | (70) ~ (all_0_6_6 = 0)
% 9.70/2.88 | (71) ! [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)))))
% 9.70/2.88 | (72) ! [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)
% 9.70/2.88 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 9.70/2.88 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 9.70/2.88 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0))
% 9.70/2.88 | (76) ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1))
% 9.70/2.88 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0)
% 9.70/2.88 | (78) ! [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))
% 9.70/2.88 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 9.70/2.88 |
% 9.70/2.88 | Instantiating formula (64) with all_0_2_2, all_0_1_1, 0 and discharging atoms ok(all_0_2_2) = all_0_1_1, yields:
% 9.70/2.88 | (80) all_0_1_1 = 0 | ~ (ok(all_0_2_2) = 0)
% 9.70/2.88 |
% 9.70/2.88 | Instantiating formula (34) with all_0_2_2, all_0_3_3, all_0_5_5 yields:
% 9.70/2.88 | (81) ~ (triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2) | findmin_cpq_res(all_0_2_2) = bottom
% 9.70/2.88 |
% 9.70/2.88 | Instantiating formula (77) with all_0_2_2, all_0_3_3, all_0_5_5 yields:
% 9.70/2.88 | (82) ~ (triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2) | check_cpq(all_0_2_2) = 0
% 9.70/2.88 |
% 9.70/2.88 | Instantiating formula (58) with all_0_2_2, all_0_3_3, all_0_5_5 yields:
% 9.70/2.88 | (83) ~ (triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2) | ? [v0] : (triple(all_0_5_5, create_slb, bad) = v0 & findmin_cpq_eff(all_0_2_2) = v0)
% 9.70/2.88 |
% 9.70/2.88 | Instantiating formula (43) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 9.70/2.88 | (84) all_0_3_3 = bad | ok(all_0_2_2) = 0
% 9.70/2.88 |
% 9.70/2.88 | Instantiating formula (47) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 9.70/2.88 | (85) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v5, bad) = v6 & findmin_cpq_eff(all_0_2_2) = v4 & update_slb(all_0_4_4, v0) = v5 & lookup_slb(all_0_4_4, v0) = v2 & contains_slb(all_0_4_4, v0) = v1 & strictly_less_than(v0, v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0) | v6 = v4))
% 9.70/2.88 |
% 9.70/2.88 | Instantiating formula (51) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 9.70/2.88 | (86) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v3, bad) = v4 & findmin_cpq_eff(all_0_2_2) = v2 & update_slb(all_0_4_4, v0) = v3 & contains_slb(all_0_4_4, v0) = v1 & (v4 = v2 | v1 = 0))
% 9.70/2.88 |
% 9.70/2.88 | Instantiating formula (8) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 9.70/2.88 | (87) all_0_4_4 = create_slb | ? [v0] : (findmin_cpq_res(all_0_2_2) = v0 & findmin_pqp_res(all_0_5_5) = v0)
% 9.70/2.88 |
% 9.70/2.88 +-Applying beta-rule and splitting (82), into two cases.
% 9.70/2.88 |-Branch one:
% 9.70/2.88 | (88) ~ (triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2)
% 9.70/2.88 |
% 9.70/2.88 +-Applying beta-rule and splitting (84), into two cases.
% 9.70/2.88 |-Branch one:
% 9.70/2.88 | (89) ok(all_0_2_2) = 0
% 9.70/2.88 |
% 9.70/2.88 +-Applying beta-rule and splitting (80), into two cases.
% 9.70/2.88 |-Branch one:
% 9.70/2.88 | (90) ~ (ok(all_0_2_2) = 0)
% 9.70/2.88 |
% 9.70/2.88 | Using (89) and (90) yields:
% 9.70/2.88 | (91) $false
% 9.70/2.88 |
% 9.70/2.88 |-The branch is then unsatisfiable
% 9.70/2.88 |-Branch two:
% 9.70/2.88 | (89) ok(all_0_2_2) = 0
% 9.70/2.88 | (93) all_0_1_1 = 0
% 9.70/2.88 |
% 9.70/2.88 | Equations (93) can reduce 33 to:
% 9.70/2.88 | (94) $false
% 9.70/2.88 |
% 9.70/2.88 |-The branch is then unsatisfiable
% 9.70/2.88 |-Branch two:
% 9.70/2.88 | (90) ~ (ok(all_0_2_2) = 0)
% 9.70/2.88 | (96) all_0_3_3 = bad
% 9.70/2.88 |
% 9.70/2.88 | From (96) and (9) follows:
% 9.70/2.88 | (97) triple(all_0_5_5, all_0_4_4, bad) = all_0_2_2
% 9.70/2.89 |
% 9.70/2.89 | From (96) and (88) follows:
% 9.70/2.89 | (98) ~ (triple(all_0_5_5, create_slb, bad) = all_0_2_2)
% 9.70/2.89 |
% 9.70/2.89 | Using (97) and (98) yields:
% 9.70/2.89 | (99) ~ (all_0_4_4 = create_slb)
% 9.70/2.89 |
% 9.70/2.89 +-Applying beta-rule and splitting (86), into two cases.
% 9.70/2.89 |-Branch one:
% 9.70/2.89 | (100) all_0_4_4 = create_slb
% 9.70/2.89 |
% 9.70/2.89 | Equations (100) can reduce 99 to:
% 9.70/2.89 | (94) $false
% 9.70/2.89 |
% 9.70/2.89 |-The branch is then unsatisfiable
% 9.70/2.89 |-Branch two:
% 9.70/2.89 | (99) ~ (all_0_4_4 = create_slb)
% 9.70/2.89 | (103) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v3, bad) = v4 & findmin_cpq_eff(all_0_2_2) = v2 & update_slb(all_0_4_4, v0) = v3 & contains_slb(all_0_4_4, v0) = v1 & (v4 = v2 | v1 = 0))
% 9.70/2.89 |
% 9.70/2.89 | Instantiating (103) with all_22_0_7, all_22_1_8, all_22_2_9, all_22_3_10, all_22_4_11 yields:
% 9.70/2.89 | (104) findmin_pqp_res(all_0_5_5) = all_22_4_11 & triple(all_0_5_5, all_22_1_8, bad) = all_22_0_7 & findmin_cpq_eff(all_0_2_2) = all_22_2_9 & update_slb(all_0_4_4, all_22_4_11) = all_22_1_8 & contains_slb(all_0_4_4, all_22_4_11) = all_22_3_10 & (all_22_0_7 = all_22_2_9 | all_22_3_10 = 0)
% 9.70/2.89 |
% 9.70/2.89 | Applying alpha-rule on (104) yields:
% 9.70/2.89 | (105) findmin_pqp_res(all_0_5_5) = all_22_4_11
% 9.70/2.89 | (106) findmin_cpq_eff(all_0_2_2) = all_22_2_9
% 9.70/2.89 | (107) all_22_0_7 = all_22_2_9 | all_22_3_10 = 0
% 9.70/2.89 | (108) triple(all_0_5_5, all_22_1_8, bad) = all_22_0_7
% 9.70/2.89 | (109) update_slb(all_0_4_4, all_22_4_11) = all_22_1_8
% 9.70/2.89 | (110) contains_slb(all_0_4_4, all_22_4_11) = all_22_3_10
% 9.70/2.89 |
% 9.70/2.89 +-Applying beta-rule and splitting (87), into two cases.
% 9.70/2.89 |-Branch one:
% 9.70/2.89 | (100) all_0_4_4 = create_slb
% 9.70/2.89 |
% 9.70/2.89 | Equations (100) can reduce 99 to:
% 9.70/2.89 | (94) $false
% 9.70/2.89 |
% 9.70/2.89 |-The branch is then unsatisfiable
% 9.70/2.89 |-Branch two:
% 9.70/2.89 | (99) ~ (all_0_4_4 = create_slb)
% 9.70/2.89 | (114) ? [v0] : (findmin_cpq_res(all_0_2_2) = v0 & findmin_pqp_res(all_0_5_5) = v0)
% 9.70/2.89 |
% 9.70/2.89 | Instantiating (114) with all_27_0_12 yields:
% 9.70/2.89 | (115) findmin_cpq_res(all_0_2_2) = all_27_0_12 & findmin_pqp_res(all_0_5_5) = all_27_0_12
% 9.70/2.89 |
% 9.70/2.89 | Applying alpha-rule on (115) yields:
% 9.70/2.89 | (116) findmin_cpq_res(all_0_2_2) = all_27_0_12
% 9.70/2.89 | (117) findmin_pqp_res(all_0_5_5) = all_27_0_12
% 9.70/2.89 |
% 9.70/2.89 +-Applying beta-rule and splitting (85), into two cases.
% 9.70/2.89 |-Branch one:
% 9.70/2.89 | (100) all_0_4_4 = create_slb
% 9.70/2.89 |
% 9.70/2.89 | Equations (100) can reduce 99 to:
% 9.70/2.89 | (94) $false
% 9.70/2.89 |
% 9.70/2.89 |-The branch is then unsatisfiable
% 9.70/2.89 |-Branch two:
% 9.70/2.89 | (99) ~ (all_0_4_4 = create_slb)
% 9.70/2.89 | (121) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (findmin_pqp_res(all_0_5_5) = v0 & triple(all_0_5_5, v5, bad) = v6 & findmin_cpq_eff(all_0_2_2) = v4 & update_slb(all_0_4_4, v0) = v5 & lookup_slb(all_0_4_4, v0) = v2 & contains_slb(all_0_4_4, v0) = v1 & strictly_less_than(v0, v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0) | v6 = v4))
% 9.70/2.89 |
% 9.70/2.89 | Instantiating (121) with all_32_0_13, all_32_1_14, all_32_2_15, all_32_3_16, all_32_4_17, all_32_5_18, all_32_6_19 yields:
% 9.70/2.89 | (122) findmin_pqp_res(all_0_5_5) = all_32_6_19 & triple(all_0_5_5, all_32_1_14, bad) = all_32_0_13 & findmin_cpq_eff(all_0_2_2) = all_32_2_15 & update_slb(all_0_4_4, all_32_6_19) = all_32_1_14 & lookup_slb(all_0_4_4, all_32_6_19) = all_32_4_17 & contains_slb(all_0_4_4, all_32_6_19) = all_32_5_18 & strictly_less_than(all_32_6_19, all_32_4_17) = all_32_3_16 & ( ~ (all_32_3_16 = 0) | ~ (all_32_5_18 = 0) | all_32_0_13 = all_32_2_15)
% 9.70/2.89 |
% 9.70/2.89 | Applying alpha-rule on (122) yields:
% 9.70/2.89 | (123) update_slb(all_0_4_4, all_32_6_19) = all_32_1_14
% 9.70/2.89 | (124) strictly_less_than(all_32_6_19, all_32_4_17) = all_32_3_16
% 9.70/2.89 | (125) lookup_slb(all_0_4_4, all_32_6_19) = all_32_4_17
% 9.70/2.89 | (126) findmin_cpq_eff(all_0_2_2) = all_32_2_15
% 9.70/2.89 | (127) ~ (all_32_3_16 = 0) | ~ (all_32_5_18 = 0) | all_32_0_13 = all_32_2_15
% 9.70/2.89 | (128) findmin_pqp_res(all_0_5_5) = all_32_6_19
% 9.70/2.89 | (129) triple(all_0_5_5, all_32_1_14, bad) = all_32_0_13
% 9.70/2.89 | (130) contains_slb(all_0_4_4, all_32_6_19) = all_32_5_18
% 9.70/2.89 |
% 9.70/2.89 | Instantiating formula (7) with all_0_5_5, all_27_0_12, all_32_6_19 and discharging atoms findmin_pqp_res(all_0_5_5) = all_32_6_19, findmin_pqp_res(all_0_5_5) = all_27_0_12, yields:
% 9.70/2.89 | (131) all_32_6_19 = all_27_0_12
% 9.70/2.89 |
% 9.70/2.89 | Instantiating formula (7) with all_0_5_5, all_22_4_11, all_32_6_19 and discharging atoms findmin_pqp_res(all_0_5_5) = all_32_6_19, findmin_pqp_res(all_0_5_5) = all_22_4_11, yields:
% 9.70/2.89 | (132) all_32_6_19 = all_22_4_11
% 9.70/2.89 |
% 9.70/2.89 | Instantiating formula (18) with all_0_5_5, all_22_1_8, bad, all_22_0_7, all_32_0_13 and discharging atoms triple(all_0_5_5, all_22_1_8, bad) = all_22_0_7, yields:
% 9.70/2.89 | (133) all_32_0_13 = all_22_0_7 | ~ (triple(all_0_5_5, all_22_1_8, bad) = all_32_0_13)
% 9.70/2.89 |
% 9.70/2.89 | Instantiating formula (37) with all_0_2_2, all_32_2_15, all_0_0_0 and discharging atoms findmin_cpq_eff(all_0_2_2) = all_32_2_15, findmin_cpq_eff(all_0_2_2) = all_0_0_0, yields:
% 9.70/2.89 | (134) all_32_2_15 = all_0_0_0
% 9.70/2.89 |
% 9.70/2.89 | Instantiating formula (37) with all_0_2_2, all_22_2_9, all_32_2_15 and discharging atoms findmin_cpq_eff(all_0_2_2) = all_32_2_15, findmin_cpq_eff(all_0_2_2) = all_22_2_9, yields:
% 9.70/2.89 | (135) all_32_2_15 = all_22_2_9
% 9.70/2.89 |
% 9.70/2.89 | Instantiating formula (15) with all_0_4_4, all_22_4_11, all_22_1_8, all_32_1_14 and discharging atoms update_slb(all_0_4_4, all_22_4_11) = all_22_1_8, yields:
% 9.70/2.89 | (136) all_32_1_14 = all_22_1_8 | ~ (update_slb(all_0_4_4, all_22_4_11) = all_32_1_14)
% 9.70/2.89 |
% 9.70/2.89 | Instantiating formula (41) with all_0_4_4, all_22_4_11, all_22_3_10, all_32_5_18 and discharging atoms contains_slb(all_0_4_4, all_22_4_11) = all_22_3_10, yields:
% 9.70/2.89 | (137) all_32_5_18 = all_22_3_10 | ~ (contains_slb(all_0_4_4, all_22_4_11) = all_32_5_18)
% 9.70/2.89 |
% 9.70/2.89 | Combining equations (134,135) yields a new equation:
% 9.70/2.89 | (138) all_22_2_9 = all_0_0_0
% 9.70/2.89 |
% 9.70/2.89 | Combining equations (132,131) yields a new equation:
% 9.70/2.89 | (139) all_27_0_12 = all_22_4_11
% 9.70/2.89 |
% 9.70/2.89 | Combining equations (139,131) yields a new equation:
% 9.70/2.89 | (132) all_32_6_19 = all_22_4_11
% 9.70/2.89 |
% 9.70/2.89 | Combining equations (138,135) yields a new equation:
% 9.70/2.89 | (134) all_32_2_15 = all_0_0_0
% 9.70/2.89 |
% 9.70/2.89 | From (139) and (117) follows:
% 9.70/2.89 | (105) findmin_pqp_res(all_0_5_5) = all_22_4_11
% 9.70/2.89 |
% 9.70/2.89 | From (138) and (106) follows:
% 9.70/2.89 | (60) findmin_cpq_eff(all_0_2_2) = all_0_0_0
% 9.70/2.89 |
% 9.70/2.89 | From (132) and (123) follows:
% 9.70/2.89 | (144) update_slb(all_0_4_4, all_22_4_11) = all_32_1_14
% 9.70/2.89 |
% 9.70/2.89 | From (132) and (125) follows:
% 9.70/2.90 | (145) lookup_slb(all_0_4_4, all_22_4_11) = all_32_4_17
% 9.70/2.90 |
% 9.70/2.90 | From (132) and (130) follows:
% 9.70/2.90 | (146) contains_slb(all_0_4_4, all_22_4_11) = all_32_5_18
% 9.70/2.90 |
% 9.70/2.90 | From (132) and (124) follows:
% 9.70/2.90 | (147) strictly_less_than(all_22_4_11, all_32_4_17) = all_32_3_16
% 9.70/2.90 |
% 9.70/2.90 +-Applying beta-rule and splitting (136), into two cases.
% 9.70/2.90 |-Branch one:
% 9.70/2.90 | (148) ~ (update_slb(all_0_4_4, all_22_4_11) = all_32_1_14)
% 9.70/2.90 |
% 9.70/2.90 | Using (144) and (148) yields:
% 9.70/2.90 | (91) $false
% 9.70/2.90 |
% 9.70/2.90 |-The branch is then unsatisfiable
% 9.70/2.90 |-Branch two:
% 9.70/2.90 | (144) update_slb(all_0_4_4, all_22_4_11) = all_32_1_14
% 9.70/2.90 | (151) all_32_1_14 = all_22_1_8
% 9.70/2.90 |
% 9.70/2.90 | From (151) and (129) follows:
% 9.70/2.90 | (152) triple(all_0_5_5, all_22_1_8, bad) = all_32_0_13
% 9.70/2.90 |
% 9.70/2.90 | From (151) and (144) follows:
% 9.70/2.90 | (109) update_slb(all_0_4_4, all_22_4_11) = all_22_1_8
% 9.70/2.90 |
% 9.70/2.90 +-Applying beta-rule and splitting (133), into two cases.
% 9.70/2.90 |-Branch one:
% 9.70/2.90 | (154) ~ (triple(all_0_5_5, all_22_1_8, bad) = all_32_0_13)
% 9.70/2.90 |
% 9.70/2.90 | Using (152) and (154) yields:
% 9.70/2.90 | (91) $false
% 9.70/2.90 |
% 9.70/2.90 |-The branch is then unsatisfiable
% 9.70/2.90 |-Branch two:
% 9.70/2.90 | (152) triple(all_0_5_5, all_22_1_8, bad) = all_32_0_13
% 9.70/2.90 | (157) all_32_0_13 = all_22_0_7
% 9.70/2.90 |
% 9.70/2.90 | From (157) and (152) follows:
% 9.70/2.90 | (108) triple(all_0_5_5, all_22_1_8, bad) = all_22_0_7
% 9.70/2.90 |
% 9.70/2.90 +-Applying beta-rule and splitting (137), into two cases.
% 9.70/2.90 |-Branch one:
% 9.70/2.90 | (159) ~ (contains_slb(all_0_4_4, all_22_4_11) = all_32_5_18)
% 9.70/2.90 |
% 9.70/2.90 | Using (146) and (159) yields:
% 9.70/2.90 | (91) $false
% 9.70/2.90 |
% 9.70/2.90 |-The branch is then unsatisfiable
% 9.70/2.90 |-Branch two:
% 9.70/2.90 | (146) contains_slb(all_0_4_4, all_22_4_11) = all_32_5_18
% 9.70/2.90 | (162) all_32_5_18 = all_22_3_10
% 9.70/2.90 |
% 9.70/2.90 | From (162) and (146) follows:
% 9.70/2.90 | (110) contains_slb(all_0_4_4, all_22_4_11) = all_22_3_10
% 9.70/2.90 |
% 9.70/2.90 | Instantiating formula (23) with all_22_0_7, all_22_1_8, all_0_5_5 and discharging atoms triple(all_0_5_5, all_22_1_8, bad) = all_22_0_7, yields:
% 9.70/2.90 | (164) ? [v0] : ( ~ (v0 = 0) & ok(all_22_0_7) = v0)
% 9.70/2.90 |
% 9.70/2.90 | Instantiating formula (5) with all_22_0_7, all_22_1_8, all_22_4_11, bad, all_0_4_4, all_0_5_5 and discharging atoms findmin_pqp_res(all_0_5_5) = all_22_4_11, triple(all_0_5_5, all_22_1_8, bad) = all_22_0_7, update_slb(all_0_4_4, all_22_4_11) = all_22_1_8, yields:
% 9.70/2.90 | (165) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (triple(all_0_5_5, all_0_4_4, bad) = v3 & findmin_cpq_eff(v3) = v4 & lookup_slb(all_0_4_4, all_22_4_11) = v1 & contains_slb(all_0_4_4, all_22_4_11) = v0 & less_than(v1, all_22_4_11) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = all_22_0_7))
% 9.70/2.90 |
% 9.70/2.90 | Instantiating formula (25) with all_32_3_16, all_32_4_17, all_22_4_11 and discharging atoms strictly_less_than(all_22_4_11, all_32_4_17) = all_32_3_16, yields:
% 9.70/2.90 | (166) all_32_3_16 = 0 | ? [v0] : ? [v1] : (less_than(all_32_4_17, all_22_4_11) = v1 & less_than(all_22_4_11, all_32_4_17) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 9.70/2.90 |
% 9.70/2.90 | Instantiating (164) with all_55_0_20 yields:
% 9.70/2.90 | (167) ~ (all_55_0_20 = 0) & ok(all_22_0_7) = all_55_0_20
% 9.70/2.90 |
% 9.70/2.90 | Applying alpha-rule on (167) yields:
% 9.70/2.90 | (168) ~ (all_55_0_20 = 0)
% 9.70/2.90 | (169) ok(all_22_0_7) = all_55_0_20
% 9.70/2.90 |
% 9.70/2.90 +-Applying beta-rule and splitting (165), into two cases.
% 9.70/2.90 |-Branch one:
% 9.70/2.90 | (100) all_0_4_4 = create_slb
% 9.70/2.90 |
% 9.70/2.90 | Equations (100) can reduce 99 to:
% 9.70/2.90 | (94) $false
% 9.70/2.90 |
% 9.70/2.90 |-The branch is then unsatisfiable
% 9.70/2.90 |-Branch two:
% 9.70/2.90 | (99) ~ (all_0_4_4 = create_slb)
% 9.70/2.90 | (173) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (triple(all_0_5_5, all_0_4_4, bad) = v3 & findmin_cpq_eff(v3) = v4 & lookup_slb(all_0_4_4, all_22_4_11) = v1 & contains_slb(all_0_4_4, all_22_4_11) = v0 & less_than(v1, all_22_4_11) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = all_22_0_7))
% 9.70/2.90 |
% 9.70/2.90 | Instantiating (173) with all_61_0_21, all_61_1_22, all_61_2_23, all_61_3_24, all_61_4_25 yields:
% 9.70/2.90 | (174) triple(all_0_5_5, all_0_4_4, bad) = all_61_1_22 & findmin_cpq_eff(all_61_1_22) = all_61_0_21 & lookup_slb(all_0_4_4, all_22_4_11) = all_61_3_24 & contains_slb(all_0_4_4, all_22_4_11) = all_61_4_25 & less_than(all_61_3_24, all_22_4_11) = all_61_2_23 & ( ~ (all_61_2_23 = 0) | ~ (all_61_4_25 = 0) | all_61_0_21 = all_22_0_7)
% 9.70/2.90 |
% 9.70/2.90 | Applying alpha-rule on (174) yields:
% 9.70/2.90 | (175) less_than(all_61_3_24, all_22_4_11) = all_61_2_23
% 9.70/2.90 | (176) triple(all_0_5_5, all_0_4_4, bad) = all_61_1_22
% 9.70/2.90 | (177) contains_slb(all_0_4_4, all_22_4_11) = all_61_4_25
% 9.70/2.90 | (178) ~ (all_61_2_23 = 0) | ~ (all_61_4_25 = 0) | all_61_0_21 = all_22_0_7
% 9.70/2.90 | (179) lookup_slb(all_0_4_4, all_22_4_11) = all_61_3_24
% 9.70/2.90 | (180) findmin_cpq_eff(all_61_1_22) = all_61_0_21
% 9.70/2.90 |
% 9.70/2.90 | Instantiating formula (64) with all_0_0_0, all_55_0_20, 0 and discharging atoms ok(all_0_0_0) = 0, yields:
% 9.70/2.90 | (181) all_55_0_20 = 0 | ~ (ok(all_0_0_0) = all_55_0_20)
% 9.70/2.90 |
% 9.70/2.90 | Instantiating formula (18) with all_0_5_5, all_0_4_4, bad, all_61_1_22, all_0_2_2 and discharging atoms triple(all_0_5_5, all_0_4_4, bad) = all_61_1_22, triple(all_0_5_5, all_0_4_4, bad) = all_0_2_2, yields:
% 9.70/2.90 | (182) all_61_1_22 = all_0_2_2
% 9.70/2.90 |
% 9.70/2.90 | Instantiating formula (37) with all_0_2_2, all_61_0_21, all_0_0_0 and discharging atoms findmin_cpq_eff(all_0_2_2) = all_0_0_0, yields:
% 9.70/2.90 | (183) all_61_0_21 = all_0_0_0 | ~ (findmin_cpq_eff(all_0_2_2) = all_61_0_21)
% 9.70/2.90 |
% 9.70/2.90 | Instantiating formula (22) with all_0_4_4, all_22_4_11, all_61_3_24, all_32_4_17 and discharging atoms lookup_slb(all_0_4_4, all_22_4_11) = all_61_3_24, lookup_slb(all_0_4_4, all_22_4_11) = all_32_4_17, yields:
% 9.70/2.90 | (184) all_61_3_24 = all_32_4_17
% 9.70/2.90 |
% 9.70/2.90 | Instantiating formula (41) with all_0_4_4, all_22_4_11, all_61_4_25, all_22_3_10 and discharging atoms contains_slb(all_0_4_4, all_22_4_11) = all_61_4_25, contains_slb(all_0_4_4, all_22_4_11) = all_22_3_10, yields:
% 9.70/2.90 | (185) all_61_4_25 = all_22_3_10
% 9.70/2.90 |
% 9.70/2.90 | From (182) and (180) follows:
% 9.70/2.90 | (186) findmin_cpq_eff(all_0_2_2) = all_61_0_21
% 9.70/2.90 |
% 9.70/2.90 | From (184) and (175) follows:
% 9.70/2.90 | (187) less_than(all_32_4_17, all_22_4_11) = all_61_2_23
% 9.70/2.90 |
% 9.70/2.90 +-Applying beta-rule and splitting (183), into two cases.
% 9.70/2.90 |-Branch one:
% 9.70/2.90 | (188) ~ (findmin_cpq_eff(all_0_2_2) = all_61_0_21)
% 9.70/2.90 |
% 9.70/2.90 | Using (186) and (188) yields:
% 9.70/2.90 | (91) $false
% 9.70/2.90 |
% 9.70/2.90 |-The branch is then unsatisfiable
% 9.70/2.90 |-Branch two:
% 9.70/2.90 | (186) findmin_cpq_eff(all_0_2_2) = all_61_0_21
% 9.70/2.90 | (191) all_61_0_21 = all_0_0_0
% 9.70/2.90 |
% 9.70/2.90 +-Applying beta-rule and splitting (107), into two cases.
% 9.70/2.90 |-Branch one:
% 9.70/2.90 | (192) all_22_3_10 = 0
% 9.70/2.90 |
% 9.70/2.90 | Combining equations (192,162) yields a new equation:
% 9.70/2.90 | (193) all_32_5_18 = 0
% 9.70/2.90 |
% 9.70/2.90 | Combining equations (192,185) yields a new equation:
% 9.70/2.90 | (194) all_61_4_25 = 0
% 9.70/2.90 |
% 9.70/2.90 +-Applying beta-rule and splitting (127), into two cases.
% 9.70/2.90 |-Branch one:
% 9.70/2.90 | (195) ~ (all_32_3_16 = 0)
% 9.70/2.90 |
% 9.70/2.90 +-Applying beta-rule and splitting (166), into two cases.
% 9.70/2.90 |-Branch one:
% 9.70/2.90 | (196) all_32_3_16 = 0
% 9.70/2.90 |
% 9.70/2.90 | Equations (196) can reduce 195 to:
% 9.70/2.90 | (94) $false
% 9.70/2.90 |
% 9.70/2.90 |-The branch is then unsatisfiable
% 9.70/2.90 |-Branch two:
% 9.70/2.90 | (195) ~ (all_32_3_16 = 0)
% 9.70/2.90 | (199) ? [v0] : ? [v1] : (less_than(all_32_4_17, all_22_4_11) = v1 & less_than(all_22_4_11, all_32_4_17) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 9.70/2.90 |
% 9.70/2.90 | Instantiating (199) with all_140_0_33, all_140_1_34 yields:
% 9.70/2.90 | (200) less_than(all_32_4_17, all_22_4_11) = all_140_0_33 & less_than(all_22_4_11, all_32_4_17) = all_140_1_34 & ( ~ (all_140_1_34 = 0) | all_140_0_33 = 0)
% 9.70/2.90 |
% 9.70/2.90 | Applying alpha-rule on (200) yields:
% 9.70/2.90 | (201) less_than(all_32_4_17, all_22_4_11) = all_140_0_33
% 9.70/2.90 | (202) less_than(all_22_4_11, all_32_4_17) = all_140_1_34
% 9.70/2.90 | (203) ~ (all_140_1_34 = 0) | all_140_0_33 = 0
% 9.70/2.90 |
% 9.70/2.90 | Instantiating formula (50) with all_32_4_17, all_22_4_11, all_140_0_33, all_61_2_23 and discharging atoms less_than(all_32_4_17, all_22_4_11) = all_140_0_33, less_than(all_32_4_17, all_22_4_11) = all_61_2_23, yields:
% 9.70/2.90 | (204) all_140_0_33 = all_61_2_23
% 9.70/2.90 |
% 9.70/2.90 | From (204) and (201) follows:
% 9.70/2.90 | (187) less_than(all_32_4_17, all_22_4_11) = all_61_2_23
% 9.70/2.90 |
% 9.70/2.91 | Instantiating formula (28) with all_140_1_34, all_32_4_17, all_22_4_11 and discharging atoms less_than(all_22_4_11, all_32_4_17) = all_140_1_34, yields:
% 9.70/2.91 | (206) all_140_1_34 = 0 | less_than(all_32_4_17, all_22_4_11) = 0
% 9.70/2.91 |
% 9.70/2.91 +-Applying beta-rule and splitting (178), into two cases.
% 9.70/2.91 |-Branch one:
% 9.70/2.91 | (207) ~ (all_61_2_23 = 0)
% 9.70/2.91 |
% 9.70/2.91 +-Applying beta-rule and splitting (206), into two cases.
% 9.70/2.91 |-Branch one:
% 9.70/2.91 | (208) less_than(all_32_4_17, all_22_4_11) = 0
% 9.70/2.91 |
% 9.70/2.91 | Instantiating formula (50) with all_32_4_17, all_22_4_11, 0, all_61_2_23 and discharging atoms less_than(all_32_4_17, all_22_4_11) = all_61_2_23, less_than(all_32_4_17, all_22_4_11) = 0, yields:
% 9.70/2.91 | (209) all_61_2_23 = 0
% 9.70/2.91 |
% 9.70/2.91 | Equations (209) can reduce 207 to:
% 9.70/2.91 | (94) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (211) ~ (less_than(all_32_4_17, all_22_4_11) = 0)
% 9.70/2.91 | (212) all_140_1_34 = 0
% 9.70/2.91 |
% 9.70/2.91 +-Applying beta-rule and splitting (203), into two cases.
% 9.70/2.91 |-Branch one:
% 9.70/2.91 | (213) ~ (all_140_1_34 = 0)
% 9.70/2.91 |
% 9.70/2.91 | Equations (212) can reduce 213 to:
% 9.70/2.91 | (94) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (212) all_140_1_34 = 0
% 9.70/2.91 | (216) all_140_0_33 = 0
% 9.70/2.91 |
% 9.70/2.91 | Combining equations (204,216) yields a new equation:
% 9.70/2.91 | (217) all_61_2_23 = 0
% 9.70/2.91 |
% 9.70/2.91 | Simplifying 217 yields:
% 9.70/2.91 | (209) all_61_2_23 = 0
% 9.70/2.91 |
% 9.70/2.91 | Equations (209) can reduce 207 to:
% 9.70/2.91 | (94) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (209) all_61_2_23 = 0
% 9.70/2.91 | (221) ~ (all_61_4_25 = 0) | all_61_0_21 = all_22_0_7
% 9.70/2.91 |
% 9.70/2.91 +-Applying beta-rule and splitting (221), into two cases.
% 9.70/2.91 |-Branch one:
% 9.70/2.91 | (222) ~ (all_61_4_25 = 0)
% 9.70/2.91 |
% 9.70/2.91 | Equations (194) can reduce 222 to:
% 9.70/2.91 | (94) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (194) all_61_4_25 = 0
% 9.70/2.91 | (225) all_61_0_21 = all_22_0_7
% 9.70/2.91 |
% 9.70/2.91 | Combining equations (225,191) yields a new equation:
% 9.70/2.91 | (226) all_22_0_7 = all_0_0_0
% 9.70/2.91 |
% 9.70/2.91 | Simplifying 226 yields:
% 9.70/2.91 | (227) all_22_0_7 = all_0_0_0
% 9.70/2.91 |
% 9.70/2.91 | From (227) and (169) follows:
% 9.70/2.91 | (228) ok(all_0_0_0) = all_55_0_20
% 9.70/2.91 |
% 9.70/2.91 +-Applying beta-rule and splitting (181), into two cases.
% 9.70/2.91 |-Branch one:
% 9.70/2.91 | (229) ~ (ok(all_0_0_0) = all_55_0_20)
% 9.70/2.91 |
% 9.70/2.91 | Using (228) and (229) yields:
% 9.70/2.91 | (91) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (228) ok(all_0_0_0) = all_55_0_20
% 9.70/2.91 | (232) all_55_0_20 = 0
% 9.70/2.91 |
% 9.70/2.91 | Equations (232) can reduce 168 to:
% 9.70/2.91 | (94) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (196) all_32_3_16 = 0
% 9.70/2.91 | (235) ~ (all_32_5_18 = 0) | all_32_0_13 = all_32_2_15
% 9.70/2.91 |
% 9.70/2.91 +-Applying beta-rule and splitting (235), into two cases.
% 9.70/2.91 |-Branch one:
% 9.70/2.91 | (236) ~ (all_32_5_18 = 0)
% 9.70/2.91 |
% 9.70/2.91 | Equations (193) can reduce 236 to:
% 9.70/2.91 | (94) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (193) all_32_5_18 = 0
% 9.70/2.91 | (239) all_32_0_13 = all_32_2_15
% 9.70/2.91 |
% 9.70/2.91 | Combining equations (157,239) yields a new equation:
% 9.70/2.91 | (240) all_32_2_15 = all_22_0_7
% 9.70/2.91 |
% 9.70/2.91 | Combining equations (240,134) yields a new equation:
% 9.70/2.91 | (226) all_22_0_7 = all_0_0_0
% 9.70/2.91 |
% 9.70/2.91 | Simplifying 226 yields:
% 9.70/2.91 | (227) all_22_0_7 = all_0_0_0
% 9.70/2.91 |
% 9.70/2.91 | From (227) and (169) follows:
% 9.70/2.91 | (228) ok(all_0_0_0) = all_55_0_20
% 9.70/2.91 |
% 9.70/2.91 +-Applying beta-rule and splitting (181), into two cases.
% 9.70/2.91 |-Branch one:
% 9.70/2.91 | (229) ~ (ok(all_0_0_0) = all_55_0_20)
% 9.70/2.91 |
% 9.70/2.91 | Using (228) and (229) yields:
% 9.70/2.91 | (91) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (228) ok(all_0_0_0) = all_55_0_20
% 9.70/2.91 | (232) all_55_0_20 = 0
% 9.70/2.91 |
% 9.70/2.91 | Equations (232) can reduce 168 to:
% 9.70/2.91 | (94) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (249) ~ (all_22_3_10 = 0)
% 9.70/2.91 | (250) all_22_0_7 = all_22_2_9
% 9.70/2.91 |
% 9.70/2.91 | Combining equations (138,250) yields a new equation:
% 9.70/2.91 | (227) all_22_0_7 = all_0_0_0
% 9.70/2.91 |
% 9.70/2.91 | From (227) and (169) follows:
% 9.70/2.91 | (228) ok(all_0_0_0) = all_55_0_20
% 9.70/2.91 |
% 9.70/2.91 +-Applying beta-rule and splitting (181), into two cases.
% 9.70/2.91 |-Branch one:
% 9.70/2.91 | (229) ~ (ok(all_0_0_0) = all_55_0_20)
% 9.70/2.91 |
% 9.70/2.91 | Using (228) and (229) yields:
% 9.70/2.91 | (91) $false
% 9.70/2.91 |
% 9.70/2.91 |-The branch is then unsatisfiable
% 9.70/2.91 |-Branch two:
% 9.70/2.91 | (228) ok(all_0_0_0) = all_55_0_20
% 10.17/2.91 | (232) all_55_0_20 = 0
% 10.17/2.91 |
% 10.17/2.91 | Equations (232) can reduce 168 to:
% 10.17/2.91 | (94) $false
% 10.17/2.91 |
% 10.17/2.91 |-The branch is then unsatisfiable
% 10.17/2.91 |-Branch two:
% 10.17/2.91 | (258) triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2
% 10.17/2.91 | (259) check_cpq(all_0_2_2) = 0
% 10.17/2.91 |
% 10.17/2.91 +-Applying beta-rule and splitting (81), into two cases.
% 10.17/2.91 |-Branch one:
% 10.17/2.91 | (88) ~ (triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2)
% 10.17/2.91 |
% 10.17/2.91 | Using (258) and (88) yields:
% 10.17/2.91 | (91) $false
% 10.17/2.91 |
% 10.17/2.91 |-The branch is then unsatisfiable
% 10.17/2.91 |-Branch two:
% 10.17/2.91 | (258) triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2
% 10.17/2.91 | (263) findmin_cpq_res(all_0_2_2) = bottom
% 10.17/2.91 |
% 10.17/2.91 +-Applying beta-rule and splitting (83), into two cases.
% 10.17/2.91 |-Branch one:
% 10.17/2.91 | (88) ~ (triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2)
% 10.17/2.91 |
% 10.17/2.91 | Using (258) and (88) yields:
% 10.17/2.91 | (91) $false
% 10.17/2.91 |
% 10.17/2.91 |-The branch is then unsatisfiable
% 10.17/2.91 |-Branch two:
% 10.17/2.91 | (258) triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2
% 10.17/2.91 | (267) ? [v0] : (triple(all_0_5_5, create_slb, bad) = v0 & findmin_cpq_eff(all_0_2_2) = v0)
% 10.17/2.91 |
% 10.17/2.91 | Instantiating (267) with all_18_0_55 yields:
% 10.17/2.91 | (268) triple(all_0_5_5, create_slb, bad) = all_18_0_55 & findmin_cpq_eff(all_0_2_2) = all_18_0_55
% 10.17/2.91 |
% 10.17/2.91 | Applying alpha-rule on (268) yields:
% 10.17/2.91 | (269) triple(all_0_5_5, create_slb, bad) = all_18_0_55
% 10.17/2.91 | (270) findmin_cpq_eff(all_0_2_2) = all_18_0_55
% 10.17/2.91 |
% 10.17/2.91 +-Applying beta-rule and splitting (84), into two cases.
% 10.17/2.91 |-Branch one:
% 10.17/2.91 | (89) ok(all_0_2_2) = 0
% 10.17/2.91 |
% 10.17/2.91 +-Applying beta-rule and splitting (80), into two cases.
% 10.17/2.91 |-Branch one:
% 10.17/2.91 | (90) ~ (ok(all_0_2_2) = 0)
% 10.17/2.91 |
% 10.17/2.91 | Using (89) and (90) yields:
% 10.17/2.91 | (91) $false
% 10.17/2.91 |
% 10.17/2.91 |-The branch is then unsatisfiable
% 10.17/2.91 |-Branch two:
% 10.17/2.91 | (89) ok(all_0_2_2) = 0
% 10.17/2.91 | (93) all_0_1_1 = 0
% 10.17/2.91 |
% 10.17/2.91 | Equations (93) can reduce 33 to:
% 10.17/2.91 | (94) $false
% 10.17/2.91 |
% 10.17/2.91 |-The branch is then unsatisfiable
% 10.17/2.91 |-Branch two:
% 10.17/2.91 | (90) ~ (ok(all_0_2_2) = 0)
% 10.17/2.91 | (96) all_0_3_3 = bad
% 10.17/2.91 |
% 10.17/2.91 | From (96) and (258) follows:
% 10.17/2.91 | (279) triple(all_0_5_5, create_slb, bad) = all_0_2_2
% 10.17/2.91 |
% 10.17/2.91 | Instantiating formula (18) with all_0_5_5, create_slb, bad, all_18_0_55, all_0_2_2 and discharging atoms triple(all_0_5_5, create_slb, bad) = all_18_0_55, triple(all_0_5_5, create_slb, bad) = all_0_2_2, yields:
% 10.17/2.91 | (280) all_18_0_55 = all_0_2_2
% 10.17/2.91 |
% 10.17/2.91 | Instantiating formula (37) with all_0_2_2, all_18_0_55, all_0_0_0 and discharging atoms findmin_cpq_eff(all_0_2_2) = all_18_0_55, findmin_cpq_eff(all_0_2_2) = all_0_0_0, yields:
% 10.17/2.91 | (281) all_18_0_55 = all_0_0_0
% 10.17/2.91 |
% 10.17/2.91 | Using (27) and (90) yields:
% 10.17/2.91 | (282) ~ (all_0_0_0 = all_0_2_2)
% 10.17/2.91 |
% 10.17/2.91 | Combining equations (280,281) yields a new equation:
% 10.17/2.91 | (283) all_0_0_0 = all_0_2_2
% 10.17/2.91 |
% 10.17/2.91 | Equations (283) can reduce 282 to:
% 10.17/2.91 | (94) $false
% 10.17/2.91 |
% 10.17/2.91 |-The branch is then unsatisfiable
% 10.17/2.91 % SZS output end Proof for theBenchmark
% 10.17/2.91
% 10.17/2.91 2270ms
%------------------------------------------------------------------------------