TSTP Solution File: SWV408+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV408+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 17:51:17 EDT 2022
% Result : Theorem 20.17s 5.34s
% Output : Proof 22.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWV408+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Wed Jun 15 16:39:29 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.13/0.45 ____ _
% 0.13/0.46 ___ / __ \_____(_)___ ________ __________
% 0.13/0.46 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.13/0.46 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.13/0.46 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.13/0.46
% 0.13/0.46 A Theorem Prover for First-Order Logic
% 0.13/0.46 (ePrincess v.1.0)
% 0.13/0.46
% 0.13/0.46 (c) Philipp Rümmer, 2009-2015
% 0.13/0.46 (c) Peter Backeman, 2014-2015
% 0.13/0.46 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.13/0.46 Free software under GNU Lesser General Public License (LGPL).
% 0.13/0.46 Bug reports to peter@backeman.se
% 0.13/0.46
% 0.13/0.46 For more information, visit http://user.uu.se/~petba168/breu/
% 0.13/0.46
% 0.13/0.46 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.13/0.50 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.81 Prover 0: Preprocessing ...
% 2.94/1.16 Prover 0: Warning: ignoring some quantifiers
% 2.94/1.19 Prover 0: Constructing countermodel ...
% 6.12/1.92 Prover 0: gave up
% 6.12/1.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.50/1.97 Prover 1: Preprocessing ...
% 6.99/2.09 Prover 1: Constructing countermodel ...
% 19.15/5.11 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 19.15/5.14 Prover 2: Preprocessing ...
% 19.55/5.22 Prover 2: Warning: ignoring some quantifiers
% 19.55/5.23 Prover 2: Constructing countermodel ...
% 20.17/5.33 Prover 2: proved (220ms)
% 20.17/5.34 Prover 1: stopped
% 20.17/5.34
% 20.17/5.34 No countermodel exists, formula is valid
% 20.17/5.34 % SZS status Theorem for theBenchmark
% 20.17/5.34
% 20.17/5.34 Generating proof ... Warning: ignoring some quantifiers
% 22.08/5.77 found it (size 98)
% 22.08/5.77
% 22.08/5.77 % SZS output start Proof for theBenchmark
% 22.08/5.77 Assumed formulas after preprocessing and simplification:
% 22.08/5.77 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v0 = 0) & findmin_cpq_res(v5) = v6 & findmin_pqp_res(v1) = v7 & triple(v1, v2, v3) = v5 & update_slb(v2, v7) = v8 & pair_in_list(v8, v4, v7) = v9 & contains_slb(v2, v4) = 0 & isnonempty_slb(create_slb) = v0 & strictly_less_than(v4, v6) = 0 & ! [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] : (( ~ (v18 = 0) & less_than(v14, v13) = v18) | (((v20 = 0 & triple(v10, v11, v12) = v19 & check_cpq(v19) = 0) | ( ~ (v18 = 0) & check_cpq(v17) = v18)) & ((v18 = 0 & check_cpq(v17) = 0) | ( ~ (v20 = 0) & triple(v10, v11, v12) = v19 & check_cpq(v19) = v20))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v10, v16, v12) = v17) | ~ (pair(v13, v14) = v15) | ~ (insert_slb(v11, v15) = v16) | ? [v18] : (( ~ (v18 = 0) & check_cpq(v17) = v18) | ( ~ (v18 = 0) & strictly_less_than(v13, v14) = v18))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (contains_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ( ~ (v17 = 0) & contains_slb(v10, v12) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (pair_in_list(v16, v12, v14) = 0) | ~ (pair(v11, v13) = v15) | ~ (insert_slb(v10, v15) = v16) | pair_in_list(v10, v12, v14) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (lookup_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ((v17 = v16 & lookup_slb(v10, v12) = v16) | ( ~ (v17 = 0) & contains_slb(v10, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (remove_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ((v18 = v16 & remove_slb(v10, v12) = v17 & insert_slb(v17, v14) = v16) | ( ~ (v17 = 0) & contains_slb(v10, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (remove_slb(v10, v12) = v15) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v15, v14) = v16) | ? [v17] : ? [v18] : ((v18 = v16 & remove_slb(v17, v12) = v16 & insert_slb(v10, v14) = v17) | ( ~ (v17 = 0) & contains_slb(v10, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (pair_in_list(v16, v12, v14) = 0) | ~ (pair(v11, v13) = v15) | ~ (insert_slb(v10, v15) = v16) | pair_in_list(v10, v12, v14) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (remove_pqp(v10, v13) = v14) | ~ (triple(v14, v15, v12) = v16) | ~ (remove_slb(v11, v13) = v15) | ? [v17] : ? [v18] : ((v18 = v16 & triple(v10, v11, v12) = v17 & remove_cpq(v17, v13) = v16) | ( ~ (v18 = 0) & lookup_slb(v11, v13) = v17 & less_than(v17, v13) = v18) | ( ~ (v17 = 0) & contains_slb(v11, v13) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (update_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : ((v19 = v16 & update_slb(v10, v12) = v17 & pair(v11, v12) = v18 & insert_slb(v17, v18) = v16) | ( ~ (v17 = 0) & strictly_less_than(v13, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (update_slb(v15, v12) = v16) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | ? [v17] : ? [v18] : ((v18 = v16 & update_slb(v10, v12) = v17 & insert_slb(v17, v14) = v16) | ( ~ (v17 = 0) & less_than(v12, v13) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (update_slb(v10, v12) = v15) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v15, v14) = v16) | ? [v17] : ? [v18] : ((v18 = v16 & update_slb(v17, v12) = v16 & insert_slb(v10, v14) = v17) | ( ~ (v17 = 0) & less_than(v12, v13) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (contains_cpq(v14, v13) = v15) | ~ (triple(v10, v11, v12) = v14) | ? [v16] : ( ~ (v16 = 0) & contains_slb(v11, v13) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (update_slb(v10, v13) = v14) | ~ (pair_in_list(v14, v11, v13) = v15) | ~ (pair_in_list(v10, v11, v12) = 0) | ? [v16] : ( ~ (v16 = 0) & strictly_less_than(v12, v13) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (update_slb(v10, v13) = v14) | ~ (pair_in_list(v14, v11, v13) = v15) | ~ (strictly_less_than(v12, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & pair_in_list(v10, v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (update_slb(v10, v13) = v14) | ~ (pair_in_list(v14, v11, v12) = v15) | ? [v16] : (( ~ (v16 = 0) & pair_in_list(v10, v11, v12) = v16) | ( ~ (v16 = 0) & less_than(v13, v12) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (pair_in_list(v14, v11, v12) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (contains_slb(v14, v11) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (contains_slb(v15, v12) = 0) | ~ (pair(v11, v13) = v14) | ~ (insert_slb(v10, v14) = v15) | contains_slb(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = create_slb | ~ (findmin_pqp_res(v10) = v13) | ~ (triple(v10, v14, v12) = v15) | ~ (update_slb(v11, v13) = v14) | ? [v16] : ? [v17] : ((v17 = v15 & triple(v10, v11, v12) = v16 & findmin_cpq_eff(v16) = v15) | ( ~ (v17 = 0) & lookup_slb(v11, v13) = v16 & less_than(v16, v13) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (remove_cpq(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v15 & remove_pqp(v10, v13) = v16 & triple(v16, v17, v12) = v15 & remove_slb(v11, v13) = v17) | ( ~ (v17 = 0) & lookup_slb(v11, v13) = v16 & less_than(v16, v13) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (remove_cpq(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v15 & remove_pqp(v10, v13) = v16 & triple(v16, v17, bad) = v15 & remove_slb(v11, v13) = v17) | ( ~ (v17 = 0) & lookup_slb(v11, v13) = v16 & strictly_less_than(v13, v16) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (remove_cpq(v14, v13) = v15) | ? [v16] : ((v16 = v15 & triple(v10, v11, bad) = v15) | (v16 = 0 & contains_slb(v11, v13) = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v10, v11, v12) = v14) | ~ (insert_cpq(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : (insert_pqp(v10, v13) = v16 & triple(v16, v18, v12) = v15 & pair(v13, bottom) = v17 & insert_slb(v11, v17) = v18)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (remove_cpq(v11, v12) = v13) | ~ (succ_cpq(v10, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & succ_cpq(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (insert_cpq(v11, v12) = v13) | ~ (succ_cpq(v10, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & succ_cpq(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (triple(v14, v13, v12) = v11) | ~ (triple(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (pair_in_list(v14, v13, v12) = v11) | ~ (pair_in_list(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = create_slb | ~ (findmin_cpq_res(v13) = v14) | ~ (triple(v10, v11, v12) = v13) | findmin_pqp_res(v10) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = create_slb | ~ (triple(v10, v11, v12) = v13) | ~ (findmin_cpq_eff(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (findmin_pqp_res(v10) = v15 & ((v17 = v14 & triple(v10, v16, v12) = v14 & update_slb(v11, v15) = v16) | ( ~ (v17 = 0) & lookup_slb(v11, v15) = v16 & less_than(v16, v15) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v15) = v16)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = create_slb | ~ (triple(v10, v11, v12) = v13) | ~ (findmin_cpq_eff(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (findmin_pqp_res(v10) = v15 & ((v17 = v14 & triple(v10, v16, bad) = v14 & update_slb(v11, v15) = v16) | (v16 = 0 & contains_slb(v11, v15) = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = create_slb | ~ (triple(v10, v11, v12) = v13) | ~ (findmin_cpq_eff(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (findmin_pqp_res(v10) = v15 & ((v17 = v14 & triple(v10, v16, bad) = v14 & update_slb(v11, v15) = v16) | ( ~ (v17 = 0) & lookup_slb(v11, v15) = v16 & strictly_less_than(v15, v16) = v17) | ( ~ (v16 = 0) & contains_slb(v11, v15) = v16)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (contains_cpq(v14, v13) = 0) | ~ (triple(v10, v11, v12) = v14) | contains_slb(v11, v13) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14) | lookup_slb(v14, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14) | remove_slb(v14, v11) = v10) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (pair(v11, v12) = v13) | ~ (insert_slb(v10, v13) = v14) | isnonempty_slb(v14) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (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(v11, v12) = 0) | ~ (less_than(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & less_than(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (less_than(v10, v12) = v13) | ~ (less_than(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & less_than(v11, v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 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] : ( ~ (pair_in_list(v10, v11, v12) = 0) | ~ (strictly_less_than(v12, v13) = 0) | ? [v14] : (update_slb(v10, v13) = v14 & pair_in_list(v14, v11, v13) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (strictly_less_than(v10, v11) = v12) | ? [v13] : ((v13 = 0 & less_than(v11, v10) = 0) | ( ~ (v13 = 0) & less_than(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (less_than(v11, v10) = v12) | less_than(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (less_than(v11, v10) = v12) | ? [v13] : ((v13 = 0 & strictly_less_than(v10, v11) = 0) | ( ~ (v13 = 0) & less_than(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (less_than(v10, v11) = v12) | less_than(v11, v10) = 0) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (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] : ! [v12] : ( ~ (less_than(v11, v12) = 0) | ~ (less_than(v10, v11) = 0) | less_than(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (less_than(v11, v10) = v12) | ? [v13] : ((v13 = 0 & ~ (v12 = 0) & less_than(v10, v11) = 0) | ( ~ (v13 = 0) & strictly_less_than(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (less_than(v10, v11) = v12) | ? [v13] : ((v12 = 0 & ~ (v13 = 0) & less_than(v11, v10) = v13) | ( ~ (v13 = 0) & strictly_less_than(v10, v11) = v13))) & ! [v10] : ! [v11] : (v11 = create_slb | ~ (update_slb(create_slb, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (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] : ( ~ (findmin_cpq_res(v10) = v11) | removemin_cpq_res(v10) = v11) & ! [v10] : ! [v11] : ( ~ (findmin_cpq_res(v10) = v11) | ? [v12] : ? [v13] : (removemin_cpq_eff(v10) = v12 & findmin_cpq_eff(v10) = v13 & remove_cpq(v13, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (removemin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : (findmin_cpq_res(v10) = v13 & findmin_cpq_eff(v10) = v12 & remove_cpq(v12, v13) = v11)) & ! [v10] : ! [v11] : ( ~ (findmin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : (findmin_cpq_res(v10) = v13 & removemin_cpq_eff(v10) = v12 & remove_cpq(v11, v13) = v12)) & ! [v10] : ! [v11] : ( ~ (succ_cpq(v10, v11) = 0) | ? [v12] : (removemin_cpq_eff(v11) = v12 & succ_cpq(v10, v12) = 0)) & ! [v10] : ! [v11] : ( ~ (succ_cpq(v10, v11) = 0) | ? [v12] : (findmin_cpq_eff(v11) = v12 & succ_cpq(v10, v12) = 0)) & ! [v10] : ! [v11] : ~ (pair_in_list(create_slb, v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (contains_slb(v10, v11) = 0) | ? [v12] : pair_in_list(v10, v11, v12) = 0) & ! [v10] : ! [v11] : ( ~ (strictly_less_than(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & less_than(v11, v10) = v12 & less_than(v10, v11) = 0)) & ! [v10] : ! [v11] : ( ~ (less_than(v10, v11) = 0) | ? [v12] : ((v12 = 0 & strictly_less_than(v10, v11) = 0) | (v12 = 0 & less_than(v11, v10) = 0))) & ! [v10] : ( ~ (pair_in_list(v8, v4, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & less_than(v7, v10) = v11)) & ! [v10] : ~ (contains_slb(create_slb, v10) = 0) & ! [v10] : ( ~ (less_than(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & pair_in_list(v8, v4, v10) = v11)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : triple(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : ? [v13] : pair_in_list(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : remove_pqp(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : insert_pqp(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : contains_cpq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : remove_cpq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : insert_cpq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : succ_cpq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : update_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : lookup_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : remove_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : contains_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : insert_slb(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : strictly_less_than(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : less_than(v11, v10) = v12 & ? [v10] : ? [v11] : removemin_cpq_res(v10) = v11 & ? [v10] : ? [v11] : findmin_cpq_res(v10) = v11 & ? [v10] : ? [v11] : findmin_pqp_res(v10) = v11 & ? [v10] : ? [v11] : ok(v10) = v11 & ? [v10] : ? [v11] : check_cpq(v10) = v11 & ? [v10] : ? [v11] : removemin_cpq_eff(v10) = v11 & ? [v10] : ? [v11] : findmin_cpq_eff(v10) = v11 & ? [v10] : ? [v11] : isnonempty_slb(v10) = v11)
% 22.25/5.82 | 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:
% 22.25/5.82 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_9_9 = 0) & findmin_cpq_res(all_0_4_4) = all_0_3_3 & findmin_pqp_res(all_0_8_8) = all_0_2_2 & triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4 & update_slb(all_0_7_7, all_0_2_2) = all_0_1_1 & pair_in_list(all_0_1_1, all_0_5_5, all_0_2_2) = all_0_0_0 & contains_slb(all_0_7_7, all_0_5_5) = 0 & isnonempty_slb(create_slb) = all_0_9_9 & strictly_less_than(all_0_5_5, all_0_3_3) = 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] : (( ~ (v8 = 0) & less_than(v4, v3) = v8) | (((v10 = 0 & triple(v0, v1, v2) = v9 & check_cpq(v9) = 0) | ( ~ (v8 = 0) & check_cpq(v7) = v8)) & ((v8 = 0 & check_cpq(v7) = 0) | ( ~ (v10 = 0) & triple(v0, v1, v2) = v9 & check_cpq(v9) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (( ~ (v8 = 0) & check_cpq(v7) = v8) | ( ~ (v8 = 0) & strictly_less_than(v3, v4) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ((v7 = v6 & lookup_slb(v0, v2) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & triple(v0, v1, v2) = v7 & remove_cpq(v7, v3) = v6) | ( ~ (v8 = 0) & lookup_slb(v1, v3) = v7 & less_than(v7, v3) = v8) | ( ~ (v7 = 0) & contains_slb(v1, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6) | ( ~ (v7 = 0) & strictly_less_than(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & less_than(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & less_than(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) = v5) | ~ (pair_in_list(v0, v1, v2) = 0) | ? [v6] : ( ~ (v6 = 0) & strictly_less_than(v2, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) = v5) | ~ (strictly_less_than(v2, v3) = 0) | ? [v6] : ( ~ (v6 = 0) & pair_in_list(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v2) = v5) | ? [v6] : (( ~ (v6 = 0) & pair_in_list(v0, v1, v2) = v6) | ( ~ (v6 = 0) & less_than(v3, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | contains_slb(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ((v7 = v5 & triple(v0, v1, v2) = v6 & findmin_cpq_eff(v6) = v5) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, v2) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, bad) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & strictly_less_than(v3, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = v5 & triple(v0, v1, bad) = v5) | (v6 = 0 & contains_slb(v1, v3) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (remove_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (insert_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, v2) = v3) | findmin_pqp_res(v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, v2) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & less_than(v6, v5) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | (v6 = 0 & contains_slb(v1, v5) = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & strictly_less_than(v5, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | lookup_slb(v4, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | remove_slb(v4, v1) = v0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (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(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & less_than(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 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] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v2, v3) = 0) | ? [v4] : (update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ((v3 = 0 & less_than(v1, v0) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | less_than(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & strictly_less_than(v0, v1) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (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] : ! [v2] : ( ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v1) = 0) | less_than(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ~ (v2 = 0) & less_than(v0, v1) = 0) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v0, v1) = v2) | ? [v3] : ((v2 = 0 & ~ (v3 = 0) & less_than(v1, v0) = v3) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (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] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | ? [v2] : ? [v3] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (findmin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2)) & ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (removemin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (findmin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0)) & ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (contains_slb(v0, v1) = 0) | ? [v2] : pair_in_list(v0, v1, v2) = 0) & ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (less_than(v0, v1) = 0) | ? [v2] : ((v2 = 0 & strictly_less_than(v0, v1) = 0) | (v2 = 0 & less_than(v1, v0) = 0))) & ! [v0] : ( ~ (pair_in_list(all_0_1_1, all_0_5_5, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & less_than(all_0_2_2, v0) = v1)) & ! [v0] : ~ (contains_slb(create_slb, v0) = 0) & ! [v0] : ( ~ (less_than(all_0_2_2, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & pair_in_list(all_0_1_1, all_0_5_5, v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : triple(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : remove_pqp(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_pqp(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : contains_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : remove_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : succ_cpq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : update_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : lookup_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : remove_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : contains_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : insert_slb(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : strictly_less_than(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : less_than(v1, v0) = v2 & ? [v0] : ? [v1] : removemin_cpq_res(v0) = v1 & ? [v0] : ? [v1] : findmin_cpq_res(v0) = v1 & ? [v0] : ? [v1] : findmin_pqp_res(v0) = v1 & ? [v0] : ? [v1] : ok(v0) = v1 & ? [v0] : ? [v1] : check_cpq(v0) = v1 & ? [v0] : ? [v1] : removemin_cpq_eff(v0) = v1 & ? [v0] : ? [v1] : findmin_cpq_eff(v0) = v1 & ? [v0] : ? [v1] : isnonempty_slb(v0) = v1
% 22.47/5.84 |
% 22.47/5.84 | Applying alpha-rule on (1) yields:
% 22.47/5.84 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 22.47/5.84 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0))
% 22.47/5.84 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6) | ( ~ (v7 = 0) & strictly_less_than(v3, v2) = v7)))
% 22.47/5.84 | (5) ? [v0] : ? [v1] : ? [v2] : contains_slb(v1, v0) = v2
% 22.47/5.84 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 22.47/5.84 | (7) pair_in_list(all_0_1_1, all_0_5_5, all_0_2_2) = all_0_0_0
% 22.47/5.84 | (8) ? [v0] : ? [v1] : ? [v2] : lookup_slb(v1, v0) = v2
% 22.47/5.84 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) = v5) | ~ (pair_in_list(v0, v1, v2) = 0) | ? [v6] : ( ~ (v6 = 0) & strictly_less_than(v2, v3) = v6))
% 22.47/5.84 | (10) ? [v0] : ? [v1] : removemin_cpq_eff(v0) = v1
% 22.47/5.84 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 22.47/5.84 | (12) ? [v0] : ? [v1] : ok(v0) = v1
% 22.47/5.84 | (13) ? [v0] : ? [v1] : removemin_cpq_res(v0) = v1
% 22.47/5.84 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0)
% 22.47/5.84 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (( ~ (v8 = 0) & check_cpq(v7) = v8) | ( ~ (v8 = 0) & strictly_less_than(v3, v4) = v8)))
% 22.47/5.84 | (16) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1))
% 22.47/5.85 | (17) ? [v0] : ? [v1] : ? [v2] : remove_cpq(v1, v0) = v2
% 22.47/5.85 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & less_than(v0, v1) = v4))
% 22.47/5.85 | (19) ? [v0] : ? [v1] : ? [v2] : succ_cpq(v1, v0) = v2
% 22.47/5.85 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = v5 & triple(v0, v1, bad) = v5) | (v6 = 0 & contains_slb(v1, v3) = 0)))
% 22.47/5.85 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 22.47/5.85 | (22) findmin_pqp_res(all_0_8_8) = all_0_2_2
% 22.47/5.85 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4))
% 22.47/5.85 | (24) ! [v0] : ! [v1] : ( ~ (less_than(v0, v1) = 0) | ? [v2] : ((v2 = 0 & strictly_less_than(v0, v1) = 0) | (v2 = 0 & less_than(v1, v0) = 0)))
% 22.47/5.85 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0))
% 22.47/5.85 | (26) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0))
% 22.47/5.85 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) = v5) | ~ (strictly_less_than(v2, v3) = 0) | ? [v6] : ( ~ (v6 = 0) & pair_in_list(v0, v1, v2) = v6))
% 22.47/5.85 | (28) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0)
% 22.47/5.85 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8))
% 22.47/5.85 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, v2) = v3) | findmin_pqp_res(v0) = v4)
% 22.47/5.85 | (31) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1))
% 22.47/5.85 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3))
% 22.47/5.85 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 22.47/5.85 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & less_than(v2, v3) = v7)))
% 22.47/5.85 | (35) ! [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))
% 22.47/5.85 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 22.47/5.85 | (37) ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (removemin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0))
% 22.47/5.85 | (38) ! [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))
% 22.47/5.85 | (39) ? [v0] : ? [v1] : ? [v2] : pair(v1, v0) = v2
% 22.47/5.85 | (40) ? [v0] : ? [v1] : findmin_pqp_res(v0) = v1
% 22.47/5.85 | (41) ~ (all_0_0_0 = 0)
% 22.47/5.85 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | remove_slb(v4, v1) = v0)
% 22.47/5.85 | (43) ? [v0] : ? [v1] : check_cpq(v0) = v1
% 22.47/5.85 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & less_than(v2, v3) = v7)))
% 22.47/5.85 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v1) = 0) | less_than(v0, v2) = 0)
% 22.47/5.85 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | lookup_slb(v4, v1) = v2)
% 22.47/5.85 | (47) ! [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))
% 22.47/5.85 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 22.47/5.85 | (49) ? [v0] : ? [v1] : ? [v2] : strictly_less_than(v1, v0) = v2
% 22.47/5.85 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 22.47/5.85 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)))
% 22.47/5.85 | (52) ? [v0] : ? [v1] : ? [v2] : update_slb(v1, v0) = v2
% 22.47/5.85 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 22.47/5.85 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v2) = v5) | ? [v6] : (( ~ (v6 = 0) & pair_in_list(v0, v1, v2) = v6) | ( ~ (v6 = 0) & less_than(v3, v2) = v6)))
% 22.47/5.85 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | (v6 = 0 & contains_slb(v1, v5) = 0))))
% 22.47/5.85 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0)
% 22.47/5.85 | (57) ? [v0] : ? [v1] : ? [v2] : insert_pqp(v1, v0) = v2
% 22.47/5.85 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ((v3 = 0 & less_than(v1, v0) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3)))
% 22.47/5.85 | (59) ! [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)
% 22.47/5.85 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, bad) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & strictly_less_than(v3, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)))
% 22.47/5.85 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 22.47/5.85 | (62) findmin_cpq_res(all_0_4_4) = all_0_3_3
% 22.47/5.85 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 22.47/5.85 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 22.47/5.86 | (65) ? [v0] : ? [v1] : ? [v2] : less_than(v1, v0) = v2
% 22.47/5.86 | (66) ? [v0] : ? [v1] : ? [v2] : insert_cpq(v1, v0) = v2
% 22.47/5.86 | (67) ! [v0] : ~ (contains_slb(create_slb, v0) = 0)
% 22.47/5.86 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 22.47/5.86 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 22.47/5.86 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ((v8 = v6 & triple(v0, v1, v2) = v7 & remove_cpq(v7, v3) = v6) | ( ~ (v8 = 0) & lookup_slb(v1, v3) = v7 & less_than(v7, v3) = v8) | ( ~ (v7 = 0) & contains_slb(v1, v3) = v7)))
% 22.47/5.86 | (71) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0)
% 22.47/5.86 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | less_than(v0, v1) = 0)
% 22.47/5.86 | (73) isnonempty_slb(create_slb) = all_0_9_9
% 22.47/5.86 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 22.47/5.86 | (75) ! [v0] : ! [v1] : ( ~ (findmin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2))
% 22.47/5.86 | (76) ! [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))
% 22.47/5.86 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 22.47/5.86 | (78) ? [v0] : ? [v1] : isnonempty_slb(v0) = v1
% 22.47/5.86 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)))
% 22.47/5.86 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 22.47/5.86 | (81) ? [v0] : ? [v1] : findmin_cpq_eff(v0) = v1
% 22.47/5.86 | (82) ~ (all_0_9_9 = 0)
% 22.47/5.86 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0))
% 22.47/5.86 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0)
% 22.47/5.86 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : (( ~ (v8 = 0) & less_than(v4, v3) = v8) | (((v10 = 0 & triple(v0, v1, v2) = v9 & check_cpq(v9) = 0) | ( ~ (v8 = 0) & check_cpq(v7) = v8)) & ((v8 = 0 & check_cpq(v7) = 0) | ( ~ (v10 = 0) & triple(v0, v1, v2) = v9 & check_cpq(v9) = v10)))))
% 22.47/5.86 | (86) strictly_less_than(all_0_5_5, all_0_3_3) = 0
% 22.47/5.86 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 22.47/5.86 | (88) ! [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)
% 22.47/5.86 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & remove_pqp(v0, v3) = v6 & triple(v6, v7, v2) = v5 & remove_slb(v1, v3) = v7) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)))
% 22.47/5.86 | (90) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | ? [v2] : ? [v3] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2))
% 22.47/5.86 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 22.47/5.86 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 22.47/5.86 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0)
% 22.47/5.86 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v0, v1) = v2) | ? [v3] : ((v2 = 0 & ~ (v3 = 0) & less_than(v1, v0) = v3) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3)))
% 22.47/5.86 | (95) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 22.47/5.86 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, v2) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & less_than(v6, v5) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6))))
% 22.47/5.86 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ((v7 = v6 & lookup_slb(v0, v2) = v6) | ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)))
% 22.47/5.86 | (98) ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3
% 22.47/5.86 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 22.47/5.86 | (100) contains_slb(all_0_7_7, all_0_5_5) = 0
% 22.47/5.86 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 22.47/5.86 | (102) triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4
% 22.47/5.86 | (103) ? [v0] : ? [v1] : ? [v2] : ? [v3] : triple(v2, v1, v0) = v3
% 22.47/5.86 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v2, v3) = 0) | ? [v4] : (update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = 0))
% 22.47/5.86 | (105) ? [v0] : ? [v1] : ? [v2] : insert_slb(v1, v0) = v2
% 22.47/5.86 | (106) ? [v0] : ? [v1] : ? [v2] : remove_slb(v1, v0) = v2
% 22.47/5.86 | (107) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 22.47/5.86 | (108) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & strictly_less_than(v0, v1) = 0) | ( ~ (v3 = 0) & less_than(v0, v1) = v3)))
% 22.47/5.86 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 22.47/5.86 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0))
% 22.47/5.86 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v5 & ((v7 = v4 & triple(v0, v6, bad) = v4 & update_slb(v1, v5) = v6) | ( ~ (v7 = 0) & lookup_slb(v1, v5) = v6 & strictly_less_than(v5, v6) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v5) = v6))))
% 22.47/5.86 | (112) ? [v0] : ? [v1] : ? [v2] : remove_pqp(v1, v0) = v2
% 22.47/5.86 | (113) ! [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))
% 22.47/5.87 | (114) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1)
% 22.47/5.87 | (115) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 22.47/5.87 | (116) ! [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)
% 22.47/5.87 | (117) update_slb(all_0_7_7, all_0_2_2) = all_0_1_1
% 22.47/5.87 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ((v7 = v5 & triple(v0, v1, v2) = v6 & findmin_cpq_eff(v6) = v5) | ( ~ (v7 = 0) & lookup_slb(v1, v3) = v6 & less_than(v6, v3) = v7) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)))
% 22.47/5.87 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ~ (v2 = 0) & less_than(v0, v1) = 0) | ( ~ (v3 = 0) & strictly_less_than(v0, v1) = v3)))
% 22.47/5.87 | (120) ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1))
% 22.47/5.87 | (121) ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (findmin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0))
% 22.47/5.87 | (122) ! [v0] : ( ~ (less_than(all_0_2_2, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & pair_in_list(all_0_1_1, all_0_5_5, v0) = v1))
% 22.47/5.87 | (123) ! [v0] : ( ~ (pair_in_list(all_0_1_1, all_0_5_5, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & less_than(all_0_2_2, v0) = v1))
% 22.47/5.87 | (124) ! [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))
% 22.47/5.87 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 22.47/5.87 | (126) ? [v0] : ? [v1] : findmin_cpq_res(v0) = v1
% 22.47/5.87 | (127) ! [v0] : ! [v1] : ( ~ (contains_slb(v0, v1) = 0) | ? [v2] : pair_in_list(v0, v1, v2) = 0)
% 22.47/5.87 | (128) ? [v0] : ? [v1] : ? [v2] : contains_cpq(v1, v0) = v2
% 22.47/5.87 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 22.47/5.87 | (130) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1))
% 22.47/5.87 |
% 22.47/5.87 | Instantiating formula (30) with all_0_3_3, all_0_4_4, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms findmin_cpq_res(all_0_4_4) = all_0_3_3, triple(all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4, yields:
% 22.47/5.87 | (131) all_0_7_7 = create_slb | findmin_pqp_res(all_0_8_8) = all_0_3_3
% 22.47/5.87 |
% 22.47/5.87 | Instantiating formula (54) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_2_2, all_0_5_5, all_0_7_7 and discharging atoms update_slb(all_0_7_7, all_0_2_2) = all_0_1_1, pair_in_list(all_0_1_1, all_0_5_5, all_0_2_2) = all_0_0_0, yields:
% 22.47/5.87 | (132) all_0_0_0 = 0 | ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & less_than(all_0_2_2, all_0_2_2) = v0))
% 22.47/5.87 |
% 22.47/5.87 | Instantiating formula (127) with all_0_5_5, all_0_7_7 and discharging atoms contains_slb(all_0_7_7, all_0_5_5) = 0, yields:
% 22.47/5.87 | (133) ? [v0] : pair_in_list(all_0_7_7, all_0_5_5, v0) = 0
% 22.47/5.87 |
% 22.47/5.87 | Instantiating (133) with all_59_0_77 yields:
% 22.47/5.87 | (134) pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = 0
% 22.47/5.87 |
% 22.47/5.87 +-Applying beta-rule and splitting (132), into two cases.
% 22.47/5.87 |-Branch one:
% 22.47/5.87 | (135) all_0_0_0 = 0
% 22.47/5.87 |
% 22.47/5.87 | Equations (135) can reduce 41 to:
% 22.47/5.87 | (136) $false
% 22.47/5.87 |
% 22.47/5.87 |-The branch is then unsatisfiable
% 22.47/5.87 |-Branch two:
% 22.47/5.87 | (41) ~ (all_0_0_0 = 0)
% 22.47/5.87 | (138) ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & less_than(all_0_2_2, all_0_2_2) = v0))
% 22.47/5.87 |
% 22.47/5.87 | Instantiating formula (9) with all_0_0_0, all_0_1_1, all_0_2_2, all_59_0_77, all_0_5_5, all_0_7_7 and discharging atoms update_slb(all_0_7_7, all_0_2_2) = all_0_1_1, pair_in_list(all_0_1_1, all_0_5_5, all_0_2_2) = all_0_0_0, pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = 0, yields:
% 22.47/5.87 | (139) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & strictly_less_than(all_59_0_77, all_0_2_2) = v0)
% 22.47/5.87 |
% 22.47/5.87 +-Applying beta-rule and splitting (139), into two cases.
% 22.47/5.87 |-Branch one:
% 22.47/5.87 | (135) all_0_0_0 = 0
% 22.47/5.87 |
% 22.47/5.87 | Equations (135) can reduce 41 to:
% 22.47/5.87 | (136) $false
% 22.47/5.87 |
% 22.47/5.87 |-The branch is then unsatisfiable
% 22.47/5.87 |-Branch two:
% 22.47/5.87 | (41) ~ (all_0_0_0 = 0)
% 22.47/5.87 | (143) ? [v0] : ( ~ (v0 = 0) & strictly_less_than(all_59_0_77, all_0_2_2) = v0)
% 22.47/5.87 |
% 22.47/5.87 | Instantiating (143) with all_84_0_83 yields:
% 22.47/5.87 | (144) ~ (all_84_0_83 = 0) & strictly_less_than(all_59_0_77, all_0_2_2) = all_84_0_83
% 22.47/5.87 |
% 22.47/5.87 | Applying alpha-rule on (144) yields:
% 22.47/5.87 | (145) ~ (all_84_0_83 = 0)
% 22.47/5.87 | (146) strictly_less_than(all_59_0_77, all_0_2_2) = all_84_0_83
% 22.47/5.87 |
% 22.47/5.87 | Instantiating formula (58) with all_84_0_83, all_0_2_2, all_59_0_77 and discharging atoms strictly_less_than(all_59_0_77, all_0_2_2) = all_84_0_83, yields:
% 22.47/5.87 | (147) all_84_0_83 = 0 | ? [v0] : ((v0 = 0 & less_than(all_0_2_2, all_59_0_77) = 0) | ( ~ (v0 = 0) & less_than(all_59_0_77, all_0_2_2) = v0))
% 22.47/5.87 |
% 22.47/5.87 +-Applying beta-rule and splitting (131), into two cases.
% 22.47/5.87 |-Branch one:
% 22.47/5.87 | (148) findmin_pqp_res(all_0_8_8) = all_0_3_3
% 22.47/5.87 |
% 22.47/5.87 +-Applying beta-rule and splitting (147), into two cases.
% 22.47/5.87 |-Branch one:
% 22.47/5.87 | (149) all_84_0_83 = 0
% 22.47/5.87 |
% 22.47/5.87 | Equations (149) can reduce 145 to:
% 22.47/5.87 | (136) $false
% 22.47/5.87 |
% 22.47/5.87 |-The branch is then unsatisfiable
% 22.47/5.87 |-Branch two:
% 22.47/5.87 | (145) ~ (all_84_0_83 = 0)
% 22.47/5.87 | (152) ? [v0] : ((v0 = 0 & less_than(all_0_2_2, all_59_0_77) = 0) | ( ~ (v0 = 0) & less_than(all_59_0_77, all_0_2_2) = v0))
% 22.47/5.87 |
% 22.47/5.87 | Instantiating (152) with all_101_0_84 yields:
% 22.47/5.87 | (153) (all_101_0_84 = 0 & less_than(all_0_2_2, all_59_0_77) = 0) | ( ~ (all_101_0_84 = 0) & less_than(all_59_0_77, all_0_2_2) = all_101_0_84)
% 22.47/5.87 |
% 22.47/5.87 | Instantiating formula (95) with all_0_8_8, all_0_3_3, all_0_2_2 and discharging atoms findmin_pqp_res(all_0_8_8) = all_0_2_2, findmin_pqp_res(all_0_8_8) = all_0_3_3, yields:
% 22.47/5.87 | (154) all_0_2_2 = all_0_3_3
% 22.47/5.87 |
% 22.47/5.87 | From (154) and (117) follows:
% 22.47/5.87 | (155) update_slb(all_0_7_7, all_0_3_3) = all_0_1_1
% 22.47/5.87 |
% 22.47/5.87 +-Applying beta-rule and splitting (153), into two cases.
% 22.47/5.87 |-Branch one:
% 22.47/5.87 | (156) all_101_0_84 = 0 & less_than(all_0_2_2, all_59_0_77) = 0
% 22.47/5.87 |
% 22.47/5.87 | Applying alpha-rule on (156) yields:
% 22.47/5.87 | (157) all_101_0_84 = 0
% 22.47/5.87 | (158) less_than(all_0_2_2, all_59_0_77) = 0
% 22.47/5.87 |
% 22.47/5.87 | From (154) and (158) follows:
% 22.47/5.87 | (159) less_than(all_0_3_3, all_59_0_77) = 0
% 22.47/5.87 |
% 22.47/5.87 | Instantiating formula (122) with all_59_0_77 yields:
% 22.47/5.87 | (160) ~ (less_than(all_0_2_2, all_59_0_77) = 0) | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = v0)
% 22.47/5.87 |
% 22.47/5.87 +-Applying beta-rule and splitting (160), into two cases.
% 22.47/5.87 |-Branch one:
% 22.47/5.87 | (161) ~ (less_than(all_0_2_2, all_59_0_77) = 0)
% 22.47/5.87 |
% 22.47/5.87 | From (154) and (161) follows:
% 22.47/5.87 | (162) ~ (less_than(all_0_3_3, all_59_0_77) = 0)
% 22.47/5.87 |
% 22.47/5.87 | Using (159) and (162) yields:
% 22.47/5.87 | (163) $false
% 22.47/5.87 |
% 22.47/5.87 |-The branch is then unsatisfiable
% 22.47/5.87 |-Branch two:
% 22.47/5.87 | (158) less_than(all_0_2_2, all_59_0_77) = 0
% 22.47/5.87 | (165) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = v0)
% 22.47/5.87 |
% 22.47/5.87 | Instantiating (165) with all_173_0_98 yields:
% 22.47/5.87 | (166) ~ (all_173_0_98 = 0) & pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = all_173_0_98
% 22.47/5.87 |
% 22.47/5.87 | Applying alpha-rule on (166) yields:
% 22.47/5.87 | (167) ~ (all_173_0_98 = 0)
% 22.47/5.87 | (168) pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = all_173_0_98
% 22.47/5.88 |
% 22.47/5.88 | From (154) and (158) follows:
% 22.47/5.88 | (159) less_than(all_0_3_3, all_59_0_77) = 0
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (54) with all_173_0_98, all_0_1_1, all_0_3_3, all_59_0_77, all_0_5_5, all_0_7_7 and discharging atoms update_slb(all_0_7_7, all_0_3_3) = all_0_1_1, pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = all_173_0_98, yields:
% 22.47/5.88 | (170) all_173_0_98 = 0 | ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = v0) | ( ~ (v0 = 0) & less_than(all_0_3_3, all_59_0_77) = v0))
% 22.47/5.88 |
% 22.47/5.88 +-Applying beta-rule and splitting (170), into two cases.
% 22.47/5.88 |-Branch one:
% 22.47/5.88 | (171) all_173_0_98 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (171) can reduce 167 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (167) ~ (all_173_0_98 = 0)
% 22.47/5.88 | (174) ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = v0) | ( ~ (v0 = 0) & less_than(all_0_3_3, all_59_0_77) = v0))
% 22.47/5.88 |
% 22.47/5.88 | Instantiating (174) with all_200_0_106 yields:
% 22.47/5.88 | (175) ( ~ (all_200_0_106 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = all_200_0_106) | ( ~ (all_200_0_106 = 0) & less_than(all_0_3_3, all_59_0_77) = all_200_0_106)
% 22.47/5.88 |
% 22.47/5.88 +-Applying beta-rule and splitting (175), into two cases.
% 22.47/5.88 |-Branch one:
% 22.47/5.88 | (176) ~ (all_200_0_106 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = all_200_0_106
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (176) yields:
% 22.47/5.88 | (177) ~ (all_200_0_106 = 0)
% 22.47/5.88 | (178) pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = all_200_0_106
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (25) with all_0_7_7, all_0_5_5, all_59_0_77, all_200_0_106, 0 and discharging atoms pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = all_200_0_106, pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = 0, yields:
% 22.47/5.88 | (179) all_200_0_106 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (179) can reduce 177 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (181) ~ (all_200_0_106 = 0) & less_than(all_0_3_3, all_59_0_77) = all_200_0_106
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (181) yields:
% 22.47/5.88 | (177) ~ (all_200_0_106 = 0)
% 22.47/5.88 | (183) less_than(all_0_3_3, all_59_0_77) = all_200_0_106
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (33) with all_0_3_3, all_59_0_77, all_200_0_106, 0 and discharging atoms less_than(all_0_3_3, all_59_0_77) = all_200_0_106, less_than(all_0_3_3, all_59_0_77) = 0, yields:
% 22.47/5.88 | (179) all_200_0_106 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (179) can reduce 177 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (186) ~ (all_101_0_84 = 0) & less_than(all_59_0_77, all_0_2_2) = all_101_0_84
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (186) yields:
% 22.47/5.88 | (187) ~ (all_101_0_84 = 0)
% 22.47/5.88 | (188) less_than(all_59_0_77, all_0_2_2) = all_101_0_84
% 22.47/5.88 |
% 22.47/5.88 | From (154) and (188) follows:
% 22.47/5.88 | (189) less_than(all_59_0_77, all_0_3_3) = all_101_0_84
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (72) with all_101_0_84, all_59_0_77, all_0_3_3 and discharging atoms less_than(all_59_0_77, all_0_3_3) = all_101_0_84, yields:
% 22.47/5.88 | (190) all_101_0_84 = 0 | less_than(all_0_3_3, all_59_0_77) = 0
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (108) with all_101_0_84, all_59_0_77, all_0_3_3 and discharging atoms less_than(all_59_0_77, all_0_3_3) = all_101_0_84, yields:
% 22.47/5.88 | (191) all_101_0_84 = 0 | ? [v0] : ((v0 = 0 & strictly_less_than(all_0_3_3, all_59_0_77) = 0) | ( ~ (v0 = 0) & less_than(all_0_3_3, all_59_0_77) = v0))
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (119) with all_101_0_84, all_59_0_77, all_0_3_3 and discharging atoms less_than(all_59_0_77, all_0_3_3) = all_101_0_84, yields:
% 22.47/5.88 | (192) ? [v0] : ((v0 = 0 & ~ (all_101_0_84 = 0) & less_than(all_0_3_3, all_59_0_77) = 0) | ( ~ (v0 = 0) & strictly_less_than(all_0_3_3, all_59_0_77) = v0))
% 22.47/5.88 |
% 22.47/5.88 | Instantiating (192) with all_166_0_107 yields:
% 22.47/5.88 | (193) (all_166_0_107 = 0 & ~ (all_101_0_84 = 0) & less_than(all_0_3_3, all_59_0_77) = 0) | ( ~ (all_166_0_107 = 0) & strictly_less_than(all_0_3_3, all_59_0_77) = all_166_0_107)
% 22.47/5.88 |
% 22.47/5.88 +-Applying beta-rule and splitting (190), into two cases.
% 22.47/5.88 |-Branch one:
% 22.47/5.88 | (159) less_than(all_0_3_3, all_59_0_77) = 0
% 22.47/5.88 |
% 22.47/5.88 +-Applying beta-rule and splitting (191), into two cases.
% 22.47/5.88 |-Branch one:
% 22.47/5.88 | (157) all_101_0_84 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (157) can reduce 187 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (187) ~ (all_101_0_84 = 0)
% 22.47/5.88 | (198) ? [v0] : ((v0 = 0 & strictly_less_than(all_0_3_3, all_59_0_77) = 0) | ( ~ (v0 = 0) & less_than(all_0_3_3, all_59_0_77) = v0))
% 22.47/5.88 |
% 22.47/5.88 | Instantiating (198) with all_177_0_108 yields:
% 22.47/5.88 | (199) (all_177_0_108 = 0 & strictly_less_than(all_0_3_3, all_59_0_77) = 0) | ( ~ (all_177_0_108 = 0) & less_than(all_0_3_3, all_59_0_77) = all_177_0_108)
% 22.47/5.88 |
% 22.47/5.88 +-Applying beta-rule and splitting (199), into two cases.
% 22.47/5.88 |-Branch one:
% 22.47/5.88 | (200) all_177_0_108 = 0 & strictly_less_than(all_0_3_3, all_59_0_77) = 0
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (200) yields:
% 22.47/5.88 | (201) all_177_0_108 = 0
% 22.47/5.88 | (202) strictly_less_than(all_0_3_3, all_59_0_77) = 0
% 22.47/5.88 |
% 22.47/5.88 +-Applying beta-rule and splitting (193), into two cases.
% 22.47/5.88 |-Branch one:
% 22.47/5.88 | (203) all_166_0_107 = 0 & ~ (all_101_0_84 = 0) & less_than(all_0_3_3, all_59_0_77) = 0
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (203) yields:
% 22.47/5.88 | (204) all_166_0_107 = 0
% 22.47/5.88 | (187) ~ (all_101_0_84 = 0)
% 22.47/5.88 | (159) less_than(all_0_3_3, all_59_0_77) = 0
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (122) with all_59_0_77 yields:
% 22.47/5.88 | (160) ~ (less_than(all_0_2_2, all_59_0_77) = 0) | ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = v0)
% 22.47/5.88 |
% 22.47/5.88 +-Applying beta-rule and splitting (160), into two cases.
% 22.47/5.88 |-Branch one:
% 22.47/5.88 | (161) ~ (less_than(all_0_2_2, all_59_0_77) = 0)
% 22.47/5.88 |
% 22.47/5.88 | From (154) and (161) follows:
% 22.47/5.88 | (162) ~ (less_than(all_0_3_3, all_59_0_77) = 0)
% 22.47/5.88 |
% 22.47/5.88 | Using (159) and (162) yields:
% 22.47/5.88 | (163) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (158) less_than(all_0_2_2, all_59_0_77) = 0
% 22.47/5.88 | (165) ? [v0] : ( ~ (v0 = 0) & pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = v0)
% 22.47/5.88 |
% 22.47/5.88 | Instantiating (165) with all_215_0_113 yields:
% 22.47/5.88 | (213) ~ (all_215_0_113 = 0) & pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = all_215_0_113
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (213) yields:
% 22.47/5.88 | (214) ~ (all_215_0_113 = 0)
% 22.47/5.88 | (215) pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = all_215_0_113
% 22.47/5.88 |
% 22.47/5.88 | From (154) and (158) follows:
% 22.47/5.88 | (159) less_than(all_0_3_3, all_59_0_77) = 0
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (54) with all_215_0_113, all_0_1_1, all_0_3_3, all_59_0_77, all_0_5_5, all_0_7_7 and discharging atoms update_slb(all_0_7_7, all_0_3_3) = all_0_1_1, pair_in_list(all_0_1_1, all_0_5_5, all_59_0_77) = all_215_0_113, yields:
% 22.47/5.88 | (217) all_215_0_113 = 0 | ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = v0) | ( ~ (v0 = 0) & less_than(all_0_3_3, all_59_0_77) = v0))
% 22.47/5.88 |
% 22.47/5.88 +-Applying beta-rule and splitting (217), into two cases.
% 22.47/5.88 |-Branch one:
% 22.47/5.88 | (218) all_215_0_113 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (218) can reduce 214 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (214) ~ (all_215_0_113 = 0)
% 22.47/5.88 | (174) ? [v0] : (( ~ (v0 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = v0) | ( ~ (v0 = 0) & less_than(all_0_3_3, all_59_0_77) = v0))
% 22.47/5.88 |
% 22.47/5.88 | Instantiating (174) with all_232_0_114 yields:
% 22.47/5.88 | (222) ( ~ (all_232_0_114 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = all_232_0_114) | ( ~ (all_232_0_114 = 0) & less_than(all_0_3_3, all_59_0_77) = all_232_0_114)
% 22.47/5.88 |
% 22.47/5.88 +-Applying beta-rule and splitting (222), into two cases.
% 22.47/5.88 |-Branch one:
% 22.47/5.88 | (223) ~ (all_232_0_114 = 0) & pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = all_232_0_114
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (223) yields:
% 22.47/5.88 | (224) ~ (all_232_0_114 = 0)
% 22.47/5.88 | (225) pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = all_232_0_114
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (25) with all_0_7_7, all_0_5_5, all_59_0_77, all_232_0_114, 0 and discharging atoms pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = all_232_0_114, pair_in_list(all_0_7_7, all_0_5_5, all_59_0_77) = 0, yields:
% 22.47/5.88 | (226) all_232_0_114 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (226) can reduce 224 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (228) ~ (all_232_0_114 = 0) & less_than(all_0_3_3, all_59_0_77) = all_232_0_114
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (228) yields:
% 22.47/5.88 | (224) ~ (all_232_0_114 = 0)
% 22.47/5.88 | (230) less_than(all_0_3_3, all_59_0_77) = all_232_0_114
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (33) with all_0_3_3, all_59_0_77, all_232_0_114, 0 and discharging atoms less_than(all_0_3_3, all_59_0_77) = all_232_0_114, less_than(all_0_3_3, all_59_0_77) = 0, yields:
% 22.47/5.88 | (226) all_232_0_114 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (226) can reduce 224 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (233) ~ (all_166_0_107 = 0) & strictly_less_than(all_0_3_3, all_59_0_77) = all_166_0_107
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (233) yields:
% 22.47/5.88 | (234) ~ (all_166_0_107 = 0)
% 22.47/5.88 | (235) strictly_less_than(all_0_3_3, all_59_0_77) = all_166_0_107
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (3) with all_0_3_3, all_59_0_77, 0, all_166_0_107 and discharging atoms strictly_less_than(all_0_3_3, all_59_0_77) = all_166_0_107, strictly_less_than(all_0_3_3, all_59_0_77) = 0, yields:
% 22.47/5.88 | (204) all_166_0_107 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (204) can reduce 234 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (238) ~ (all_177_0_108 = 0) & less_than(all_0_3_3, all_59_0_77) = all_177_0_108
% 22.47/5.88 |
% 22.47/5.88 | Applying alpha-rule on (238) yields:
% 22.47/5.88 | (239) ~ (all_177_0_108 = 0)
% 22.47/5.88 | (240) less_than(all_0_3_3, all_59_0_77) = all_177_0_108
% 22.47/5.88 |
% 22.47/5.88 | Instantiating formula (33) with all_0_3_3, all_59_0_77, 0, all_177_0_108 and discharging atoms less_than(all_0_3_3, all_59_0_77) = all_177_0_108, less_than(all_0_3_3, all_59_0_77) = 0, yields:
% 22.47/5.88 | (201) all_177_0_108 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (201) can reduce 239 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.88 |-Branch two:
% 22.47/5.88 | (162) ~ (less_than(all_0_3_3, all_59_0_77) = 0)
% 22.47/5.88 | (157) all_101_0_84 = 0
% 22.47/5.88 |
% 22.47/5.88 | Equations (157) can reduce 187 to:
% 22.47/5.88 | (136) $false
% 22.47/5.88 |
% 22.47/5.88 |-The branch is then unsatisfiable
% 22.47/5.89 |-Branch two:
% 22.47/5.89 | (246) ~ (findmin_pqp_res(all_0_8_8) = all_0_3_3)
% 22.47/5.89 | (247) all_0_7_7 = create_slb
% 22.47/5.89 |
% 22.47/5.89 | From (247) and (100) follows:
% 22.47/5.89 | (248) contains_slb(create_slb, all_0_5_5) = 0
% 22.47/5.89 |
% 22.47/5.89 | Instantiating formula (67) with all_0_5_5 and discharging atoms contains_slb(create_slb, all_0_5_5) = 0, yields:
% 22.47/5.89 | (163) $false
% 22.47/5.89 |
% 22.47/5.89 |-The branch is then unsatisfiable
% 22.47/5.89 % SZS output end Proof for theBenchmark
% 22.47/5.89
% 22.47/5.89 5420ms
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