TSTP Solution File: SWV404+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV404+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 17:51:16 EDT 2022
% Result : Theorem 8.49s 2.57s
% Output : Proof 11.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV404+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n004.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 14:15:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.59 ____ _
% 0.59/0.59 ___ / __ \_____(_)___ ________ __________
% 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.59
% 0.59/0.59 A Theorem Prover for First-Order Logic
% 0.59/0.59 (ePrincess v.1.0)
% 0.59/0.59
% 0.59/0.59 (c) Philipp Rümmer, 2009-2015
% 0.59/0.59 (c) Peter Backeman, 2014-2015
% 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.59 Bug reports to peter@backeman.se
% 0.59/0.59
% 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.59
% 0.59/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.83/0.96 Prover 0: Preprocessing ...
% 2.89/1.30 Prover 0: Warning: ignoring some quantifiers
% 3.18/1.33 Prover 0: Constructing countermodel ...
% 5.43/1.85 Prover 0: gave up
% 5.43/1.86 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.43/1.90 Prover 1: Preprocessing ...
% 6.21/2.02 Prover 1: Constructing countermodel ...
% 6.81/2.21 Prover 1: gave up
% 6.81/2.21 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 7.21/2.24 Prover 2: Preprocessing ...
% 7.60/2.36 Prover 2: Warning: ignoring some quantifiers
% 7.60/2.37 Prover 2: Constructing countermodel ...
% 8.49/2.57 Prover 2: proved (356ms)
% 8.49/2.57
% 8.49/2.57 No countermodel exists, formula is valid
% 8.49/2.57 % SZS status Theorem for theBenchmark
% 8.49/2.57
% 8.49/2.57 Generating proof ... Warning: ignoring some quantifiers
% 10.76/3.08 found it (size 145)
% 10.76/3.08
% 10.76/3.08 % SZS output start Proof for theBenchmark
% 10.76/3.08 Assumed formulas after preprocessing and simplification:
% 10.76/3.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v0 = 0) & ok(v5) = 0 & triple(v1, v2, v3) = v4 & check_cpq(v5) = 0 & check_cpq(v4) = v6 & removemin_cpq_eff(v4) = v5 & 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] : (( ~ (v15 = 0) & less_than(v11, v10) = v15) | (((v17 = 0 & triple(v7, v8, v9) = v16 & check_cpq(v16) = 0) | ( ~ (v15 = 0) & check_cpq(v14) = v15)) & ((v15 = 0 & check_cpq(v14) = 0) | ( ~ (v17 = 0) & triple(v7, v8, v9) = v16 & check_cpq(v16) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (triple(v7, v13, v9) = v14) | ~ (pair(v10, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & check_cpq(v14) = v15) | ( ~ (v15 = 0) & strictly_less_than(v10, v11) = v15))) & ! [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] : ((v14 = v13 & lookup_slb(v7, v9) = v13) | ( ~ (v14 = 0) & contains_slb(v7, v9) = v14))) & ! [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] : ((v15 = v13 & remove_slb(v7, v9) = v14 & insert_slb(v14, v11) = v13) | ( ~ (v14 = 0) & contains_slb(v7, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (remove_slb(v7, v9) = v12) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v12, v11) = v13) | ? [v14] : ? [v15] : ((v15 = v13 & remove_slb(v14, v9) = v13 & insert_slb(v7, v11) = v14) | ( ~ (v14 = 0) & contains_slb(v7, v9) = v14))) & ! [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] : ((v15 = v13 & triple(v7, v8, v9) = v14 & remove_cpq(v14, v10) = v13) | ( ~ (v15 = 0) & lookup_slb(v8, v10) = v14 & less_than(v14, v10) = v15) | ( ~ (v14 = 0) & contains_slb(v8, v10) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : ((v16 = v13 & update_slb(v7, v9) = v14 & pair(v8, v9) = v15 & insert_slb(v14, v15) = v13) | ( ~ (v14 = 0) & strictly_less_than(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v12, v9) = v13) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v7, v11) = v12) | ? [v14] : ? [v15] : ((v15 = v13 & update_slb(v7, v9) = v14 & insert_slb(v14, v11) = v13) | ( ~ (v14 = 0) & less_than(v9, v10) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (update_slb(v7, v9) = v12) | ~ (pair(v8, v10) = v11) | ~ (insert_slb(v12, v11) = v13) | ? [v14] : ? [v15] : ((v15 = v13 & update_slb(v14, v9) = v13 & insert_slb(v7, v11) = v14) | ( ~ (v14 = 0) & less_than(v9, v10) = v14))) & ! [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] : ((v14 = v12 & triple(v7, v8, v9) = v13 & findmin_cpq_eff(v13) = v12) | ( ~ (v14 = 0) & lookup_slb(v8, v10) = v13 & less_than(v13, v10) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v15 = v12 & remove_pqp(v7, v10) = v13 & triple(v13, v14, v9) = v12 & remove_slb(v8, v10) = v14) | ( ~ (v14 = 0) & lookup_slb(v8, v10) = v13 & less_than(v13, v10) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v15 = v12 & remove_pqp(v7, v10) = v13 & triple(v13, v14, bad) = v12 & remove_slb(v8, v10) = v14) | ( ~ (v14 = 0) & lookup_slb(v8, v10) = v13 & strictly_less_than(v10, v13) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ((v13 = v12 & triple(v7, v8, bad) = v12) | (v13 = 0 & contains_slb(v8, v10) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (remove_cpq(v11, v10) = v12) | ? [v13] : ((v13 = 0 & check_cpq(v11) = 0) | ( ~ (v13 = 0) & ok(v12) = v13) | ( ~ (v13 = 0) & check_cpq(v12) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v7, v8, v9) = v11) | ~ (insert_cpq(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : (insert_pqp(v7, v10) = v13 & triple(v13, v15, v9) = v12 & pair(v10, bottom) = v14 & insert_slb(v8, v14) = v15)) & ! [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] : (v8 = create_slb | ~ (findmin_cpq_res(v10) = v11) | ~ (triple(v7, v8, v9) = v10) | findmin_pqp_res(v7) = v11) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ~ (findmin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (findmin_pqp_res(v7) = v12 & ((v14 = v11 & triple(v7, v13, v9) = v11 & update_slb(v8, v12) = v13) | ( ~ (v14 = 0) & lookup_slb(v8, v12) = v13 & less_than(v13, v12) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v12) = v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ~ (findmin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (findmin_pqp_res(v7) = v12 & ((v14 = v11 & triple(v7, v13, bad) = v11 & update_slb(v8, v12) = v13) | (v13 = 0 & contains_slb(v8, v12) = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = create_slb | ~ (triple(v7, v8, v9) = v10) | ~ (findmin_cpq_eff(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (findmin_pqp_res(v7) = v12 & ((v14 = v11 & triple(v7, v13, bad) = v11 & update_slb(v8, v12) = v13) | ( ~ (v14 = 0) & lookup_slb(v8, v12) = v13 & strictly_less_than(v12, v13) = v14) | ( ~ (v13 = 0) & contains_slb(v8, v12) = v13)))) & ! [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) | lookup_slb(v11, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (pair(v8, v9) = v10) | ~ (insert_slb(v7, v10) = v11) | remove_slb(v11, v8) = v7) & ! [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(v8, v9) = 0) | ~ (less_than(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & less_than(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] : ( ~ (triple(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ((v11 = 0 & check_cpq(v10) = 0) | ( ~ (v12 = 0) & check_cpq(v11) = v12 & findmin_cpq_eff(v10) = v11))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (strictly_less_than(v7, v8) = v9) | ? [v10] : ((v10 = 0 & less_than(v8, v7) = 0) | ( ~ (v10 = 0) & less_than(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(v8, v7) = v9) | less_than(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less_than(v8, v7) = v9) | ? [v10] : ((v10 = 0 & strictly_less_than(v7, v8) = 0) | ( ~ (v10 = 0) & less_than(v7, v8) = v10))) & ! [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] : ! [v9] : ( ~ (less_than(v8, v9) = 0) | ~ (less_than(v7, v8) = 0) | less_than(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (less_than(v8, v7) = v9) | ? [v10] : ((v10 = 0 & ~ (v9 = 0) & less_than(v7, v8) = 0) | ( ~ (v10 = 0) & strictly_less_than(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (less_than(v7, v8) = v9) | ? [v10] : ((v9 = 0 & ~ (v10 = 0) & less_than(v8, v7) = v10) | ( ~ (v10 = 0) & strictly_less_than(v7, v8) = 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] : ( ~ (findmin_cpq_res(v7) = v8) | removemin_cpq_res(v7) = v8) & ! [v7] : ! [v8] : ( ~ (findmin_cpq_res(v7) = v8) | ? [v9] : ? [v10] : (removemin_cpq_eff(v7) = v9 & findmin_cpq_eff(v7) = v10 & remove_cpq(v10, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (removemin_cpq_eff(v7) = v8) | ? [v9] : ? [v10] : (findmin_cpq_res(v7) = v10 & findmin_cpq_eff(v7) = v9 & remove_cpq(v9, v10) = v8)) & ! [v7] : ! [v8] : ( ~ (findmin_cpq_eff(v7) = v8) | ? [v9] : ? [v10] : (findmin_cpq_res(v7) = v10 & removemin_cpq_eff(v7) = v9 & remove_cpq(v8, v10) = v9)) & ! [v7] : ! [v8] : ( ~ (succ_cpq(v7, v8) = 0) | ? [v9] : (removemin_cpq_eff(v8) = v9 & succ_cpq(v7, v9) = 0)) & ! [v7] : ! [v8] : ( ~ (succ_cpq(v7, v8) = 0) | ? [v9] : (findmin_cpq_eff(v8) = v9 & succ_cpq(v7, v9) = 0)) & ! [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] : ! [v8] : ( ~ (less_than(v7, v8) = 0) | ? [v9] : ((v9 = 0 & strictly_less_than(v7, v8) = 0) | (v9 = 0 & less_than(v8, v7) = 0))) & ! [v7] : ~ (contains_slb(create_slb, v7) = 0) & ? [v7] : ? [v8] : ? [v9] : ? [v10] : triple(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : pair_in_list(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : remove_pqp(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : insert_pqp(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : contains_cpq(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : remove_cpq(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : insert_cpq(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : succ_cpq(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : update_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : lookup_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : remove_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : contains_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : pair(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : insert_slb(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : strictly_less_than(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : less_than(v8, v7) = v9 & ? [v7] : ? [v8] : removemin_cpq_res(v7) = v8 & ? [v7] : ? [v8] : findmin_cpq_res(v7) = v8 & ? [v7] : ? [v8] : findmin_pqp_res(v7) = v8 & ? [v7] : ? [v8] : ok(v7) = v8 & ? [v7] : ? [v8] : check_cpq(v7) = v8 & ? [v7] : ? [v8] : removemin_cpq_eff(v7) = v8 & ? [v7] : ? [v8] : findmin_cpq_eff(v7) = v8 & ? [v7] : ? [v8] : isnonempty_slb(v7) = v8)
% 11.19/3.14 | 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:
% 11.19/3.14 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_6_6 = 0) & ok(all_0_1_1) = 0 & triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2 & check_cpq(all_0_1_1) = 0 & check_cpq(all_0_2_2) = all_0_0_0 & removemin_cpq_eff(all_0_2_2) = all_0_1_1 & 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] : (( ~ (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 | ~ (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) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = 0 & check_cpq(v4) = 0) | ( ~ (v6 = 0) & ok(v5) = v6) | ( ~ (v6 = 0) & check_cpq(v5) = v6))) & ! [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] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = 0 & check_cpq(v3) = 0) | ( ~ (v5 = 0) & check_cpq(v4) = v5 & findmin_cpq_eff(v3) = v4))) & ! [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] : ( ~ (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] : ~ (contains_slb(create_slb, v0) = 0) & ? [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
% 11.19/3.17 |
% 11.19/3.17 | Applying alpha-rule on (1) yields:
% 11.19/3.17 | (2) check_cpq(all_0_1_1) = 0
% 11.19/3.17 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 11.19/3.17 | (4) ! [v0] : ! [v1] : ( ~ (findmin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2))
% 11.19/3.17 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0))
% 11.19/3.17 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 11.19/3.17 | (7) ok(all_0_1_1) = 0
% 11.19/3.17 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 11.19/3.17 | (9) ~ (all_0_6_6 = 0)
% 11.19/3.17 | (10) triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2
% 11.19/3.17 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 11.19/3.17 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 11.19/3.17 | (13) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0)
% 11.19/3.17 | (14) ! [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)
% 11.19/3.17 | (15) ! [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)
% 11.19/3.17 | (16) ! [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)))
% 11.19/3.17 | (17) ! [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)))
% 11.19/3.17 | (18) ! [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))))
% 11.19/3.17 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0)
% 11.19/3.17 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | less_than(v0, v1) = 0)
% 11.19/3.17 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0))
% 11.19/3.17 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 11.19/3.17 | (23) ? [v0] : ? [v1] : removemin_cpq_eff(v0) = v1
% 11.19/3.17 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 11.19/3.17 | (25) ! [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)))
% 11.19/3.18 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 11.19/3.18 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0))
% 11.19/3.18 | (28) ? [v0] : ? [v1] : ? [v2] : remove_slb(v1, v0) = v2
% 11.19/3.18 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | remove_slb(v4, v1) = v0)
% 11.19/3.18 | (30) ! [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)))
% 11.19/3.18 | (31) ? [v0] : ? [v1] : ? [v2] : succ_cpq(v1, v0) = v2
% 11.19/3.18 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0)
% 11.19/3.18 | (33) ! [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)))))
% 11.19/3.18 | (34) ? [v0] : ? [v1] : ? [v2] : insert_cpq(v1, v0) = v2
% 11.19/3.18 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0))
% 11.19/3.18 | (36) ! [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))
% 11.19/3.18 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4))
% 11.19/3.18 | (38) ? [v0] : ? [v1] : ? [v2] : insert_pqp(v1, v0) = v2
% 11.19/3.18 | (39) ? [v0] : ? [v1] : removemin_cpq_res(v0) = v1
% 11.19/3.18 | (40) ! [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)))
% 11.19/3.18 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 11.19/3.18 | (42) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0))
% 11.19/3.18 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 11.19/3.18 | (44) ? [v0] : ? [v1] : ? [v2] : lookup_slb(v1, v0) = v2
% 11.19/3.18 | (45) ? [v0] : ? [v1] : ? [v2] : ? [v3] : pair_in_list(v2, v1, v0) = v3
% 11.19/3.18 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 11.19/3.18 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 11.19/3.18 | (48) ! [v0] : ! [v1] : ( ~ (less_than(v0, v1) = 0) | ? [v2] : ((v2 = 0 & strictly_less_than(v0, v1) = 0) | (v2 = 0 & less_than(v1, v0) = 0)))
% 11.19/3.18 | (49) ! [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)))
% 11.19/3.18 | (50) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 11.19/3.18 | (51) ? [v0] : ? [v1] : ? [v2] : pair(v1, v0) = v2
% 11.19/3.18 | (52) ! [v0] : ~ (contains_slb(create_slb, v0) = 0)
% 11.19/3.18 | (53) ! [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))))
% 11.19/3.18 | (54) ? [v0] : ? [v1] : findmin_pqp_res(v0) = v1
% 11.19/3.18 | (55) ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (removemin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0))
% 11.19/3.18 | (56) ! [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)))
% 11.19/3.18 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 11.19/3.18 | (58) ! [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))))
% 11.19/3.18 | (59) ! [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)))
% 11.19/3.18 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0)
% 11.19/3.18 | (61) check_cpq(all_0_2_2) = all_0_0_0
% 11.19/3.18 | (62) ! [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))
% 11.19/3.19 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & less_than(v0, v1) = v4))
% 11.19/3.19 | (64) ? [v0] : ? [v1] : findmin_cpq_eff(v0) = v1
% 11.19/3.19 | (65) ? [v0] : ? [v1] : isnonempty_slb(v0) = v1
% 11.19/3.19 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3))
% 11.19/3.19 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 11.19/3.19 | (68) ! [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)))
% 11.19/3.19 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 11.19/3.19 | (70) ? [v0] : ? [v1] : ? [v2] : update_slb(v1, v0) = v2
% 11.19/3.19 | (71) ! [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))
% 11.19/3.19 | (72) ? [v0] : ? [v1] : ? [v2] : less_than(v1, v0) = v2
% 11.19/3.19 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0)
% 11.19/3.19 | (74) ? [v0] : ? [v1] : check_cpq(v0) = v1
% 11.19/3.19 | (75) ! [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)))
% 11.19/3.19 | (76) ! [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)))
% 11.19/3.19 | (77) isnonempty_slb(create_slb) = all_0_6_6
% 11.19/3.19 | (78) ? [v0] : ? [v1] : ? [v2] : contains_cpq(v1, v0) = v2
% 11.19/3.19 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 11.19/3.19 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = 0 & check_cpq(v3) = 0) | ( ~ (v5 = 0) & check_cpq(v4) = v5 & findmin_cpq_eff(v3) = v4)))
% 11.19/3.19 | (81) ? [v0] : ? [v1] : ? [v2] : contains_slb(v1, v0) = v2
% 11.19/3.19 | (82) ! [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))
% 11.19/3.19 | (83) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | ? [v2] : ? [v3] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2))
% 11.19/3.19 | (84) ? [v0] : ? [v1] : ? [v2] : ? [v3] : triple(v2, v1, v0) = v3
% 11.19/3.19 | (85) ! [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))
% 11.19/3.19 | (86) removemin_cpq_eff(all_0_2_2) = all_0_1_1
% 11.19/3.19 | (87) ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1))
% 11.19/3.19 | (88) ? [v0] : ? [v1] : findmin_cpq_res(v0) = v1
% 11.19/3.19 | (89) ? [v0] : ? [v1] : ? [v2] : remove_cpq(v1, v0) = v2
% 11.19/3.19 | (90) ! [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)))
% 11.19/3.19 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, v2) = v3) | findmin_pqp_res(v0) = v4)
% 11.19/3.19 | (92) ? [v0] : ? [v1] : ? [v2] : insert_slb(v1, v0) = v2
% 11.19/3.19 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 11.19/3.19 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 11.19/3.19 | (95) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1))
% 11.19/3.19 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 11.19/3.19 | (97) ! [v0] : ! [v1] : ( ~ (succ_cpq(v0, v1) = 0) | ? [v2] : (findmin_cpq_eff(v1) = v2 & succ_cpq(v0, v2) = 0))
% 11.19/3.19 | (98) ! [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)))
% 11.19/3.19 | (99) ? [v0] : ? [v1] : ? [v2] : remove_pqp(v1, v0) = v2
% 11.19/3.19 | (100) ~ (all_0_0_0 = 0)
% 11.19/3.19 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 11.19/3.19 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 11.19/3.19 | (103) ! [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))
% 11.19/3.19 | (104) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1))
% 11.19/3.19 | (105) ? [v0] : ? [v1] : ? [v2] : strictly_less_than(v1, v0) = v2
% 11.19/3.19 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 11.19/3.19 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 11.19/3.19 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 11.19/3.19 | (109) ! [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)))
% 11.19/3.19 | (110) ! [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)
% 11.19/3.19 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (less_than(v1, v2) = 0) | ~ (less_than(v0, v1) = 0) | less_than(v0, v2) = 0)
% 11.19/3.19 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ((v6 = 0 & check_cpq(v4) = 0) | ( ~ (v6 = 0) & ok(v5) = v6) | ( ~ (v6 = 0) & check_cpq(v5) = v6)))
% 11.19/3.19 | (113) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1)
% 11.19/3.19 | (114) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 11.19/3.19 | (115) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1))
% 11.19/3.19 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0)
% 11.19/3.20 | (117) ! [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)))
% 11.19/3.20 | (118) ? [v0] : ? [v1] : ok(v0) = v1
% 11.19/3.20 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | lookup_slb(v4, v1) = v2)
% 11.19/3.20 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 11.19/3.20 | (121) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 11.19/3.20 | (122) ! [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)))
% 11.19/3.20 | (123) ! [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))
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (80) 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:
% 11.19/3.20 | (124) ? [v0] : ? [v1] : ((v0 = 0 & check_cpq(all_0_2_2) = 0) | ( ~ (v1 = 0) & check_cpq(v0) = v1 & findmin_cpq_eff(all_0_2_2) = v0))
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (104) with all_0_1_1, all_0_2_2 and discharging atoms removemin_cpq_eff(all_0_2_2) = all_0_1_1, yields:
% 11.19/3.20 | (125) ? [v0] : ? [v1] : (findmin_cpq_res(all_0_2_2) = v1 & findmin_cpq_eff(all_0_2_2) = v0 & remove_cpq(v0, v1) = all_0_1_1)
% 11.19/3.20 |
% 11.19/3.20 | Instantiating (125) with all_56_0_73, all_56_1_74 yields:
% 11.19/3.20 | (126) findmin_cpq_res(all_0_2_2) = all_56_0_73 & findmin_cpq_eff(all_0_2_2) = all_56_1_74 & remove_cpq(all_56_1_74, all_56_0_73) = all_0_1_1
% 11.19/3.20 |
% 11.19/3.20 | Applying alpha-rule on (126) yields:
% 11.19/3.20 | (127) findmin_cpq_res(all_0_2_2) = all_56_0_73
% 11.19/3.20 | (128) findmin_cpq_eff(all_0_2_2) = all_56_1_74
% 11.19/3.20 | (129) remove_cpq(all_56_1_74, all_56_0_73) = all_0_1_1
% 11.19/3.20 |
% 11.19/3.20 | Instantiating (124) with all_58_0_75, all_58_1_76 yields:
% 11.19/3.20 | (130) (all_58_1_76 = 0 & check_cpq(all_0_2_2) = 0) | ( ~ (all_58_0_75 = 0) & check_cpq(all_58_1_76) = all_58_0_75 & findmin_cpq_eff(all_0_2_2) = all_58_1_76)
% 11.19/3.20 |
% 11.19/3.20 +-Applying beta-rule and splitting (130), into two cases.
% 11.19/3.20 |-Branch one:
% 11.19/3.20 | (131) all_58_1_76 = 0 & check_cpq(all_0_2_2) = 0
% 11.19/3.20 |
% 11.19/3.20 | Applying alpha-rule on (131) yields:
% 11.19/3.20 | (132) all_58_1_76 = 0
% 11.19/3.20 | (133) check_cpq(all_0_2_2) = 0
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (79) with all_0_2_2, 0, all_0_0_0 and discharging atoms check_cpq(all_0_2_2) = all_0_0_0, check_cpq(all_0_2_2) = 0, yields:
% 11.19/3.20 | (134) all_0_0_0 = 0
% 11.19/3.20 |
% 11.19/3.20 | Equations (134) can reduce 100 to:
% 11.19/3.20 | (135) $false
% 11.19/3.20 |
% 11.19/3.20 |-The branch is then unsatisfiable
% 11.19/3.20 |-Branch two:
% 11.19/3.20 | (136) ~ (all_58_0_75 = 0) & check_cpq(all_58_1_76) = all_58_0_75 & findmin_cpq_eff(all_0_2_2) = all_58_1_76
% 11.19/3.20 |
% 11.19/3.20 | Applying alpha-rule on (136) yields:
% 11.19/3.20 | (137) ~ (all_58_0_75 = 0)
% 11.19/3.20 | (138) check_cpq(all_58_1_76) = all_58_0_75
% 11.19/3.20 | (139) findmin_cpq_eff(all_0_2_2) = all_58_1_76
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (69) with all_0_2_2, all_56_1_74, all_58_1_76 and discharging atoms findmin_cpq_eff(all_0_2_2) = all_58_1_76, findmin_cpq_eff(all_0_2_2) = all_56_1_74, yields:
% 11.19/3.20 | (140) all_58_1_76 = all_56_1_74
% 11.19/3.20 |
% 11.19/3.20 | From (140) and (138) follows:
% 11.19/3.20 | (141) check_cpq(all_56_1_74) = all_58_0_75
% 11.19/3.20 |
% 11.19/3.20 | From (140) and (139) follows:
% 11.19/3.20 | (128) findmin_cpq_eff(all_0_2_2) = all_56_1_74
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (91) with all_56_0_73, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms findmin_cpq_res(all_0_2_2) = all_56_0_73, triple(all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 11.19/3.20 | (143) all_0_4_4 = create_slb | findmin_pqp_res(all_0_5_5) = all_56_0_73
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (18) with all_56_1_74, 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, findmin_cpq_eff(all_0_2_2) = all_56_1_74, yields:
% 11.19/3.20 | (144) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, all_0_3_3) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | ( ~ (v2 = 0) & lookup_slb(all_0_4_4, v0) = v1 & less_than(v1, v0) = v2) | ( ~ (v1 = 0) & contains_slb(all_0_4_4, v0) = v1)))
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (53) with all_56_1_74, 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, findmin_cpq_eff(all_0_2_2) = all_56_1_74, yields:
% 11.19/3.20 | (145) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | (v1 = 0 & contains_slb(all_0_4_4, v0) = 0)))
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (58) with all_56_1_74, 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, findmin_cpq_eff(all_0_2_2) = all_56_1_74, yields:
% 11.19/3.20 | (146) all_0_4_4 = create_slb | ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | ( ~ (v2 = 0) & lookup_slb(all_0_4_4, v0) = v1 & strictly_less_than(v0, v1) = v2) | ( ~ (v1 = 0) & contains_slb(all_0_4_4, v0) = v1)))
% 11.19/3.20 |
% 11.19/3.20 +-Applying beta-rule and splitting (143), into two cases.
% 11.19/3.20 |-Branch one:
% 11.19/3.20 | (147) findmin_pqp_res(all_0_5_5) = all_56_0_73
% 11.19/3.20 |
% 11.19/3.20 +-Applying beta-rule and splitting (145), into two cases.
% 11.19/3.20 |-Branch one:
% 11.19/3.20 | (148) all_0_4_4 = create_slb
% 11.19/3.20 |
% 11.19/3.20 | From (148) and (10) follows:
% 11.19/3.20 | (149) triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (116) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2, yields:
% 11.19/3.20 | (133) check_cpq(all_0_2_2) = 0
% 11.19/3.20 |
% 11.19/3.20 | Instantiating formula (79) with all_0_2_2, 0, all_0_0_0 and discharging atoms check_cpq(all_0_2_2) = all_0_0_0, check_cpq(all_0_2_2) = 0, yields:
% 11.19/3.20 | (134) all_0_0_0 = 0
% 11.19/3.20 |
% 11.19/3.20 | Equations (134) can reduce 100 to:
% 11.19/3.20 | (135) $false
% 11.19/3.20 |
% 11.19/3.20 |-The branch is then unsatisfiable
% 11.19/3.20 |-Branch two:
% 11.19/3.20 | (153) ~ (all_0_4_4 = create_slb)
% 11.19/3.20 | (154) ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | (v1 = 0 & contains_slb(all_0_4_4, v0) = 0)))
% 11.19/3.20 |
% 11.19/3.20 | Instantiating (154) with all_94_0_78, all_94_1_79, all_94_2_80 yields:
% 11.19/3.20 | (155) findmin_pqp_res(all_0_5_5) = all_94_2_80 & ((all_94_0_78 = all_56_1_74 & triple(all_0_5_5, all_94_1_79, bad) = all_56_1_74 & update_slb(all_0_4_4, all_94_2_80) = all_94_1_79) | (all_94_1_79 = 0 & contains_slb(all_0_4_4, all_94_2_80) = 0))
% 11.19/3.20 |
% 11.19/3.20 | Applying alpha-rule on (155) yields:
% 11.19/3.20 | (156) findmin_pqp_res(all_0_5_5) = all_94_2_80
% 11.19/3.21 | (157) (all_94_0_78 = all_56_1_74 & triple(all_0_5_5, all_94_1_79, bad) = all_56_1_74 & update_slb(all_0_4_4, all_94_2_80) = all_94_1_79) | (all_94_1_79 = 0 & contains_slb(all_0_4_4, all_94_2_80) = 0)
% 11.19/3.21 |
% 11.19/3.21 +-Applying beta-rule and splitting (144), into two cases.
% 11.19/3.21 |-Branch one:
% 11.19/3.21 | (148) all_0_4_4 = create_slb
% 11.19/3.21 |
% 11.19/3.21 | Equations (148) can reduce 153 to:
% 11.19/3.21 | (135) $false
% 11.19/3.21 |
% 11.19/3.21 |-The branch is then unsatisfiable
% 11.19/3.21 |-Branch two:
% 11.19/3.21 | (153) ~ (all_0_4_4 = create_slb)
% 11.19/3.21 | (161) ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, all_0_3_3) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | ( ~ (v2 = 0) & lookup_slb(all_0_4_4, v0) = v1 & less_than(v1, v0) = v2) | ( ~ (v1 = 0) & contains_slb(all_0_4_4, v0) = v1)))
% 11.19/3.21 |
% 11.19/3.21 | Instantiating (161) with all_100_0_81, all_100_1_82, all_100_2_83 yields:
% 11.19/3.21 | (162) findmin_pqp_res(all_0_5_5) = all_100_2_83 & ((all_100_0_81 = all_56_1_74 & triple(all_0_5_5, all_100_1_82, all_0_3_3) = all_56_1_74 & update_slb(all_0_4_4, all_100_2_83) = all_100_1_82) | ( ~ (all_100_0_81 = 0) & lookup_slb(all_0_4_4, all_100_2_83) = all_100_1_82 & less_than(all_100_1_82, all_100_2_83) = all_100_0_81) | ( ~ (all_100_1_82 = 0) & contains_slb(all_0_4_4, all_100_2_83) = all_100_1_82))
% 11.19/3.21 |
% 11.19/3.21 | Applying alpha-rule on (162) yields:
% 11.19/3.21 | (163) findmin_pqp_res(all_0_5_5) = all_100_2_83
% 11.19/3.21 | (164) (all_100_0_81 = all_56_1_74 & triple(all_0_5_5, all_100_1_82, all_0_3_3) = all_56_1_74 & update_slb(all_0_4_4, all_100_2_83) = all_100_1_82) | ( ~ (all_100_0_81 = 0) & lookup_slb(all_0_4_4, all_100_2_83) = all_100_1_82 & less_than(all_100_1_82, all_100_2_83) = all_100_0_81) | ( ~ (all_100_1_82 = 0) & contains_slb(all_0_4_4, all_100_2_83) = all_100_1_82)
% 11.19/3.21 |
% 11.19/3.21 +-Applying beta-rule and splitting (146), into two cases.
% 11.19/3.21 |-Branch one:
% 11.19/3.21 | (148) all_0_4_4 = create_slb
% 11.19/3.21 |
% 11.19/3.21 | Equations (148) can reduce 153 to:
% 11.19/3.21 | (135) $false
% 11.19/3.21 |
% 11.19/3.21 |-The branch is then unsatisfiable
% 11.19/3.21 |-Branch two:
% 11.19/3.21 | (153) ~ (all_0_4_4 = create_slb)
% 11.19/3.21 | (168) ? [v0] : ? [v1] : ? [v2] : (findmin_pqp_res(all_0_5_5) = v0 & ((v2 = all_56_1_74 & triple(all_0_5_5, v1, bad) = all_56_1_74 & update_slb(all_0_4_4, v0) = v1) | ( ~ (v2 = 0) & lookup_slb(all_0_4_4, v0) = v1 & strictly_less_than(v0, v1) = v2) | ( ~ (v1 = 0) & contains_slb(all_0_4_4, v0) = v1)))
% 11.19/3.21 |
% 11.19/3.21 | Instantiating (168) with all_105_0_84, all_105_1_85, all_105_2_86 yields:
% 11.19/3.21 | (169) findmin_pqp_res(all_0_5_5) = all_105_2_86 & ((all_105_0_84 = all_56_1_74 & triple(all_0_5_5, all_105_1_85, bad) = all_56_1_74 & update_slb(all_0_4_4, all_105_2_86) = all_105_1_85) | ( ~ (all_105_0_84 = 0) & lookup_slb(all_0_4_4, all_105_2_86) = all_105_1_85 & strictly_less_than(all_105_2_86, all_105_1_85) = all_105_0_84) | ( ~ (all_105_1_85 = 0) & contains_slb(all_0_4_4, all_105_2_86) = all_105_1_85))
% 11.19/3.21 |
% 11.19/3.21 | Applying alpha-rule on (169) yields:
% 11.19/3.21 | (170) findmin_pqp_res(all_0_5_5) = all_105_2_86
% 11.19/3.21 | (171) (all_105_0_84 = all_56_1_74 & triple(all_0_5_5, all_105_1_85, bad) = all_56_1_74 & update_slb(all_0_4_4, all_105_2_86) = all_105_1_85) | ( ~ (all_105_0_84 = 0) & lookup_slb(all_0_4_4, all_105_2_86) = all_105_1_85 & strictly_less_than(all_105_2_86, all_105_1_85) = all_105_0_84) | ( ~ (all_105_1_85 = 0) & contains_slb(all_0_4_4, all_105_2_86) = all_105_1_85)
% 11.19/3.21 |
% 11.19/3.21 | Instantiating formula (22) with all_0_5_5, all_105_2_86, all_56_0_73 and discharging atoms findmin_pqp_res(all_0_5_5) = all_105_2_86, findmin_pqp_res(all_0_5_5) = all_56_0_73, yields:
% 11.19/3.21 | (172) all_105_2_86 = all_56_0_73
% 11.19/3.21 |
% 11.19/3.21 | Instantiating formula (22) with all_0_5_5, all_100_2_83, all_105_2_86 and discharging atoms findmin_pqp_res(all_0_5_5) = all_105_2_86, findmin_pqp_res(all_0_5_5) = all_100_2_83, yields:
% 11.19/3.21 | (173) all_105_2_86 = all_100_2_83
% 11.19/3.21 |
% 11.19/3.21 | Instantiating formula (22) with all_0_5_5, all_94_2_80, all_100_2_83 and discharging atoms findmin_pqp_res(all_0_5_5) = all_100_2_83, findmin_pqp_res(all_0_5_5) = all_94_2_80, yields:
% 11.19/3.21 | (174) all_100_2_83 = all_94_2_80
% 11.19/3.21 |
% 11.19/3.21 | Combining equations (173,172) yields a new equation:
% 11.19/3.21 | (175) all_100_2_83 = all_56_0_73
% 11.19/3.21 |
% 11.19/3.21 | Simplifying 175 yields:
% 11.19/3.21 | (176) all_100_2_83 = all_56_0_73
% 11.19/3.21 |
% 11.19/3.21 | Combining equations (174,176) yields a new equation:
% 11.19/3.21 | (177) all_94_2_80 = all_56_0_73
% 11.19/3.21 |
% 11.19/3.21 | Simplifying 177 yields:
% 11.19/3.21 | (178) all_94_2_80 = all_56_0_73
% 11.19/3.21 |
% 11.19/3.21 +-Applying beta-rule and splitting (157), into two cases.
% 11.19/3.21 |-Branch one:
% 11.19/3.21 | (179) all_94_0_78 = all_56_1_74 & triple(all_0_5_5, all_94_1_79, bad) = all_56_1_74 & update_slb(all_0_4_4, all_94_2_80) = all_94_1_79
% 11.19/3.21 |
% 11.19/3.21 | Applying alpha-rule on (179) yields:
% 11.19/3.21 | (180) all_94_0_78 = all_56_1_74
% 11.19/3.21 | (181) triple(all_0_5_5, all_94_1_79, bad) = all_56_1_74
% 11.19/3.21 | (182) update_slb(all_0_4_4, all_94_2_80) = all_94_1_79
% 11.19/3.21 |
% 11.19/3.21 | Instantiating formula (112) with all_0_1_1, all_56_1_74, all_56_0_73, bad, all_94_1_79, all_0_5_5 and discharging atoms triple(all_0_5_5, all_94_1_79, bad) = all_56_1_74, remove_cpq(all_56_1_74, all_56_0_73) = all_0_1_1, yields:
% 11.19/3.21 | (183) ? [v0] : ((v0 = 0 & check_cpq(all_56_1_74) = 0) | ( ~ (v0 = 0) & ok(all_0_1_1) = v0) | ( ~ (v0 = 0) & check_cpq(all_0_1_1) = v0))
% 11.19/3.21 |
% 11.19/3.21 | Instantiating (183) with all_124_0_89 yields:
% 11.19/3.21 | (184) (all_124_0_89 = 0 & check_cpq(all_56_1_74) = 0) | ( ~ (all_124_0_89 = 0) & ok(all_0_1_1) = all_124_0_89) | ( ~ (all_124_0_89 = 0) & check_cpq(all_0_1_1) = all_124_0_89)
% 11.19/3.21 |
% 11.19/3.21 +-Applying beta-rule and splitting (184), into two cases.
% 11.19/3.21 |-Branch one:
% 11.19/3.21 | (185) (all_124_0_89 = 0 & check_cpq(all_56_1_74) = 0) | ( ~ (all_124_0_89 = 0) & ok(all_0_1_1) = all_124_0_89)
% 11.19/3.21 |
% 11.19/3.21 +-Applying beta-rule and splitting (185), into two cases.
% 11.19/3.21 |-Branch one:
% 11.19/3.21 | (186) all_124_0_89 = 0 & check_cpq(all_56_1_74) = 0
% 11.19/3.21 |
% 11.19/3.21 | Applying alpha-rule on (186) yields:
% 11.19/3.21 | (187) all_124_0_89 = 0
% 11.19/3.21 | (188) check_cpq(all_56_1_74) = 0
% 11.19/3.21 |
% 11.19/3.21 | Instantiating formula (79) with all_56_1_74, 0, all_58_0_75 and discharging atoms check_cpq(all_56_1_74) = all_58_0_75, check_cpq(all_56_1_74) = 0, yields:
% 11.19/3.21 | (189) all_58_0_75 = 0
% 11.19/3.21 |
% 11.19/3.21 | Equations (189) can reduce 137 to:
% 11.19/3.21 | (135) $false
% 11.19/3.21 |
% 11.19/3.21 |-The branch is then unsatisfiable
% 11.19/3.21 |-Branch two:
% 11.19/3.21 | (191) ~ (all_124_0_89 = 0) & ok(all_0_1_1) = all_124_0_89
% 11.19/3.21 |
% 11.19/3.21 | Applying alpha-rule on (191) yields:
% 11.19/3.21 | (192) ~ (all_124_0_89 = 0)
% 11.19/3.21 | (193) ok(all_0_1_1) = all_124_0_89
% 11.19/3.21 |
% 11.19/3.21 | Instantiating formula (12) with all_0_1_1, all_124_0_89, 0 and discharging atoms ok(all_0_1_1) = all_124_0_89, ok(all_0_1_1) = 0, yields:
% 11.19/3.21 | (187) all_124_0_89 = 0
% 11.19/3.21 |
% 11.19/3.21 | Equations (187) can reduce 192 to:
% 11.19/3.21 | (135) $false
% 11.19/3.21 |
% 11.19/3.21 |-The branch is then unsatisfiable
% 11.19/3.21 |-Branch two:
% 11.19/3.21 | (196) ~ (all_124_0_89 = 0) & check_cpq(all_0_1_1) = all_124_0_89
% 11.19/3.21 |
% 11.19/3.21 | Applying alpha-rule on (196) yields:
% 11.19/3.21 | (192) ~ (all_124_0_89 = 0)
% 11.19/3.21 | (198) check_cpq(all_0_1_1) = all_124_0_89
% 11.19/3.21 |
% 11.19/3.21 | Instantiating formula (79) with all_0_1_1, all_124_0_89, 0 and discharging atoms check_cpq(all_0_1_1) = all_124_0_89, check_cpq(all_0_1_1) = 0, yields:
% 11.19/3.21 | (187) all_124_0_89 = 0
% 11.19/3.21 |
% 11.19/3.21 | Equations (187) can reduce 192 to:
% 11.19/3.21 | (135) $false
% 11.19/3.21 |
% 11.19/3.21 |-The branch is then unsatisfiable
% 11.19/3.21 |-Branch two:
% 11.19/3.21 | (201) all_94_1_79 = 0 & contains_slb(all_0_4_4, all_94_2_80) = 0
% 11.19/3.21 |
% 11.68/3.21 | Applying alpha-rule on (201) yields:
% 11.68/3.21 | (202) all_94_1_79 = 0
% 11.68/3.21 | (203) contains_slb(all_0_4_4, all_94_2_80) = 0
% 11.68/3.21 |
% 11.68/3.21 | From (178) and (203) follows:
% 11.68/3.21 | (204) contains_slb(all_0_4_4, all_56_0_73) = 0
% 11.68/3.21 |
% 11.68/3.21 +-Applying beta-rule and splitting (164), into two cases.
% 11.68/3.21 |-Branch one:
% 11.68/3.21 | (205) (all_100_0_81 = all_56_1_74 & triple(all_0_5_5, all_100_1_82, all_0_3_3) = all_56_1_74 & update_slb(all_0_4_4, all_100_2_83) = all_100_1_82) | ( ~ (all_100_0_81 = 0) & lookup_slb(all_0_4_4, all_100_2_83) = all_100_1_82 & less_than(all_100_1_82, all_100_2_83) = all_100_0_81)
% 11.68/3.21 |
% 11.68/3.21 +-Applying beta-rule and splitting (205), into two cases.
% 11.68/3.21 |-Branch one:
% 11.68/3.21 | (206) all_100_0_81 = all_56_1_74 & triple(all_0_5_5, all_100_1_82, all_0_3_3) = all_56_1_74 & update_slb(all_0_4_4, all_100_2_83) = all_100_1_82
% 11.68/3.21 |
% 11.68/3.21 | Applying alpha-rule on (206) yields:
% 11.68/3.21 | (207) all_100_0_81 = all_56_1_74
% 11.68/3.21 | (208) triple(all_0_5_5, all_100_1_82, all_0_3_3) = all_56_1_74
% 11.68/3.21 | (209) update_slb(all_0_4_4, all_100_2_83) = all_100_1_82
% 11.68/3.21 |
% 11.68/3.21 | Instantiating formula (112) with all_0_1_1, all_56_1_74, all_56_0_73, all_0_3_3, all_100_1_82, all_0_5_5 and discharging atoms triple(all_0_5_5, all_100_1_82, all_0_3_3) = all_56_1_74, remove_cpq(all_56_1_74, all_56_0_73) = all_0_1_1, yields:
% 11.68/3.21 | (183) ? [v0] : ((v0 = 0 & check_cpq(all_56_1_74) = 0) | ( ~ (v0 = 0) & ok(all_0_1_1) = v0) | ( ~ (v0 = 0) & check_cpq(all_0_1_1) = v0))
% 11.68/3.21 |
% 11.68/3.21 | Instantiating (183) with all_134_0_111 yields:
% 11.68/3.21 | (211) (all_134_0_111 = 0 & check_cpq(all_56_1_74) = 0) | ( ~ (all_134_0_111 = 0) & ok(all_0_1_1) = all_134_0_111) | ( ~ (all_134_0_111 = 0) & check_cpq(all_0_1_1) = all_134_0_111)
% 11.68/3.21 |
% 11.68/3.21 +-Applying beta-rule and splitting (211), into two cases.
% 11.68/3.21 |-Branch one:
% 11.68/3.21 | (212) (all_134_0_111 = 0 & check_cpq(all_56_1_74) = 0) | ( ~ (all_134_0_111 = 0) & ok(all_0_1_1) = all_134_0_111)
% 11.68/3.21 |
% 11.68/3.21 +-Applying beta-rule and splitting (212), into two cases.
% 11.68/3.21 |-Branch one:
% 11.68/3.21 | (213) all_134_0_111 = 0 & check_cpq(all_56_1_74) = 0
% 11.68/3.21 |
% 11.68/3.21 | Applying alpha-rule on (213) yields:
% 11.68/3.21 | (214) all_134_0_111 = 0
% 11.68/3.21 | (188) check_cpq(all_56_1_74) = 0
% 11.68/3.21 |
% 11.68/3.21 | Instantiating formula (79) with all_56_1_74, 0, all_58_0_75 and discharging atoms check_cpq(all_56_1_74) = all_58_0_75, check_cpq(all_56_1_74) = 0, yields:
% 11.68/3.21 | (189) all_58_0_75 = 0
% 11.68/3.21 |
% 11.68/3.21 | Equations (189) can reduce 137 to:
% 11.68/3.21 | (135) $false
% 11.68/3.21 |
% 11.68/3.21 |-The branch is then unsatisfiable
% 11.68/3.21 |-Branch two:
% 11.68/3.21 | (218) ~ (all_134_0_111 = 0) & ok(all_0_1_1) = all_134_0_111
% 11.68/3.21 |
% 11.68/3.21 | Applying alpha-rule on (218) yields:
% 11.68/3.21 | (219) ~ (all_134_0_111 = 0)
% 11.68/3.21 | (220) ok(all_0_1_1) = all_134_0_111
% 11.68/3.21 |
% 11.68/3.21 | Instantiating formula (12) with all_0_1_1, all_134_0_111, 0 and discharging atoms ok(all_0_1_1) = all_134_0_111, ok(all_0_1_1) = 0, yields:
% 11.68/3.21 | (214) all_134_0_111 = 0
% 11.68/3.21 |
% 11.68/3.21 | Equations (214) can reduce 219 to:
% 11.68/3.21 | (135) $false
% 11.68/3.21 |
% 11.68/3.21 |-The branch is then unsatisfiable
% 11.68/3.21 |-Branch two:
% 11.68/3.21 | (223) ~ (all_134_0_111 = 0) & check_cpq(all_0_1_1) = all_134_0_111
% 11.68/3.21 |
% 11.68/3.21 | Applying alpha-rule on (223) yields:
% 11.68/3.21 | (219) ~ (all_134_0_111 = 0)
% 11.68/3.21 | (225) check_cpq(all_0_1_1) = all_134_0_111
% 11.68/3.21 |
% 11.68/3.21 | Instantiating formula (79) with all_0_1_1, all_134_0_111, 0 and discharging atoms check_cpq(all_0_1_1) = all_134_0_111, check_cpq(all_0_1_1) = 0, yields:
% 11.68/3.22 | (214) all_134_0_111 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (214) can reduce 219 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (228) ~ (all_100_0_81 = 0) & lookup_slb(all_0_4_4, all_100_2_83) = all_100_1_82 & less_than(all_100_1_82, all_100_2_83) = all_100_0_81
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (228) yields:
% 11.68/3.22 | (229) ~ (all_100_0_81 = 0)
% 11.68/3.22 | (230) lookup_slb(all_0_4_4, all_100_2_83) = all_100_1_82
% 11.68/3.22 | (231) less_than(all_100_1_82, all_100_2_83) = all_100_0_81
% 11.68/3.22 |
% 11.68/3.22 | From (176) and (230) follows:
% 11.68/3.22 | (232) lookup_slb(all_0_4_4, all_56_0_73) = all_100_1_82
% 11.68/3.22 |
% 11.68/3.22 | From (176) and (231) follows:
% 11.68/3.22 | (233) less_than(all_100_1_82, all_56_0_73) = all_100_0_81
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (20) with all_100_0_81, all_100_1_82, all_56_0_73 and discharging atoms less_than(all_100_1_82, all_56_0_73) = all_100_0_81, yields:
% 11.68/3.22 | (234) all_100_0_81 = 0 | less_than(all_56_0_73, all_100_1_82) = 0
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (117) with all_100_0_81, all_100_1_82, all_56_0_73 and discharging atoms less_than(all_100_1_82, all_56_0_73) = all_100_0_81, yields:
% 11.68/3.22 | (235) all_100_0_81 = 0 | ? [v0] : ((v0 = 0 & strictly_less_than(all_56_0_73, all_100_1_82) = 0) | ( ~ (v0 = 0) & less_than(all_56_0_73, all_100_1_82) = v0))
% 11.68/3.22 |
% 11.68/3.22 +-Applying beta-rule and splitting (171), into two cases.
% 11.68/3.22 |-Branch one:
% 11.68/3.22 | (236) (all_105_0_84 = all_56_1_74 & triple(all_0_5_5, all_105_1_85, bad) = all_56_1_74 & update_slb(all_0_4_4, all_105_2_86) = all_105_1_85) | ( ~ (all_105_0_84 = 0) & lookup_slb(all_0_4_4, all_105_2_86) = all_105_1_85 & strictly_less_than(all_105_2_86, all_105_1_85) = all_105_0_84)
% 11.68/3.22 |
% 11.68/3.22 +-Applying beta-rule and splitting (236), into two cases.
% 11.68/3.22 |-Branch one:
% 11.68/3.22 | (237) all_105_0_84 = all_56_1_74 & triple(all_0_5_5, all_105_1_85, bad) = all_56_1_74 & update_slb(all_0_4_4, all_105_2_86) = all_105_1_85
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (237) yields:
% 11.68/3.22 | (238) all_105_0_84 = all_56_1_74
% 11.68/3.22 | (239) triple(all_0_5_5, all_105_1_85, bad) = all_56_1_74
% 11.68/3.22 | (240) update_slb(all_0_4_4, all_105_2_86) = all_105_1_85
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (112) with all_0_1_1, all_56_1_74, all_56_0_73, bad, all_105_1_85, all_0_5_5 and discharging atoms triple(all_0_5_5, all_105_1_85, bad) = all_56_1_74, remove_cpq(all_56_1_74, all_56_0_73) = all_0_1_1, yields:
% 11.68/3.22 | (183) ? [v0] : ((v0 = 0 & check_cpq(all_56_1_74) = 0) | ( ~ (v0 = 0) & ok(all_0_1_1) = v0) | ( ~ (v0 = 0) & check_cpq(all_0_1_1) = v0))
% 11.68/3.22 |
% 11.68/3.22 | Instantiating (183) with all_163_0_124 yields:
% 11.68/3.22 | (242) (all_163_0_124 = 0 & check_cpq(all_56_1_74) = 0) | ( ~ (all_163_0_124 = 0) & ok(all_0_1_1) = all_163_0_124) | ( ~ (all_163_0_124 = 0) & check_cpq(all_0_1_1) = all_163_0_124)
% 11.68/3.22 |
% 11.68/3.22 +-Applying beta-rule and splitting (242), into two cases.
% 11.68/3.22 |-Branch one:
% 11.68/3.22 | (243) (all_163_0_124 = 0 & check_cpq(all_56_1_74) = 0) | ( ~ (all_163_0_124 = 0) & ok(all_0_1_1) = all_163_0_124)
% 11.68/3.22 |
% 11.68/3.22 +-Applying beta-rule and splitting (243), into two cases.
% 11.68/3.22 |-Branch one:
% 11.68/3.22 | (244) all_163_0_124 = 0 & check_cpq(all_56_1_74) = 0
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (244) yields:
% 11.68/3.22 | (245) all_163_0_124 = 0
% 11.68/3.22 | (188) check_cpq(all_56_1_74) = 0
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (79) with all_56_1_74, 0, all_58_0_75 and discharging atoms check_cpq(all_56_1_74) = all_58_0_75, check_cpq(all_56_1_74) = 0, yields:
% 11.68/3.22 | (189) all_58_0_75 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (189) can reduce 137 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (249) ~ (all_163_0_124 = 0) & ok(all_0_1_1) = all_163_0_124
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (249) yields:
% 11.68/3.22 | (250) ~ (all_163_0_124 = 0)
% 11.68/3.22 | (251) ok(all_0_1_1) = all_163_0_124
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (12) with all_0_1_1, all_163_0_124, 0 and discharging atoms ok(all_0_1_1) = all_163_0_124, ok(all_0_1_1) = 0, yields:
% 11.68/3.22 | (245) all_163_0_124 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (245) can reduce 250 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (254) ~ (all_163_0_124 = 0) & check_cpq(all_0_1_1) = all_163_0_124
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (254) yields:
% 11.68/3.22 | (250) ~ (all_163_0_124 = 0)
% 11.68/3.22 | (256) check_cpq(all_0_1_1) = all_163_0_124
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (79) with all_0_1_1, all_163_0_124, 0 and discharging atoms check_cpq(all_0_1_1) = all_163_0_124, check_cpq(all_0_1_1) = 0, yields:
% 11.68/3.22 | (245) all_163_0_124 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (245) can reduce 250 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (259) ~ (all_105_0_84 = 0) & lookup_slb(all_0_4_4, all_105_2_86) = all_105_1_85 & strictly_less_than(all_105_2_86, all_105_1_85) = all_105_0_84
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (259) yields:
% 11.68/3.22 | (260) ~ (all_105_0_84 = 0)
% 11.68/3.22 | (261) lookup_slb(all_0_4_4, all_105_2_86) = all_105_1_85
% 11.68/3.22 | (262) strictly_less_than(all_105_2_86, all_105_1_85) = all_105_0_84
% 11.68/3.22 |
% 11.68/3.22 | From (172) and (261) follows:
% 11.68/3.22 | (263) lookup_slb(all_0_4_4, all_56_0_73) = all_105_1_85
% 11.68/3.22 |
% 11.68/3.22 | From (172) and (262) follows:
% 11.68/3.22 | (264) strictly_less_than(all_56_0_73, all_105_1_85) = all_105_0_84
% 11.68/3.22 |
% 11.68/3.22 +-Applying beta-rule and splitting (234), into two cases.
% 11.68/3.22 |-Branch one:
% 11.68/3.22 | (265) less_than(all_56_0_73, all_100_1_82) = 0
% 11.68/3.22 |
% 11.68/3.22 +-Applying beta-rule and splitting (235), into two cases.
% 11.68/3.22 |-Branch one:
% 11.68/3.22 | (266) all_100_0_81 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (266) can reduce 229 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (229) ~ (all_100_0_81 = 0)
% 11.68/3.22 | (269) ? [v0] : ((v0 = 0 & strictly_less_than(all_56_0_73, all_100_1_82) = 0) | ( ~ (v0 = 0) & less_than(all_56_0_73, all_100_1_82) = v0))
% 11.68/3.22 |
% 11.68/3.22 | Instantiating (269) with all_142_0_138 yields:
% 11.68/3.22 | (270) (all_142_0_138 = 0 & strictly_less_than(all_56_0_73, all_100_1_82) = 0) | ( ~ (all_142_0_138 = 0) & less_than(all_56_0_73, all_100_1_82) = all_142_0_138)
% 11.68/3.22 |
% 11.68/3.22 +-Applying beta-rule and splitting (270), into two cases.
% 11.68/3.22 |-Branch one:
% 11.68/3.22 | (271) all_142_0_138 = 0 & strictly_less_than(all_56_0_73, all_100_1_82) = 0
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (271) yields:
% 11.68/3.22 | (272) all_142_0_138 = 0
% 11.68/3.22 | (273) strictly_less_than(all_56_0_73, all_100_1_82) = 0
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (24) with all_0_4_4, all_56_0_73, all_105_1_85, all_100_1_82 and discharging atoms lookup_slb(all_0_4_4, all_56_0_73) = all_105_1_85, lookup_slb(all_0_4_4, all_56_0_73) = all_100_1_82, yields:
% 11.68/3.22 | (274) all_105_1_85 = all_100_1_82
% 11.68/3.22 |
% 11.68/3.22 | From (274) and (264) follows:
% 11.68/3.22 | (275) strictly_less_than(all_56_0_73, all_100_1_82) = all_105_0_84
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (21) with all_56_0_73, all_100_1_82, all_105_0_84, 0 and discharging atoms strictly_less_than(all_56_0_73, all_100_1_82) = all_105_0_84, strictly_less_than(all_56_0_73, all_100_1_82) = 0, yields:
% 11.68/3.22 | (276) all_105_0_84 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (276) can reduce 260 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (278) ~ (all_142_0_138 = 0) & less_than(all_56_0_73, all_100_1_82) = all_142_0_138
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (278) yields:
% 11.68/3.22 | (279) ~ (all_142_0_138 = 0)
% 11.68/3.22 | (280) less_than(all_56_0_73, all_100_1_82) = all_142_0_138
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (57) with all_56_0_73, all_100_1_82, 0, all_142_0_138 and discharging atoms less_than(all_56_0_73, all_100_1_82) = all_142_0_138, less_than(all_56_0_73, all_100_1_82) = 0, yields:
% 11.68/3.22 | (272) all_142_0_138 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (272) can reduce 279 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (283) ~ (less_than(all_56_0_73, all_100_1_82) = 0)
% 11.68/3.22 | (266) all_100_0_81 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (266) can reduce 229 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (286) ~ (all_105_1_85 = 0) & contains_slb(all_0_4_4, all_105_2_86) = all_105_1_85
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (286) yields:
% 11.68/3.22 | (287) ~ (all_105_1_85 = 0)
% 11.68/3.22 | (288) contains_slb(all_0_4_4, all_105_2_86) = all_105_1_85
% 11.68/3.22 |
% 11.68/3.22 | From (172) and (288) follows:
% 11.68/3.22 | (289) contains_slb(all_0_4_4, all_56_0_73) = all_105_1_85
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (94) with all_0_4_4, all_56_0_73, all_105_1_85, 0 and discharging atoms contains_slb(all_0_4_4, all_56_0_73) = all_105_1_85, contains_slb(all_0_4_4, all_56_0_73) = 0, yields:
% 11.68/3.22 | (290) all_105_1_85 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (290) can reduce 287 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (292) ~ (all_100_1_82 = 0) & contains_slb(all_0_4_4, all_100_2_83) = all_100_1_82
% 11.68/3.22 |
% 11.68/3.22 | Applying alpha-rule on (292) yields:
% 11.68/3.22 | (293) ~ (all_100_1_82 = 0)
% 11.68/3.22 | (294) contains_slb(all_0_4_4, all_100_2_83) = all_100_1_82
% 11.68/3.22 |
% 11.68/3.22 | From (176) and (294) follows:
% 11.68/3.22 | (295) contains_slb(all_0_4_4, all_56_0_73) = all_100_1_82
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (94) with all_0_4_4, all_56_0_73, all_100_1_82, 0 and discharging atoms contains_slb(all_0_4_4, all_56_0_73) = all_100_1_82, contains_slb(all_0_4_4, all_56_0_73) = 0, yields:
% 11.68/3.22 | (296) all_100_1_82 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (296) can reduce 293 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 |-Branch two:
% 11.68/3.22 | (298) ~ (findmin_pqp_res(all_0_5_5) = all_56_0_73)
% 11.68/3.22 | (148) all_0_4_4 = create_slb
% 11.68/3.22 |
% 11.68/3.22 | From (148) and (10) follows:
% 11.68/3.22 | (149) triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (116) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms triple(all_0_5_5, create_slb, all_0_3_3) = all_0_2_2, yields:
% 11.68/3.22 | (133) check_cpq(all_0_2_2) = 0
% 11.68/3.22 |
% 11.68/3.22 | Instantiating formula (79) with all_0_2_2, 0, all_0_0_0 and discharging atoms check_cpq(all_0_2_2) = all_0_0_0, check_cpq(all_0_2_2) = 0, yields:
% 11.68/3.22 | (134) all_0_0_0 = 0
% 11.68/3.22 |
% 11.68/3.22 | Equations (134) can reduce 100 to:
% 11.68/3.22 | (135) $false
% 11.68/3.22 |
% 11.68/3.22 |-The branch is then unsatisfiable
% 11.68/3.22 % SZS output end Proof for theBenchmark
% 11.68/3.23
% 11.68/3.23 2626ms
%------------------------------------------------------------------------------