TSTP Solution File: SWV408+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV408+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 4.87s 1.74s
% Output : Proof 7.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV408+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 23:10:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.58/0.59 ____ _
% 0.58/0.59 ___ / __ \_____(_)___ ________ __________
% 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.59
% 0.58/0.59 A Theorem Prover for First-Order Logic
% 0.58/0.59 (ePrincess v.1.0)
% 0.58/0.59
% 0.58/0.59 (c) Philipp Rümmer, 2009-2015
% 0.58/0.59 (c) Peter Backeman, 2014-2015
% 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.59 Bug reports to peter@backeman.se
% 0.58/0.59
% 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.59
% 0.58/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.86/0.99 Prover 0: Preprocessing ...
% 3.29/1.34 Prover 0: Warning: ignoring some quantifiers
% 3.29/1.37 Prover 0: Constructing countermodel ...
% 4.87/1.74 Prover 0: proved (1099ms)
% 4.87/1.74
% 4.87/1.74 No countermodel exists, formula is valid
% 4.87/1.74 % SZS status Theorem for theBenchmark
% 4.87/1.74
% 4.87/1.74 Generating proof ... Warning: ignoring some quantifiers
% 6.70/2.13 found it (size 62)
% 6.70/2.13
% 6.70/2.13 % SZS output start Proof for theBenchmark
% 6.70/2.13 Assumed formulas after preprocessing and simplification:
% 6.70/2.13 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (findmin_cpq_res(v4) = v5 & findmin_pqp_res(v0) = v6 & triple(v0, v1, v2) = v4 & update_slb(v1, v6) = v7 & contains_slb(v1, v3) & strictly_less_than(v3, v5) & ~ pair_in_list(v7, v3, v6) & ~ isnonempty_slb(create_slb) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (insert_pqp(v8, v11) = v12) | ~ (triple(v12, v14, v10) = v15) | ~ (pair(v11, bottom) = v13) | ~ (insert_slb(v9, v13) = v14) | ? [v16] : (triple(v8, v9, v10) = v16 & insert_cpq(v16, v11) = v15)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v8, v14, v10) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ~ check_cpq(v15) | ~ strictly_less_than(v11, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (triple(v8, v14, v10) = v15) | ~ (pair(v11, v12) = v13) | ~ (insert_slb(v9, v13) = v14) | ~ less_than(v12, v11) | ? [v16] : (triple(v8, v9, v10) = v16 & ( ~ check_cpq(v16) | check_cpq(v15)) & ( ~ check_cpq(v15) | check_cpq(v16)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (pair(v9, v11) = v13) | ~ (insert_slb(v8, v13) = v14) | ~ pair_in_list(v14, v10, v12) | pair_in_list(v8, v10, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (lookup_slb(v13, v10) = v14) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ~ contains_slb(v8, v10) | lookup_slb(v8, v10) = v14) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (remove_slb(v13, v10) = v14) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ~ contains_slb(v8, v10) | ? [v15] : (remove_slb(v8, v10) = v15 & insert_slb(v15, v12) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (remove_slb(v8, v10) = v13) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v13, v12) = v14) | ~ contains_slb(v8, v10) | ? [v15] : (remove_slb(v15, v10) = v14 & insert_slb(v8, v12) = v15)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (pair(v9, v11) = v13) | ~ (insert_slb(v8, v13) = v14) | ~ pair_in_list(v14, v10, v12) | pair_in_list(v8, v10, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (remove_pqp(v8, v11) = v12) | ~ (triple(v12, v13, v10) = v14) | ~ (remove_slb(v9, v11) = v13) | ~ contains_slb(v9, v11) | ? [v15] : ? [v16] : ? [v17] : (triple(v8, v9, v10) = v16 & remove_cpq(v16, v11) = v17 & lookup_slb(v9, v11) = v15 & (v17 = v14 | ~ less_than(v15, v11)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (update_slb(v13, v10) = v14) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ~ strictly_less_than(v11, v10) | ? [v15] : ? [v16] : (update_slb(v8, v10) = v15 & pair(v9, v10) = v16 & insert_slb(v15, v16) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (update_slb(v13, v10) = v14) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ~ less_than(v10, v11) | ? [v15] : (update_slb(v8, v10) = v15 & insert_slb(v15, v12) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (update_slb(v8, v10) = v13) | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v13, v12) = v14) | ~ less_than(v10, v11) | ? [v15] : (update_slb(v15, v10) = v14 & insert_slb(v8, v12) = v15)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (pair(v9, v11) = v13) | ~ (insert_slb(v8, v13) = v14) | ~ pair_in_list(v8, v10, v12) | pair_in_list(v14, v10, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (lookup_slb(v12, v9) = v13) | ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v8 | ~ (remove_slb(v12, v9) = v13) | ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ~ contains_slb(v13, v10) | contains_slb(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = create_slb | ~ (findmin_pqp_res(v8) = v11) | ~ (triple(v8, v12, v10) = v13) | ~ (update_slb(v9, v11) = v12) | ~ contains_slb(v9, v11) | ? [v14] : ? [v15] : ? [v16] : (triple(v8, v9, v10) = v15 & findmin_cpq_eff(v15) = v16 & lookup_slb(v9, v11) = v14 & (v16 = v13 | ~ less_than(v14, v11)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v8, v9, v10) = v12) | ~ (remove_cpq(v12, v11) = v13) | ~ contains_slb(v9, v11) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (remove_pqp(v8, v11) = v15 & triple(v15, v16, v10) = v17 & lookup_slb(v9, v11) = v14 & remove_slb(v9, v11) = v16 & (v17 = v13 | ~ less_than(v14, v11)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v8, v9, v10) = v12) | ~ (remove_cpq(v12, v11) = v13) | ~ contains_slb(v9, v11) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (remove_pqp(v8, v11) = v15 & triple(v15, v16, bad) = v17 & lookup_slb(v9, v11) = v14 & remove_slb(v9, v11) = v16 & (v17 = v13 | ~ strictly_less_than(v11, v14)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v8, v9, v10) = v12) | ~ (remove_cpq(v12, v11) = v13) | triple(v8, v9, bad) = v13 | contains_slb(v9, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (triple(v8, v9, v10) = v12) | ~ (insert_cpq(v12, v11) = v13) | ? [v14] : ? [v15] : ? [v16] : (insert_pqp(v8, v11) = v14 & triple(v14, v16, v10) = v13 & pair(v11, bottom) = v15 & insert_slb(v9, v15) = v16)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (pair(v9, v11) = v12) | ~ (insert_slb(v8, v12) = v13) | ~ contains_slb(v8, v10) | contains_slb(v13, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (triple(v12, v11, v10) = v9) | ~ (triple(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v8, v9, v10) = v12) | ~ contains_cpq(v12, v11) | contains_slb(v9, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (triple(v8, v9, v10) = v12) | ~ contains_slb(v9, v11) | contains_cpq(v12, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12) | pair_in_list(v12, v9, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12) | contains_slb(v12, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (pair(v9, v10) = v11) | ~ (insert_slb(v8, v11) = v12) | isnonempty_slb(v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = bad | ~ (triple(v8, v9, v10) = v11) | ok(v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (remove_pqp(v11, v10) = v9) | ~ (remove_pqp(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (insert_pqp(v11, v10) = v9) | ~ (insert_pqp(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (remove_cpq(v11, v10) = v9) | ~ (remove_cpq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (insert_cpq(v11, v10) = v9) | ~ (insert_cpq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (update_slb(v11, v10) = v9) | ~ (update_slb(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (lookup_slb(v11, v10) = v9) | ~ (lookup_slb(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (remove_slb(v11, v10) = v9) | ~ (remove_slb(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (pair(v11, v10) = v9) | ~ (pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (insert_slb(v11, v10) = v9) | ~ (insert_slb(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = create_slb | ~ (triple(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (findmin_pqp_res(v8) = v12 & triple(v8, v15, v10) = v16 & findmin_cpq_eff(v11) = v14 & update_slb(v9, v12) = v15 & lookup_slb(v9, v12) = v13 & (v16 = v14 | ~ contains_slb(v9, v12) | ~ less_than(v13, v12)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = create_slb | ~ (triple(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (findmin_pqp_res(v8) = v12 & triple(v8, v15, bad) = v16 & findmin_cpq_eff(v11) = v14 & update_slb(v9, v12) = v15 & lookup_slb(v9, v12) = v13 & (v16 = v14 | ~ contains_slb(v9, v12) | ~ strictly_less_than(v12, v13)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = create_slb | ~ (triple(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (findmin_pqp_res(v8) = v12 & triple(v8, v14, bad) = v15 & findmin_cpq_eff(v11) = v13 & update_slb(v9, v12) = v14 & (v15 = v13 | contains_slb(v9, v12)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = create_slb | ~ (triple(v8, v9, v10) = v11) | ? [v12] : (findmin_cpq_res(v11) = v12 & findmin_pqp_res(v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (findmin_cpq_res(v8) = v10) | ~ (findmin_cpq_eff(v8) = v9) | ~ (remove_cpq(v9, v10) = v11) | removemin_cpq_eff(v8) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (remove_cpq(v9, v10) = v11) | ~ succ_cpq(v8, v9) | succ_cpq(v8, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (insert_cpq(v9, v10) = v11) | ~ succ_cpq(v8, v9) | succ_cpq(v8, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (update_slb(v8, v10) = v11) | ~ contains_slb(v8, v9) | ~ strictly_less_than(v9, v10) | pair_in_list(v11, v9, v10) | ? [v12] : (pair_in_list(v11, v9, v12) & less_than(v10, v12))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (removemin_cpq_res(v10) = v9) | ~ (removemin_cpq_res(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (findmin_cpq_res(v10) = v9) | ~ (findmin_cpq_res(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (findmin_pqp_res(v10) = v9) | ~ (findmin_pqp_res(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (removemin_cpq_eff(v10) = v9) | ~ (removemin_cpq_eff(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (findmin_cpq_eff(v10) = v9) | ~ (findmin_cpq_eff(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v8, v9, bad) = v10) | ~ ok(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v8, create_slb, v9) = v10) | findmin_cpq_res(v10) = bottom) & ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v8, create_slb, v9) = v10) | check_cpq(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (triple(v8, create_slb, v9) = v10) | ? [v11] : (triple(v8, create_slb, bad) = v11 & findmin_cpq_eff(v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (removemin_cpq_eff(v9) = v10) | ~ succ_cpq(v8, v9) | succ_cpq(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (findmin_cpq_eff(v9) = v10) | ~ succ_cpq(v8, v9) | succ_cpq(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ less_than(v9, v10) | ~ less_than(v8, v9) | less_than(v8, v10)) & ! [v8] : ! [v9] : (v9 = create_slb | ~ (update_slb(create_slb, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (removemin_cpq_res(v8) = v9) | findmin_cpq_res(v8) = v9) & ! [v8] : ! [v9] : ( ~ (findmin_cpq_res(v8) = v9) | removemin_cpq_res(v8) = v9) & ! [v8] : ! [v9] : ( ~ (removemin_cpq_eff(v8) = v9) | ? [v10] : ? [v11] : (findmin_cpq_res(v8) = v11 & findmin_cpq_eff(v8) = v10 & remove_cpq(v10, v11) = v9)) & ! [v8] : ! [v9] : ~ pair_in_list(create_slb, v8, v9) & ! [v8] : ! [v9] : ( ~ strictly_less_than(v8, v9) | ~ less_than(v9, v8)) & ! [v8] : ! [v9] : ( ~ strictly_less_than(v8, v9) | less_than(v8, v9)) & ! [v8] : ! [v9] : ( ~ less_than(v8, v9) | strictly_less_than(v8, v9) | less_than(v9, v8)) & ! [v8] : ( ~ pair_in_list(v7, v3, v8) | ~ less_than(v6, v8)) & ! [v8] : ~ contains_slb(create_slb, v8) & ? [v8] : ? [v9] : (less_than(v9, v8) | less_than(v8, v9)) & ? [v8] : succ_cpq(v8, v8) & ? [v8] : less_than(v8, v8) & ? [v8] : less_than(bottom, v8))
% 6.70/2.18 | 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 yields:
% 6.70/2.18 | (1) findmin_cpq_res(all_0_3_3) = all_0_2_2 & findmin_pqp_res(all_0_7_7) = all_0_1_1 & triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_3_3 & update_slb(all_0_6_6, all_0_1_1) = all_0_0_0 & contains_slb(all_0_6_6, all_0_4_4) & strictly_less_than(all_0_4_4, all_0_2_2) & ~ pair_in_list(all_0_0_0, all_0_4_4, all_0_1_1) & ~ isnonempty_slb(create_slb) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (insert_pqp(v0, v3) = v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ check_cpq(v7) | ~ strictly_less_than(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ less_than(v4, v3) | ? [v8] : (triple(v0, v1, v2) = v8 & ( ~ check_cpq(v8) | check_cpq(v7)) & ( ~ check_cpq(v7) | check_cpq(v8)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | lookup_slb(v0, v2) = v6) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ~ contains_slb(v1, v3) | ? [v7] : ? [v8] : ? [v9] : (triple(v0, v1, v2) = v8 & remove_cpq(v8, v3) = v9 & lookup_slb(v1, v3) = v7 & (v9 = v6 | ~ less_than(v7, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ strictly_less_than(v3, v2) | ? [v7] : ? [v8] : (update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v0, v2, v4) | pair_in_list(v6, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v5, v2) | contains_slb(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : (triple(v0, v1, v2) = v7 & findmin_cpq_eff(v7) = v8 & lookup_slb(v1, v3) = v6 & (v8 = v5 | ~ less_than(v6, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, v2) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ less_than(v6, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, bad) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ strictly_less_than(v3, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | triple(v0, v1, bad) = v5 | contains_slb(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, v2) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ less_than(v5, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, bad) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ strictly_less_than(v4, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v4 & triple(v0, v6, bad) = v7 & findmin_cpq_eff(v3) = v5 & update_slb(v1, v4) = v6 & (v7 = v5 | contains_slb(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (update_slb(v0, v2) = v3) | ~ contains_slb(v0, v1) | ~ strictly_less_than(v1, v2) | pair_in_list(v3, v1, v2) | ? [v4] : (pair_in_list(v3, v1, v4) & less_than(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2)) & ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1)) & ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1) & ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0)) & ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1)) & ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0)) & ! [v0] : ( ~ pair_in_list(all_0_0_0, all_0_4_4, v0) | ~ less_than(all_0_1_1, v0)) & ! [v0] : ~ contains_slb(create_slb, v0) & ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1)) & ? [v0] : succ_cpq(v0, v0) & ? [v0] : less_than(v0, v0) & ? [v0] : less_than(bottom, v0)
% 6.70/2.21 |
% 6.70/2.21 | Applying alpha-rule on (1) yields:
% 6.70/2.21 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3)
% 6.70/2.21 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, v2) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ less_than(v6, v3))))
% 6.70/2.21 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 6.70/2.21 | (5) update_slb(all_0_6_6, all_0_1_1) = all_0_0_0
% 6.70/2.21 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (insert_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3))
% 6.70/2.21 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 6.70/2.21 | (8) ? [v0] : less_than(bottom, v0)
% 6.70/2.21 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 6.70/2.21 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 6.70/2.21 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 6.70/2.21 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ less_than(v4, v3) | ? [v8] : (triple(v0, v1, v2) = v8 & ( ~ check_cpq(v8) | check_cpq(v7)) & ( ~ check_cpq(v7) | check_cpq(v8))))
% 6.70/2.21 | (13) ! [v0] : ! [v1] : ( ~ (removemin_cpq_eff(v0) = v1) | ? [v2] : ? [v3] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1))
% 6.70/2.21 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 6.70/2.21 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4))
% 6.70/2.21 | (16) ! [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))
% 6.70/2.21 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (findmin_pqp_res(v0) = v4 & triple(v0, v6, bad) = v7 & findmin_cpq_eff(v3) = v5 & update_slb(v1, v4) = v6 & (v7 = v5 | contains_slb(v1, v4))))
% 6.70/2.21 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4))
% 6.70/2.21 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | triple(v0, v1, bad) = v5 | contains_slb(v1, v3))
% 6.70/2.21 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ check_cpq(v7) | ~ strictly_less_than(v3, v4))
% 6.70/2.21 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v6, v2, v4) | pair_in_list(v0, v2, v4))
% 6.70/2.21 | (22) contains_slb(all_0_6_6, all_0_4_4)
% 6.70/2.21 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 6.70/2.21 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ~ contains_slb(v1, v3) | ? [v7] : ? [v8] : ? [v9] : (triple(v0, v1, v2) = v8 & remove_cpq(v8, v3) = v9 & lookup_slb(v1, v3) = v7 & (v9 = v6 | ~ less_than(v7, v3))))
% 6.70/2.21 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 6.70/2.21 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (findmin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2))
% 6.70/2.21 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | lookup_slb(v0, v2) = v6)
% 6.70/2.21 | (28) ! [v0] : ! [v1] : ( ~ (findmin_cpq_res(v0) = v1) | removemin_cpq_res(v0) = v1)
% 6.70/2.21 | (29) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 6.70/2.21 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 6.70/2.21 | (31) ? [v0] : ? [v1] : (less_than(v1, v0) | less_than(v0, v1))
% 6.70/2.21 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 6.70/2.21 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7))
% 6.70/2.22 | (34) ~ isnonempty_slb(create_slb)
% 6.70/2.22 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 6.70/2.22 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v5, v2) | contains_slb(v0, v2))
% 6.70/2.22 | (37) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 6.70/2.22 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 6.70/2.22 | (39) ? [v0] : succ_cpq(v0, v0)
% 6.70/2.22 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : (triple(v0, v1, v2) = v7 & findmin_cpq_eff(v7) = v8 & lookup_slb(v1, v3) = v6 & (v8 = v5 | ~ less_than(v6, v3))))
% 6.70/2.22 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2))
% 6.70/2.22 | (42) ? [v0] : less_than(v0, v0)
% 6.70/2.22 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | pair_in_list(v4, v1, v2))
% 6.70/2.22 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, v2) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ less_than(v5, v4))))
% 6.70/2.22 | (45) ! [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))
% 6.70/2.22 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (remove_cpq(v1, v2) = v3) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v3))
% 6.70/2.22 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_cpq_eff(v1) = v2) | ~ succ_cpq(v0, v1) | succ_cpq(v0, v2))
% 6.70/2.22 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (update_slb(v0, v2) = v3) | ~ contains_slb(v0, v1) | ~ strictly_less_than(v1, v2) | pair_in_list(v3, v1, v2) | ? [v4] : (pair_in_list(v3, v1, v4) & less_than(v2, v4)))
% 6.70/2.22 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 6.70/2.22 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 6.70/2.22 | (51) strictly_less_than(all_0_4_4, all_0_2_2)
% 6.70/2.22 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ contains_slb(v1, v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (remove_pqp(v0, v3) = v7 & triple(v7, v8, bad) = v9 & lookup_slb(v1, v3) = v6 & remove_slb(v1, v3) = v8 & (v9 = v5 | ~ strictly_less_than(v3, v6))))
% 6.70/2.22 | (53) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | less_than(v0, v1))
% 6.70/2.22 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2))
% 6.70/2.22 | (55) findmin_pqp_res(all_0_7_7) = all_0_1_1
% 6.70/2.22 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 6.70/2.22 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3))
% 6.70/2.22 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (triple(v0, v1, v2) = v4) | ~ contains_cpq(v4, v3) | contains_slb(v1, v3))
% 6.70/2.22 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v5, v4) = v6) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v7, v2) = v6 & insert_slb(v0, v4) = v7))
% 6.70/2.22 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ~ ok(v2))
% 6.70/2.22 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3))
% 6.70/2.22 | (62) ! [v0] : ! [v1] : ~ pair_in_list(create_slb, v0, v1)
% 6.70/2.22 | (63) ! [v0] : ! [v1] : ( ~ strictly_less_than(v0, v1) | ~ less_than(v1, v0))
% 6.70/2.22 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 6.70/2.22 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ pair_in_list(v0, v2, v4) | pair_in_list(v6, v2, v4))
% 6.70/2.22 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 6.70/2.22 | (67) ~ pair_in_list(all_0_0_0, all_0_4_4, all_0_1_1)
% 6.70/2.22 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | contains_slb(v5, v2))
% 6.70/2.22 | (69) findmin_cpq_res(all_0_3_3) = all_0_2_2
% 6.70/2.23 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 6.70/2.23 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | contains_slb(v4, v1))
% 6.70/2.23 | (72) ! [v0] : ! [v1] : ( ~ less_than(v0, v1) | strictly_less_than(v0, v1) | less_than(v1, v0))
% 6.70/2.23 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ contains_slb(v0, v2) | ? [v7] : (remove_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6))
% 6.70/2.23 | (74) triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_3_3
% 6.70/2.23 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4))
% 6.70/2.23 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ less_than(v2, v3) | ? [v7] : (update_slb(v0, v2) = v7 & insert_slb(v7, v4) = v6))
% 6.70/2.23 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 6.70/2.23 | (78) ! [v0] : ( ~ pair_in_list(all_0_0_0, all_0_4_4, v0) | ~ less_than(all_0_1_1, v0))
% 6.70/2.23 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, bad) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & lookup_slb(v1, v4) = v5 & (v8 = v6 | ~ contains_slb(v1, v4) | ~ strictly_less_than(v4, v5))))
% 7.22/2.23 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ strictly_less_than(v3, v2) | ? [v7] : ? [v8] : (update_slb(v0, v2) = v7 & pair(v1, v2) = v8 & insert_slb(v7, v8) = v6))
% 7.22/2.23 | (81) ! [v0] : ~ contains_slb(create_slb, v0)
% 7.22/2.23 |
% 7.22/2.23 | Instantiating formula (44) with all_0_3_3, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 7.22/2.23 | (82) all_0_6_6 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_7_7) = v0 & triple(all_0_7_7, v3, all_0_5_5) = v4 & findmin_cpq_eff(all_0_3_3) = v2 & update_slb(all_0_6_6, v0) = v3 & lookup_slb(all_0_6_6, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_6_6, v0) | ~ less_than(v1, v0)))
% 7.22/2.23 |
% 7.22/2.23 | Instantiating formula (79) with all_0_3_3, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 7.22/2.23 | (83) all_0_6_6 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_7_7) = v0 & triple(all_0_7_7, v3, bad) = v4 & findmin_cpq_eff(all_0_3_3) = v2 & update_slb(all_0_6_6, v0) = v3 & lookup_slb(all_0_6_6, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_6_6, v0) | ~ strictly_less_than(v0, v1)))
% 7.22/2.23 |
% 7.22/2.23 | Instantiating formula (17) with all_0_3_3, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 7.22/2.23 | (84) all_0_6_6 = create_slb | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (findmin_pqp_res(all_0_7_7) = v0 & triple(all_0_7_7, v2, bad) = v3 & findmin_cpq_eff(all_0_3_3) = v1 & update_slb(all_0_6_6, v0) = v2 & (v3 = v1 | contains_slb(all_0_6_6, v0)))
% 7.22/2.23 |
% 7.22/2.23 | Instantiating formula (75) with all_0_3_3, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms triple(all_0_7_7, all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 7.22/2.24 | (85) all_0_6_6 = create_slb | ? [v0] : (findmin_cpq_res(all_0_3_3) = v0 & findmin_pqp_res(all_0_7_7) = v0)
% 7.22/2.24 |
% 7.22/2.24 +-Applying beta-rule and splitting (82), into two cases.
% 7.22/2.24 |-Branch one:
% 7.22/2.24 | (86) all_0_6_6 = create_slb
% 7.22/2.24 |
% 7.22/2.24 | From (86) and (22) follows:
% 7.22/2.24 | (87) contains_slb(create_slb, all_0_4_4)
% 7.22/2.24 |
% 7.22/2.24 | Instantiating formula (81) with all_0_4_4 and discharging atoms contains_slb(create_slb, all_0_4_4), yields:
% 7.22/2.24 | (88) $false
% 7.22/2.24 |
% 7.22/2.24 |-The branch is then unsatisfiable
% 7.22/2.24 |-Branch two:
% 7.22/2.24 | (89) ~ (all_0_6_6 = create_slb)
% 7.22/2.24 | (90) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_7_7) = v0 & triple(all_0_7_7, v3, all_0_5_5) = v4 & findmin_cpq_eff(all_0_3_3) = v2 & update_slb(all_0_6_6, v0) = v3 & lookup_slb(all_0_6_6, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_6_6, v0) | ~ less_than(v1, v0)))
% 7.22/2.24 |
% 7.22/2.24 | Instantiating (90) with all_43_0_13, all_43_1_14, all_43_2_15, all_43_3_16, all_43_4_17 yields:
% 7.22/2.24 | (91) findmin_pqp_res(all_0_7_7) = all_43_4_17 & triple(all_0_7_7, all_43_1_14, all_0_5_5) = all_43_0_13 & findmin_cpq_eff(all_0_3_3) = all_43_2_15 & update_slb(all_0_6_6, all_43_4_17) = all_43_1_14 & lookup_slb(all_0_6_6, all_43_4_17) = all_43_3_16 & (all_43_0_13 = all_43_2_15 | ~ contains_slb(all_0_6_6, all_43_4_17) | ~ less_than(all_43_3_16, all_43_4_17))
% 7.22/2.24 |
% 7.22/2.24 | Applying alpha-rule on (91) yields:
% 7.22/2.24 | (92) findmin_pqp_res(all_0_7_7) = all_43_4_17
% 7.22/2.24 | (93) update_slb(all_0_6_6, all_43_4_17) = all_43_1_14
% 7.22/2.24 | (94) all_43_0_13 = all_43_2_15 | ~ contains_slb(all_0_6_6, all_43_4_17) | ~ less_than(all_43_3_16, all_43_4_17)
% 7.22/2.24 | (95) lookup_slb(all_0_6_6, all_43_4_17) = all_43_3_16
% 7.22/2.24 | (96) findmin_cpq_eff(all_0_3_3) = all_43_2_15
% 7.22/2.24 | (97) triple(all_0_7_7, all_43_1_14, all_0_5_5) = all_43_0_13
% 7.22/2.24 |
% 7.22/2.24 +-Applying beta-rule and splitting (85), into two cases.
% 7.22/2.24 |-Branch one:
% 7.22/2.24 | (86) all_0_6_6 = create_slb
% 7.22/2.24 |
% 7.22/2.24 | Equations (86) can reduce 89 to:
% 7.22/2.24 | (99) $false
% 7.22/2.24 |
% 7.22/2.24 |-The branch is then unsatisfiable
% 7.22/2.24 |-Branch two:
% 7.22/2.24 | (89) ~ (all_0_6_6 = create_slb)
% 7.22/2.24 | (101) ? [v0] : (findmin_cpq_res(all_0_3_3) = v0 & findmin_pqp_res(all_0_7_7) = v0)
% 7.22/2.24 |
% 7.22/2.24 | Instantiating (101) with all_49_0_18 yields:
% 7.22/2.24 | (102) findmin_cpq_res(all_0_3_3) = all_49_0_18 & findmin_pqp_res(all_0_7_7) = all_49_0_18
% 7.22/2.24 |
% 7.22/2.24 | Applying alpha-rule on (102) yields:
% 7.22/2.24 | (103) findmin_cpq_res(all_0_3_3) = all_49_0_18
% 7.22/2.24 | (104) findmin_pqp_res(all_0_7_7) = all_49_0_18
% 7.22/2.24 |
% 7.22/2.24 +-Applying beta-rule and splitting (83), into two cases.
% 7.22/2.24 |-Branch one:
% 7.22/2.24 | (86) all_0_6_6 = create_slb
% 7.22/2.24 |
% 7.22/2.24 | Equations (86) can reduce 89 to:
% 7.22/2.24 | (99) $false
% 7.22/2.24 |
% 7.22/2.24 |-The branch is then unsatisfiable
% 7.22/2.24 |-Branch two:
% 7.22/2.24 | (89) ~ (all_0_6_6 = create_slb)
% 7.22/2.24 | (108) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (findmin_pqp_res(all_0_7_7) = v0 & triple(all_0_7_7, v3, bad) = v4 & findmin_cpq_eff(all_0_3_3) = v2 & update_slb(all_0_6_6, v0) = v3 & lookup_slb(all_0_6_6, v0) = v1 & (v4 = v2 | ~ contains_slb(all_0_6_6, v0) | ~ strictly_less_than(v0, v1)))
% 7.22/2.24 |
% 7.22/2.24 | Instantiating (108) with all_54_0_19, all_54_1_20, all_54_2_21, all_54_3_22, all_54_4_23 yields:
% 7.22/2.24 | (109) findmin_pqp_res(all_0_7_7) = all_54_4_23 & triple(all_0_7_7, all_54_1_20, bad) = all_54_0_19 & findmin_cpq_eff(all_0_3_3) = all_54_2_21 & update_slb(all_0_6_6, all_54_4_23) = all_54_1_20 & lookup_slb(all_0_6_6, all_54_4_23) = all_54_3_22 & (all_54_0_19 = all_54_2_21 | ~ contains_slb(all_0_6_6, all_54_4_23) | ~ strictly_less_than(all_54_4_23, all_54_3_22))
% 7.22/2.24 |
% 7.22/2.24 | Applying alpha-rule on (109) yields:
% 7.22/2.24 | (110) lookup_slb(all_0_6_6, all_54_4_23) = all_54_3_22
% 7.22/2.24 | (111) update_slb(all_0_6_6, all_54_4_23) = all_54_1_20
% 7.22/2.24 | (112) all_54_0_19 = all_54_2_21 | ~ contains_slb(all_0_6_6, all_54_4_23) | ~ strictly_less_than(all_54_4_23, all_54_3_22)
% 7.22/2.24 | (113) triple(all_0_7_7, all_54_1_20, bad) = all_54_0_19
% 7.22/2.24 | (114) findmin_cpq_eff(all_0_3_3) = all_54_2_21
% 7.22/2.24 | (115) findmin_pqp_res(all_0_7_7) = all_54_4_23
% 7.22/2.24 |
% 7.22/2.24 +-Applying beta-rule and splitting (84), into two cases.
% 7.22/2.24 |-Branch one:
% 7.22/2.24 | (86) all_0_6_6 = create_slb
% 7.22/2.24 |
% 7.22/2.24 | Equations (86) can reduce 89 to:
% 7.22/2.24 | (99) $false
% 7.22/2.24 |
% 7.22/2.24 |-The branch is then unsatisfiable
% 7.22/2.24 |-Branch two:
% 7.22/2.24 | (89) ~ (all_0_6_6 = create_slb)
% 7.22/2.24 | (119) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (findmin_pqp_res(all_0_7_7) = v0 & triple(all_0_7_7, v2, bad) = v3 & findmin_cpq_eff(all_0_3_3) = v1 & update_slb(all_0_6_6, v0) = v2 & (v3 = v1 | contains_slb(all_0_6_6, v0)))
% 7.22/2.24 |
% 7.22/2.24 | Instantiating (119) with all_59_0_24, all_59_1_25, all_59_2_26, all_59_3_27 yields:
% 7.22/2.24 | (120) findmin_pqp_res(all_0_7_7) = all_59_3_27 & triple(all_0_7_7, all_59_1_25, bad) = all_59_0_24 & findmin_cpq_eff(all_0_3_3) = all_59_2_26 & update_slb(all_0_6_6, all_59_3_27) = all_59_1_25 & (all_59_0_24 = all_59_2_26 | contains_slb(all_0_6_6, all_59_3_27))
% 7.22/2.24 |
% 7.22/2.24 | Applying alpha-rule on (120) yields:
% 7.22/2.24 | (121) findmin_cpq_eff(all_0_3_3) = all_59_2_26
% 7.22/2.24 | (122) all_59_0_24 = all_59_2_26 | contains_slb(all_0_6_6, all_59_3_27)
% 7.22/2.24 | (123) triple(all_0_7_7, all_59_1_25, bad) = all_59_0_24
% 7.22/2.24 | (124) update_slb(all_0_6_6, all_59_3_27) = all_59_1_25
% 7.22/2.24 | (125) findmin_pqp_res(all_0_7_7) = all_59_3_27
% 7.22/2.24 |
% 7.22/2.24 | Instantiating formula (77) with all_0_3_3, all_49_0_18, all_0_2_2 and discharging atoms findmin_cpq_res(all_0_3_3) = all_49_0_18, findmin_cpq_res(all_0_3_3) = all_0_2_2, yields:
% 7.22/2.24 | (126) all_49_0_18 = all_0_2_2
% 7.22/2.24 |
% 7.22/2.24 | Instantiating formula (25) with all_0_7_7, all_54_4_23, all_59_3_27 and discharging atoms findmin_pqp_res(all_0_7_7) = all_59_3_27, findmin_pqp_res(all_0_7_7) = all_54_4_23, yields:
% 7.22/2.24 | (127) all_59_3_27 = all_54_4_23
% 7.22/2.24 |
% 7.22/2.24 | Instantiating formula (25) with all_0_7_7, all_49_0_18, all_0_1_1 and discharging atoms findmin_pqp_res(all_0_7_7) = all_49_0_18, findmin_pqp_res(all_0_7_7) = all_0_1_1, yields:
% 7.22/2.24 | (128) all_49_0_18 = all_0_1_1
% 7.22/2.24 |
% 7.22/2.24 | Instantiating formula (25) with all_0_7_7, all_49_0_18, all_59_3_27 and discharging atoms findmin_pqp_res(all_0_7_7) = all_59_3_27, findmin_pqp_res(all_0_7_7) = all_49_0_18, yields:
% 7.22/2.24 | (129) all_59_3_27 = all_49_0_18
% 7.22/2.24 |
% 7.22/2.24 | Instantiating formula (25) with all_0_7_7, all_43_4_17, all_59_3_27 and discharging atoms findmin_pqp_res(all_0_7_7) = all_59_3_27, findmin_pqp_res(all_0_7_7) = all_43_4_17, yields:
% 7.22/2.24 | (130) all_59_3_27 = all_43_4_17
% 7.22/2.24 |
% 7.22/2.25 | Combining equations (130,127) yields a new equation:
% 7.22/2.25 | (131) all_54_4_23 = all_43_4_17
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (129,127) yields a new equation:
% 7.22/2.25 | (132) all_54_4_23 = all_49_0_18
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (132,131) yields a new equation:
% 7.22/2.25 | (133) all_49_0_18 = all_43_4_17
% 7.22/2.25 |
% 7.22/2.25 | Simplifying 133 yields:
% 7.22/2.25 | (134) all_49_0_18 = all_43_4_17
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (126,134) yields a new equation:
% 7.22/2.25 | (135) all_43_4_17 = all_0_2_2
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (128,134) yields a new equation:
% 7.22/2.25 | (136) all_43_4_17 = all_0_1_1
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (135,136) yields a new equation:
% 7.22/2.25 | (137) all_0_1_1 = all_0_2_2
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (137,136) yields a new equation:
% 7.22/2.25 | (135) all_43_4_17 = all_0_2_2
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (135,131) yields a new equation:
% 7.22/2.25 | (139) all_54_4_23 = all_0_2_2
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (139,127) yields a new equation:
% 7.22/2.25 | (140) all_59_3_27 = all_0_2_2
% 7.22/2.25 |
% 7.22/2.25 | From (140) and (124) follows:
% 7.22/2.25 | (141) update_slb(all_0_6_6, all_0_2_2) = all_59_1_25
% 7.22/2.25 |
% 7.22/2.25 | From (139) and (111) follows:
% 7.22/2.25 | (142) update_slb(all_0_6_6, all_0_2_2) = all_54_1_20
% 7.22/2.25 |
% 7.22/2.25 | From (135) and (93) follows:
% 7.22/2.25 | (143) update_slb(all_0_6_6, all_0_2_2) = all_43_1_14
% 7.22/2.25 |
% 7.22/2.25 | From (137) and (5) follows:
% 7.22/2.25 | (144) update_slb(all_0_6_6, all_0_2_2) = all_0_0_0
% 7.22/2.25 |
% 7.22/2.25 | From (137) and (67) follows:
% 7.22/2.25 | (145) ~ pair_in_list(all_0_0_0, all_0_4_4, all_0_2_2)
% 7.22/2.25 |
% 7.22/2.25 | Instantiating formula (32) with all_0_6_6, all_0_2_2, all_54_1_20, all_59_1_25 and discharging atoms update_slb(all_0_6_6, all_0_2_2) = all_59_1_25, update_slb(all_0_6_6, all_0_2_2) = all_54_1_20, yields:
% 7.22/2.25 | (146) all_59_1_25 = all_54_1_20
% 7.22/2.25 |
% 7.22/2.25 | Instantiating formula (32) with all_0_6_6, all_0_2_2, all_43_1_14, all_54_1_20 and discharging atoms update_slb(all_0_6_6, all_0_2_2) = all_54_1_20, update_slb(all_0_6_6, all_0_2_2) = all_43_1_14, yields:
% 7.22/2.25 | (147) all_54_1_20 = all_43_1_14
% 7.22/2.25 |
% 7.22/2.25 | Instantiating formula (32) with all_0_6_6, all_0_2_2, all_0_0_0, all_59_1_25 and discharging atoms update_slb(all_0_6_6, all_0_2_2) = all_59_1_25, update_slb(all_0_6_6, all_0_2_2) = all_0_0_0, yields:
% 7.22/2.25 | (148) all_59_1_25 = all_0_0_0
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (146,148) yields a new equation:
% 7.22/2.25 | (149) all_54_1_20 = all_0_0_0
% 7.22/2.25 |
% 7.22/2.25 | Simplifying 149 yields:
% 7.22/2.25 | (150) all_54_1_20 = all_0_0_0
% 7.22/2.25 |
% 7.22/2.25 | Combining equations (147,150) yields a new equation:
% 7.22/2.25 | (151) all_43_1_14 = all_0_0_0
% 7.22/2.25 |
% 7.22/2.25 | Simplifying 151 yields:
% 7.22/2.25 | (152) all_43_1_14 = all_0_0_0
% 7.22/2.25 |
% 7.22/2.25 | From (152) and (143) follows:
% 7.22/2.25 | (144) update_slb(all_0_6_6, all_0_2_2) = all_0_0_0
% 7.22/2.25 |
% 7.22/2.25 | Instantiating formula (48) with all_0_0_0, all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms update_slb(all_0_6_6, all_0_2_2) = all_0_0_0, contains_slb(all_0_6_6, all_0_4_4), strictly_less_than(all_0_4_4, all_0_2_2), ~ pair_in_list(all_0_0_0, all_0_4_4, all_0_2_2), yields:
% 7.22/2.25 | (154) ? [v0] : (pair_in_list(all_0_0_0, all_0_4_4, v0) & less_than(all_0_2_2, v0))
% 7.22/2.25 |
% 7.22/2.25 | Instantiating (154) with all_78_0_28 yields:
% 7.22/2.25 | (155) pair_in_list(all_0_0_0, all_0_4_4, all_78_0_28) & less_than(all_0_2_2, all_78_0_28)
% 7.22/2.25 |
% 7.22/2.25 | Applying alpha-rule on (155) yields:
% 7.22/2.25 | (156) pair_in_list(all_0_0_0, all_0_4_4, all_78_0_28)
% 7.22/2.25 | (157) less_than(all_0_2_2, all_78_0_28)
% 7.22/2.25 |
% 7.22/2.25 | Instantiating formula (78) with all_78_0_28 and discharging atoms pair_in_list(all_0_0_0, all_0_4_4, all_78_0_28), yields:
% 7.22/2.25 | (158) ~ less_than(all_0_1_1, all_78_0_28)
% 7.22/2.25 |
% 7.22/2.25 | From (137) and (158) follows:
% 7.22/2.25 | (159) ~ less_than(all_0_2_2, all_78_0_28)
% 7.22/2.25 |
% 7.22/2.25 | Using (157) and (159) yields:
% 7.22/2.25 | (88) $false
% 7.22/2.25 |
% 7.22/2.25 |-The branch is then unsatisfiable
% 7.22/2.25 % SZS output end Proof for theBenchmark
% 7.22/2.25
% 7.22/2.25 1652ms
%------------------------------------------------------------------------------