TSTP Solution File: SWV366+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 17:51:08 EDT 2022
% Result : Theorem 22.27s 6.31s
% Output : Proof 24.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 05:29:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.50/0.58 ____ _
% 0.50/0.58 ___ / __ \_____(_)___ ________ __________
% 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.58
% 0.50/0.58 A Theorem Prover for First-Order Logic
% 0.50/0.58 (ePrincess v.1.0)
% 0.50/0.58
% 0.50/0.58 (c) Philipp Rümmer, 2009-2015
% 0.50/0.58 (c) Peter Backeman, 2014-2015
% 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.58 Bug reports to peter@backeman.se
% 0.50/0.58
% 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.58
% 0.50/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.50/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.99/1.02 Prover 0: Preprocessing ...
% 3.42/1.43 Prover 0: Warning: ignoring some quantifiers
% 3.69/1.46 Prover 0: Constructing countermodel ...
% 20.59/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.05/6.00 Prover 1: Preprocessing ...
% 21.79/6.19 Prover 1: Constructing countermodel ...
% 22.27/6.31 Prover 1: proved (390ms)
% 22.27/6.31 Prover 0: stopped
% 22.27/6.31
% 22.27/6.31 No countermodel exists, formula is valid
% 22.27/6.31 % SZS status Theorem for theBenchmark
% 22.27/6.31
% 22.27/6.31 Generating proof ... found it (size 47)
% 24.25/6.72
% 24.25/6.72 % SZS output start Proof for theBenchmark
% 24.25/6.72 Assumed formulas after preprocessing and simplification:
% 24.25/6.72 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ( ~ (v14 = v12) & ~ (v1 = 0) & ~ (v0 = 0) & i(v13) = v14 & i(v11) = v12 & triple(v4, v10, v6) = v13 & triple(v3, v10, v5) = v11 & pair(v7, v8) = v9 & insert_slb(v2, v9) = v10 & isnonempty_slb(create_slb) = v1 & isnonempty_pq(create_pq) = v0 & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (pair_in_list(v21, v17, v19) = v22) | ~ (pair(v16, v18) = v20) | ~ (insert_slb(v15, v20) = v21) | ? [v23] : ( ~ (v23 = 0) & pair_in_list(v15, v17, v19) = v23)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (insert_pqp(v15, v18) = v19) | ~ (triple(v19, v21, v17) = v22) | ~ (pair(v18, bottom) = v20) | ~ (insert_slb(v16, v20) = v21) | ? [v23] : (triple(v15, v16, v17) = v23 & insert_cpq(v23, v18) = v22)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (triple(v15, v21, v17) = v22) | ~ (pair(v18, v19) = v20) | ~ (insert_slb(v16, v20) = v21) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (triple(v15, v16, v17) = v25 & check_cpq(v25) = v26 & check_cpq(v22) = v24 & less_than(v19, v18) = v23 & ( ~ (v23 = 0) | (( ~ (v26 = 0) | v24 = 0) & ( ~ (v24 = 0) | v26 = 0))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (triple(v15, v21, v17) = v22) | ~ (pair(v18, v19) = v20) | ~ (insert_slb(v16, v20) = v21) | ? [v23] : ? [v24] : ? [v25] : (i(v24) = v25 & i(v22) = v23 & triple(v15, v16, v17) = v24 & insert_pq(v25, v18) = v23)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (triple(v15, v21, v17) = v22) | ~ (pair(v18, v19) = v20) | ~ (insert_slb(v16, v20) = v21) | ? [v23] : ? [v24] : (check_cpq(v22) = v24 & strictly_less_than(v18, v19) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (contains_slb(v20, v17) = v21) | ~ (pair(v16, v18) = v19) | ~ (insert_slb(v15, v19) = v20) | ? [v22] : ( ~ (v22 = 0) & contains_slb(v15, v17) = v22)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (pair_in_list(v21, v17, v19) = 0) | ~ (pair(v16, v18) = v20) | ~ (insert_slb(v15, v20) = v21) | pair_in_list(v15, v17, v19) = 0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v17 = v16 | ~ (lookup_slb(v20, v17) = v21) | ~ (pair(v16, v18) = v19) | ~ (insert_slb(v15, v19) = v20) | ? [v22] : ? [v23] : (lookup_slb(v15, v17) = v23 & contains_slb(v15, v17) = v22 & ( ~ (v22 = 0) | v23 = v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v17 = v16 | ~ (remove_slb(v20, v17) = v21) | ~ (pair(v16, v18) = v19) | ~ (insert_slb(v15, v19) = v20) | ? [v22] : ? [v23] : ? [v24] : (remove_slb(v15, v17) = v23 & contains_slb(v15, v17) = v22 & insert_slb(v23, v19) = v24 & ( ~ (v22 = 0) | v24 = v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v17 = v16 | ~ (pair_in_list(v21, v17, v19) = 0) | ~ (pair(v16, v18) = v20) | ~ (insert_slb(v15, v20) = v21) | pair_in_list(v15, v17, v19) = 0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (remove_pqp(v15, v18) = v19) | ~ (triple(v19, v20, v17) = v21) | ~ (remove_slb(v16, v18) = v20) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (triple(v15, v16, v17) = v25 & remove_cpq(v25, v18) = v26 & lookup_slb(v16, v18) = v23 & contains_slb(v16, v18) = v22 & less_than(v23, v18) = v24 & ( ~ (v24 = 0) | ~ (v22 = 0) | v26 = v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (update_slb(v20, v17) = v21) | ~ (pair(v16, v18) = v19) | ~ (insert_slb(v15, v19) = v20) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (update_slb(v15, v17) = v23 & pair(v16, v17) = v24 & insert_slb(v23, v24) = v25 & strictly_less_than(v18, v17) = v22 & ( ~ (v22 = 0) | v25 = v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (update_slb(v20, v17) = v21) | ~ (pair(v16, v18) = v19) | ~ (insert_slb(v15, v19) = v20) | ? [v22] : ? [v23] : ? [v24] : (update_slb(v15, v17) = v23 & insert_slb(v23, v19) = v24 & less_than(v17, v18) = v22 & ( ~ (v22 = 0) | v24 = v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (lookup_slb(v19, v16) = v20) | ~ (pair(v16, v17) = v18) | ~ (insert_slb(v15, v18) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v15 | ~ (remove_slb(v19, v16) = v20) | ~ (pair(v16, v17) = v18) | ~ (insert_slb(v15, v18) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (contains_cpq(v19, v18) = v20) | ~ (triple(v15, v16, v17) = v19) | ? [v21] : ( ~ (v21 = 0) & contains_slb(v16, v18) = v21)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (pair_in_list(v19, v16, v17) = v20) | ~ (pair(v16, v17) = v18) | ~ (insert_slb(v15, v18) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (contains_slb(v19, v16) = v20) | ~ (pair(v16, v17) = v18) | ~ (insert_slb(v15, v18) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v17 = v16 | ~ (contains_slb(v20, v17) = 0) | ~ (pair(v16, v18) = v19) | ~ (insert_slb(v15, v19) = v20) | contains_slb(v15, v17) = 0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v16 = create_slb | ~ (findmin_pqp_res(v15) = v18) | ~ (triple(v15, v19, v17) = v20) | ~ (update_slb(v16, v18) = v19) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (triple(v15, v16, v17) = v24 & findmin_cpq_eff(v24) = v25 & lookup_slb(v16, v18) = v22 & contains_slb(v16, v18) = v21 & less_than(v22, v18) = v23 & ( ~ (v23 = 0) | ~ (v21 = 0) | v25 = v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (triple(v16, v2, v18) = v20) | ~ (triple(v15, v2, v17) = v19) | ? [v21] : (i(v20) = v21 & i(v19) = v21)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (triple(v15, v16, v17) = v19) | ~ (remove_cpq(v19, v18) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (remove_pqp(v15, v18) = v24 & triple(v24, v25, bad) = v26 & lookup_slb(v16, v18) = v22 & remove_slb(v16, v18) = v25 & contains_slb(v16, v18) = v21 & strictly_less_than(v18, v22) = v23 & ( ~ (v23 = 0) | ~ (v21 = 0) | v26 = v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (triple(v15, v16, v17) = v19) | ~ (remove_cpq(v19, v18) = v20) | ? [v21] : ? [v22] : (triple(v15, v16, bad) = v22 & contains_slb(v16, v18) = v21 & (v22 = v20 | v21 = 0))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (remove_cpq(v16, v17) = v18) | ~ (succ_cpq(v15, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & succ_cpq(v15, v16) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (insert_cpq(v16, v17) = v18) | ~ (succ_cpq(v15, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & succ_cpq(v15, v16) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (contains_pq(v18, v17) = v19) | ~ (insert_pq(v15, v16) = v18) | ? [v20] : ( ~ (v20 = 0) & contains_pq(v15, v17) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (remove_pq(v18, v17) = v19) | ~ (insert_pq(v15, v16) = v18) | ? [v20] : ? [v21] : ? [v22] : (remove_pq(v15, v17) = v21 & contains_pq(v15, v17) = v20 & insert_pq(v21, v16) = v22 & ( ~ (v20 = 0) | v22 = v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = v15 | ~ (triple(v19, v18, v17) = v16) | ~ (triple(v19, v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = v15 | ~ (pair_in_list(v19, v18, v17) = v16) | ~ (pair_in_list(v19, v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (contains_cpq(v19, v18) = 0) | ~ (triple(v15, v16, v17) = v19) | contains_slb(v16, v18) = 0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (pair(v16, v17) = v18) | ~ (insert_slb(v15, v18) = v19) | isnonempty_slb(v19) = 0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (insert_pq(v18, v17) = v19) | ~ (insert_pq(v15, v16) = v18) | ? [v20] : (insert_pq(v20, v16) = v19 & insert_pq(v15, v17) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (remove_pq(v17, v16) = v18) | ~ (insert_pq(v15, v16) = v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (pi_sharp_remove(v17, v16) = v18) | ~ (i(v15) = v17) | ? [v19] : ( ~ (v19 = 0) & pi_remove(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (removemin_cpq_eff(v16) = v17) | ~ (succ_cpq(v15, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & succ_cpq(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (findmin_cpq_eff(v16) = v17) | ~ (succ_cpq(v15, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & succ_cpq(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (issmallestelement_pq(v15, v16) = 0) | ~ (less_than(v16, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & contains_pq(v15, v17) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (contains_pq(v17, v16) = v18) | ~ (insert_pq(v15, v16) = v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (less_than(v15, v17) = v18) | ~ (less_than(v15, v16) = 0) | ? [v19] : ( ~ (v19 = 0) & less_than(v16, v17) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (contains_pq(v18, v17) = 0) | ~ (insert_pq(v15, v16) = v18) | contains_pq(v15, v17) = 0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = bad | ~ (triple(v15, v16, v17) = v18) | ok(v18) = 0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (pi_sharp_removemin(v18, v17) = v16) | ~ (pi_sharp_removemin(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (pi_sharp_find_min(v18, v17) = v16) | ~ (pi_sharp_find_min(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (pi_remove(v18, v17) = v16) | ~ (pi_remove(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (pi_sharp_remove(v18, v17) = v16) | ~ (pi_sharp_remove(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (remove_pqp(v18, v17) = v16) | ~ (remove_pqp(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (insert_pqp(v18, v17) = v16) | ~ (insert_pqp(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (contains_cpq(v18, v17) = v16) | ~ (contains_cpq(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (remove_cpq(v18, v17) = v16) | ~ (remove_cpq(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (insert_cpq(v18, v17) = v16) | ~ (insert_cpq(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (succ_cpq(v18, v17) = v16) | ~ (succ_cpq(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (update_slb(v18, v17) = v16) | ~ (update_slb(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (lookup_slb(v18, v17) = v16) | ~ (lookup_slb(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (remove_slb(v18, v17) = v16) | ~ (remove_slb(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (contains_slb(v18, v17) = v16) | ~ (contains_slb(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (pair(v18, v17) = v16) | ~ (pair(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (insert_slb(v18, v17) = v16) | ~ (insert_slb(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (removemin_pq_res(v18, v17) = v16) | ~ (removemin_pq_res(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (removemin_pq_eff(v18, v17) = v16) | ~ (removemin_pq_eff(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (findmin_pq_res(v18, v17) = v16) | ~ (findmin_pq_res(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (findmin_pq_eff(v18, v17) = v16) | ~ (findmin_pq_eff(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (remove_pq(v18, v17) = v16) | ~ (remove_pq(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (issmallestelement_pq(v18, v17) = v16) | ~ (issmallestelement_pq(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (contains_pq(v18, v17) = v16) | ~ (contains_pq(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (insert_pq(v18, v17) = v16) | ~ (insert_pq(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (strictly_less_than(v18, v17) = v16) | ~ (strictly_less_than(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (less_than(v18, v17) = v16) | ~ (less_than(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = create_slb | ~ (triple(v15, v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (findmin_pqp_res(v15) = v19 & triple(v15, v24, bad) = v25 & findmin_cpq_eff(v18) = v23 & update_slb(v16, v19) = v24 & lookup_slb(v16, v19) = v21 & contains_slb(v16, v19) = v20 & strictly_less_than(v19, v21) = v22 & ( ~ (v22 = 0) | ~ (v20 = 0) | v25 = v23))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = create_slb | ~ (triple(v15, v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (findmin_pqp_res(v15) = v19 & triple(v15, v22, bad) = v23 & findmin_cpq_eff(v18) = v21 & update_slb(v16, v19) = v22 & contains_slb(v16, v19) = v20 & (v23 = v21 | v20 = 0))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = create_slb | ~ (triple(v15, v16, v17) = v18) | ? [v19] : (findmin_cpq_res(v18) = v19 & findmin_pqp_res(v15) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (findmin_cpq_res(v15) = v17) | ~ (findmin_cpq_eff(v15) = v16) | ~ (remove_cpq(v16, v17) = v18) | removemin_cpq_eff(v15) = v18) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (removemin_pq_res(v15, v16) = v17) | ? [v18] : ? [v19] : (issmallestelement_pq(v15, v16) = v19 & contains_pq(v15, v16) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (findmin_pq_res(v15, v16) = v17) | ? [v18] : ? [v19] : (issmallestelement_pq(v15, v16) = v19 & contains_pq(v15, v16) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (findmin_pq_eff(v15, v16) = v17) | ? [v18] : ? [v19] : (issmallestelement_pq(v15, v16) = v19 & contains_pq(v15, v16) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (pi_sharp_removemin(v15, v16) = v17) | ? [v18] : ? [v19] : (issmallestelement_pq(v15, v16) = v19 & contains_pq(v15, v16) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (pi_sharp_find_min(v15, v16) = v17) | ? [v18] : ? [v19] : (issmallestelement_pq(v15, v16) = v19 & contains_pq(v15, v16) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (pi_sharp_remove(v15, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & contains_pq(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (issmallestelement_pq(v15, v16) = v17) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & contains_pq(v15, v18) = 0 & less_than(v16, v18) = v19)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (strictly_less_than(v15, v16) = v17) | ? [v18] : ? [v19] : (less_than(v16, v15) = v19 & less_than(v15, v16) = v18 & ( ~ (v18 = 0) | v19 = 0))) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (less_than(v15, v16) = v17) | less_than(v16, v15) = 0) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (phi(v17) = v16) | ~ (phi(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (pi_removemin(v17) = v16) | ~ (pi_removemin(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (pi_find_min(v17) = v16) | ~ (pi_find_min(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (i(v17) = v16) | ~ (i(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (removemin_cpq_res(v17) = v16) | ~ (removemin_cpq_res(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (findmin_cpq_res(v17) = v16) | ~ (findmin_cpq_res(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (findmin_pqp_res(v17) = v16) | ~ (findmin_pqp_res(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (ok(v17) = v16) | ~ (ok(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (check_cpq(v17) = v16) | ~ (check_cpq(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (removemin_cpq_eff(v17) = v16) | ~ (removemin_cpq_eff(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (findmin_cpq_eff(v17) = v16) | ~ (findmin_cpq_eff(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (isnonempty_slb(v17) = v16) | ~ (isnonempty_slb(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (isnonempty_pq(v17) = v16) | ~ (isnonempty_pq(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (phi(v15) = v16) | ~ (ok(v17) = 0) | ? [v18] : ? [v19] : (check_cpq(v17) = v19 & succ_cpq(v15, v17) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (pi_sharp_remove(v17, v16) = 0) | ~ (i(v15) = v17) | pi_remove(v15, v16) = 0) & ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v15, v16, bad) = v17) | ? [v18] : ( ~ (v18 = 0) & ok(v17) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v15, create_slb, v16) = v17) | i(v17) = create_pq) & ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v15, create_slb, v16) = v17) | findmin_cpq_res(v17) = bottom) & ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v15, create_slb, v16) = v17) | check_cpq(v17) = 0) & ! [v15] : ! [v16] : ! [v17] : ( ~ (triple(v15, create_slb, v16) = v17) | ? [v18] : (triple(v15, create_slb, bad) = v18 & findmin_cpq_eff(v17) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (removemin_pq_eff(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (remove_pq(v15, v16) = v20 & issmallestelement_pq(v15, v16) = v19 & contains_pq(v15, v16) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | v20 = v17))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (insert_pq(v15, v16) = v17) | isnonempty_pq(v17) = 0) & ! [v15] : ! [v16] : (v16 = create_slb | ~ (update_slb(create_slb, v15) = v16)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (pi_removemin(v15) = v16) | ? [v17] : (i(v15) = v17 & ! [v18] : ~ (pi_sharp_find_min(v17, v18) = 0))) & ! [v15] : ! [v16] : (v16 = 0 | ~ (pi_find_min(v15) = v16) | ? [v17] : (i(v15) = v17 & ! [v18] : ~ (pi_sharp_find_min(v17, v18) = 0))) & ! [v15] : ! [v16] : (v16 = 0 | ~ (succ_cpq(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (less_than(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (less_than(bottom, v15) = v16)) & ! [v15] : ! [v16] : ( ~ (pi_sharp_removemin(v15, v16) = 0) | (issmallestelement_pq(v15, v16) = 0 & contains_pq(v15, v16) = 0)) & ! [v15] : ! [v16] : ( ~ (pi_sharp_find_min(v15, v16) = 0) | (issmallestelement_pq(v15, v16) = 0 & contains_pq(v15, v16) = 0)) & ! [v15] : ! [v16] : ( ~ (pi_sharp_remove(v15, v16) = 0) | contains_pq(v15, v16) = 0) & ! [v15] : ! [v16] : ( ~ (removemin_cpq_res(v15) = v16) | findmin_cpq_res(v15) = v16) & ! [v15] : ! [v16] : ~ (pair_in_list(create_slb, v15, v16) = 0) & ! [v15] : ! [v16] : ( ~ (strictly_less_than(v15, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & less_than(v16, v15) = v17 & less_than(v15, v16) = 0)) & ! [v15] : ( ~ (phi(v15) = 0) | ? [v16] : (ok(v16) = 0 & check_cpq(v16) = 0 & succ_cpq(v15, v16) = 0)) & ! [v15] : ( ~ (pi_removemin(v15) = 0) | ? [v16] : ? [v17] : (pi_sharp_find_min(v16, v17) = 0 & i(v15) = v16)) & ! [v15] : ( ~ (pi_find_min(v15) = 0) | ? [v16] : ? [v17] : (pi_sharp_find_min(v16, v17) = 0 & i(v15) = v16)) & ! [v15] : ~ (contains_slb(create_slb, v15) = 0) & ! [v15] : ~ (contains_pq(create_pq, v15) = 0))
% 24.41/6.78 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14 yields:
% 24.41/6.78 | (1) ~ (all_0_0_0 = all_0_2_2) & ~ (all_0_13_13 = 0) & ~ (all_0_14_14 = 0) & i(all_0_1_1) = all_0_0_0 & i(all_0_3_3) = all_0_2_2 & triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1 & triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3 & pair(all_0_7_7, all_0_6_6) = all_0_5_5 & insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4 & isnonempty_slb(create_slb) = all_0_13_13 & isnonempty_pq(create_pq) = all_0_14_14 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & pair_in_list(v0, v2, v4) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (insert_pqp(v0, v3) = v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 & check_cpq(v7) = v9 & less_than(v4, v3) = v8 & ( ~ (v8 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : (check_cpq(v7) = v9 & strictly_less_than(v3, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & contains_slb(v0, v2) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : (lookup_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & ( ~ (v7 = 0) | v8 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (remove_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & insert_slb(v8, v4) = v9 & ( ~ (v7 = 0) | v9 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | pair_in_list(v0, v2, v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v11 & lookup_slb(v1, v3) = v8 & contains_slb(v1, v3) = v7 & less_than(v8, v3) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (update_slb(v0, v2) = v8 & pair(v1, v2) = v9 & insert_slb(v8, v9) = v10 & strictly_less_than(v3, v2) = v7 & ( ~ (v7 = 0) | v10 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (update_slb(v0, v2) = v8 & insert_slb(v8, v4) = v9 & less_than(v2, v3) = v7 & ( ~ (v7 = 0) | v9 = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = v4) | ? [v6] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | contains_slb(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v1, all_0_12_12, v3) = v5) | ~ (triple(v0, all_0_12_12, v2) = v4) | ? [v6] : (i(v5) = v6 & i(v4) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v11 & lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & strictly_less_than(v3, v7) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v11 = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 & (v7 = v5 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (remove_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (insert_cpq(v1, v2) = v3) | ~ (succ_cpq(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & succ_cpq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (contains_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & contains_pq(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (remove_pq(v0, v2) = v6 & contains_pq(v0, v2) = v5 & insert_pq(v6, v1) = v7 & ( ~ (v5 = 0) | v7 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : (insert_pq(v5, v1) = v4 & insert_pq(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (remove_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pi_sharp_remove(v2, v1) = v3) | ~ (i(v0) = v2) | ? [v4] : ( ~ (v4 = 0) & pi_remove(v0, v1) = v4)) & ! [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 | ~ (issmallestelement_pq(v0, v1) = 0) | ~ (less_than(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & contains_pq(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (contains_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2)) & ! [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 = v1 | ~ (contains_pq(v3, v2) = 0) | ~ (insert_pq(v0, v1) = v3) | contains_pq(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~ (pi_sharp_find_min(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) = v0)) & ! [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 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~ (issmallestelement_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (findmin_pqp_res(v0) = v4 & triple(v0, v9, bad) = v10 & findmin_cpq_eff(v3) = v8 & update_slb(v1, v4) = v9 & lookup_slb(v1, v4) = v6 & contains_slb(v1, v4) = v5 & strictly_less_than(v4, v6) = v7 & ( ~ (v7 = 0) | ~ (v5 = 0) | v10 = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, bad) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & contains_slb(v1, v4) = v5 & (v8 = v6 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_removemin(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_find_min(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_remove(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & contains_pq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (issmallestelement_pq(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & contains_pq(v0, v3) = 0 & less_than(v1, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ? [v4] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pi_removemin(v2) = v1) | ~ (pi_removemin(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~ (pi_find_min(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [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] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (phi(v0) = v1) | ~ (ok(v2) = 0) | ? [v3] : ? [v4] : (check_cpq(v2) = v4 & succ_cpq(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (pi_sharp_remove(v2, v1) = 0) | ~ (i(v0) = v2) | pi_remove(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq) & ! [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] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (remove_pq(v0, v1) = v5 & issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2) = 0) & ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pi_removemin(v0) = v1) | ? [v2] : (i(v0) = v2 & ! [v3] : ~ (pi_sharp_find_min(v2, v3) = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pi_find_min(v0) = v1) | ? [v2] : (i(v0) = v2 & ! [v3] : ~ (pi_sharp_find_min(v2, v3) = 0))) & ! [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] : ( ~ (pi_sharp_removemin(v0, v1) = 0) | (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (pi_sharp_find_min(v0, v1) = 0) | (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (pi_sharp_remove(v0, v1) = 0) | contains_pq(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1) & ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0] : ( ~ (phi(v0) = 0) | ? [v1] : (ok(v1) = 0 & check_cpq(v1) = 0 & succ_cpq(v0, v1) = 0)) & ! [v0] : ( ~ (pi_removemin(v0) = 0) | ? [v1] : ? [v2] : (pi_sharp_find_min(v1, v2) = 0 & i(v0) = v1)) & ! [v0] : ( ~ (pi_find_min(v0) = 0) | ? [v1] : ? [v2] : (pi_sharp_find_min(v1, v2) = 0 & i(v0) = v1)) & ! [v0] : ~ (contains_slb(create_slb, v0) = 0) & ! [v0] : ~ (contains_pq(create_pq, v0) = 0)
% 24.41/6.81 |
% 24.41/6.81 | Applying alpha-rule on (1) yields:
% 24.41/6.81 | (2) ! [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)
% 24.41/6.81 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (removemin_pq_res(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 24.41/6.81 | (4) ! [v0] : ! [v1] : ( ~ (strictly_less_than(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0))
% 24.41/6.81 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (contains_pq(v3, v2) = 0) | ~ (insert_pq(v0, v1) = v3) | contains_pq(v0, v2) = 0)
% 24.41/6.81 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | i(v2) = create_pq)
% 24.41/6.81 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (insert_pq(v0, v1) = v2) | isnonempty_pq(v2) = 0)
% 24.41/6.81 | (8) ! [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)
% 24.41/6.81 | (9) ! [v0] : ~ (contains_slb(create_slb, v0) = 0)
% 24.41/6.81 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = v0))
% 24.41/6.81 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(bottom, v0) = v1))
% 24.41/6.81 | (12) i(all_0_1_1) = all_0_0_0
% 24.41/6.81 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | contains_slb(v1, v3) = 0)
% 24.41/6.81 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 24.41/6.81 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ (removemin_pq_res(v3, v2) = v0))
% 24.41/6.81 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | less_than(v1, v0) = 0)
% 24.41/6.81 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | ? [v3] : (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3))
% 24.41/6.81 | (18) ! [v0] : ( ~ (pi_removemin(v0) = 0) | ? [v1] : ? [v2] : (pi_sharp_find_min(v1, v2) = 0 & i(v0) = v1))
% 24.41/6.81 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 24.41/6.81 | (20) ! [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))
% 24.41/6.81 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : (findmin_cpq_res(v3) = v4 & findmin_pqp_res(v0) = v4))
% 24.41/6.81 | (22) isnonempty_pq(create_pq) = all_0_14_14
% 24.41/6.81 | (23) ! [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))
% 24.41/6.81 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (contains_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & contains_pq(v0, v2) = v5))
% 24.41/6.81 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strictly_less_than(v0, v1) = v2) | ? [v3] : ? [v4] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 24.41/6.81 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 24.41/6.81 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 24.41/6.81 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 & check_cpq(v7) = v9 & less_than(v4, v3) = v8 & ( ~ (v8 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0)))))
% 24.41/6.82 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (remove_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (remove_pq(v0, v2) = v6 & contains_pq(v0, v2) = v5 & insert_pq(v6, v1) = v7 & ( ~ (v5 = 0) | v7 = v4)))
% 24.41/6.82 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_removemin(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 24.41/6.82 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | findmin_cpq_res(v2) = bottom)
% 24.41/6.82 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = bad | ~ (triple(v0, v1, v2) = v3) | ok(v3) = 0)
% 24.41/6.82 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 24.41/6.82 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (findmin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 24.41/6.82 | (35) pair(all_0_7_7, all_0_6_6) = all_0_5_5
% 24.41/6.82 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | isnonempty_slb(v4) = 0)
% 24.41/6.82 | (37) ! [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))
% 24.41/6.82 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 24.41/6.82 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (findmin_pq_res(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 24.41/6.82 | (40) ! [v0] : ! [v1] : (v1 = 0 | ~ (pi_find_min(v0) = v1) | ? [v2] : (i(v0) = v2 & ! [v3] : ~ (pi_sharp_find_min(v2, v3) = 0)))
% 24.41/6.82 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0))
% 24.41/6.82 | (42) ! [v0] : ! [v1] : ( ~ (pi_sharp_removemin(v0, v1) = 0) | (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0))
% 24.41/6.82 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v11 & lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & strictly_less_than(v3, v7) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v11 = v5)))
% 24.41/6.82 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0))
% 24.41/6.82 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ (removemin_pq_eff(v3, v2) = v0))
% 24.41/6.82 | (46) ! [v0] : ! [v1] : ( ~ (removemin_cpq_res(v0) = v1) | findmin_cpq_res(v0) = v1)
% 24.41/6.82 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = v0))
% 24.41/6.82 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v0 | ~ (remove_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 24.41/6.82 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (contains_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2))
% 24.41/6.82 | (50) triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3
% 24.41/6.82 | (51) ! [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)
% 24.41/6.82 | (52) i(all_0_3_3) = all_0_2_2
% 24.41/6.82 | (53) ! [v0] : ! [v1] : ~ (pair_in_list(create_slb, v0, v1) = 0)
% 24.41/6.82 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v1, all_0_12_12, v3) = v5) | ~ (triple(v0, all_0_12_12, v2) = v4) | ? [v6] : (i(v5) = v6 & i(v4) = v6))
% 24.41/6.82 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (insert_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ? [v5] : (insert_pq(v5, v1) = v4 & insert_pq(v0, v2) = v5))
% 24.41/6.82 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5)))
% 24.41/6.82 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0))
% 24.41/6.82 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0))
% 24.41/6.82 | (59) ! [v0] : ! [v1] : (v1 = create_slb | ~ (update_slb(create_slb, v0) = v1))
% 24.41/6.82 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 24.41/6.82 | (61) ! [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))
% 24.41/6.82 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (removemin_pq_eff(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (remove_pq(v0, v1) = v5 & issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 24.41/6.82 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0))
% 24.41/6.82 | (64) ~ (all_0_14_14 = 0)
% 24.41/6.82 | (65) triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1
% 24.41/6.82 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) = v0))
% 24.41/6.82 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ (pair_in_list(v4, v3, v2) = v0))
% 24.41/6.82 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 24.41/6.82 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~ (pi_find_min(v2) = v0))
% 24.41/6.82 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0))
% 24.41/6.82 | (71) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 24.41/6.82 | (72) ! [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))
% 24.41/6.83 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~ (issmallestelement_pq(v3, v2) = v0))
% 24.41/6.83 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 24.41/6.83 | (75) isnonempty_slb(create_slb) = all_0_13_13
% 24.41/6.83 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 24.41/6.83 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 24.41/6.83 | (78) ! [v0] : ! [v1] : ( ~ (pi_sharp_remove(v0, v1) = 0) | contains_pq(v0, v1) = 0)
% 24.41/6.83 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v11 & lookup_slb(v1, v3) = v8 & contains_slb(v1, v3) = v7 & less_than(v8, v3) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = v6)))
% 24.41/6.83 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (pi_sharp_remove(v2, v1) = 0) | ~ (i(v0) = v2) | pi_remove(v0, v1) = 0)
% 24.41/6.83 | (81) ! [v0] : ! [v1] : (v1 = 0 | ~ (succ_cpq(v0, v0) = v1))
% 24.41/6.83 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0))
% 24.41/6.83 | (83) insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4
% 24.41/6.83 | (84) ~ (all_0_0_0 = all_0_2_2)
% 24.41/6.83 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0))
% 24.41/6.83 | (86) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0))
% 24.41/6.83 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0))
% 24.41/6.83 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 24.41/6.83 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less_than(v1, v2) = v4))
% 24.41/6.83 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, v1, bad) = v2) | ? [v3] : ( ~ (v3 = 0) & ok(v2) = v3))
% 24.41/6.83 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (findmin_cpq_res(v0) = v2) | ~ (findmin_cpq_eff(v0) = v1) | ~ (remove_cpq(v1, v2) = v3) | removemin_cpq_eff(v0) = v3)
% 24.41/6.83 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 24.41/6.83 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : (lookup_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & ( ~ (v7 = 0) | v8 = v6)))
% 24.41/6.83 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~ (pi_sharp_find_min(v3, v2) = v0))
% 24.41/6.83 | (95) ! [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))
% 24.41/6.83 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (lookup_slb(v4, v1) = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4))
% 24.41/6.83 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ? [v6] : ? [v7] : (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 & (v7 = v5 | v6 = 0)))
% 24.41/6.83 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0))
% 24.41/6.83 | (99) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (findmin_pq_eff(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 24.41/6.83 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pi_sharp_remove(v2, v1) = v3) | ~ (i(v0) = v2) | ? [v4] : ( ~ (v4 = 0) & pi_remove(v0, v1) = v4))
% 24.41/6.83 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (update_slb(v0, v2) = v8 & pair(v1, v2) = v9 & insert_slb(v8, v9) = v10 & strictly_less_than(v3, v2) = v7 & ( ~ (v7 = 0) | v10 = v6)))
% 24.41/6.83 | (102) ! [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] : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = v8))
% 24.41/6.83 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (removemin_cpq_eff(v1) = v2) | ~ (succ_cpq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & succ_cpq(v0, v1) = v4))
% 24.41/6.83 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (remove_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & insert_slb(v8, v4) = v9 & ( ~ (v7 = 0) | v9 = v6)))
% 24.41/6.83 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (findmin_pqp_res(v0) = v4 & triple(v0, v9, bad) = v10 & findmin_cpq_eff(v3) = v8 & update_slb(v1, v4) = v9 & lookup_slb(v1, v4) = v6 & contains_slb(v1, v4) = v5 & strictly_less_than(v4, v6) = v7 & ( ~ (v7 = 0) | ~ (v5 = 0) | v10 = v8)))
% 24.41/6.83 | (106) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_remove(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & contains_pq(v0, v1) = v3))
% 24.41/6.83 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 24.41/6.83 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : (update_slb(v0, v2) = v8 & insert_slb(v8, v4) = v9 & less_than(v2, v3) = v7 & ( ~ (v7 = 0) | v9 = v6)))
% 24.41/6.83 | (109) ~ (all_0_13_13 = 0)
% 24.41/6.83 | (110) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pi_removemin(v2) = v1) | ~ (pi_removemin(v2) = v0))
% 24.41/6.83 | (111) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_than(v0, v0) = v1))
% 24.41/6.83 | (112) ! [v0] : ( ~ (phi(v0) = 0) | ? [v1] : (ok(v1) = 0 & check_cpq(v1) = 0 & succ_cpq(v0, v1) = 0))
% 24.41/6.83 | (113) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0))
% 24.41/6.83 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0))
% 24.41/6.83 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (findmin_pqp_res(v0) = v4 & triple(v0, v7, bad) = v8 & findmin_cpq_eff(v3) = v6 & update_slb(v1, v4) = v7 & contains_slb(v1, v4) = v5 & (v8 = v6 | v5 = 0)))
% 24.41/6.83 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (triple(v0, create_slb, v1) = v2) | check_cpq(v2) = 0)
% 24.41/6.83 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (issmallestelement_pq(v0, v1) = 0) | ~ (less_than(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & contains_pq(v0, v2) = v4))
% 24.41/6.83 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (triple(v0, v6, v2) = v7) | ~ (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ? [v8] : ? [v9] : (check_cpq(v7) = v9 & strictly_less_than(v3, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))
% 24.41/6.83 | (119) ! [v0] : ! [v1] : (v1 = 0 | ~ (pi_removemin(v0) = v1) | ? [v2] : (i(v0) = v2 & ! [v3] : ~ (pi_sharp_find_min(v2, v3) = 0)))
% 24.90/6.83 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0))
% 24.90/6.83 | (121) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (issmallestelement_pq(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & contains_pq(v0, v3) = 0 & less_than(v1, v3) = v4))
% 24.90/6.83 | (122) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pi_sharp_find_min(v0, v1) = v2) | ? [v3] : ? [v4] : (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 24.90/6.83 | (123) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0))
% 24.90/6.83 | (124) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (phi(v0) = v1) | ~ (ok(v2) = 0) | ? [v3] : ? [v4] : (check_cpq(v2) = v4 & succ_cpq(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 24.90/6.83 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ (findmin_pq_eff(v3, v2) = v0))
% 24.90/6.84 | (126) ! [v0] : ~ (contains_pq(create_pq, v0) = 0)
% 24.90/6.84 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 24.90/6.84 | (128) ! [v0] : ! [v1] : ( ~ (pi_sharp_find_min(v0, v1) = 0) | (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0))
% 24.90/6.84 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (succ_cpq(v3, v2) = v1) | ~ (succ_cpq(v3, v2) = v0))
% 24.90/6.84 | (130) ! [v0] : ( ~ (pi_find_min(v0) = 0) | ? [v1] : ? [v2] : (pi_sharp_find_min(v1, v2) = 0 & i(v0) = v1))
% 24.90/6.84 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (remove_pq(v2, v1) = v3) | ~ (insert_pq(v0, v1) = v2))
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (123) with all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms i(all_0_3_3) = all_0_2_2, yields:
% 24.90/6.84 | (132) all_0_0_0 = all_0_2_2 | ~ (i(all_0_3_3) = all_0_0_0)
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (28) with all_0_1_1, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_12_12, all_0_10_10 and discharging atoms triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1, pair(all_0_7_7, all_0_6_6) = all_0_5_5, insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4, yields:
% 24.90/6.84 | (133) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (triple(all_0_10_10, all_0_12_12, all_0_8_8) = v2 & check_cpq(v2) = v3 & check_cpq(all_0_1_1) = v1 & less_than(all_0_6_6, all_0_7_7) = v0 & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (102) with all_0_1_1, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_12_12, all_0_10_10 and discharging atoms triple(all_0_10_10, all_0_4_4, all_0_8_8) = all_0_1_1, pair(all_0_7_7, all_0_6_6) = all_0_5_5, insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4, yields:
% 24.90/6.84 | (134) ? [v0] : ? [v1] : ? [v2] : (i(v1) = v2 & i(all_0_1_1) = v0 & triple(all_0_10_10, all_0_12_12, all_0_8_8) = v1 & insert_pq(v2, all_0_7_7) = v0)
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (28) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_9_9, all_0_12_12, all_0_11_11 and discharging atoms triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3, pair(all_0_7_7, all_0_6_6) = all_0_5_5, insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4, yields:
% 24.90/6.84 | (135) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (triple(all_0_11_11, all_0_12_12, all_0_9_9) = v2 & check_cpq(v2) = v3 & check_cpq(all_0_3_3) = v1 & less_than(all_0_6_6, all_0_7_7) = v0 & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (102) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_9_9, all_0_12_12, all_0_11_11 and discharging atoms triple(all_0_11_11, all_0_4_4, all_0_9_9) = all_0_3_3, pair(all_0_7_7, all_0_6_6) = all_0_5_5, insert_slb(all_0_12_12, all_0_5_5) = all_0_4_4, yields:
% 24.90/6.84 | (136) ? [v0] : ? [v1] : ? [v2] : (i(v1) = v2 & i(all_0_3_3) = v0 & triple(all_0_11_11, all_0_12_12, all_0_9_9) = v1 & insert_pq(v2, all_0_7_7) = v0)
% 24.90/6.84 |
% 24.90/6.84 | Instantiating (136) with all_9_0_15, all_9_1_16, all_9_2_17 yields:
% 24.90/6.84 | (137) i(all_9_1_16) = all_9_0_15 & i(all_0_3_3) = all_9_2_17 & triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_9_1_16 & insert_pq(all_9_0_15, all_0_7_7) = all_9_2_17
% 24.90/6.84 |
% 24.90/6.84 | Applying alpha-rule on (137) yields:
% 24.90/6.84 | (138) i(all_9_1_16) = all_9_0_15
% 24.90/6.84 | (139) i(all_0_3_3) = all_9_2_17
% 24.90/6.84 | (140) triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_9_1_16
% 24.90/6.84 | (141) insert_pq(all_9_0_15, all_0_7_7) = all_9_2_17
% 24.90/6.84 |
% 24.90/6.84 | Instantiating (135) with all_11_0_18, all_11_1_19, all_11_2_20, all_11_3_21 yields:
% 24.90/6.84 | (142) triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_11_1_19 & check_cpq(all_11_1_19) = all_11_0_18 & check_cpq(all_0_3_3) = all_11_2_20 & less_than(all_0_6_6, all_0_7_7) = all_11_3_21 & ( ~ (all_11_3_21 = 0) | (( ~ (all_11_0_18 = 0) | all_11_2_20 = 0) & ( ~ (all_11_2_20 = 0) | all_11_0_18 = 0)))
% 24.90/6.84 |
% 24.90/6.84 | Applying alpha-rule on (142) yields:
% 24.90/6.84 | (143) check_cpq(all_11_1_19) = all_11_0_18
% 24.90/6.84 | (144) check_cpq(all_0_3_3) = all_11_2_20
% 24.90/6.84 | (145) ~ (all_11_3_21 = 0) | (( ~ (all_11_0_18 = 0) | all_11_2_20 = 0) & ( ~ (all_11_2_20 = 0) | all_11_0_18 = 0))
% 24.90/6.84 | (146) less_than(all_0_6_6, all_0_7_7) = all_11_3_21
% 24.90/6.84 | (147) triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_11_1_19
% 24.90/6.84 |
% 24.90/6.84 | Instantiating (133) with all_17_0_26, all_17_1_27, all_17_2_28, all_17_3_29 yields:
% 24.90/6.84 | (148) triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_17_1_27 & check_cpq(all_17_1_27) = all_17_0_26 & check_cpq(all_0_1_1) = all_17_2_28 & less_than(all_0_6_6, all_0_7_7) = all_17_3_29 & ( ~ (all_17_3_29 = 0) | (( ~ (all_17_0_26 = 0) | all_17_2_28 = 0) & ( ~ (all_17_2_28 = 0) | all_17_0_26 = 0)))
% 24.90/6.84 |
% 24.90/6.84 | Applying alpha-rule on (148) yields:
% 24.90/6.84 | (149) check_cpq(all_0_1_1) = all_17_2_28
% 24.90/6.84 | (150) ~ (all_17_3_29 = 0) | (( ~ (all_17_0_26 = 0) | all_17_2_28 = 0) & ( ~ (all_17_2_28 = 0) | all_17_0_26 = 0))
% 24.90/6.84 | (151) less_than(all_0_6_6, all_0_7_7) = all_17_3_29
% 24.90/6.84 | (152) triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_17_1_27
% 24.90/6.84 | (153) check_cpq(all_17_1_27) = all_17_0_26
% 24.90/6.84 |
% 24.90/6.84 | Instantiating (134) with all_19_0_30, all_19_1_31, all_19_2_32 yields:
% 24.90/6.84 | (154) i(all_19_1_31) = all_19_0_30 & i(all_0_1_1) = all_19_2_32 & triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_19_1_31 & insert_pq(all_19_0_30, all_0_7_7) = all_19_2_32
% 24.90/6.84 |
% 24.90/6.84 | Applying alpha-rule on (154) yields:
% 24.90/6.84 | (155) i(all_19_1_31) = all_19_0_30
% 24.90/6.84 | (156) i(all_0_1_1) = all_19_2_32
% 24.90/6.84 | (157) triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_19_1_31
% 24.90/6.84 | (158) insert_pq(all_19_0_30, all_0_7_7) = all_19_2_32
% 24.90/6.84 |
% 24.90/6.84 +-Applying beta-rule and splitting (132), into two cases.
% 24.90/6.84 |-Branch one:
% 24.90/6.84 | (159) ~ (i(all_0_3_3) = all_0_0_0)
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (123) with all_0_1_1, all_19_2_32, all_0_0_0 and discharging atoms i(all_0_1_1) = all_19_2_32, i(all_0_1_1) = all_0_0_0, yields:
% 24.90/6.84 | (160) all_19_2_32 = all_0_0_0
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (123) with all_0_3_3, all_9_2_17, all_0_2_2 and discharging atoms i(all_0_3_3) = all_9_2_17, i(all_0_3_3) = all_0_2_2, yields:
% 24.90/6.84 | (161) all_9_2_17 = all_0_2_2
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (68) with all_0_10_10, all_0_12_12, all_0_8_8, all_17_1_27, all_19_1_31 and discharging atoms triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_19_1_31, triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_17_1_27, yields:
% 24.90/6.84 | (162) all_19_1_31 = all_17_1_27
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (68) with all_0_11_11, all_0_12_12, all_0_9_9, all_9_1_16, all_11_1_19 and discharging atoms triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_11_1_19, triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_9_1_16, yields:
% 24.90/6.84 | (163) all_11_1_19 = all_9_1_16
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (44) with all_9_0_15, all_0_7_7, all_9_2_17, all_19_2_32 and discharging atoms insert_pq(all_9_0_15, all_0_7_7) = all_9_2_17, yields:
% 24.90/6.84 | (164) all_19_2_32 = all_9_2_17 | ~ (insert_pq(all_9_0_15, all_0_7_7) = all_19_2_32)
% 24.90/6.84 |
% 24.90/6.84 | Using (139) and (159) yields:
% 24.90/6.84 | (165) ~ (all_9_2_17 = all_0_0_0)
% 24.90/6.84 |
% 24.90/6.84 | Equations (161) can reduce 165 to:
% 24.90/6.84 | (166) ~ (all_0_0_0 = all_0_2_2)
% 24.90/6.84 |
% 24.90/6.84 | Simplifying 166 yields:
% 24.90/6.84 | (84) ~ (all_0_0_0 = all_0_2_2)
% 24.90/6.84 |
% 24.90/6.84 | From (162) and (155) follows:
% 24.90/6.84 | (168) i(all_17_1_27) = all_19_0_30
% 24.90/6.84 |
% 24.90/6.84 | From (162) and (157) follows:
% 24.90/6.84 | (152) triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_17_1_27
% 24.90/6.84 |
% 24.90/6.84 | From (163) and (147) follows:
% 24.90/6.84 | (140) triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_9_1_16
% 24.90/6.84 |
% 24.90/6.84 | From (160) and (158) follows:
% 24.90/6.84 | (171) insert_pq(all_19_0_30, all_0_7_7) = all_0_0_0
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (54) with all_9_1_16, all_17_1_27, all_0_9_9, all_0_8_8, all_0_11_11, all_0_10_10 and discharging atoms triple(all_0_10_10, all_0_12_12, all_0_8_8) = all_17_1_27, triple(all_0_11_11, all_0_12_12, all_0_9_9) = all_9_1_16, yields:
% 24.90/6.84 | (172) ? [v0] : (i(all_17_1_27) = v0 & i(all_9_1_16) = v0)
% 24.90/6.84 |
% 24.90/6.84 | Instantiating (172) with all_35_0_33 yields:
% 24.90/6.84 | (173) i(all_17_1_27) = all_35_0_33 & i(all_9_1_16) = all_35_0_33
% 24.90/6.84 |
% 24.90/6.84 | Applying alpha-rule on (173) yields:
% 24.90/6.84 | (174) i(all_17_1_27) = all_35_0_33
% 24.90/6.84 | (175) i(all_9_1_16) = all_35_0_33
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (123) with all_17_1_27, all_35_0_33, all_19_0_30 and discharging atoms i(all_17_1_27) = all_35_0_33, i(all_17_1_27) = all_19_0_30, yields:
% 24.90/6.84 | (176) all_35_0_33 = all_19_0_30
% 24.90/6.84 |
% 24.90/6.84 | Instantiating formula (123) with all_9_1_16, all_35_0_33, all_9_0_15 and discharging atoms i(all_9_1_16) = all_35_0_33, i(all_9_1_16) = all_9_0_15, yields:
% 24.90/6.84 | (177) all_35_0_33 = all_9_0_15
% 24.90/6.84 |
% 24.90/6.84 | Combining equations (176,177) yields a new equation:
% 24.90/6.84 | (178) all_19_0_30 = all_9_0_15
% 24.90/6.84 |
% 24.90/6.84 | Simplifying 178 yields:
% 24.90/6.85 | (179) all_19_0_30 = all_9_0_15
% 24.90/6.85 |
% 24.90/6.85 | From (179) and (171) follows:
% 24.90/6.85 | (180) insert_pq(all_9_0_15, all_0_7_7) = all_0_0_0
% 24.90/6.85 |
% 24.90/6.85 +-Applying beta-rule and splitting (164), into two cases.
% 24.90/6.85 |-Branch one:
% 24.90/6.85 | (181) ~ (insert_pq(all_9_0_15, all_0_7_7) = all_19_2_32)
% 24.90/6.85 |
% 24.90/6.85 | From (160) and (181) follows:
% 24.90/6.85 | (182) ~ (insert_pq(all_9_0_15, all_0_7_7) = all_0_0_0)
% 24.90/6.85 |
% 24.90/6.85 | Using (180) and (182) yields:
% 24.90/6.85 | (183) $false
% 24.90/6.85 |
% 24.90/6.85 |-The branch is then unsatisfiable
% 24.90/6.85 |-Branch two:
% 24.90/6.85 | (184) insert_pq(all_9_0_15, all_0_7_7) = all_19_2_32
% 24.90/6.85 | (185) all_19_2_32 = all_9_2_17
% 24.90/6.85 |
% 24.90/6.85 | Combining equations (185,160) yields a new equation:
% 24.90/6.85 | (186) all_9_2_17 = all_0_0_0
% 24.90/6.85 |
% 24.90/6.85 | Simplifying 186 yields:
% 24.90/6.85 | (187) all_9_2_17 = all_0_0_0
% 24.90/6.85 |
% 24.90/6.85 | Combining equations (161,187) yields a new equation:
% 24.90/6.85 | (188) all_0_0_0 = all_0_2_2
% 24.90/6.85 |
% 24.90/6.85 | Equations (188) can reduce 84 to:
% 24.90/6.85 | (189) $false
% 24.90/6.85 |
% 24.90/6.85 |-The branch is then unsatisfiable
% 24.90/6.85 |-Branch two:
% 24.90/6.85 | (190) i(all_0_3_3) = all_0_0_0
% 24.90/6.85 | (188) all_0_0_0 = all_0_2_2
% 24.90/6.85 |
% 24.90/6.85 | Equations (188) can reduce 84 to:
% 24.90/6.85 | (189) $false
% 24.90/6.85 |
% 24.90/6.85 |-The branch is then unsatisfiable
% 24.90/6.85 % SZS output end Proof for theBenchmark
% 24.90/6.85
% 24.90/6.85 6258ms
%------------------------------------------------------------------------------