%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV176+1 : TPTP v8.1.2. Bugfixed v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n028.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 : 300s % DateTime : Thu Aug 31 22:55:13 EDT 2023 % Result : Theorem 14.83s 2.74s % Output : Proof 18.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SWV176+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n028.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 07:48:40 EDT 2023 % 0.13/0.34 % CPUTime : % 0.60/0.68 ________ _____ % 0.60/0.68 ___ __ \_________(_)________________________________ % 0.60/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.60/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.60/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.60/0.68 % 0.60/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.60/0.68 (2023-06-19) % 0.60/0.68 % 0.60/0.68 (c) Philipp Rümmer, 2009-2023 % 0.60/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.60/0.68 Amanda Stjerna. % 0.60/0.68 Free software under BSD-3-Clause. % 0.60/0.68 % 0.60/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.60/0.68 % 0.60/0.68 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.60/0.70 Running up to 7 provers in parallel. % 0.60/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.60/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.60/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.82/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.82/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.82/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.82/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.69/1.37 Prover 1: Preprocessing ... % 4.69/1.38 Prover 4: Preprocessing ... % 4.69/1.42 Prover 5: Preprocessing ... % 4.69/1.42 Prover 0: Preprocessing ... % 4.69/1.42 Prover 3: Preprocessing ... % 4.69/1.42 Prover 2: Preprocessing ... % 4.69/1.42 Prover 6: Preprocessing ... % 10.98/2.27 Prover 1: Warning: ignoring some quantifiers % 11.47/2.31 Prover 3: Warning: ignoring some quantifiers % 11.47/2.35 Prover 1: Constructing countermodel ... % 11.47/2.35 Prover 3: Constructing countermodel ... % 12.37/2.42 Prover 6: Proving ... % 13.10/2.50 Prover 4: Warning: ignoring some quantifiers % 13.67/2.59 Prover 2: Proving ... % 13.67/2.60 Prover 4: Constructing countermodel ... % 13.67/2.61 Prover 5: Proving ... % 13.67/2.66 Prover 0: Proving ... % 14.83/2.74 Prover 3: proved (2032ms) % 14.83/2.74 % 14.83/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.83/2.74 % 14.83/2.75 Prover 5: stopped % 14.83/2.75 Prover 2: stopped % 14.83/2.76 Prover 6: stopped % 14.83/2.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.83/2.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.83/2.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.83/2.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.83/2.76 Prover 0: stopped % 14.83/2.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.98/2.88 Prover 7: Preprocessing ... % 15.98/2.89 Prover 8: Preprocessing ... % 15.98/2.90 Prover 10: Preprocessing ... % 15.98/2.94 Prover 13: Preprocessing ... % 15.98/2.97 Prover 11: Preprocessing ... % 16.72/2.98 Prover 1: Found proof (size 20) % 16.72/2.99 Prover 1: proved (2284ms) % 16.72/2.99 Prover 4: stopped % 16.72/2.99 Prover 10: stopped % 16.91/3.00 Prover 7: stopped % 16.91/3.03 Prover 13: stopped % 16.91/3.04 Prover 11: stopped % 17.41/3.13 Prover 8: Warning: ignoring some quantifiers % 17.41/3.15 Prover 8: Constructing countermodel ... % 17.76/3.17 Prover 8: stopped % 17.76/3.17 % 17.76/3.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.76/3.17 % 17.84/3.17 % SZS output start Proof for theBenchmark % 17.84/3.18 Assumptions after simplification: % 17.84/3.18 --------------------------------- % 17.84/3.18 % 17.84/3.18 (cl5_nebula_init_0056) % 18.02/3.22 $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(center_init) & % 18.02/3.22 $i(sigma_init) & $i(mu_init) & $i(rho_init) & $i(init) & $i(q_init) & % 18.02/3.22 $i(loopcounter) & $i(n135299) & $i(pv44) & $i(pv40) & $i(n4) & $i(n1) & $i(n0) % 18.02/3.22 & ? [v0: $i] : (pred(pv40) = v0 & leq(pv44, n135299) = 0 & leq(pv40, n4) = 0 % 18.02/3.22 & leq(n0, pv44) = 0 & leq(n0, pv40) = 0 & gt(loopcounter, n1) = 0 & $i(v0) & % 18.02/3.22 ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select3(center_init, v1, n0) % 18.02/3.22 = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & % 18.02/3.22 leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: % 18.02/3.22 $i] : (v2 = init | ~ (a_select2(sigmaold_init, v1) = v2) | ~ $i(v1) | ? % 18.02/3.22 [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 % 18.02/3.22 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 18.02/3.22 (a_select2(rhoold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 18.02/3.22 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 18.02/3.22 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 18.02/3.22 (a_select2(muold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] % 18.02/3.22 : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & % 18.02/3.22 ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select2(rho_init, v1) = v2) | % 18.02/3.22 ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = % 18.02/3.22 v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) % 18.02/3.22 | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : (a_select2(sigma_init, v1) = v3 % 18.02/3.22 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = init))) & ! [v1: $i] % 18.02/3.22 : ( ~ (leq(v1, v0) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : % 18.02/3.22 (a_select2(mu_init, v1) = v3 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | % 18.02/3.22 v3 = init))) & ! [v1: $i] : ( ~ (leq(v1, n135299) = 0) | ~ $i(v1) | % 18.02/3.22 ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] % 18.02/3.22 : (v3 = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4: % 18.02/3.22 any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = % 18.02/3.22 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 18.02/3.22 & a_select2(muold_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = 0 & % 18.02/3.22 $i(v2) & $i(v1))) % 18.02/3.22 % 18.02/3.22 (function-axioms) % 18.02/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.02/3.23 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 18.02/3.23 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.02/3.23 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 18.02/3.23 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.02/3.23 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 18.02/3.23 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.02/3.23 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 18.02/3.23 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.02/3.23 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 18.02/3.23 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.02/3.23 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 18.02/3.23 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 18.02/3.23 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 18.02/3.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 18.02/3.23 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.02/3.23 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 18.02/3.23 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 18.02/3.23 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 18.02/3.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 18.02/3.23 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 18.02/3.23 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 18.02/3.23 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 18.02/3.23 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 18.02/3.23 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.02/3.23 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 18.02/3.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 18.02/3.23 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 18.02/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.02/3.23 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 18.02/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.02/3.23 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 18.02/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.02/3.23 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 18.02/3.23 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 18.02/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 18.02/3.23 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.02/3.23 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.02/3.23 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 18.02/3.23 % 18.02/3.23 Further assumptions not needed in the proof: % 18.02/3.23 -------------------------------------------- % 18.02/3.23 const_array1_select, const_array2_select, defuse, finite_domain_0, % 18.02/3.23 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 18.02/3.23 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, % 18.02/3.23 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, % 18.02/3.23 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, % 18.02/3.23 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, % 18.02/3.23 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 18.02/3.23 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, % 18.02/3.23 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 18.02/3.23 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 18.02/3.23 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 18.02/3.23 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 18.02/3.23 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 18.02/3.23 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 18.02/3.23 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 18.02/3.23 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 18.02/3.23 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 18.02/3.23 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 18.02/3.23 % 18.02/3.23 Those formulas are unsatisfiable: % 18.02/3.23 --------------------------------- % 18.02/3.23 % 18.02/3.23 Begin of proof % 18.02/3.23 | % 18.02/3.23 | ALPHA: (cl5_nebula_init_0056) implies: % 18.02/3.24 | (1) ? [v0: $i] : (pred(pv40) = v0 & leq(pv44, n135299) = 0 & leq(pv40, n4) % 18.02/3.24 | = 0 & leq(n0, pv44) = 0 & leq(n0, pv40) = 0 & gt(loopcounter, n1) = 0 % 18.02/3.24 | & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 18.02/3.24 | (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | ? [v3: any] : % 18.02/3.24 | ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 18.02/3.24 | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 18.02/3.24 | (a_select2(sigmaold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 18.02/3.24 | [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 18.02/3.24 | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 18.02/3.24 | (a_select2(rhoold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 18.02/3.24 | [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 18.02/3.24 | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 18.02/3.24 | (a_select2(muold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 18.02/3.24 | [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 18.02/3.24 | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 18.02/3.24 | (a_select2(rho_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 18.02/3.24 | any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ % 18.02/3.24 | (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) | ~ $i(v1) | % 18.02/3.24 | ? [v2: any] : ? [v3: $i] : (a_select2(sigma_init, v1) = v3 & % 18.02/3.24 | leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = init))) & ! [v1: % 18.02/3.24 | $i] : ( ~ (leq(v1, v0) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: % 18.02/3.24 | $i] : (a_select2(mu_init, v1) = v3 & leq(n0, v1) = v2 & $i(v3) & % 18.02/3.24 | ( ~ (v2 = 0) | v3 = init))) & ! [v1: $i] : ( ~ (leq(v1, n135299) % 18.02/3.24 | = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = % 18.02/3.24 | v2) | ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 18.02/3.24 | (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 18.02/3.24 | [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | % 18.02/3.24 | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 18.02/3.24 | & a_select2(muold_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = % 18.02/3.24 | 0 & $i(v2) & $i(v1))) % 18.02/3.24 | % 18.02/3.24 | ALPHA: (function-axioms) implies: % 18.16/3.24 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.16/3.24 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 18.16/3.24 | % 18.16/3.24 | DELTA: instantiating (1) with fresh symbol all_76_0 gives: % 18.16/3.24 | (3) pred(pv40) = all_76_0 & leq(pv44, n135299) = 0 & leq(pv40, n4) = 0 & % 18.16/3.24 | leq(n0, pv44) = 0 & leq(n0, pv40) = 0 & gt(loopcounter, n1) = 0 & % 18.16/3.24 | $i(all_76_0) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 18.16/3.24 | (a_select3(center_init, v0, n0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 18.16/3.24 | [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 18.16/3.24 | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 18.16/3.24 | (a_select2(sigmaold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 18.16/3.24 | [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 18.16/3.24 | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 18.16/3.24 | (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 18.16/3.24 | [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 18.16/3.24 | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 18.16/3.24 | (a_select2(muold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 18.16/3.24 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 18.16/3.24 | = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 18.16/3.24 | (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 18.16/3.24 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 18.16/3.24 | = 0)))) & ! [v0: $i] : ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0) % 18.16/3.24 | | ? [v1: any] : ? [v2: $i] : (a_select2(sigma_init, v0) = v2 & % 18.16/3.24 | leq(n0, v0) = v1 & $i(v2) & ( ~ (v1 = 0) | v2 = init))) & ! [v0: % 18.16/3.24 | $i] : ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 18.16/3.24 | [v2: $i] : (a_select2(mu_init, v0) = v2 & leq(n0, v0) = v1 & $i(v2) & % 18.16/3.24 | ( ~ (v1 = 0) | v2 = init))) & ! [v0: $i] : ( ~ (leq(v0, n135299) = % 18.16/3.24 | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | % 18.16/3.24 | ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select3(q_init, v0, v1) % 18.16/3.24 | = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = % 18.16/3.24 | v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ? [v0: % 18.16/3.24 | $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(muold_init, v0) = v1 % 18.16/3.24 | & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 18.16/3.24 | % 18.16/3.24 | ALPHA: (3) implies: % 18.16/3.24 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(muold_init, v0) % 18.16/3.24 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 % 18.16/3.24 | & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 18.16/3.25 | (5) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(muold_init, v0) % 18.16/3.25 | = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 18.16/3.25 | % 18.16/3.25 | DELTA: instantiating (5) with fresh symbols all_79_0, all_79_1 gives: % 18.16/3.25 | (6) ~ (all_79_0 = init) & a_select2(muold_init, all_79_1) = all_79_0 & % 18.16/3.25 | leq(all_79_1, n4) = 0 & leq(n0, all_79_1) = 0 & $i(all_79_0) & % 18.16/3.25 | $i(all_79_1) % 18.16/3.25 | % 18.16/3.25 | ALPHA: (6) implies: % 18.16/3.25 | (7) ~ (all_79_0 = init) % 18.16/3.25 | (8) $i(all_79_1) % 18.16/3.25 | (9) leq(n0, all_79_1) = 0 % 18.16/3.25 | (10) leq(all_79_1, n4) = 0 % 18.16/3.25 | (11) a_select2(muold_init, all_79_1) = all_79_0 % 18.16/3.25 | % 18.16/3.25 | GROUND_INST: instantiating (4) with all_79_1, all_79_0, simplifying with (8), % 18.16/3.25 | (11) gives: % 18.16/3.25 | (12) all_79_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = % 18.16/3.25 | v1 & leq(n0, all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 18.16/3.25 | % 18.16/3.25 | BETA: splitting (12) gives: % 18.16/3.25 | % 18.16/3.25 | Case 1: % 18.16/3.25 | | % 18.16/3.25 | | (13) all_79_0 = init % 18.16/3.25 | | % 18.16/3.25 | | REDUCE: (7), (13) imply: % 18.16/3.25 | | (14) $false % 18.16/3.25 | | % 18.16/3.25 | | CLOSE: (14) is inconsistent. % 18.16/3.25 | | % 18.16/3.25 | Case 2: % 18.16/3.25 | | % 18.16/3.25 | | (15) ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = v1 & leq(n0, % 18.16/3.25 | | all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 18.16/3.25 | | % 18.16/3.25 | | DELTA: instantiating (15) with fresh symbols all_110_0, all_110_1 gives: % 18.16/3.25 | | (16) leq(all_79_1, n4) = all_110_0 & leq(n0, all_79_1) = all_110_1 & ( ~ % 18.16/3.25 | | (all_110_0 = 0) | ~ (all_110_1 = 0)) % 18.16/3.25 | | % 18.16/3.25 | | ALPHA: (16) implies: % 18.16/3.25 | | (17) leq(n0, all_79_1) = all_110_1 % 18.16/3.25 | | (18) leq(all_79_1, n4) = all_110_0 % 18.16/3.25 | | (19) ~ (all_110_0 = 0) | ~ (all_110_1 = 0) % 18.16/3.25 | | % 18.16/3.25 | | GROUND_INST: instantiating (2) with 0, all_110_1, all_79_1, n0, simplifying % 18.16/3.25 | | with (9), (17) gives: % 18.16/3.25 | | (20) all_110_1 = 0 % 18.16/3.25 | | % 18.16/3.25 | | GROUND_INST: instantiating (2) with 0, all_110_0, n4, all_79_1, simplifying % 18.16/3.25 | | with (10), (18) gives: % 18.16/3.25 | | (21) all_110_0 = 0 % 18.16/3.25 | | % 18.16/3.25 | | BETA: splitting (19) gives: % 18.16/3.25 | | % 18.16/3.25 | | Case 1: % 18.16/3.25 | | | % 18.16/3.25 | | | (22) ~ (all_110_0 = 0) % 18.16/3.25 | | | % 18.16/3.25 | | | REDUCE: (21), (22) imply: % 18.16/3.25 | | | (23) $false % 18.16/3.25 | | | % 18.16/3.25 | | | CLOSE: (23) is inconsistent. % 18.16/3.25 | | | % 18.16/3.25 | | Case 2: % 18.16/3.25 | | | % 18.16/3.25 | | | (24) ~ (all_110_1 = 0) % 18.16/3.25 | | | % 18.16/3.25 | | | REDUCE: (20), (24) imply: % 18.16/3.25 | | | (25) $false % 18.16/3.25 | | | % 18.16/3.25 | | | CLOSE: (25) is inconsistent. % 18.16/3.25 | | | % 18.16/3.25 | | End of split % 18.16/3.25 | | % 18.16/3.25 | End of split % 18.16/3.25 | % 18.16/3.25 End of proof % 18.16/3.25 % SZS output end Proof for theBenchmark % 18.16/3.25 % 18.16/3.25 2571ms %------------------------------------------------------------------------------