%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV178+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 : n021.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 22:55:14 EDT 2023 % Result : Theorem 14.12s 2.65s % Output : Proof 17.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV178+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n021.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 07:29:59 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.91/1.41 Prover 4: Preprocessing ... % 4.91/1.41 Prover 1: Preprocessing ... % 4.91/1.45 Prover 0: Preprocessing ... % 4.91/1.45 Prover 5: Preprocessing ... % 4.91/1.45 Prover 3: Preprocessing ... % 4.91/1.45 Prover 6: Preprocessing ... % 4.91/1.45 Prover 2: Preprocessing ... % 10.76/2.21 Prover 1: Warning: ignoring some quantifiers % 10.76/2.27 Prover 3: Warning: ignoring some quantifiers % 11.54/2.30 Prover 1: Constructing countermodel ... % 11.67/2.31 Prover 6: Proving ... % 11.72/2.32 Prover 3: Constructing countermodel ... % 11.72/2.32 Prover 4: Warning: ignoring some quantifiers % 11.72/2.36 Prover 5: Proving ... % 11.72/2.41 Prover 2: Proving ... % 11.72/2.43 Prover 4: Constructing countermodel ... % 12.51/2.46 Prover 0: Proving ... % 14.12/2.64 Prover 3: proved (2010ms) % 14.12/2.65 % 14.12/2.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.12/2.65 % 14.12/2.65 Prover 0: stopped % 14.12/2.66 Prover 2: stopped % 14.12/2.66 Prover 5: stopped % 14.12/2.66 Prover 6: stopped % 14.12/2.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.12/2.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.12/2.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.12/2.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.12/2.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.12/2.78 Prover 1: Found proof (size 19) % 15.12/2.78 Prover 1: proved (2147ms) % 15.12/2.78 Prover 4: stopped % 15.73/2.88 Prover 7: Preprocessing ... % 15.73/2.89 Prover 11: Preprocessing ... % 15.73/2.90 Prover 10: Preprocessing ... % 15.73/2.92 Prover 8: Preprocessing ... % 15.73/2.92 Prover 13: Preprocessing ... % 16.43/2.96 Prover 7: stopped % 16.43/2.97 Prover 10: stopped % 16.43/2.99 Prover 11: stopped % 16.87/3.00 Prover 13: stopped % 17.17/3.08 Prover 8: Warning: ignoring some quantifiers % 17.17/3.10 Prover 8: Constructing countermodel ... % 17.27/3.12 Prover 8: stopped % 17.27/3.12 % 17.27/3.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.27/3.12 % 17.27/3.12 % SZS output start Proof for theBenchmark % 17.27/3.13 Assumptions after simplification: % 17.27/3.13 --------------------------------- % 17.27/3.13 % 17.27/3.13 (cl5_nebula_init_0066) % 17.64/3.17 $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(center_init) & % 17.64/3.17 $i(sigma_init) & $i(mu_init) & $i(rho_init) & $i(init) & $i(q_init) & % 17.64/3.17 $i(n135299) & $i(loopcounter) & $i(pv40) & $i(n4) & $i(n1) & $i(n0) & ? [v0: % 17.64/3.17 $i] : (pred(pv40) = v0 & leq(pv40, n4) = 0 & leq(n0, pv40) = 0 & % 17.64/3.17 gt(loopcounter, n1) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = init | % 17.64/3.17 ~ (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | ? [v3: any] : ? % 17.64/3.17 [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 17.64/3.17 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 17.64/3.17 (a_select2(sigmaold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 17.64/3.17 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 17.64/3.17 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 17.64/3.17 (a_select2(rhoold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 17.64/3.17 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 17.64/3.17 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 17.64/3.17 (a_select2(muold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] % 17.64/3.17 : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & % 17.64/3.17 ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select2(rho_init, v1) = v2) | % 17.64/3.17 ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = % 17.64/3.17 v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) % 17.64/3.17 | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : (a_select2(sigma_init, v1) = v3 % 17.64/3.17 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = init))) & ! [v1: $i] % 17.64/3.17 : ( ~ (leq(v1, v0) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : % 17.64/3.17 (a_select2(mu_init, v1) = v3 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | % 17.64/3.17 v3 = init))) & ! [v1: $i] : ( ~ (leq(v1, n135299) = 0) | ~ $i(v1) | % 17.64/3.17 ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] % 17.64/3.17 : (v3 = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4: % 17.64/3.17 any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = % 17.64/3.17 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 17.64/3.17 & a_select2(sigmaold_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = 0 & % 17.64/3.17 $i(v2) & $i(v1))) % 17.64/3.17 % 17.64/3.17 (function-axioms) % 17.64/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.64/3.18 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 17.64/3.18 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.64/3.18 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 17.64/3.18 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.64/3.18 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 17.64/3.18 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.64/3.18 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 17.64/3.18 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.64/3.18 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 17.64/3.18 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.64/3.18 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 17.64/3.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.64/3.18 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 17.64/3.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 17.64/3.18 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.64/3.18 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 17.64/3.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 17.64/3.18 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 17.64/3.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 17.64/3.18 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 17.64/3.18 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 17.64/3.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.64/3.18 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 17.64/3.18 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.64/3.18 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 17.64/3.18 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.64/3.18 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 17.64/3.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.64/3.18 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 17.64/3.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.64/3.18 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 17.64/3.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.64/3.18 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 17.64/3.18 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 17.64/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 17.64/3.18 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.64/3.18 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.64/3.18 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 17.64/3.18 % 17.64/3.18 Further assumptions not needed in the proof: % 17.64/3.18 -------------------------------------------- % 17.64/3.18 const_array1_select, const_array2_select, defuse, finite_domain_0, % 17.64/3.18 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 17.64/3.18 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, % 17.64/3.18 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, % 17.64/3.18 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, % 17.64/3.18 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, % 17.64/3.18 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 17.64/3.18 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, % 17.64/3.18 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 17.64/3.18 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 17.64/3.18 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 17.64/3.18 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 17.64/3.18 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 17.64/3.18 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 17.64/3.18 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 17.64/3.18 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 17.64/3.18 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 17.64/3.18 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 17.64/3.18 % 17.64/3.18 Those formulas are unsatisfiable: % 17.64/3.18 --------------------------------- % 17.64/3.18 % 17.64/3.18 Begin of proof % 17.64/3.18 | % 17.64/3.18 | ALPHA: (cl5_nebula_init_0066) implies: % 17.64/3.18 | (1) ? [v0: $i] : (pred(pv40) = v0 & leq(pv40, n4) = 0 & leq(n0, pv40) = 0 % 17.64/3.18 | & gt(loopcounter, n1) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 % 17.64/3.18 | = init | ~ (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | ? % 17.64/3.18 | [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( % 17.64/3.18 | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = % 17.64/3.18 | init | ~ (a_select2(sigmaold_init, v1) = v2) | ~ $i(v1) | ? [v3: % 17.64/3.18 | any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ % 17.64/3.18 | (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = % 17.64/3.18 | init | ~ (a_select2(rhoold_init, v1) = v2) | ~ $i(v1) | ? [v3: % 17.64/3.18 | any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ % 17.64/3.18 | (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = % 17.64/3.18 | init | ~ (a_select2(muold_init, v1) = v2) | ~ $i(v1) | ? [v3: % 17.64/3.18 | any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ % 17.64/3.18 | (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = % 17.64/3.18 | init | ~ (a_select2(rho_init, v1) = v2) | ~ $i(v1) | ? [v3: any] % 17.64/3.18 | : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = % 17.64/3.18 | 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) | % 17.64/3.18 | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : (a_select2(sigma_init, v1) % 17.64/3.18 | = v3 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = init))) & % 17.64/3.18 | ! [v1: $i] : ( ~ (leq(v1, v0) = 0) | ~ $i(v1) | ? [v2: any] : ? % 17.64/3.18 | [v3: $i] : (a_select2(mu_init, v1) = v3 & leq(n0, v1) = v2 & $i(v3) % 17.64/3.19 | & ( ~ (v2 = 0) | v3 = init))) & ! [v1: $i] : ( ~ (leq(v1, % 17.64/3.19 | n135299) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & % 17.64/3.19 | leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 17.64/3.19 | (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 17.64/3.19 | [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | % 17.64/3.19 | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 17.64/3.19 | & a_select2(sigmaold_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) % 17.64/3.19 | = 0 & $i(v2) & $i(v1))) % 17.64/3.19 | % 17.64/3.19 | ALPHA: (function-axioms) implies: % 17.64/3.19 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.64/3.19 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 17.64/3.19 | % 17.64/3.19 | DELTA: instantiating (1) with fresh symbol all_76_0 gives: % 17.82/3.19 | (3) pred(pv40) = all_76_0 & leq(pv40, n4) = 0 & leq(n0, pv40) = 0 & % 17.82/3.19 | gt(loopcounter, n1) = 0 & $i(all_76_0) & ! [v0: $i] : ! [v1: $i] : % 17.82/3.19 | (v1 = init | ~ (a_select3(center_init, v0, n0) = v1) | ~ $i(v0) | ? % 17.82/3.19 | [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ % 17.82/3.19 | (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = % 17.82/3.19 | init | ~ (a_select2(sigmaold_init, v0) = v1) | ~ $i(v0) | ? [v2: % 17.82/3.19 | any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ % 17.82/3.19 | (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = % 17.82/3.19 | init | ~ (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ? [v2: % 17.82/3.19 | any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ % 17.82/3.19 | (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = % 17.82/3.19 | init | ~ (a_select2(muold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] % 17.82/3.19 | : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) % 17.82/3.19 | | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 17.82/3.19 | (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 17.82/3.19 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 17.82/3.19 | = 0)))) & ! [v0: $i] : ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0) % 17.82/3.19 | | ? [v1: any] : ? [v2: $i] : (a_select2(sigma_init, v0) = v2 & % 17.82/3.19 | leq(n0, v0) = v1 & $i(v2) & ( ~ (v1 = 0) | v2 = init))) & ! [v0: % 17.82/3.19 | $i] : ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 17.82/3.19 | [v2: $i] : (a_select2(mu_init, v0) = v2 & leq(n0, v0) = v1 & $i(v2) & % 17.82/3.19 | ( ~ (v1 = 0) | v2 = init))) & ! [v0: $i] : ( ~ (leq(v0, n135299) = % 17.82/3.19 | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | % 17.82/3.19 | ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select3(q_init, v0, v1) % 17.82/3.19 | = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = % 17.82/3.19 | v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ? [v0: % 17.82/3.19 | $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(sigmaold_init, v0) = % 17.82/3.19 | v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 17.82/3.19 | % 17.82/3.19 | ALPHA: (3) implies: % 17.82/3.19 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(sigmaold_init, % 17.82/3.19 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, % 17.82/3.19 | n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 17.82/3.19 | (5) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(sigmaold_init, % 17.82/3.19 | v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 17.82/3.19 | % 17.82/3.19 | DELTA: instantiating (5) with fresh symbols all_79_0, all_79_1 gives: % 17.82/3.19 | (6) ~ (all_79_0 = init) & a_select2(sigmaold_init, all_79_1) = all_79_0 & % 17.82/3.19 | leq(all_79_1, n4) = 0 & leq(n0, all_79_1) = 0 & $i(all_79_0) & % 17.82/3.19 | $i(all_79_1) % 17.82/3.19 | % 17.82/3.19 | ALPHA: (6) implies: % 17.82/3.20 | (7) ~ (all_79_0 = init) % 17.82/3.20 | (8) $i(all_79_1) % 17.82/3.20 | (9) leq(n0, all_79_1) = 0 % 17.82/3.20 | (10) leq(all_79_1, n4) = 0 % 17.82/3.20 | (11) a_select2(sigmaold_init, all_79_1) = all_79_0 % 17.82/3.20 | % 17.82/3.20 | GROUND_INST: instantiating (4) with all_79_1, all_79_0, simplifying with (8), % 17.82/3.20 | (11) gives: % 17.82/3.20 | (12) all_79_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = % 17.82/3.20 | v1 & leq(n0, all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 17.82/3.20 | % 17.82/3.20 | BETA: splitting (12) gives: % 17.82/3.20 | % 17.82/3.20 | Case 1: % 17.82/3.20 | | % 17.82/3.20 | | (13) all_79_0 = init % 17.82/3.20 | | % 17.82/3.20 | | REDUCE: (7), (13) imply: % 17.82/3.20 | | (14) $false % 17.82/3.20 | | % 17.82/3.20 | | CLOSE: (14) is inconsistent. % 17.82/3.20 | | % 17.82/3.20 | Case 2: % 17.82/3.20 | | % 17.82/3.20 | | (15) ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = v1 & leq(n0, % 17.82/3.20 | | all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 17.82/3.20 | | % 17.82/3.20 | | DELTA: instantiating (15) with fresh symbols all_107_0, all_107_1 gives: % 17.82/3.20 | | (16) leq(all_79_1, n4) = all_107_0 & leq(n0, all_79_1) = all_107_1 & ( ~ % 17.82/3.20 | | (all_107_0 = 0) | ~ (all_107_1 = 0)) % 17.82/3.20 | | % 17.82/3.20 | | ALPHA: (16) implies: % 17.82/3.20 | | (17) leq(n0, all_79_1) = all_107_1 % 17.82/3.20 | | (18) leq(all_79_1, n4) = all_107_0 % 17.82/3.20 | | (19) ~ (all_107_0 = 0) | ~ (all_107_1 = 0) % 17.82/3.20 | | % 17.82/3.20 | | GROUND_INST: instantiating (2) with 0, all_107_1, all_79_1, n0, simplifying % 17.82/3.20 | | with (9), (17) gives: % 17.82/3.20 | | (20) all_107_1 = 0 % 17.82/3.20 | | % 17.82/3.20 | | GROUND_INST: instantiating (2) with 0, all_107_0, n4, all_79_1, simplifying % 17.82/3.20 | | with (10), (18) gives: % 17.82/3.20 | | (21) all_107_0 = 0 % 17.82/3.20 | | % 17.82/3.20 | | BETA: splitting (19) gives: % 17.82/3.20 | | % 17.82/3.20 | | Case 1: % 17.82/3.20 | | | % 17.82/3.20 | | | (22) ~ (all_107_0 = 0) % 17.82/3.20 | | | % 17.82/3.20 | | | REDUCE: (21), (22) imply: % 17.82/3.20 | | | (23) $false % 17.82/3.20 | | | % 17.82/3.20 | | | CLOSE: (23) is inconsistent. % 17.82/3.20 | | | % 17.82/3.20 | | Case 2: % 17.82/3.20 | | | % 17.82/3.20 | | | (24) ~ (all_107_1 = 0) % 17.82/3.20 | | | % 17.82/3.20 | | | REDUCE: (20), (24) imply: % 17.82/3.20 | | | (25) $false % 17.82/3.20 | | | % 17.82/3.20 | | | CLOSE: (25) is inconsistent. % 17.82/3.20 | | | % 17.82/3.20 | | End of split % 17.82/3.20 | | % 17.82/3.20 | End of split % 17.82/3.20 | % 17.82/3.20 End of proof % 17.82/3.20 % SZS output end Proof for theBenchmark % 17.82/3.20 % 17.82/3.20 2590ms %------------------------------------------------------------------------------