%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV171+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 : n001.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 22:55:12 EDT 2023 % Result : Theorem 20.38s 3.62s % Output : Proof 25.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SWV171+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.31 % Computer : n001.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Tue Aug 29 09:51:36 EDT 2023 % 0.10/0.31 % CPUTime : % 0.16/0.59 ________ _____ % 0.16/0.59 ___ __ \_________(_)________________________________ % 0.16/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.59 % 0.16/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.59 (2023-06-19) % 0.16/0.59 % 0.16/0.59 (c) Philipp Rümmer, 2009-2023 % 0.16/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.59 Amanda Stjerna. % 0.16/0.59 Free software under BSD-3-Clause. % 0.16/0.59 % 0.16/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.59 % 0.16/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.61 Running up to 7 provers in parallel. % 0.16/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.80/1.51 Prover 1: Preprocessing ... % 4.80/1.51 Prover 4: Preprocessing ... % 4.80/1.59 Prover 5: Preprocessing ... % 4.80/1.59 Prover 2: Preprocessing ... % 4.80/1.59 Prover 6: Preprocessing ... % 4.80/1.59 Prover 3: Preprocessing ... % 4.80/1.59 Prover 0: Preprocessing ... % 14.92/2.84 Prover 1: Warning: ignoring some quantifiers % 14.92/2.88 Prover 3: Warning: ignoring some quantifiers % 15.47/2.91 Prover 1: Constructing countermodel ... % 15.47/2.92 Prover 6: Proving ... % 15.47/2.95 Prover 4: Warning: ignoring some quantifiers % 15.47/2.96 Prover 3: Constructing countermodel ... % 16.03/3.12 Prover 4: Constructing countermodel ... % 16.03/3.24 Prover 2: Proving ... % 17.29/3.27 Prover 5: Proving ... % 18.09/3.30 Prover 0: Proving ... % 20.38/3.61 Prover 3: proved (2964ms) % 20.38/3.61 % 20.38/3.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.38/3.62 % 20.58/3.62 Prover 5: stopped % 20.58/3.62 Prover 6: stopped % 20.58/3.62 Prover 2: stopped % 20.62/3.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.62/3.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.62/3.63 Prover 0: stopped % 20.62/3.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.62/3.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.62/3.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.20/3.85 Prover 1: Found proof (size 18) % 21.20/3.85 Prover 1: proved (3232ms) % 21.20/3.85 Prover 4: stopped % 21.20/3.88 Prover 10: Preprocessing ... % 21.20/3.94 Prover 8: Preprocessing ... % 22.56/4.02 Prover 7: Preprocessing ... % 22.56/4.02 Prover 13: Preprocessing ... % 22.56/4.03 Prover 10: stopped % 22.56/4.06 Prover 11: Preprocessing ... % 23.84/4.09 Prover 7: stopped % 24.25/4.15 Prover 11: stopped % 24.25/4.16 Prover 13: stopped % 24.70/4.22 Prover 8: Warning: ignoring some quantifiers % 24.70/4.25 Prover 8: Constructing countermodel ... % 25.05/4.29 Prover 8: stopped % 25.05/4.29 % 25.05/4.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 25.05/4.29 % 25.05/4.29 % SZS output start Proof for theBenchmark % 25.05/4.30 Assumptions after simplification: % 25.05/4.30 --------------------------------- % 25.05/4.30 % 25.05/4.30 (cl5_nebula_init_0031) % 25.05/4.36 $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(loopcounter) & % 25.05/4.36 $i(center_init) & $i(sigma_init) & $i(mu_init) & $i(rho_init) & $i(init) & % 25.05/4.36 $i(q_init) & $i(n135299) & $i(pv54) & $i(pv52) & $i(pv10) & $i(n4) & $i(n1) & % 25.05/4.36 $i(n0) & ? [v0: any] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(sigma_init, % 25.05/4.36 pv52) = v1 & leq(pv54, n4) = 0 & leq(pv52, n4) = 0 & leq(pv10, n135299) = % 25.05/4.36 0 & leq(n0, pv54) = 0 & leq(n0, pv52) = 0 & leq(n0, pv10) = 0 & % 25.05/4.36 gt(loopcounter, n1) = v0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : (v3 = init | % 25.05/4.36 ~ (a_select3(center_init, v2, n0) = v3) | ~ $i(v2) | ? [v4: any] : ? % 25.05/4.36 [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 25.05/4.36 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 25.05/4.36 (a_select2(sigma_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] % 25.05/4.36 : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & % 25.05/4.36 ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ (a_select2(mu_init, v2) = v3) | % 25.05/4.36 ~ $i(v2) | ? [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = % 25.05/4.36 v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = % 25.05/4.36 init | ~ (a_select2(rho_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 25.05/4.36 [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 25.05/4.36 0)))) & ! [v2: $i] : ( ~ (leq(v2, n135299) = 0) | ~ $i(v2) | ? % 25.05/4.36 [v3: int] : ( ~ (v3 = 0) & leq(n0, v2) = v3) | ! [v3: $i] : ! [v4: $i] : % 25.05/4.36 (v4 = init | ~ (a_select3(q_init, v2, v3) = v4) | ~ $i(v3) | ? [v5: % 25.05/4.36 any] : ? [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = % 25.05/4.36 0) | ~ (v5 = 0))))) & ( ~ (v0 = 0) | ! [v2: $i] : ! [v3: $i] : % 25.05/4.36 (v3 = init | ~ (a_select2(sigmaold_init, v2) = v3) | ~ $i(v2) | ? [v4: % 25.05/4.36 any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = % 25.05/4.36 0) | ~ (v4 = 0))))) & ( ~ (v0 = 0) | ! [v2: $i] : ! [v3: $i] : % 25.05/4.36 (v3 = init | ~ (a_select2(rhoold_init, v2) = v3) | ~ $i(v2) | ? [v4: % 25.05/4.36 any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = % 25.05/4.36 0) | ~ (v4 = 0))))) & ( ~ (v0 = 0) | ! [v2: $i] : ! [v3: $i] : % 25.05/4.36 (v3 = init | ~ (a_select2(muold_init, v2) = v3) | ~ $i(v2) | ? [v4: % 25.05/4.36 any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = % 25.05/4.36 0) | ~ (v4 = 0)))))) % 25.05/4.36 % 25.05/4.36 (function-axioms) % 25.50/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 25.50/4.38 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 25.50/4.38 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 25.50/4.38 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 25.50/4.38 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 25.50/4.38 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 25.50/4.38 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 25.50/4.38 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 25.50/4.38 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 25.50/4.38 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 25.50/4.38 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 25.50/4.38 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 25.50/4.38 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 25.50/4.38 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 25.50/4.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 25.50/4.38 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 25.50/4.38 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 25.50/4.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 25.50/4.38 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 25.50/4.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 25.50/4.38 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 25.50/4.38 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 25.50/4.38 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 25.50/4.38 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 25.50/4.38 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.50/4.38 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 25.50/4.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 25.50/4.38 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 25.50/4.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 25.50/4.38 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 25.50/4.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 25.50/4.38 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 25.50/4.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 25.50/4.38 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 25.50/4.38 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 25.50/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 25.50/4.38 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 25.50/4.38 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 25.50/4.38 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 25.50/4.38 % 25.50/4.38 Further assumptions not needed in the proof: % 25.50/4.38 -------------------------------------------- % 25.50/4.38 const_array1_select, const_array2_select, defuse, finite_domain_0, % 25.50/4.38 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 25.50/4.38 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, % 25.50/4.38 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, % 25.50/4.38 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, % 25.50/4.38 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, % 25.50/4.38 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 25.50/4.38 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, % 25.50/4.38 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 25.50/4.38 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 25.50/4.38 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 25.50/4.38 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 25.50/4.38 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 25.50/4.38 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 25.50/4.38 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 25.50/4.38 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 25.50/4.38 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 25.50/4.38 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 25.50/4.38 % 25.50/4.38 Those formulas are unsatisfiable: % 25.50/4.38 --------------------------------- % 25.50/4.38 % 25.50/4.38 Begin of proof % 25.50/4.38 | % 25.50/4.38 | ALPHA: (cl5_nebula_init_0031) implies: % 25.50/4.38 | (1) $i(pv52) % 25.61/4.39 | (2) ? [v0: any] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(sigma_init, % 25.61/4.39 | pv52) = v1 & leq(pv54, n4) = 0 & leq(pv52, n4) = 0 & leq(pv10, % 25.61/4.39 | n135299) = 0 & leq(n0, pv54) = 0 & leq(n0, pv52) = 0 & leq(n0, % 25.61/4.39 | pv10) = 0 & gt(loopcounter, n1) = v0 & $i(v1) & ! [v2: $i] : ! % 25.61/4.39 | [v3: $i] : (v3 = init | ~ (a_select3(center_init, v2, n0) = v3) | ~ % 25.61/4.39 | $i(v2) | ? [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, % 25.61/4.39 | v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2: $i] : ! % 25.61/4.39 | [v3: $i] : (v3 = init | ~ (a_select2(sigma_init, v2) = v3) | ~ % 25.61/4.39 | $i(v2) | ? [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, % 25.61/4.39 | v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2: $i] : ! % 25.61/4.39 | [v3: $i] : (v3 = init | ~ (a_select2(mu_init, v2) = v3) | ~ $i(v2) % 25.61/4.39 | | ? [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = % 25.61/4.39 | v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : % 25.61/4.39 | (v3 = init | ~ (a_select2(rho_init, v2) = v3) | ~ $i(v2) | ? [v4: % 25.61/4.39 | any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ % 25.61/4.39 | (v5 = 0) | ~ (v4 = 0)))) & ! [v2: $i] : ( ~ (leq(v2, n135299) % 25.61/4.39 | = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & leq(n0, v2) = % 25.61/4.39 | v3) | ! [v3: $i] : ! [v4: $i] : (v4 = init | ~ % 25.61/4.39 | (a_select3(q_init, v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? % 25.61/4.39 | [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | % 25.61/4.39 | ~ (v5 = 0))))) & ( ~ (v0 = 0) | ! [v2: $i] : ! [v3: $i] : % 25.61/4.39 | (v3 = init | ~ (a_select2(sigmaold_init, v2) = v3) | ~ $i(v2) | % 25.61/4.39 | ? [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 % 25.61/4.39 | & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ( ~ (v0 = 0) | ! [v2: $i] : % 25.61/4.39 | ! [v3: $i] : (v3 = init | ~ (a_select2(rhoold_init, v2) = v3) | % 25.61/4.39 | ~ $i(v2) | ? [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & % 25.61/4.39 | leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ( ~ (v0 = % 25.61/4.40 | 0) | ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 25.61/4.40 | (a_select2(muold_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 25.61/4.40 | [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | % 25.61/4.40 | ~ (v4 = 0)))))) % 25.61/4.40 | % 25.61/4.40 | ALPHA: (function-axioms) implies: % 25.61/4.40 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 25.61/4.40 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 25.61/4.40 | % 25.61/4.40 | DELTA: instantiating (2) with fresh symbols all_76_0, all_76_1 gives: % 25.61/4.41 | (4) ~ (all_76_0 = init) & a_select2(sigma_init, pv52) = all_76_0 & % 25.61/4.41 | leq(pv54, n4) = 0 & leq(pv52, n4) = 0 & leq(pv10, n135299) = 0 & % 25.61/4.41 | leq(n0, pv54) = 0 & leq(n0, pv52) = 0 & leq(n0, pv10) = 0 & % 25.61/4.41 | gt(loopcounter, n1) = all_76_1 & $i(all_76_0) & ! [v0: $i] : ! [v1: % 25.61/4.41 | $i] : (v1 = init | ~ (a_select3(center_init, v0, n0) = v1) | ~ % 25.61/4.41 | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, % 25.61/4.41 | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: % 25.61/4.41 | $i] : (v1 = init | ~ (a_select2(sigma_init, v0) = v1) | ~ $i(v0) | % 25.61/4.41 | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( % 25.61/4.41 | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = % 25.61/4.41 | init | ~ (a_select2(mu_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 25.61/4.41 | ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | % 25.61/4.41 | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 25.61/4.41 | (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 25.61/4.41 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 25.61/4.41 | = 0)))) & ! [v0: $i] : ( ~ (leq(v0, n135299) = 0) | ~ $i(v0) % 25.61/4.41 | | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! % 25.61/4.41 | [v2: $i] : (v2 = init | ~ (a_select3(q_init, v0, v1) = v2) | ~ % 25.61/4.41 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, % 25.61/4.41 | v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ( ~ (all_76_1 = 0) % 25.61/4.41 | | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 25.61/4.41 | (a_select2(sigmaold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 25.61/4.41 | [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | % 25.61/4.41 | ~ (v2 = 0))))) & ( ~ (all_76_1 = 0) | ! [v0: $i] : ! [v1: $i] % 25.61/4.41 | : (v1 = init | ~ (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ? % 25.61/4.41 | [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( % 25.61/4.41 | ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ (all_76_1 = 0) | ! [v0: $i] % 25.61/4.41 | : ! [v1: $i] : (v1 = init | ~ (a_select2(muold_init, v0) = v1) | ~ % 25.61/4.41 | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, % 25.61/4.41 | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 25.61/4.41 | % 25.61/4.41 | ALPHA: (4) implies: % 25.61/4.41 | (5) ~ (all_76_0 = init) % 25.61/4.41 | (6) leq(n0, pv52) = 0 % 25.61/4.41 | (7) leq(pv52, n4) = 0 % 25.61/4.41 | (8) a_select2(sigma_init, pv52) = all_76_0 % 25.61/4.41 | (9) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(sigma_init, v0) % 25.61/4.41 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 % 25.61/4.41 | & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 25.61/4.41 | % 25.61/4.41 | GROUND_INST: instantiating (9) with pv52, all_76_0, simplifying with (1), (8) % 25.61/4.41 | gives: % 25.61/4.41 | (10) all_76_0 = init | ? [v0: any] : ? [v1: any] : (leq(pv52, n4) = v1 & % 25.61/4.41 | leq(n0, pv52) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 25.61/4.41 | % 25.61/4.41 | BETA: splitting (10) gives: % 25.61/4.41 | % 25.61/4.41 | Case 1: % 25.61/4.41 | | % 25.61/4.41 | | (11) all_76_0 = init % 25.61/4.41 | | % 25.61/4.41 | | REDUCE: (5), (11) imply: % 25.61/4.41 | | (12) $false % 25.61/4.42 | | % 25.61/4.42 | | CLOSE: (12) is inconsistent. % 25.61/4.42 | | % 25.61/4.42 | Case 2: % 25.61/4.42 | | % 25.61/4.42 | | (13) ? [v0: any] : ? [v1: any] : (leq(pv52, n4) = v1 & leq(n0, pv52) = % 25.61/4.42 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 25.61/4.42 | | % 25.61/4.42 | | DELTA: instantiating (13) with fresh symbols all_105_0, all_105_1 gives: % 25.61/4.42 | | (14) leq(pv52, n4) = all_105_0 & leq(n0, pv52) = all_105_1 & ( ~ % 25.61/4.42 | | (all_105_0 = 0) | ~ (all_105_1 = 0)) % 25.61/4.42 | | % 25.61/4.42 | | ALPHA: (14) implies: % 25.61/4.42 | | (15) leq(n0, pv52) = all_105_1 % 25.61/4.42 | | (16) leq(pv52, n4) = all_105_0 % 25.75/4.42 | | (17) ~ (all_105_0 = 0) | ~ (all_105_1 = 0) % 25.75/4.42 | | % 25.75/4.42 | | GROUND_INST: instantiating (3) with 0, all_105_1, pv52, n0, simplifying with % 25.75/4.42 | | (6), (15) gives: % 25.75/4.42 | | (18) all_105_1 = 0 % 25.75/4.42 | | % 25.75/4.42 | | GROUND_INST: instantiating (3) with 0, all_105_0, n4, pv52, simplifying with % 25.75/4.42 | | (7), (16) gives: % 25.75/4.42 | | (19) all_105_0 = 0 % 25.75/4.42 | | % 25.75/4.42 | | BETA: splitting (17) gives: % 25.75/4.42 | | % 25.75/4.42 | | Case 1: % 25.75/4.42 | | | % 25.75/4.42 | | | (20) ~ (all_105_0 = 0) % 25.75/4.42 | | | % 25.75/4.42 | | | REDUCE: (19), (20) imply: % 25.75/4.42 | | | (21) $false % 25.75/4.42 | | | % 25.75/4.42 | | | CLOSE: (21) is inconsistent. % 25.75/4.42 | | | % 25.75/4.42 | | Case 2: % 25.75/4.42 | | | % 25.75/4.42 | | | (22) ~ (all_105_1 = 0) % 25.75/4.42 | | | % 25.75/4.42 | | | REDUCE: (18), (22) imply: % 25.75/4.42 | | | (23) $false % 25.75/4.42 | | | % 25.75/4.42 | | | CLOSE: (23) is inconsistent. % 25.75/4.42 | | | % 25.75/4.42 | | End of split % 25.75/4.42 | | % 25.75/4.42 | End of split % 25.75/4.42 | % 25.75/4.42 End of proof % 25.75/4.42 % SZS output end Proof for theBenchmark % 25.75/4.42 % 25.75/4.42 3831ms %------------------------------------------------------------------------------