%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV193+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 : n009.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 22:55:17 EDT 2023 % Result : Theorem 14.82s 2.74s % Output : Proof 19.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV193+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.33 % Computer : n009.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 05:35:20 EDT 2023 % 0.14/0.34 % CPUTime : % 0.58/0.61 ________ _____ % 0.58/0.61 ___ __ \_________(_)________________________________ % 0.58/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.58/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.58/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.58/0.61 % 0.58/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.58/0.61 (2023-06-19) % 0.58/0.61 % 0.58/0.61 (c) Philipp Rümmer, 2009-2023 % 0.58/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.58/0.61 Amanda Stjerna. % 0.58/0.61 Free software under BSD-3-Clause. % 0.58/0.61 % 0.58/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.58/0.61 % 0.58/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.58/0.63 Running up to 7 provers in parallel. % 0.71/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.07/1.40 Prover 1: Preprocessing ... % 5.07/1.40 Prover 4: Preprocessing ... % 5.07/1.43 Prover 3: Preprocessing ... % 5.07/1.43 Prover 0: Preprocessing ... % 5.07/1.43 Prover 5: Preprocessing ... % 5.07/1.43 Prover 2: Preprocessing ... % 5.07/1.43 Prover 6: Preprocessing ... % 11.34/2.25 Prover 1: Warning: ignoring some quantifiers % 11.34/2.29 Prover 3: Warning: ignoring some quantifiers % 11.94/2.35 Prover 3: Constructing countermodel ... % 11.94/2.35 Prover 1: Constructing countermodel ... % 12.55/2.39 Prover 6: Proving ... % 12.55/2.44 Prover 4: Warning: ignoring some quantifiers % 13.46/2.53 Prover 5: Proving ... % 13.46/2.55 Prover 4: Constructing countermodel ... % 13.46/2.56 Prover 0: Proving ... % 14.20/2.62 Prover 2: Proving ... % 14.82/2.74 Prover 3: proved (2099ms) % 14.82/2.74 % 14.82/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.82/2.74 % 14.82/2.74 Prover 5: stopped % 14.82/2.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.82/2.74 Prover 0: stopped % 14.82/2.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.82/2.75 Prover 2: stopped % 14.82/2.77 Prover 6: stopped % 14.82/2.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.82/2.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.82/2.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.59/2.95 Prover 1: Found proof (size 30) % 16.59/2.95 Prover 1: proved (2316ms) % 16.59/2.95 Prover 4: stopped % 17.10/3.00 Prover 8: Preprocessing ... % 17.10/3.00 Prover 11: Preprocessing ... % 17.10/3.00 Prover 13: Preprocessing ... % 17.10/3.00 Prover 7: Preprocessing ... % 17.10/3.01 Prover 10: Preprocessing ... % 17.97/3.12 Prover 10: stopped % 17.97/3.13 Prover 7: stopped % 18.17/3.14 Prover 11: stopped % 18.17/3.16 Prover 13: stopped % 18.67/3.25 Prover 8: Warning: ignoring some quantifiers % 18.67/3.27 Prover 8: Constructing countermodel ... % 18.67/3.28 Prover 8: stopped % 18.67/3.28 % 18.67/3.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.67/3.28 % 19.00/3.29 % SZS output start Proof for theBenchmark % 19.00/3.30 Assumptions after simplification: % 19.00/3.30 --------------------------------- % 19.00/3.30 % 19.00/3.30 (finite_domain_0) % 19.00/3.34 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.00/3.34 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.00/3.34 % 19.00/3.34 (quaternion_ds1_inuse_0004) % 19.00/3.35 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) & % 19.00/3.35 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & % 19.00/3.35 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) % 19.00/3.35 & ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, % 19.00/3.35 n0) = use & a_select3(u_defuse, n0, n0) = use & % 19.00/3.35 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4) % 19.00/3.35 = use & a_select2(xinit_noise_defuse, n3) = use & % 19.00/3.35 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1) % 19.00/3.35 = use & a_select2(xinit_noise_defuse, n0) = use & % 19.00/3.35 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) = % 19.00/3.35 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 19.00/3.35 n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 19.00/3.35 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use & % 19.00/3.35 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use & % 19.00/3.35 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use & % 19.00/3.35 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use & % 19.00/3.35 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use & % 19.00/3.35 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 19.00/3.35 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 & % 19.00/3.35 leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & ! [v1: $i] % 19.00/3.35 : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | % 19.00/3.35 ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 19.00/3.35 (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & % 19.00/3.35 $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & ! [v1: $i] : ! % 19.00/3.35 [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ % 19.00/3.35 $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : (a_select3(u_defuse, % 19.00/3.35 v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 % 19.00/3.35 = 0) | ~ (v3 = 0) | v5 = use))) & ? [v1: $i] : ? [v2: $i] : ? % 19.00/3.35 [v3: $i] : ( ~ (v3 = use) & a_select3(z_defuse, v1, v2) = v3 & leq(v2, v0) = % 19.00/3.35 0 & leq(v1, n2) = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) % 19.00/3.35 & $i(v1) & ( ~ (v2 = pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) % 19.00/3.35 & ( ~ (v2 = pv5) | ~ (v1 = n0)))) % 19.00/3.35 % 19.00/3.35 (function-axioms) % 19.00/3.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.00/3.36 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.00/3.36 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.00/3.36 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.00/3.36 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.00/3.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.00/3.36 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.00/3.36 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.00/3.36 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.00/3.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.00/3.36 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.00/3.36 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 19.00/3.36 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.00/3.36 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 19.00/3.36 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 19.00/3.36 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.00/3.36 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 19.00/3.36 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.00/3.36 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 19.00/3.36 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 19.00/3.36 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.00/3.36 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 19.00/3.36 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.00/3.36 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 19.00/3.36 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.00/3.36 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 19.00/3.36 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.00/3.36 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.00/3.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.00/3.36 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.00/3.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.00/3.36 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.00/3.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.00/3.36 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.00/3.36 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 19.00/3.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 19.00/3.36 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.00/3.36 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.00/3.36 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 19.00/3.36 % 19.00/3.36 Further assumptions not needed in the proof: % 19.00/3.36 -------------------------------------------- % 19.00/3.36 const_array1_select, const_array2_select, defuse, finite_domain_1, % 19.00/3.36 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 19.00/3.36 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, % 19.00/3.36 gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, % 19.00/3.36 gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, % 19.00/3.36 gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, % 19.00/3.36 gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, % 19.00/3.36 leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, lt_gt, % 19.00/3.36 matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 19.00/3.36 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.00/3.36 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 19.00/3.36 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 19.00/3.36 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 19.00/3.36 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 19.00/3.36 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2, % 19.00/3.36 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float, % 19.00/3.36 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 19.00/3.36 uniform_int_rand_ranges_lo % 19.00/3.36 % 19.00/3.36 Those formulas are unsatisfiable: % 19.00/3.36 --------------------------------- % 19.00/3.36 % 19.00/3.36 Begin of proof % 19.00/3.36 | % 19.00/3.36 | ALPHA: (finite_domain_0) implies: % 19.00/3.36 | (1) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.00/3.36 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.00/3.36 | % 19.00/3.36 | ALPHA: (quaternion_ds1_inuse_0004) implies: % 19.00/3.36 | (2) $i(pv5) % 19.33/3.37 | (3) ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, % 19.33/3.37 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use & % 19.33/3.37 | a_select2(xinit_noise_defuse, n5) = use & % 19.33/3.37 | a_select2(xinit_noise_defuse, n4) = use & % 19.33/3.37 | a_select2(xinit_noise_defuse, n3) = use & % 19.33/3.37 | a_select2(xinit_noise_defuse, n2) = use & % 19.33/3.37 | a_select2(xinit_noise_defuse, n1) = use & % 19.33/3.37 | a_select2(xinit_noise_defuse, n0) = use & % 19.33/3.37 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 19.33/3.37 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 19.33/3.37 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 19.33/3.37 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 19.33/3.37 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use % 19.33/3.37 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = % 19.33/3.37 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) % 19.33/3.37 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, % 19.33/3.37 | n1) = use & a_select2(sigma_defuse, n0) = use & % 19.33/3.37 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 19.33/3.37 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 % 19.33/3.37 | & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & ! % 19.33/3.37 | [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) % 19.33/3.37 | | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] % 19.33/3.37 | : (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, % 19.33/3.37 | v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & % 19.33/3.37 | ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = % 19.33/3.37 | 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? % 19.33/3.37 | [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & % 19.33/3.37 | leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = % 19.33/3.37 | use))) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = % 19.33/3.37 | use) & a_select3(z_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & % 19.33/3.37 | leq(v1, n2) = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & % 19.33/3.37 | $i(v2) & $i(v1) & ( ~ (v2 = pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | % 19.33/3.37 | ~ (v1 = n1)) & ( ~ (v2 = pv5) | ~ (v1 = n0)))) % 19.33/3.37 | % 19.33/3.37 | ALPHA: (function-axioms) implies: % 19.33/3.37 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.33/3.37 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 19.33/3.37 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.33/3.37 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 19.33/3.37 | = v0)) % 19.33/3.37 | % 19.33/3.37 | DELTA: instantiating (3) with fresh symbol all_76_0 gives: % 19.33/3.38 | (6) a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use & % 19.33/3.38 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = % 19.33/3.38 | use & a_select2(xinit_noise_defuse, n4) = use & % 19.33/3.38 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse, % 19.33/3.38 | n2) = use & a_select2(xinit_noise_defuse, n1) = use & % 19.33/3.38 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse, % 19.33/3.38 | n5) = use & a_select2(xinit_mean_defuse, n4) = use & % 19.33/3.38 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 19.33/3.38 | n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 19.33/3.38 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = % 19.33/3.38 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = % 19.33/3.38 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = % 19.33/3.38 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = % 19.33/3.38 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = % 19.33/3.38 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use % 19.33/3.38 | & a_select2(rho_defuse, n0) = use & pred(pv5) = all_76_0 & leq(pv5, % 19.33/3.38 | n998) = 0 & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & % 19.33/3.38 | $i(all_76_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) % 19.33/3.38 | | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 19.33/3.38 | [v3: any] : ? [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, % 19.33/3.38 | v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 19.33/3.38 | | v4 = use))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, % 19.33/3.38 | all_76_0) = 0) | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | % 19.33/3.38 | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (a_select3(u_defuse, v0, % 19.33/3.38 | v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 % 19.33/3.38 | = 0) | ~ (v2 = 0) | v4 = use))) & ? [v0: $i] : ? [v1: $i] : % 19.33/3.38 | ? [v2: $i] : ( ~ (v2 = use) & a_select3(z_defuse, v0, v1) = v2 & % 19.33/3.38 | leq(v1, all_76_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, % 19.33/3.38 | v0) = 0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) % 19.33/3.38 | & ( ~ (v1 = pv5) | ~ (v0 = n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0))) % 19.33/3.38 | % 19.33/3.38 | ALPHA: (6) implies: % 19.39/3.38 | (7) leq(n0, pv5) = 0 % 19.39/3.38 | (8) leq(pv5, n0) = 0 % 19.39/3.38 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0, % 19.39/3.38 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 19.39/3.38 | ? [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & % 19.39/3.38 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = % 19.39/3.38 | use))) % 19.39/3.38 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = use) & % 19.39/3.38 | a_select3(z_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 & leq(v0, % 19.39/3.38 | n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & % 19.39/3.38 | $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 = % 19.39/3.38 | n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0))) % 19.39/3.38 | % 19.39/3.38 | DELTA: instantiating (10) with fresh symbols all_79_0, all_79_1, all_79_2 % 19.39/3.38 | gives: % 19.39/3.39 | (11) ~ (all_79_0 = use) & a_select3(z_defuse, all_79_2, all_79_1) = % 19.39/3.39 | all_79_0 & leq(all_79_1, all_76_0) = 0 & leq(all_79_2, n2) = 0 & % 19.39/3.39 | leq(n0, all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) & % 19.39/3.39 | $i(all_79_1) & $i(all_79_2) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 = % 19.39/3.39 | n2)) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 = n1)) & ( ~ (all_79_1 % 19.39/3.39 | = pv5) | ~ (all_79_2 = n0)) % 19.39/3.39 | % 19.39/3.39 | ALPHA: (11) implies: % 19.39/3.39 | (12) ~ (all_79_0 = use) % 19.39/3.39 | (13) $i(all_79_2) % 19.39/3.39 | (14) $i(all_79_1) % 19.39/3.39 | (15) leq(n0, all_79_2) = 0 % 19.39/3.39 | (16) leq(n0, all_79_1) = 0 % 19.39/3.39 | (17) leq(all_79_2, n2) = 0 % 19.39/3.39 | (18) leq(all_79_1, all_76_0) = 0 % 19.39/3.39 | (19) a_select3(z_defuse, all_79_2, all_79_1) = all_79_0 % 19.39/3.39 | % 19.39/3.39 | GROUND_INST: instantiating (1) with pv5, simplifying with (2), (7) gives: % 19.39/3.39 | (20) pv5 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0) % 19.39/3.39 | % 19.39/3.39 | GROUND_INST: instantiating (9) with all_79_2, all_79_1, simplifying with (13), % 19.39/3.39 | (14), (17), (18) gives: % 19.39/3.39 | (21) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (a_select3(z_defuse, % 19.39/3.39 | all_79_2, all_79_1) = v2 & leq(n0, all_79_1) = v1 & leq(n0, % 19.39/3.39 | all_79_2) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = use)) % 19.39/3.39 | % 19.39/3.39 | DELTA: instantiating (21) with fresh symbols all_105_0, all_105_1, all_105_2 % 19.39/3.39 | gives: % 19.39/3.39 | (22) a_select3(z_defuse, all_79_2, all_79_1) = all_105_0 & leq(n0, % 19.39/3.39 | all_79_1) = all_105_1 & leq(n0, all_79_2) = all_105_2 & % 19.39/3.39 | $i(all_105_0) & ( ~ (all_105_1 = 0) | ~ (all_105_2 = 0) | all_105_0 = % 19.39/3.39 | use) % 19.39/3.39 | % 19.39/3.39 | ALPHA: (22) implies: % 19.39/3.39 | (23) leq(n0, all_79_2) = all_105_2 % 19.39/3.39 | (24) leq(n0, all_79_1) = all_105_1 % 19.39/3.39 | (25) a_select3(z_defuse, all_79_2, all_79_1) = all_105_0 % 19.39/3.39 | (26) ~ (all_105_1 = 0) | ~ (all_105_2 = 0) | all_105_0 = use % 19.39/3.39 | % 19.39/3.39 | BETA: splitting (20) gives: % 19.39/3.39 | % 19.39/3.39 | Case 1: % 19.39/3.39 | | % 19.39/3.39 | | % 19.39/3.39 | | GROUND_INST: instantiating (4) with 0, all_105_2, all_79_2, n0, simplifying % 19.39/3.39 | | with (15), (23) gives: % 19.39/3.39 | | (27) all_105_2 = 0 % 19.39/3.39 | | % 19.39/3.39 | | GROUND_INST: instantiating (4) with 0, all_105_1, all_79_1, n0, simplifying % 19.39/3.39 | | with (16), (24) gives: % 19.39/3.39 | | (28) all_105_1 = 0 % 19.39/3.39 | | % 19.39/3.39 | | GROUND_INST: instantiating (5) with all_79_0, all_105_0, all_79_1, all_79_2, % 19.39/3.39 | | z_defuse, simplifying with (19), (25) gives: % 19.39/3.39 | | (29) all_105_0 = all_79_0 % 19.39/3.39 | | % 19.39/3.39 | | BETA: splitting (26) gives: % 19.39/3.39 | | % 19.39/3.39 | | Case 1: % 19.39/3.39 | | | % 19.39/3.39 | | | (30) ~ (all_105_1 = 0) % 19.39/3.39 | | | % 19.39/3.39 | | | REDUCE: (28), (30) imply: % 19.39/3.39 | | | (31) $false % 19.39/3.40 | | | % 19.39/3.40 | | | CLOSE: (31) is inconsistent. % 19.39/3.40 | | | % 19.39/3.40 | | Case 2: % 19.39/3.40 | | | % 19.39/3.40 | | | (32) ~ (all_105_2 = 0) | all_105_0 = use % 19.39/3.40 | | | % 19.39/3.40 | | | BETA: splitting (32) gives: % 19.39/3.40 | | | % 19.39/3.40 | | | Case 1: % 19.39/3.40 | | | | % 19.39/3.40 | | | | (33) ~ (all_105_2 = 0) % 19.39/3.40 | | | | % 19.39/3.40 | | | | REDUCE: (27), (33) imply: % 19.39/3.40 | | | | (34) $false % 19.39/3.40 | | | | % 19.39/3.40 | | | | CLOSE: (34) is inconsistent. % 19.39/3.40 | | | | % 19.39/3.40 | | | Case 2: % 19.39/3.40 | | | | % 19.39/3.40 | | | | (35) all_105_0 = use % 19.39/3.40 | | | | % 19.39/3.40 | | | | COMBINE_EQS: (29), (35) imply: % 19.39/3.40 | | | | (36) all_79_0 = use % 19.39/3.40 | | | | % 19.39/3.40 | | | | REDUCE: (12), (36) imply: % 19.39/3.40 | | | | (37) $false % 19.39/3.40 | | | | % 19.39/3.40 | | | | CLOSE: (37) is inconsistent. % 19.39/3.40 | | | | % 19.39/3.40 | | | End of split % 19.39/3.40 | | | % 19.39/3.40 | | End of split % 19.39/3.40 | | % 19.39/3.40 | Case 2: % 19.39/3.40 | | % 19.39/3.40 | | (38) ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0) % 19.39/3.40 | | % 19.39/3.40 | | DELTA: instantiating (38) with fresh symbol all_111_0 gives: % 19.39/3.40 | | (39) ~ (all_111_0 = 0) & leq(pv5, n0) = all_111_0 % 19.39/3.40 | | % 19.39/3.40 | | ALPHA: (39) implies: % 19.39/3.40 | | (40) ~ (all_111_0 = 0) % 19.39/3.40 | | (41) leq(pv5, n0) = all_111_0 % 19.39/3.40 | | % 19.39/3.40 | | GROUND_INST: instantiating (4) with 0, all_111_0, n0, pv5, simplifying with % 19.39/3.40 | | (8), (41) gives: % 19.39/3.40 | | (42) all_111_0 = 0 % 19.39/3.40 | | % 19.39/3.40 | | REDUCE: (40), (42) imply: % 19.39/3.40 | | (43) $false % 19.39/3.40 | | % 19.39/3.40 | | CLOSE: (43) is inconsistent. % 19.39/3.40 | | % 19.39/3.40 | End of split % 19.39/3.40 | % 19.39/3.40 End of proof % 19.39/3.40 % SZS output end Proof for theBenchmark % 19.39/3.40 % 19.39/3.40 2784ms %------------------------------------------------------------------------------