%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV195+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 : n026.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 22:55:18 EDT 2023 % Result : Theorem 14.68s 2.95s % Output : Proof 19.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SWV195+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 06:48:05 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.17/1.47 Prover 1: Preprocessing ... % 4.17/1.48 Prover 4: Preprocessing ... % 4.17/1.52 Prover 0: Preprocessing ... % 4.69/1.52 Prover 5: Preprocessing ... % 4.69/1.52 Prover 3: Preprocessing ... % 4.69/1.52 Prover 2: Preprocessing ... % 4.69/1.52 Prover 6: Preprocessing ... % 11.70/2.39 Prover 1: Warning: ignoring some quantifiers % 11.70/2.44 Prover 3: Warning: ignoring some quantifiers % 12.60/2.49 Prover 3: Constructing countermodel ... % 12.60/2.50 Prover 1: Constructing countermodel ... % 12.60/2.50 Prover 6: Proving ... % 12.60/2.51 Prover 4: Warning: ignoring some quantifiers % 13.55/2.64 Prover 4: Constructing countermodel ... % 13.83/2.67 Prover 0: Proving ... % 13.83/2.69 Prover 5: Proving ... % 13.83/2.70 Prover 2: Proving ... % 14.68/2.95 Prover 3: proved (2288ms) % 14.68/2.95 % 14.68/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.68/2.95 % 14.68/2.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.68/2.95 Prover 2: stopped % 14.68/2.95 Prover 6: stopped % 14.68/2.96 Prover 5: stopped % 14.68/2.98 Prover 0: stopped % 15.39/2.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.39/2.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.39/2.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.39/2.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.69/3.14 Prover 8: Preprocessing ... % 16.69/3.14 Prover 7: Preprocessing ... % 16.69/3.14 Prover 10: Preprocessing ... % 16.69/3.15 Prover 11: Preprocessing ... % 17.40/3.18 Prover 13: Preprocessing ... % 17.94/3.25 Prover 1: Found proof (size 50) % 17.94/3.25 Prover 1: proved (2602ms) % 17.94/3.25 Prover 4: stopped % 17.94/3.27 Prover 10: stopped % 17.94/3.27 Prover 7: stopped % 17.94/3.30 Prover 11: stopped % 18.41/3.34 Prover 13: stopped % 18.76/3.37 Prover 8: Warning: ignoring some quantifiers % 18.76/3.39 Prover 8: Constructing countermodel ... % 18.76/3.41 Prover 8: stopped % 18.76/3.41 % 18.76/3.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.76/3.41 % 18.76/3.42 % SZS output start Proof for theBenchmark % 18.76/3.42 Assumptions after simplification: % 18.76/3.42 --------------------------------- % 18.76/3.42 % 18.76/3.42 (finite_domain_0) % 18.76/3.45 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 18.76/3.45 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 18.76/3.45 % 18.76/3.45 (finite_domain_2) % 18.76/3.45 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 18.76/3.45 (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = % 18.76/3.45 v1)) % 18.76/3.45 % 18.76/3.45 (quaternion_ds1_inuse_0006) % 18.76/3.46 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) & % 18.76/3.46 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & % 18.76/3.46 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) % 18.76/3.46 & ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, % 18.76/3.46 n0) = use & a_select3(u_defuse, n0, n0) = use & % 18.76/3.46 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4) % 18.76/3.46 = use & a_select2(xinit_noise_defuse, n3) = use & % 18.76/3.46 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1) % 18.76/3.46 = use & a_select2(xinit_noise_defuse, n0) = use & % 18.76/3.46 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) = % 18.76/3.46 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 18.76/3.46 n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 18.76/3.46 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use & % 18.76/3.46 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use & % 18.76/3.46 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use & % 18.76/3.46 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use & % 18.76/3.46 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use & % 18.76/3.46 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 18.76/3.46 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 & % 18.76/3.46 leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & ! [v1: $i] % 18.76/3.46 : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | % 18.76/3.46 ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 18.76/3.46 (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & % 18.76/3.46 $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & ! [v1: $i] : ! % 19.24/3.46 [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ % 19.24/3.46 $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : (a_select3(u_defuse, % 19.24/3.46 v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 % 19.24/3.46 = 0) | ~ (v3 = 0) | v5 = use))) & ? [v1: $i] : ? [v2: $i] : ? % 19.24/3.46 [v3: $i] : ( ~ (v3 = use) & a_select3(u_defuse, v1, v2) = v3 & leq(v2, pv5) % 19.24/3.46 = 0 & leq(v1, n2) = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & % 19.24/3.46 $i(v2) & $i(v1) & ( ~ (v2 = pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 % 19.24/3.46 = n1)) & ( ~ (v2 = pv5) | ~ (v1 = n0)))) % 19.24/3.46 % 19.24/3.46 (function-axioms) % 19.24/3.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.24/3.47 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.24/3.47 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.24/3.47 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.24/3.47 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.24/3.47 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.24/3.47 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.24/3.47 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.24/3.47 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.24/3.47 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.24/3.47 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.24/3.47 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 19.24/3.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.24/3.47 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 19.24/3.47 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 19.24/3.47 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.24/3.47 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 19.24/3.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.24/3.47 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 19.24/3.47 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 19.24/3.47 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.24/3.47 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 19.24/3.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.24/3.47 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 19.24/3.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.24/3.47 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 19.24/3.47 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.24/3.47 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.24/3.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.24/3.47 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.24/3.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.24/3.47 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.24/3.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.24/3.47 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.24/3.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 19.24/3.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 19.24/3.47 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.24/3.47 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.24/3.47 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 19.24/3.47 % 19.24/3.47 Further assumptions not needed in the proof: % 19.24/3.47 -------------------------------------------- % 19.24/3.47 const_array1_select, const_array2_select, defuse, finite_domain_1, % 19.24/3.47 finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0, % 19.24/3.47 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, % 19.24/3.47 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, % 19.24/3.47 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_998_0, gt_998_1, gt_998_2, % 19.24/3.47 gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, gt_succ, irreflexivity_gt, % 19.24/3.47 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, % 19.24/3.47 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 19.24/3.47 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 19.24/3.47 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 19.24/3.47 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 19.24/3.47 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 19.24/3.47 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 19.24/3.47 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 19.24/3.47 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 19.24/3.47 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 19.24/3.47 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 19.24/3.47 % 19.24/3.47 Those formulas are unsatisfiable: % 19.24/3.47 --------------------------------- % 19.24/3.47 % 19.24/3.47 Begin of proof % 19.24/3.47 | % 19.24/3.47 | ALPHA: (finite_domain_0) implies: % 19.24/3.47 | (1) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.24/3.47 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.24/3.47 | % 19.24/3.47 | ALPHA: (finite_domain_2) implies: % 19.24/3.47 | (2) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n2) = 0) | ~ % 19.24/3.47 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) % 19.24/3.47 | % 19.24/3.47 | ALPHA: (quaternion_ds1_inuse_0006) implies: % 19.24/3.48 | (3) $i(pv5) % 19.24/3.48 | (4) ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, % 19.24/3.48 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use & % 19.24/3.48 | a_select2(xinit_noise_defuse, n5) = use & % 19.24/3.48 | a_select2(xinit_noise_defuse, n4) = use & % 19.24/3.48 | a_select2(xinit_noise_defuse, n3) = use & % 19.24/3.48 | a_select2(xinit_noise_defuse, n2) = use & % 19.24/3.48 | a_select2(xinit_noise_defuse, n1) = use & % 19.24/3.48 | a_select2(xinit_noise_defuse, n0) = use & % 19.24/3.48 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 19.24/3.48 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 19.24/3.48 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 19.24/3.48 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 19.24/3.48 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use % 19.24/3.48 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = % 19.24/3.48 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) % 19.24/3.48 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, % 19.24/3.48 | n1) = use & a_select2(sigma_defuse, n0) = use & % 19.24/3.48 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 19.24/3.48 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 % 19.24/3.48 | & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & ! % 19.24/3.48 | [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) % 19.24/3.48 | | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] % 19.24/3.48 | : (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, % 19.24/3.48 | v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & % 19.24/3.48 | ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = % 19.24/3.48 | 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? % 19.24/3.48 | [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & % 19.24/3.48 | leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = % 19.24/3.48 | use))) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = % 19.24/3.48 | use) & a_select3(u_defuse, v1, v2) = v3 & leq(v2, pv5) = 0 & % 19.24/3.48 | leq(v1, n2) = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & % 19.24/3.48 | $i(v2) & $i(v1) & ( ~ (v2 = pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | % 19.24/3.48 | ~ (v1 = n1)) & ( ~ (v2 = pv5) | ~ (v1 = n0)))) % 19.24/3.48 | % 19.24/3.48 | ALPHA: (function-axioms) implies: % 19.24/3.48 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.24/3.48 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 19.24/3.48 | % 19.24/3.48 | DELTA: instantiating (4) with fresh symbol all_76_0 gives: % 19.24/3.49 | (6) a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use & % 19.24/3.49 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = % 19.24/3.49 | use & a_select2(xinit_noise_defuse, n4) = use & % 19.24/3.49 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse, % 19.24/3.49 | n2) = use & a_select2(xinit_noise_defuse, n1) = use & % 19.24/3.49 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse, % 19.24/3.49 | n5) = use & a_select2(xinit_mean_defuse, n4) = use & % 19.24/3.49 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 19.24/3.49 | n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 19.24/3.49 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = % 19.24/3.49 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = % 19.24/3.49 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = % 19.24/3.49 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = % 19.24/3.49 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = % 19.24/3.49 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use % 19.24/3.49 | & a_select2(rho_defuse, n0) = use & pred(pv5) = all_76_0 & leq(pv5, % 19.24/3.49 | n998) = 0 & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & % 19.24/3.49 | $i(all_76_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) % 19.24/3.49 | | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 19.24/3.49 | [v3: any] : ? [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, % 19.24/3.49 | v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 19.24/3.49 | | v4 = use))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, % 19.24/3.49 | all_76_0) = 0) | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | % 19.24/3.49 | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (a_select3(u_defuse, v0, % 19.24/3.49 | v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 % 19.24/3.49 | = 0) | ~ (v2 = 0) | v4 = use))) & ? [v0: $i] : ? [v1: $i] : % 19.24/3.49 | ? [v2: $i] : ( ~ (v2 = use) & a_select3(u_defuse, v0, v1) = v2 & % 19.24/3.49 | leq(v1, pv5) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = % 19.24/3.49 | 0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) & ( ~ % 19.24/3.49 | (v1 = pv5) | ~ (v0 = n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0))) % 19.24/3.49 | % 19.24/3.49 | ALPHA: (6) implies: % 19.24/3.49 | (7) leq(n0, pv5) = 0 % 19.24/3.49 | (8) leq(pv5, n0) = 0 % 19.24/3.49 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = use) & % 19.24/3.49 | a_select3(u_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 & leq(v0, n2) = 0 % 19.24/3.49 | & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0) & ( ~ % 19.24/3.49 | (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 = n1)) & ( ~ % 19.24/3.49 | (v1 = pv5) | ~ (v0 = n0))) % 19.24/3.49 | % 19.24/3.49 | DELTA: instantiating (9) with fresh symbols all_79_0, all_79_1, all_79_2 % 19.24/3.49 | gives: % 19.24/3.49 | (10) ~ (all_79_0 = use) & a_select3(u_defuse, all_79_2, all_79_1) = % 19.24/3.49 | all_79_0 & leq(all_79_1, pv5) = 0 & leq(all_79_2, n2) = 0 & leq(n0, % 19.24/3.49 | all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) & $i(all_79_1) % 19.24/3.49 | & $i(all_79_2) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 = n2)) & ( ~ % 19.24/3.49 | (all_79_1 = pv5) | ~ (all_79_2 = n1)) & ( ~ (all_79_1 = pv5) | ~ % 19.24/3.49 | (all_79_2 = n0)) % 19.24/3.49 | % 19.24/3.49 | ALPHA: (10) implies: % 19.24/3.49 | (11) $i(all_79_2) % 19.24/3.49 | (12) $i(all_79_1) % 19.24/3.49 | (13) leq(n0, all_79_2) = 0 % 19.24/3.49 | (14) leq(n0, all_79_1) = 0 % 19.24/3.49 | (15) leq(all_79_2, n2) = 0 % 19.24/3.49 | (16) leq(all_79_1, pv5) = 0 % 19.24/3.49 | (17) ~ (all_79_1 = pv5) | ~ (all_79_2 = n0) % 19.24/3.50 | (18) ~ (all_79_1 = pv5) | ~ (all_79_2 = n1) % 19.24/3.50 | (19) ~ (all_79_1 = pv5) | ~ (all_79_2 = n2) % 19.24/3.50 | % 19.24/3.50 | GROUND_INST: instantiating (1) with pv5, simplifying with (3), (7) gives: % 19.40/3.50 | (20) pv5 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0) % 19.40/3.50 | % 19.40/3.50 | GROUND_INST: instantiating (1) with all_79_1, simplifying with (12), (14) % 19.40/3.50 | gives: % 19.40/3.50 | (21) all_79_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0) % 19.40/3.50 | % 19.40/3.50 | GROUND_INST: instantiating (2) with all_79_2, simplifying with (11), (15) % 19.40/3.50 | gives: % 19.40/3.50 | (22) all_79_2 = n2 | all_79_2 = n1 | all_79_2 = n0 | ? [v0: int] : ( ~ (v0 % 19.40/3.50 | = 0) & leq(n0, all_79_2) = v0) % 19.40/3.50 | % 19.40/3.50 | BETA: splitting (20) gives: % 19.40/3.50 | % 19.40/3.50 | Case 1: % 19.40/3.50 | | % 19.40/3.50 | | (23) pv5 = n0 % 19.40/3.50 | | % 19.40/3.50 | | REDUCE: (16), (23) imply: % 19.40/3.50 | | (24) leq(all_79_1, n0) = 0 % 19.40/3.50 | | % 19.40/3.50 | | BETA: splitting (21) gives: % 19.40/3.50 | | % 19.40/3.50 | | Case 1: % 19.40/3.50 | | | % 19.40/3.50 | | | (25) all_79_1 = n0 % 19.40/3.50 | | | % 19.40/3.50 | | | BETA: splitting (19) gives: % 19.40/3.50 | | | % 19.40/3.50 | | | Case 1: % 19.40/3.50 | | | | % 19.40/3.50 | | | | (26) ~ (all_79_1 = pv5) % 19.40/3.50 | | | | % 19.40/3.50 | | | | REDUCE: (23), (25), (26) imply: % 19.40/3.50 | | | | (27) $false % 19.40/3.50 | | | | % 19.40/3.50 | | | | CLOSE: (27) is inconsistent. % 19.40/3.50 | | | | % 19.40/3.50 | | | Case 2: % 19.40/3.50 | | | | % 19.40/3.50 | | | | (28) all_79_1 = pv5 % 19.40/3.50 | | | | (29) ~ (all_79_2 = n2) % 19.40/3.50 | | | | % 19.40/3.50 | | | | COMBINE_EQS: (25), (28) imply: % 19.40/3.50 | | | | (30) pv5 = n0 % 19.40/3.50 | | | | % 19.40/3.50 | | | | BETA: splitting (17) gives: % 19.40/3.50 | | | | % 19.40/3.50 | | | | Case 1: % 19.40/3.50 | | | | | % 19.40/3.50 | | | | | (31) ~ (all_79_2 = n0) % 19.40/3.50 | | | | | % 19.40/3.50 | | | | | BETA: splitting (22) gives: % 19.40/3.50 | | | | | % 19.40/3.50 | | | | | Case 1: % 19.40/3.50 | | | | | | % 19.40/3.50 | | | | | | (32) all_79_2 = n0 % 19.40/3.50 | | | | | | % 19.40/3.50 | | | | | | REDUCE: (31), (32) imply: % 19.40/3.50 | | | | | | (33) $false % 19.40/3.50 | | | | | | % 19.40/3.50 | | | | | | CLOSE: (33) is inconsistent. % 19.40/3.50 | | | | | | % 19.40/3.50 | | | | | Case 2: % 19.40/3.50 | | | | | | % 19.40/3.50 | | | | | | (34) all_79_2 = n2 | all_79_2 = n1 | ? [v0: int] : ( ~ (v0 = 0) % 19.40/3.50 | | | | | | & leq(n0, all_79_2) = v0) % 19.40/3.50 | | | | | | % 19.40/3.50 | | | | | | BETA: splitting (34) gives: % 19.40/3.50 | | | | | | % 19.40/3.50 | | | | | | Case 1: % 19.40/3.50 | | | | | | | % 19.40/3.50 | | | | | | | (35) all_79_2 = n2 % 19.40/3.50 | | | | | | | % 19.40/3.50 | | | | | | | REDUCE: (29), (35) imply: % 19.40/3.50 | | | | | | | (36) $false % 19.40/3.50 | | | | | | | % 19.40/3.50 | | | | | | | CLOSE: (36) is inconsistent. % 19.40/3.50 | | | | | | | % 19.40/3.50 | | | | | | Case 2: % 19.40/3.50 | | | | | | | % 19.40/3.50 | | | | | | | (37) all_79_2 = n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0, % 19.40/3.50 | | | | | | | all_79_2) = v0) % 19.40/3.50 | | | | | | | % 19.40/3.50 | | | | | | | BETA: splitting (37) gives: % 19.40/3.50 | | | | | | | % 19.40/3.50 | | | | | | | Case 1: % 19.40/3.50 | | | | | | | | % 19.40/3.50 | | | | | | | | (38) all_79_2 = n1 % 19.40/3.50 | | | | | | | | % 19.40/3.50 | | | | | | | | BETA: splitting (18) gives: % 19.40/3.50 | | | | | | | | % 19.40/3.50 | | | | | | | | Case 1: % 19.40/3.50 | | | | | | | | | % 19.40/3.50 | | | | | | | | | (39) ~ (all_79_1 = pv5) % 19.40/3.50 | | | | | | | | | % 19.40/3.51 | | | | | | | | | REDUCE: (23), (25), (39) imply: % 19.40/3.51 | | | | | | | | | (40) $false % 19.40/3.51 | | | | | | | | | % 19.40/3.51 | | | | | | | | | CLOSE: (40) is inconsistent. % 19.40/3.51 | | | | | | | | | % 19.40/3.51 | | | | | | | | Case 2: % 19.40/3.51 | | | | | | | | | % 19.40/3.51 | | | | | | | | | (41) ~ (all_79_2 = n1) % 19.40/3.51 | | | | | | | | | % 19.40/3.51 | | | | | | | | | REDUCE: (38), (41) imply: % 19.40/3.51 | | | | | | | | | (42) $false % 19.40/3.51 | | | | | | | | | % 19.40/3.51 | | | | | | | | | CLOSE: (42) is inconsistent. % 19.40/3.51 | | | | | | | | | % 19.40/3.51 | | | | | | | | End of split % 19.40/3.51 | | | | | | | | % 19.40/3.51 | | | | | | | Case 2: % 19.40/3.51 | | | | | | | | % 19.40/3.51 | | | | | | | | (43) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_79_2) = v0) % 19.40/3.51 | | | | | | | | % 19.40/3.51 | | | | | | | | DELTA: instantiating (43) with fresh symbol all_131_0 gives: % 19.40/3.51 | | | | | | | | (44) ~ (all_131_0 = 0) & leq(n0, all_79_2) = all_131_0 % 19.40/3.51 | | | | | | | | % 19.40/3.51 | | | | | | | | ALPHA: (44) implies: % 19.40/3.51 | | | | | | | | (45) ~ (all_131_0 = 0) % 19.40/3.51 | | | | | | | | (46) leq(n0, all_79_2) = all_131_0 % 19.40/3.51 | | | | | | | | % 19.40/3.51 | | | | | | | | GROUND_INST: instantiating (5) with 0, all_131_0, all_79_2, n0, % 19.40/3.51 | | | | | | | | simplifying with (13), (46) gives: % 19.40/3.51 | | | | | | | | (47) all_131_0 = 0 % 19.40/3.51 | | | | | | | | % 19.40/3.51 | | | | | | | | REDUCE: (45), (47) imply: % 19.40/3.51 | | | | | | | | (48) $false % 19.40/3.51 | | | | | | | | % 19.40/3.51 | | | | | | | | CLOSE: (48) is inconsistent. % 19.40/3.51 | | | | | | | | % 19.40/3.51 | | | | | | | End of split % 19.40/3.51 | | | | | | | % 19.40/3.51 | | | | | | End of split % 19.40/3.51 | | | | | | % 19.40/3.51 | | | | | End of split % 19.40/3.51 | | | | | % 19.40/3.51 | | | | Case 2: % 19.40/3.51 | | | | | % 19.40/3.51 | | | | | (49) ~ (all_79_1 = pv5) % 19.40/3.51 | | | | | % 19.40/3.51 | | | | | REDUCE: (23), (25), (49) imply: % 19.40/3.51 | | | | | (50) $false % 19.40/3.51 | | | | | % 19.40/3.51 | | | | | CLOSE: (50) is inconsistent. % 19.40/3.51 | | | | | % 19.40/3.51 | | | | End of split % 19.40/3.51 | | | | % 19.40/3.51 | | | End of split % 19.40/3.51 | | | % 19.40/3.51 | | Case 2: % 19.40/3.51 | | | % 19.40/3.51 | | | (51) ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0) % 19.40/3.51 | | | % 19.40/3.51 | | | DELTA: instantiating (51) with fresh symbol all_111_0 gives: % 19.40/3.51 | | | (52) ~ (all_111_0 = 0) & leq(all_79_1, n0) = all_111_0 % 19.40/3.51 | | | % 19.40/3.51 | | | ALPHA: (52) implies: % 19.40/3.51 | | | (53) ~ (all_111_0 = 0) % 19.40/3.51 | | | (54) leq(all_79_1, n0) = all_111_0 % 19.40/3.51 | | | % 19.40/3.51 | | | GROUND_INST: instantiating (5) with 0, all_111_0, n0, all_79_1, % 19.40/3.51 | | | simplifying with (24), (54) gives: % 19.40/3.51 | | | (55) all_111_0 = 0 % 19.40/3.51 | | | % 19.40/3.51 | | | REDUCE: (53), (55) imply: % 19.40/3.51 | | | (56) $false % 19.40/3.51 | | | % 19.40/3.51 | | | CLOSE: (56) is inconsistent. % 19.40/3.51 | | | % 19.40/3.51 | | End of split % 19.40/3.51 | | % 19.40/3.51 | Case 2: % 19.40/3.51 | | % 19.40/3.51 | | (57) ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0) % 19.40/3.51 | | % 19.40/3.51 | | DELTA: instantiating (57) with fresh symbol all_107_0 gives: % 19.40/3.51 | | (58) ~ (all_107_0 = 0) & leq(pv5, n0) = all_107_0 % 19.40/3.51 | | % 19.40/3.51 | | ALPHA: (58) implies: % 19.40/3.51 | | (59) ~ (all_107_0 = 0) % 19.40/3.51 | | (60) leq(pv5, n0) = all_107_0 % 19.40/3.51 | | % 19.40/3.51 | | GROUND_INST: instantiating (5) with 0, all_107_0, n0, pv5, simplifying with % 19.40/3.51 | | (8), (60) gives: % 19.40/3.51 | | (61) all_107_0 = 0 % 19.40/3.51 | | % 19.40/3.51 | | REDUCE: (59), (61) imply: % 19.40/3.51 | | (62) $false % 19.40/3.51 | | % 19.40/3.51 | | CLOSE: (62) is inconsistent. % 19.40/3.51 | | % 19.40/3.51 | End of split % 19.40/3.51 | % 19.40/3.51 End of proof % 19.40/3.51 % SZS output end Proof for theBenchmark % 19.40/3.51 % 19.40/3.51 2883ms %------------------------------------------------------------------------------