%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV198+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 : n011.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 22:55:19 EDT 2023 % Result : Theorem 17.36s 3.09s % Output : Proof 23.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV198+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n011.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % 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 03:02:11 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.87/1.42 Prover 1: Preprocessing ... % 4.87/1.42 Prover 4: Preprocessing ... % 5.22/1.46 Prover 3: Preprocessing ... % 5.22/1.46 Prover 6: Preprocessing ... % 5.22/1.46 Prover 0: Preprocessing ... % 5.22/1.46 Prover 5: Preprocessing ... % 5.22/1.46 Prover 2: Preprocessing ... % 10.08/2.22 Prover 1: Warning: ignoring some quantifiers % 11.61/2.29 Prover 1: Constructing countermodel ... % 11.61/2.31 Prover 3: Warning: ignoring some quantifiers % 11.61/2.33 Prover 6: Proving ... % 11.61/2.33 Prover 3: Constructing countermodel ... % 12.15/2.39 Prover 4: Warning: ignoring some quantifiers % 12.73/2.48 Prover 4: Constructing countermodel ... % 12.73/2.51 Prover 5: Proving ... % 12.73/2.51 Prover 0: Proving ... % 13.42/2.56 Prover 2: Proving ... % 17.36/3.09 Prover 6: proved (2457ms) % 17.36/3.09 % 17.36/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.36/3.09 % 17.36/3.10 Prover 2: stopped % 17.74/3.11 Prover 5: stopped % 17.74/3.11 Prover 0: stopped % 17.74/3.11 Prover 3: stopped % 17.74/3.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.74/3.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.74/3.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.74/3.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.74/3.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 19.12/3.33 Prover 7: Preprocessing ... % 19.51/3.35 Prover 8: Preprocessing ... % 19.51/3.39 Prover 10: Preprocessing ... % 19.51/3.39 Prover 11: Preprocessing ... % 19.51/3.40 Prover 13: Preprocessing ... % 21.30/3.62 Prover 10: Warning: ignoring some quantifiers % 21.30/3.64 Prover 10: Constructing countermodel ... % 21.30/3.64 Prover 7: Warning: ignoring some quantifiers % 21.74/3.66 Prover 8: Warning: ignoring some quantifiers % 21.74/3.66 Prover 7: Constructing countermodel ... % 21.74/3.69 Prover 8: Constructing countermodel ... % 21.74/3.72 Prover 13: Warning: ignoring some quantifiers % 21.74/3.74 Prover 1: Found proof (size 53) % 21.74/3.74 Prover 1: proved (3111ms) % 21.74/3.74 Prover 4: stopped % 21.74/3.74 Prover 8: stopped % 21.74/3.74 Prover 10: stopped % 21.74/3.74 Prover 7: stopped % 21.74/3.75 Prover 13: Constructing countermodel ... % 22.43/3.77 Prover 13: stopped % 22.43/3.78 Prover 11: Warning: ignoring some quantifiers % 22.62/3.80 Prover 11: Constructing countermodel ... % 22.62/3.82 Prover 11: stopped % 22.62/3.82 % 22.62/3.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.62/3.82 % 22.62/3.82 % SZS output start Proof for theBenchmark % 22.62/3.83 Assumptions after simplification: % 22.62/3.83 --------------------------------- % 22.62/3.83 % 22.62/3.83 (finite_domain_0) % 22.84/3.85 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 22.84/3.85 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 22.84/3.85 % 22.84/3.85 (finite_domain_2) % 22.84/3.85 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 22.84/3.85 (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = % 22.84/3.85 v1)) % 22.84/3.85 % 22.84/3.85 (quaternion_ds1_inuse_0009) % 22.84/3.87 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) & % 22.84/3.87 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & % 22.84/3.87 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) % 22.84/3.87 & ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, % 22.84/3.87 n0) = use & a_select3(u_defuse, n0, n0) = use & % 22.84/3.87 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4) % 22.84/3.87 = use & a_select2(xinit_noise_defuse, n3) = use & % 22.84/3.87 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1) % 22.84/3.87 = use & a_select2(xinit_noise_defuse, n0) = use & % 22.84/3.87 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) = % 22.84/3.87 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 22.84/3.87 n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 22.84/3.87 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use & % 22.84/3.87 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use & % 22.84/3.87 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use & % 22.84/3.87 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use & % 22.84/3.87 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use & % 22.84/3.87 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 22.84/3.87 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 & % 22.84/3.87 leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 22.84/3.87 ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ? % 22.84/3.87 [v3: any] : ? [v4: any] : ? [v5: $i] : (a_select3(z_defuse, v1, v2) = v5 % 22.84/3.87 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = % 22.84/3.87 0) | v5 = use))) & ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) % 22.84/3.87 | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 22.84/3.87 any] : ? [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = % 22.84/3.87 v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = % 22.84/3.87 use))) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) & % 22.84/3.87 a_select3(u_defuse, v1, v2) = v3 & leq(v2, pv5) = 0 & leq(v1, n2) = 0 & % 22.84/3.87 leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1))) % 22.84/3.87 % 22.84/3.87 (function-axioms) % 22.84/3.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.84/3.87 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 22.84/3.87 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 22.84/3.87 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 22.84/3.87 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 22.84/3.87 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 22.84/3.87 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 22.84/3.87 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 22.84/3.87 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 22.84/3.87 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 22.84/3.88 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 22.84/3.88 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 22.84/3.88 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 22.84/3.88 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 22.84/3.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 22.84/3.88 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 22.84/3.88 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 22.84/3.88 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 22.84/3.88 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 22.84/3.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 22.84/3.88 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 22.84/3.88 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 22.84/3.88 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 22.84/3.88 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 22.84/3.88 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.84/3.88 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 22.84/3.88 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 22.84/3.88 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 22.84/3.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.84/3.88 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 22.84/3.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.84/3.88 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 22.84/3.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.84/3.88 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 22.84/3.88 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 22.84/3.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 22.84/3.88 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.84/3.88 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 22.84/3.88 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 22.84/3.88 % 22.84/3.88 Further assumptions not needed in the proof: % 22.84/3.88 -------------------------------------------- % 22.84/3.88 const_array1_select, const_array2_select, defuse, finite_domain_1, % 22.84/3.88 finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0, % 22.84/3.88 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, % 22.84/3.88 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, % 22.84/3.88 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, % 22.84/3.88 gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, gt_succ, irreflexivity_gt, % 22.84/3.88 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, % 22.84/3.88 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 22.84/3.88 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 22.84/3.88 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 22.84/3.88 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 22.84/3.88 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 22.84/3.88 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 22.84/3.88 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 22.84/3.88 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 22.84/3.88 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 22.84/3.88 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 22.84/3.88 % 22.84/3.88 Those formulas are unsatisfiable: % 22.84/3.88 --------------------------------- % 22.84/3.88 % 22.84/3.88 Begin of proof % 22.84/3.88 | % 22.84/3.88 | ALPHA: (finite_domain_0) implies: % 22.84/3.88 | (1) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 22.84/3.88 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 22.84/3.88 | % 22.84/3.88 | ALPHA: (finite_domain_2) implies: % 22.84/3.88 | (2) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n2) = 0) | ~ % 22.84/3.88 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) % 22.84/3.88 | % 22.84/3.88 | ALPHA: (quaternion_ds1_inuse_0009) implies: % 22.84/3.88 | (3) $i(pv5) % 22.84/3.89 | (4) ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, % 22.84/3.89 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use & % 22.84/3.89 | a_select2(xinit_noise_defuse, n5) = use & % 22.84/3.89 | a_select2(xinit_noise_defuse, n4) = use & % 22.84/3.89 | a_select2(xinit_noise_defuse, n3) = use & % 22.84/3.89 | a_select2(xinit_noise_defuse, n2) = use & % 22.84/3.89 | a_select2(xinit_noise_defuse, n1) = use & % 22.84/3.89 | a_select2(xinit_noise_defuse, n0) = use & % 22.84/3.89 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 22.84/3.89 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 22.84/3.89 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 22.84/3.89 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 22.84/3.89 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use % 22.84/3.89 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = % 22.84/3.89 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) % 22.84/3.89 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, % 22.84/3.89 | n1) = use & a_select2(sigma_defuse, n0) = use & % 22.84/3.89 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 22.84/3.89 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 % 22.84/3.89 | & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) & ! [v1: $i] : ! % 22.84/3.89 | [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | % 22.84/3.89 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 22.84/3.89 | (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) % 22.84/3.89 | = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & ! % 22.84/3.89 | [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) % 22.84/3.89 | | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] % 22.84/3.89 | : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, % 22.84/3.89 | v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & % 22.84/3.89 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) & % 22.84/3.89 | a_select3(u_defuse, v1, v2) = v3 & leq(v2, pv5) = 0 & leq(v1, n2) = % 22.84/3.89 | 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1))) % 22.84/3.89 | % 22.84/3.89 | ALPHA: (function-axioms) implies: % 22.84/3.89 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.84/3.89 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 22.84/3.89 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 22.84/3.89 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 22.84/3.89 | = v0)) % 22.84/3.89 | % 22.84/3.89 | DELTA: instantiating (4) with fresh symbol all_74_0 gives: % 22.84/3.89 | (7) a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use & % 22.84/3.89 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = % 22.84/3.89 | use & a_select2(xinit_noise_defuse, n4) = use & % 22.84/3.89 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse, % 22.84/3.89 | n2) = use & a_select2(xinit_noise_defuse, n1) = use & % 22.84/3.89 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse, % 22.84/3.89 | n5) = use & a_select2(xinit_mean_defuse, n4) = use & % 22.84/3.89 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 22.84/3.89 | n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 22.84/3.89 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = % 22.84/3.90 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = % 22.84/3.90 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = % 22.84/3.90 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = % 22.84/3.90 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = % 22.84/3.90 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use % 22.84/3.90 | & a_select2(rho_defuse, n0) = use & pred(pv5) = all_74_0 & leq(pv5, % 22.84/3.90 | n998) = 0 & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(all_74_0) & ! % 22.84/3.90 | [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_74_0) = 0) | ~ (leq(v0, n2) % 22.84/3.90 | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? % 22.84/3.90 | [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & % 22.84/3.90 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = % 22.84/3.90 | use))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_74_0) = 0) % 22.84/3.90 | | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 22.84/3.90 | [v3: any] : ? [v4: $i] : (a_select3(u_defuse, v0, v1) = v4 & leq(n0, % 22.84/3.90 | v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 22.84/3.90 | | v4 = use))) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 % 22.84/3.90 | = use) & a_select3(u_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 & % 22.84/3.90 | leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) % 22.84/3.90 | & $i(v0)) % 22.84/3.90 | % 22.84/3.90 | ALPHA: (7) implies: % 22.84/3.90 | (8) leq(n0, pv5) = 0 % 22.84/3.90 | (9) leq(pv5, n0) = 0 % 22.84/3.90 | (10) a_select3(u_defuse, n0, n0) = use % 22.84/3.90 | (11) a_select3(u_defuse, n1, n0) = use % 22.84/3.90 | (12) a_select3(u_defuse, n2, n0) = use % 22.84/3.90 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = use) & % 22.84/3.90 | a_select3(u_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 & leq(v0, n2) = % 22.84/3.90 | 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 22.84/3.90 | % 22.84/3.90 | DELTA: instantiating (13) with fresh symbols all_79_0, all_79_1, all_79_2 % 22.84/3.90 | gives: % 22.84/3.90 | (14) ~ (all_79_0 = use) & a_select3(u_defuse, all_79_2, all_79_1) = % 22.84/3.90 | all_79_0 & leq(all_79_1, pv5) = 0 & leq(all_79_2, n2) = 0 & leq(n0, % 22.84/3.90 | all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) & $i(all_79_1) % 22.84/3.90 | & $i(all_79_2) % 22.84/3.90 | % 22.84/3.90 | ALPHA: (14) implies: % 22.84/3.90 | (15) ~ (all_79_0 = use) % 22.84/3.90 | (16) $i(all_79_2) % 22.84/3.90 | (17) $i(all_79_1) % 22.84/3.90 | (18) leq(n0, all_79_2) = 0 % 22.84/3.90 | (19) leq(n0, all_79_1) = 0 % 22.84/3.90 | (20) leq(all_79_2, n2) = 0 % 22.84/3.90 | (21) leq(all_79_1, pv5) = 0 % 22.84/3.90 | (22) a_select3(u_defuse, all_79_2, all_79_1) = all_79_0 % 22.84/3.90 | % 23.14/3.90 | GROUND_INST: instantiating (1) with pv5, simplifying with (3), (8) gives: % 23.14/3.90 | (23) pv5 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0) % 23.14/3.90 | % 23.14/3.90 | GROUND_INST: instantiating (1) with all_79_2, simplifying with (16), (18) % 23.14/3.90 | gives: % 23.14/3.90 | (24) all_79_2 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_2, n0) = v0) % 23.14/3.90 | % 23.14/3.90 | GROUND_INST: instantiating (1) with all_79_1, simplifying with (17), (19) % 23.14/3.90 | gives: % 23.14/3.90 | (25) all_79_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0) % 23.14/3.90 | % 23.14/3.90 | GROUND_INST: instantiating (2) with all_79_2, simplifying with (16), (20) % 23.14/3.90 | gives: % 23.14/3.91 | (26) all_79_2 = n2 | all_79_2 = n1 | all_79_2 = n0 | ? [v0: int] : ( ~ (v0 % 23.14/3.91 | = 0) & leq(n0, all_79_2) = v0) % 23.14/3.91 | % 23.14/3.91 | BETA: splitting (23) gives: % 23.14/3.91 | % 23.14/3.91 | Case 1: % 23.14/3.91 | | % 23.14/3.91 | | (27) pv5 = n0 % 23.14/3.91 | | % 23.14/3.91 | | REDUCE: (21), (27) imply: % 23.14/3.91 | | (28) leq(all_79_1, n0) = 0 % 23.14/3.91 | | % 23.14/3.91 | | BETA: splitting (25) gives: % 23.14/3.91 | | % 23.14/3.91 | | Case 1: % 23.14/3.91 | | | % 23.14/3.91 | | | (29) all_79_1 = n0 % 23.14/3.91 | | | % 23.14/3.91 | | | REDUCE: (22), (29) imply: % 23.14/3.91 | | | (30) a_select3(u_defuse, all_79_2, n0) = all_79_0 % 23.14/3.91 | | | % 23.14/3.91 | | | BETA: splitting (24) gives: % 23.14/3.91 | | | % 23.14/3.91 | | | Case 1: % 23.14/3.91 | | | | % 23.14/3.91 | | | | (31) all_79_2 = n0 % 23.14/3.91 | | | | % 23.14/3.91 | | | | REDUCE: (30), (31) imply: % 23.14/3.91 | | | | (32) a_select3(u_defuse, n0, n0) = all_79_0 % 23.14/3.91 | | | | % 23.14/3.91 | | | | GROUND_INST: instantiating (6) with use, all_79_0, n0, n0, u_defuse, % 23.14/3.91 | | | | simplifying with (10), (32) gives: % 23.14/3.91 | | | | (33) all_79_0 = use % 23.14/3.91 | | | | % 23.14/3.91 | | | | REDUCE: (15), (33) imply: % 23.14/3.91 | | | | (34) $false % 23.14/3.91 | | | | % 23.14/3.91 | | | | CLOSE: (34) is inconsistent. % 23.14/3.91 | | | | % 23.14/3.91 | | | Case 2: % 23.14/3.91 | | | | % 23.14/3.91 | | | | (35) ~ (all_79_2 = n0) % 23.14/3.91 | | | | % 23.14/3.91 | | | | BETA: splitting (26) gives: % 23.14/3.91 | | | | % 23.14/3.91 | | | | Case 1: % 23.14/3.91 | | | | | % 23.14/3.91 | | | | | (36) all_79_2 = n0 % 23.14/3.91 | | | | | % 23.14/3.91 | | | | | REDUCE: (35), (36) imply: % 23.14/3.91 | | | | | (37) $false % 23.14/3.91 | | | | | % 23.14/3.91 | | | | | CLOSE: (37) is inconsistent. % 23.14/3.91 | | | | | % 23.14/3.91 | | | | Case 2: % 23.14/3.91 | | | | | % 23.14/3.91 | | | | | (38) all_79_2 = n2 | all_79_2 = n1 | ? [v0: int] : ( ~ (v0 = 0) & % 23.14/3.91 | | | | | leq(n0, all_79_2) = v0) % 23.14/3.91 | | | | | % 23.14/3.91 | | | | | BETA: splitting (38) gives: % 23.14/3.91 | | | | | % 23.14/3.91 | | | | | Case 1: % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | | (39) all_79_2 = n2 % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | | REDUCE: (30), (39) imply: % 23.14/3.91 | | | | | | (40) a_select3(u_defuse, n2, n0) = all_79_0 % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | | GROUND_INST: instantiating (6) with use, all_79_0, n0, n2, u_defuse, % 23.14/3.91 | | | | | | simplifying with (12), (40) gives: % 23.14/3.91 | | | | | | (41) all_79_0 = use % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | | REDUCE: (15), (41) imply: % 23.14/3.91 | | | | | | (42) $false % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | | CLOSE: (42) is inconsistent. % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | Case 2: % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | | (43) all_79_2 = n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0, % 23.14/3.91 | | | | | | all_79_2) = v0) % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | | BETA: splitting (43) gives: % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | | Case 1: % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | (44) all_79_2 = n1 % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | REDUCE: (30), (44) imply: % 23.14/3.91 | | | | | | | (45) a_select3(u_defuse, n1, n0) = all_79_0 % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | GROUND_INST: instantiating (6) with use, all_79_0, n0, n1, % 23.14/3.91 | | | | | | | u_defuse, simplifying with (11), (45) gives: % 23.14/3.91 | | | | | | | (46) all_79_0 = use % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | REDUCE: (15), (46) imply: % 23.14/3.91 | | | | | | | (47) $false % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | CLOSE: (47) is inconsistent. % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | Case 2: % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | (48) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_79_2) = v0) % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | DELTA: instantiating (48) with fresh symbol all_488_0 gives: % 23.14/3.91 | | | | | | | (49) ~ (all_488_0 = 0) & leq(n0, all_79_2) = all_488_0 % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | ALPHA: (49) implies: % 23.14/3.91 | | | | | | | (50) ~ (all_488_0 = 0) % 23.14/3.91 | | | | | | | (51) leq(n0, all_79_2) = all_488_0 % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | GROUND_INST: instantiating (5) with 0, all_488_0, all_79_2, n0, % 23.14/3.91 | | | | | | | simplifying with (18), (51) gives: % 23.14/3.91 | | | | | | | (52) all_488_0 = 0 % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | REDUCE: (50), (52) imply: % 23.14/3.91 | | | | | | | (53) $false % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | | CLOSE: (53) is inconsistent. % 23.14/3.91 | | | | | | | % 23.14/3.91 | | | | | | End of split % 23.14/3.91 | | | | | | % 23.14/3.91 | | | | | End of split % 23.14/3.91 | | | | | % 23.14/3.91 | | | | End of split % 23.14/3.91 | | | | % 23.14/3.91 | | | End of split % 23.14/3.91 | | | % 23.14/3.91 | | Case 2: % 23.14/3.91 | | | % 23.14/3.91 | | | (54) ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0) % 23.14/3.91 | | | % 23.14/3.92 | | | DELTA: instantiating (54) with fresh symbol all_111_0 gives: % 23.14/3.92 | | | (55) ~ (all_111_0 = 0) & leq(all_79_1, n0) = all_111_0 % 23.14/3.92 | | | % 23.14/3.92 | | | ALPHA: (55) implies: % 23.14/3.92 | | | (56) ~ (all_111_0 = 0) % 23.14/3.92 | | | (57) leq(all_79_1, n0) = all_111_0 % 23.14/3.92 | | | % 23.14/3.92 | | | GROUND_INST: instantiating (5) with 0, all_111_0, n0, all_79_1, % 23.14/3.92 | | | simplifying with (28), (57) gives: % 23.14/3.92 | | | (58) all_111_0 = 0 % 23.14/3.92 | | | % 23.14/3.92 | | | REDUCE: (56), (58) imply: % 23.14/3.92 | | | (59) $false % 23.14/3.92 | | | % 23.14/3.92 | | | CLOSE: (59) is inconsistent. % 23.14/3.92 | | | % 23.14/3.92 | | End of split % 23.14/3.92 | | % 23.14/3.92 | Case 2: % 23.14/3.92 | | % 23.14/3.92 | | (60) ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0) % 23.14/3.92 | | % 23.14/3.92 | | DELTA: instantiating (60) with fresh symbol all_107_0 gives: % 23.14/3.92 | | (61) ~ (all_107_0 = 0) & leq(pv5, n0) = all_107_0 % 23.14/3.92 | | % 23.14/3.92 | | ALPHA: (61) implies: % 23.14/3.92 | | (62) ~ (all_107_0 = 0) % 23.14/3.92 | | (63) leq(pv5, n0) = all_107_0 % 23.14/3.92 | | % 23.14/3.92 | | GROUND_INST: instantiating (5) with 0, all_107_0, n0, pv5, simplifying with % 23.14/3.92 | | (9), (63) gives: % 23.14/3.92 | | (64) all_107_0 = 0 % 23.14/3.92 | | % 23.14/3.92 | | REDUCE: (62), (64) imply: % 23.14/3.92 | | (65) $false % 23.14/3.92 | | % 23.14/3.92 | | CLOSE: (65) is inconsistent. % 23.14/3.92 | | % 23.14/3.92 | End of split % 23.14/3.92 | % 23.14/3.92 End of proof % 23.14/3.92 % SZS output end Proof for theBenchmark % 23.14/3.92 % 23.14/3.92 3311ms %------------------------------------------------------------------------------