%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV200+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 : n016.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 14.67s 2.67s % Output : Proof 17.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SWV200+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n016.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 10:01:00 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.65/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.65/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.65/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.65/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.65/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.65/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.65/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 4.18/1.32 Prover 4: Preprocessing ... % 4.18/1.32 Prover 1: Preprocessing ... % 4.90/1.37 Prover 5: Preprocessing ... % 4.90/1.37 Prover 3: Preprocessing ... % 4.90/1.37 Prover 0: Preprocessing ... % 4.90/1.38 Prover 6: Preprocessing ... % 4.90/1.38 Prover 2: Preprocessing ... % 11.30/2.17 Prover 3: Warning: ignoring some quantifiers % 11.64/2.21 Prover 3: Constructing countermodel ... % 11.83/2.23 Prover 1: Warning: ignoring some quantifiers % 11.83/2.29 Prover 1: Constructing countermodel ... % 12.48/2.34 Prover 6: Proving ... % 13.02/2.46 Prover 4: Warning: ignoring some quantifiers % 13.58/2.48 Prover 0: Proving ... % 13.58/2.48 Prover 5: Proving ... % 13.96/2.52 Prover 2: Proving ... % 13.96/2.53 Prover 4: Constructing countermodel ... % 14.67/2.67 Prover 3: proved (2058ms) % 14.67/2.67 % 14.67/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.67/2.67 % 14.67/2.67 Prover 2: stopped % 14.67/2.67 Prover 6: stopped % 14.67/2.67 Prover 0: stopped % 14.67/2.68 Prover 5: stopped % 15.25/2.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.25/2.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.25/2.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.25/2.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.25/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.32/2.82 Prover 1: Found proof (size 29) % 16.32/2.83 Prover 1: proved (2216ms) % 16.32/2.83 Prover 4: stopped % 16.32/2.84 Prover 13: Preprocessing ... % 16.32/2.85 Prover 8: Preprocessing ... % 16.32/2.86 Prover 7: Preprocessing ... % 16.32/2.86 Prover 11: Preprocessing ... % 16.32/2.87 Prover 10: Preprocessing ... % 17.06/2.93 Prover 7: stopped % 17.06/2.95 Prover 11: stopped % 17.06/2.95 Prover 10: stopped % 17.06/2.96 Prover 13: stopped % 17.54/3.05 Prover 8: Warning: ignoring some quantifiers % 17.54/3.06 Prover 8: Constructing countermodel ... % 17.94/3.08 Prover 8: stopped % 17.94/3.08 % 17.94/3.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.94/3.08 % 17.94/3.09 % SZS output start Proof for theBenchmark % 17.94/3.10 Assumptions after simplification: % 17.94/3.10 --------------------------------- % 17.94/3.10 % 17.94/3.10 (quaternion_ds1_inuse_0011) % 17.94/3.13 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) & % 17.94/3.13 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & % 17.94/3.13 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) % 17.94/3.13 & ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, % 17.94/3.13 n0) = use & a_select3(u_defuse, n0, n0) = use & % 17.94/3.13 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4) % 17.94/3.13 = use & a_select2(xinit_noise_defuse, n3) = use & % 17.94/3.13 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1) % 17.94/3.13 = use & a_select2(xinit_noise_defuse, n0) = use & % 17.94/3.13 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) = % 17.94/3.13 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 17.94/3.13 n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 17.94/3.13 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use & % 17.94/3.13 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use & % 17.94/3.13 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use & % 17.94/3.13 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use & % 17.94/3.13 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use & % 17.94/3.14 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 17.94/3.14 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 & % 17.94/3.14 leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 17.94/3.14 ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ? % 17.94/3.14 [v3: any] : ? [v4: any] : ? [v5: $i] : (a_select3(z_defuse, v1, v2) = v5 % 17.94/3.14 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = % 17.94/3.14 0) | v5 = use))) & ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) % 17.94/3.14 | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 17.94/3.14 any] : ? [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = % 17.94/3.14 v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = % 17.94/3.14 use))) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) & % 17.94/3.14 a_select3(u_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) = 0 & % 17.94/3.14 leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & ( ~ (v2 = % 17.94/3.14 pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5) % 17.94/3.14 | ~ (v1 = n0)))) % 17.94/3.14 % 17.94/3.14 (function-axioms) % 17.94/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.94/3.14 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 17.94/3.14 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.94/3.14 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 17.94/3.14 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.94/3.14 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 17.94/3.14 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.94/3.14 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 17.94/3.14 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.94/3.14 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 17.94/3.14 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.94/3.14 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 17.94/3.14 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.94/3.14 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 17.94/3.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 17.94/3.14 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.94/3.14 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 17.94/3.14 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 17.94/3.14 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 17.94/3.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 17.94/3.14 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 17.94/3.14 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 17.94/3.14 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.94/3.15 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 17.94/3.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.94/3.15 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 17.94/3.15 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.94/3.15 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 17.94/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.94/3.15 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 17.94/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.94/3.15 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 17.94/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.94/3.15 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 17.94/3.15 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 17.94/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 17.94/3.15 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.94/3.15 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.94/3.15 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 17.94/3.15 % 17.94/3.15 Further assumptions not needed in the proof: % 17.94/3.15 -------------------------------------------- % 17.94/3.15 const_array1_select, const_array2_select, defuse, finite_domain_0, % 17.94/3.15 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 17.94/3.15 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, % 17.94/3.15 gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1, % 17.94/3.15 gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, % 17.94/3.15 gt_5_tptp_minus_1, gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5, % 17.94/3.15 gt_998_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2, % 17.94/3.15 leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, % 17.94/3.15 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 17.94/3.15 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 17.94/3.15 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 17.94/3.15 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 17.94/3.15 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 17.94/3.15 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 17.94/3.15 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2, % 17.94/3.15 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float, % 17.94/3.15 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 17.94/3.15 uniform_int_rand_ranges_lo % 17.94/3.15 % 17.94/3.15 Those formulas are unsatisfiable: % 17.94/3.15 --------------------------------- % 17.94/3.15 % 17.94/3.15 Begin of proof % 17.94/3.15 | % 17.94/3.15 | ALPHA: (quaternion_ds1_inuse_0011) implies: % 17.94/3.15 | (1) ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, % 17.94/3.15 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use & % 17.94/3.15 | a_select2(xinit_noise_defuse, n5) = use & % 17.94/3.15 | a_select2(xinit_noise_defuse, n4) = use & % 17.94/3.15 | a_select2(xinit_noise_defuse, n3) = use & % 17.94/3.15 | a_select2(xinit_noise_defuse, n2) = use & % 17.94/3.15 | a_select2(xinit_noise_defuse, n1) = use & % 17.94/3.15 | a_select2(xinit_noise_defuse, n0) = use & % 17.94/3.15 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 17.94/3.15 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 17.94/3.15 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 17.94/3.15 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 17.94/3.15 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use % 17.94/3.15 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = % 17.94/3.15 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) % 17.94/3.15 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, % 17.94/3.15 | n1) = use & a_select2(sigma_defuse, n0) = use & % 17.94/3.15 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 17.94/3.15 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 % 17.94/3.15 | & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: % 17.94/3.15 | $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ % 17.94/3.15 | $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 17.94/3.15 | (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) % 17.94/3.15 | = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & ! % 17.94/3.15 | [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) % 17.94/3.15 | | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] % 17.94/3.15 | : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, % 17.94/3.15 | v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & % 17.94/3.15 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) & % 17.94/3.15 | a_select3(u_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) = % 17.94/3.15 | 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & % 17.94/3.15 | ( ~ (v2 = pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( % 17.94/3.15 | ~ (v2 = pv5) | ~ (v1 = n0)))) % 17.94/3.15 | % 17.94/3.15 | ALPHA: (function-axioms) implies: % 17.94/3.16 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.94/3.16 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 17.94/3.16 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.94/3.16 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 17.94/3.16 | = v0)) % 17.94/3.16 | % 17.94/3.16 | DELTA: instantiating (1) with fresh symbol all_76_0 gives: % 17.94/3.16 | (4) a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use & % 17.94/3.16 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = % 17.94/3.16 | use & a_select2(xinit_noise_defuse, n4) = use & % 17.94/3.16 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse, % 17.94/3.16 | n2) = use & a_select2(xinit_noise_defuse, n1) = use & % 17.94/3.16 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse, % 17.94/3.16 | n5) = use & a_select2(xinit_mean_defuse, n4) = use & % 17.94/3.16 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 17.94/3.16 | n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 17.94/3.16 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = % 17.94/3.16 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = % 17.94/3.16 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = % 17.94/3.16 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = % 17.94/3.16 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = % 17.94/3.16 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use % 17.94/3.16 | & a_select2(rho_defuse, n0) = use & pred(pv5) = all_76_0 & leq(pv5, % 17.94/3.16 | n998) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(all_76_0) & ! % 17.94/3.16 | [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0, n2) % 17.94/3.16 | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? % 17.94/3.16 | [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & % 17.94/3.16 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = % 17.94/3.16 | use))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) % 17.94/3.16 | | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 17.94/3.16 | [v3: any] : ? [v4: $i] : (a_select3(u_defuse, v0, v1) = v4 & leq(n0, % 17.94/3.16 | v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 17.94/3.16 | | v4 = use))) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 % 17.94/3.16 | = use) & a_select3(u_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 & % 17.94/3.16 | leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) % 17.94/3.16 | & $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 = % 17.94/3.16 | n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0))) % 17.94/3.16 | % 17.94/3.16 | ALPHA: (4) implies: % 17.94/3.16 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0, % 17.94/3.16 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 17.94/3.16 | ? [v4: $i] : (a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & % 17.94/3.16 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = % 17.94/3.16 | use))) % 17.94/3.16 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0, % 17.94/3.16 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 17.94/3.16 | ? [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & % 17.94/3.16 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = % 17.94/3.16 | use))) % 17.94/3.17 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = use) & % 17.94/3.17 | a_select3(u_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 & leq(v0, % 17.94/3.17 | n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & % 17.94/3.17 | $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 = % 17.94/3.17 | n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0))) % 17.94/3.17 | % 17.94/3.17 | DELTA: instantiating (7) with fresh symbols all_79_0, all_79_1, all_79_2 % 17.94/3.17 | gives: % 17.94/3.17 | (8) ~ (all_79_0 = use) & a_select3(u_defuse, all_79_2, all_79_1) = % 17.94/3.17 | all_79_0 & leq(all_79_1, all_76_0) = 0 & leq(all_79_2, n2) = 0 & % 17.94/3.17 | leq(n0, all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) & % 17.94/3.17 | $i(all_79_1) & $i(all_79_2) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 = % 17.94/3.17 | n2)) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 = n1)) & ( ~ (all_79_1 = % 17.94/3.17 | pv5) | ~ (all_79_2 = n0)) % 17.94/3.17 | % 17.94/3.17 | ALPHA: (8) implies: % 17.94/3.17 | (9) ~ (all_79_0 = use) % 17.94/3.17 | (10) $i(all_79_2) % 17.94/3.17 | (11) $i(all_79_1) % 17.94/3.17 | (12) leq(n0, all_79_2) = 0 % 17.94/3.17 | (13) leq(n0, all_79_1) = 0 % 17.94/3.17 | (14) leq(all_79_2, n2) = 0 % 17.94/3.17 | (15) leq(all_79_1, all_76_0) = 0 % 17.94/3.17 | (16) a_select3(u_defuse, all_79_2, all_79_1) = all_79_0 % 17.94/3.17 | % 17.94/3.17 | GROUND_INST: instantiating (6) with all_79_2, all_79_1, simplifying with (10), % 17.94/3.17 | (11), (14), (15) gives: % 17.94/3.17 | (17) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (a_select3(z_defuse, % 17.94/3.17 | all_79_2, all_79_1) = v2 & leq(n0, all_79_1) = v1 & leq(n0, % 17.94/3.17 | all_79_2) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = use)) % 17.94/3.17 | % 17.94/3.17 | GROUND_INST: instantiating (5) with all_79_2, all_79_1, simplifying with (10), % 17.94/3.17 | (11), (14), (15) gives: % 17.94/3.17 | (18) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (a_select3(u_defuse, % 17.94/3.17 | all_79_2, all_79_1) = v2 & leq(n0, all_79_1) = v1 & leq(n0, % 17.94/3.17 | all_79_2) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = use)) % 17.94/3.17 | % 17.94/3.17 | DELTA: instantiating (18) with fresh symbols all_103_0, all_103_1, all_103_2 % 17.94/3.17 | gives: % 17.94/3.17 | (19) a_select3(u_defuse, all_79_2, all_79_1) = all_103_0 & leq(n0, % 17.94/3.17 | all_79_1) = all_103_1 & leq(n0, all_79_2) = all_103_2 & % 17.94/3.17 | $i(all_103_0) & ( ~ (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 = % 17.94/3.17 | use) % 17.94/3.17 | % 17.94/3.17 | ALPHA: (19) implies: % 17.94/3.17 | (20) leq(n0, all_79_2) = all_103_2 % 17.94/3.17 | (21) leq(n0, all_79_1) = all_103_1 % 17.94/3.17 | (22) a_select3(u_defuse, all_79_2, all_79_1) = all_103_0 % 17.94/3.17 | (23) ~ (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 = use % 17.94/3.17 | % 17.94/3.17 | DELTA: instantiating (17) with fresh symbols all_105_0, all_105_1, all_105_2 % 17.94/3.17 | gives: % 17.94/3.17 | (24) a_select3(z_defuse, all_79_2, all_79_1) = all_105_0 & leq(n0, % 17.94/3.17 | all_79_1) = all_105_1 & leq(n0, all_79_2) = all_105_2 & % 17.94/3.17 | $i(all_105_0) & ( ~ (all_105_1 = 0) | ~ (all_105_2 = 0) | all_105_0 = % 17.94/3.17 | use) % 17.94/3.17 | % 17.94/3.17 | ALPHA: (24) implies: % 17.94/3.17 | (25) leq(n0, all_79_2) = all_105_2 % 17.94/3.17 | (26) leq(n0, all_79_1) = all_105_1 % 17.94/3.17 | % 17.94/3.17 | GROUND_INST: instantiating (2) with 0, all_105_2, all_79_2, n0, simplifying % 17.94/3.17 | with (12), (25) gives: % 17.94/3.17 | (27) all_105_2 = 0 % 17.94/3.17 | % 17.94/3.18 | GROUND_INST: instantiating (2) with all_103_2, all_105_2, all_79_2, n0, % 17.94/3.18 | simplifying with (20), (25) gives: % 17.94/3.18 | (28) all_105_2 = all_103_2 % 17.94/3.18 | % 17.94/3.18 | GROUND_INST: instantiating (2) with 0, all_105_1, all_79_1, n0, simplifying % 17.94/3.18 | with (13), (26) gives: % 17.94/3.18 | (29) all_105_1 = 0 % 17.94/3.18 | % 17.94/3.18 | GROUND_INST: instantiating (2) with all_103_1, all_105_1, all_79_1, n0, % 17.94/3.18 | simplifying with (21), (26) gives: % 17.94/3.18 | (30) all_105_1 = all_103_1 % 17.94/3.18 | % 17.94/3.18 | GROUND_INST: instantiating (3) with all_79_0, all_103_0, all_79_1, all_79_2, % 17.94/3.18 | u_defuse, simplifying with (16), (22) gives: % 17.94/3.18 | (31) all_103_0 = all_79_0 % 17.94/3.18 | % 17.94/3.18 | COMBINE_EQS: (29), (30) imply: % 17.94/3.18 | (32) all_103_1 = 0 % 17.94/3.18 | % 17.94/3.18 | COMBINE_EQS: (27), (28) imply: % 17.94/3.18 | (33) all_103_2 = 0 % 17.94/3.18 | % 17.94/3.18 | BETA: splitting (23) gives: % 17.94/3.18 | % 17.94/3.18 | Case 1: % 17.94/3.18 | | % 17.94/3.18 | | (34) ~ (all_103_1 = 0) % 17.94/3.18 | | % 17.94/3.18 | | REDUCE: (32), (34) imply: % 17.94/3.18 | | (35) $false % 17.94/3.18 | | % 17.94/3.18 | | CLOSE: (35) is inconsistent. % 17.94/3.18 | | % 17.94/3.18 | Case 2: % 17.94/3.18 | | % 17.94/3.18 | | (36) ~ (all_103_2 = 0) | all_103_0 = use % 17.94/3.18 | | % 17.94/3.18 | | BETA: splitting (36) gives: % 17.94/3.18 | | % 17.94/3.18 | | Case 1: % 17.94/3.18 | | | % 17.94/3.18 | | | (37) ~ (all_103_2 = 0) % 17.94/3.18 | | | % 17.94/3.18 | | | REDUCE: (33), (37) imply: % 17.94/3.18 | | | (38) $false % 17.94/3.18 | | | % 17.94/3.18 | | | CLOSE: (38) is inconsistent. % 17.94/3.18 | | | % 17.94/3.18 | | Case 2: % 17.94/3.18 | | | % 17.94/3.18 | | | (39) all_103_0 = use % 17.94/3.18 | | | % 17.94/3.18 | | | COMBINE_EQS: (31), (39) imply: % 17.94/3.18 | | | (40) all_79_0 = use % 17.94/3.18 | | | % 17.94/3.18 | | | SIMP: (40) implies: % 17.94/3.18 | | | (41) all_79_0 = use % 17.94/3.18 | | | % 17.94/3.18 | | | REDUCE: (9), (41) imply: % 17.94/3.18 | | | (42) $false % 17.94/3.18 | | | % 17.94/3.18 | | | CLOSE: (42) is inconsistent. % 17.94/3.18 | | | % 17.94/3.18 | | End of split % 17.94/3.18 | | % 17.94/3.18 | End of split % 17.94/3.18 | % 17.94/3.18 End of proof % 17.94/3.18 % SZS output end Proof for theBenchmark % 17.94/3.18 % 17.94/3.18 2589ms %------------------------------------------------------------------------------