%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV098+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 : n006.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 22:54:54 EDT 2023 % Result : Theorem 16.69s 2.91s % Output : Proof 20.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV098+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n006.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 08:55:06 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.88/1.33 Prover 4: Preprocessing ... % 4.88/1.33 Prover 1: Preprocessing ... % 4.88/1.36 Prover 3: Preprocessing ... % 4.88/1.36 Prover 5: Preprocessing ... % 4.88/1.36 Prover 0: Preprocessing ... % 4.88/1.36 Prover 6: Preprocessing ... % 4.88/1.36 Prover 2: Preprocessing ... % 11.13/2.22 Prover 1: Warning: ignoring some quantifiers % 11.13/2.23 Prover 3: Warning: ignoring some quantifiers % 12.02/2.29 Prover 4: Warning: ignoring some quantifiers % 12.02/2.30 Prover 3: Constructing countermodel ... % 12.02/2.31 Prover 1: Constructing countermodel ... % 12.02/2.33 Prover 6: Proving ... % 12.50/2.43 Prover 4: Constructing countermodel ... % 13.25/2.49 Prover 0: Proving ... % 13.82/2.53 Prover 5: Proving ... % 13.82/2.56 Prover 2: Proving ... % 16.69/2.90 Prover 3: proved (2264ms) % 16.69/2.90 % 16.69/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.69/2.91 % 16.69/2.91 Prover 6: stopped % 16.69/2.91 Prover 0: stopped % 16.69/2.91 Prover 5: stopped % 16.69/2.91 Prover 2: stopped % 16.69/2.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.69/2.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.69/2.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.69/2.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.69/2.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.95/3.12 Prover 10: Preprocessing ... % 17.95/3.12 Prover 7: Preprocessing ... % 17.95/3.14 Prover 13: Preprocessing ... % 18.32/3.15 Prover 8: Preprocessing ... % 18.32/3.15 Prover 11: Preprocessing ... % 18.32/3.15 Prover 1: Found proof (size 42) % 18.32/3.15 Prover 1: proved (2526ms) % 18.32/3.15 Prover 4: stopped % 18.79/3.19 Prover 10: stopped % 18.91/3.20 Prover 7: stopped % 19.01/3.23 Prover 11: stopped % 19.01/3.25 Prover 13: stopped % 19.54/3.36 Prover 8: Warning: ignoring some quantifiers % 19.54/3.37 Prover 8: Constructing countermodel ... % 19.54/3.39 Prover 8: stopped % 19.54/3.39 % 19.54/3.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.54/3.39 % 19.94/3.41 % SZS output start Proof for theBenchmark % 19.94/3.42 Assumptions after simplification: % 19.94/3.42 --------------------------------- % 19.94/3.42 % 19.94/3.42 (pred_minus_1) % 19.94/3.45 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 19.94/3.45 (pred(v0) = v1 & $i(v1))) % 19.94/3.45 % 19.94/3.45 (pred_succ) % 19.94/3.45 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 19.94/3.45 % 19.94/3.45 (quaternion_ds1_inuse_0010) % 19.94/3.46 $i(z_defuse) & $i(n999) & $i(pv5) & $i(xinit_noise_defuse) & % 19.94/3.46 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & % 19.94/3.46 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) % 19.94/3.46 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (minus(v2, n1) = v3 % 19.94/3.46 & minus(n999, n1) = v0 & minus(pv5, n1) = v1 & plus(n1, pv5) = v2 & % 19.94/3.46 a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use & % 19.94/3.46 a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use % 19.94/3.46 & a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse, % 19.94/3.46 n3) = use & a_select2(xinit_noise_defuse, n2) = use & % 19.94/3.46 a_select2(xinit_noise_defuse, n1) = use & a_select2(xinit_noise_defuse, n0) % 19.94/3.46 = use & a_select2(xinit_mean_defuse, n5) = use & % 19.94/3.46 a_select2(xinit_mean_defuse, n4) = use & a_select2(xinit_mean_defuse, n3) = % 19.94/3.46 use & a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 19.94/3.46 n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 19.94/3.46 a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use & % 19.94/3.46 a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use & % 19.94/3.46 a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use & % 19.94/3.46 a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use & % 19.94/3.46 a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use & % 19.94/3.46 a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use & leq(pv5, % 19.94/3.46 v0) = 0 & leq(n0, pv5) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 19.94/3.46 $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (a_select3(z_defuse, v4, v5) = v6) | % 19.94/3.46 ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] : ? [v9: any] : ? % 19.94/3.46 [v10: any] : ? [v11: $i] : (a_select3(u_defuse, v4, v5) = v11 & leq(v5, % 19.94/3.46 pv5) = v10 & leq(v4, n2) = v9 & leq(n0, v5) = v8 & leq(n0, v4) = v7 & % 19.94/3.46 $i(v11) & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | (v11 % 19.94/3.46 = use & v6 = use)))) & ! [v4: $i] : ! [v5: $i] : ( ~ (leq(v5, v1) % 19.94/3.46 = 0) | ~ (leq(v4, n2) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v6: any] : ? % 19.94/3.46 [v7: any] : ? [v8: $i] : ? [v9: $i] : (a_select3(z_defuse, v4, v5) = v9 % 19.94/3.46 & a_select3(u_defuse, v4, v5) = v8 & leq(n0, v5) = v7 & leq(n0, v4) = v6 % 19.94/3.46 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | (v9 = use & v8 = % 19.94/3.46 use)))) & ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 19.94/3.46 (a_select3(z_defuse, v4, v5) = v7 & a_select3(u_defuse, v4, v5) = v6 & % 19.94/3.47 leq(v5, v3) = 0 & leq(v4, n2) = 0 & leq(n0, v5) = 0 & leq(n0, v4) = 0 & % 19.94/3.47 $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v7 = use) | ~ (v6 = use)))) % 19.94/3.47 % 19.94/3.47 (succ_plus_1_l) % 19.94/3.47 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (plus(n1, v0) = v1) | ~ $i(v0) | % 19.94/3.47 (succ(v0) = v1 & $i(v1))) % 19.94/3.47 % 19.94/3.47 (function-axioms) % 19.94/3.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.94/3.47 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.94/3.47 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.94/3.47 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.94/3.47 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.94/3.47 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.94/3.47 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.94/3.47 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.94/3.47 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.94/3.47 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.94/3.47 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.94/3.47 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 19.94/3.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.94/3.47 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 19.94/3.47 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 19.94/3.47 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.94/3.47 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 19.94/3.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.94/3.47 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 19.94/3.47 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 19.94/3.47 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.94/3.47 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 19.94/3.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.94/3.47 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 19.94/3.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.94/3.47 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 19.94/3.47 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.94/3.47 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.94/3.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.94/3.47 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.94/3.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.94/3.47 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.94/3.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.94/3.47 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.94/3.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 19.94/3.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 19.94/3.47 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.94/3.47 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.94/3.47 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 19.94/3.47 % 19.94/3.47 Further assumptions not needed in the proof: % 19.94/3.47 -------------------------------------------- % 19.94/3.47 const_array1_select, const_array2_select, defuse, finite_domain_0, % 19.94/3.47 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 19.94/3.47 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, % 19.94/3.47 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, % 19.94/3.47 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, % 19.94/3.47 gt_5_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2, gt_999_3, gt_999_4, gt_999_5, % 19.94/3.47 gt_999_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2, % 19.94/3.47 leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, % 19.94/3.47 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 19.94/3.47 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.94/3.47 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 19.94/3.47 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_r, % 19.94/3.47 succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, % 19.94/3.47 succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, % 19.94/3.47 successor_1, successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 19.94/3.47 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 19.94/3.47 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 19.94/3.47 % 19.94/3.47 Those formulas are unsatisfiable: % 19.94/3.47 --------------------------------- % 19.94/3.47 % 19.94/3.47 Begin of proof % 19.94/3.47 | % 19.94/3.47 | ALPHA: (succ_plus_1_l) implies: % 19.94/3.48 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (plus(n1, v0) = v1) | ~ $i(v0) | % 19.94/3.48 | (succ(v0) = v1 & $i(v1))) % 19.94/3.48 | % 19.94/3.48 | ALPHA: (pred_minus_1) implies: % 19.94/3.48 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 19.94/3.48 | (pred(v0) = v1 & $i(v1))) % 19.94/3.48 | % 19.94/3.48 | ALPHA: (quaternion_ds1_inuse_0010) implies: % 19.94/3.48 | (3) $i(pv5) % 20.35/3.48 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (minus(v2, n1) % 20.35/3.48 | = v3 & minus(n999, n1) = v0 & minus(pv5, n1) = v1 & plus(n1, pv5) = % 20.35/3.48 | v2 & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) % 20.35/3.48 | = use & a_select3(u_defuse, n0, n0) = use & % 20.35/3.48 | a_select2(xinit_noise_defuse, n5) = use & % 20.35/3.48 | a_select2(xinit_noise_defuse, n4) = use & % 20.35/3.48 | a_select2(xinit_noise_defuse, n3) = use & % 20.35/3.48 | a_select2(xinit_noise_defuse, n2) = use & % 20.35/3.48 | a_select2(xinit_noise_defuse, n1) = use & % 20.35/3.48 | a_select2(xinit_noise_defuse, n0) = use & % 20.35/3.48 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 20.35/3.48 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 20.35/3.48 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 20.35/3.48 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 20.35/3.48 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use % 20.35/3.48 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = % 20.35/3.48 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) % 20.35/3.48 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, % 20.35/3.48 | n1) = use & a_select2(sigma_defuse, n0) = use & % 20.35/3.48 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 20.35/3.48 | a_select2(rho_defuse, n0) = use & leq(pv5, v0) = 0 & leq(n0, pv5) = 0 % 20.35/3.48 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 20.35/3.48 | [v6: $i] : ( ~ (a_select3(z_defuse, v4, v5) = v6) | ~ $i(v5) | ~ % 20.35/3.48 | $i(v4) | ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] % 20.35/3.48 | : ? [v11: $i] : (a_select3(u_defuse, v4, v5) = v11 & leq(v5, pv5) % 20.35/3.48 | = v10 & leq(v4, n2) = v9 & leq(n0, v5) = v8 & leq(n0, v4) = v7 & % 20.35/3.48 | $i(v11) & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) % 20.35/3.48 | | (v11 = use & v6 = use)))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 20.35/3.48 | (leq(v5, v1) = 0) | ~ (leq(v4, n2) = 0) | ~ $i(v5) | ~ $i(v4) | % 20.35/3.48 | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : % 20.35/3.48 | (a_select3(z_defuse, v4, v5) = v9 & a_select3(u_defuse, v4, v5) = % 20.35/3.48 | v8 & leq(n0, v5) = v7 & leq(n0, v4) = v6 & $i(v9) & $i(v8) & ( ~ % 20.35/3.48 | (v7 = 0) | ~ (v6 = 0) | (v9 = use & v8 = use)))) & ? [v4: $i] % 20.35/3.48 | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (a_select3(z_defuse, v4, % 20.35/3.48 | v5) = v7 & a_select3(u_defuse, v4, v5) = v6 & leq(v5, v3) = 0 & % 20.35/3.48 | leq(v4, n2) = 0 & leq(n0, v5) = 0 & leq(n0, v4) = 0 & $i(v7) & % 20.35/3.48 | $i(v6) & $i(v5) & $i(v4) & ( ~ (v7 = use) | ~ (v6 = use)))) % 20.35/3.48 | % 20.35/3.48 | ALPHA: (function-axioms) implies: % 20.35/3.48 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) % 20.35/3.48 | | ~ (pred(v2) = v0)) % 20.35/3.48 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.35/3.48 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 20.35/3.48 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.35/3.48 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 20.35/3.48 | = v0)) % 20.35/3.48 | % 20.35/3.49 | DELTA: instantiating (4) with fresh symbols all_76_0, all_76_1, all_76_2, % 20.35/3.49 | all_76_3 gives: % 20.35/3.49 | (8) minus(all_76_1, n1) = all_76_0 & minus(n999, n1) = all_76_3 & % 20.35/3.49 | minus(pv5, n1) = all_76_2 & plus(n1, pv5) = all_76_1 & % 20.35/3.49 | a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use & % 20.35/3.49 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = % 20.35/3.49 | use & a_select2(xinit_noise_defuse, n4) = use & % 20.35/3.49 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse, % 20.35/3.49 | n2) = use & a_select2(xinit_noise_defuse, n1) = use & % 20.35/3.49 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse, % 20.35/3.49 | n5) = use & a_select2(xinit_mean_defuse, n4) = use & % 20.35/3.49 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 20.35/3.49 | n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 20.35/3.49 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = % 20.35/3.49 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = % 20.35/3.49 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = % 20.35/3.49 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = % 20.35/3.49 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = % 20.35/3.49 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use % 20.35/3.49 | & a_select2(rho_defuse, n0) = use & leq(pv5, all_76_3) = 0 & leq(n0, % 20.35/3.49 | pv5) = 0 & $i(all_76_0) & $i(all_76_1) & $i(all_76_2) & $i(all_76_3) % 20.35/3.49 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(z_defuse, % 20.35/3.49 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 20.35/3.49 | any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] : % 20.35/3.49 | (a_select3(u_defuse, v0, v1) = v7 & leq(v1, pv5) = v6 & leq(v0, n2) = % 20.35/3.49 | v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3 & $i(v7) & ( ~ (v6 = 0) | % 20.35/3.49 | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v7 = use & v2 = use)))) % 20.35/3.49 | & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_2) = 0) | ~ (leq(v0, % 20.35/3.49 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 20.35/3.49 | ? [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v0, v1) = v5 & % 20.35/3.49 | a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) = % 20.35/3.49 | v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = use & v4 % 20.35/3.49 | = use)))) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 20.35/3.49 | $i] : (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) % 20.35/3.49 | = v2 & leq(v1, all_76_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & % 20.35/3.49 | leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) % 20.35/3.49 | | ~ (v2 = use))) % 20.35/3.49 | % 20.35/3.49 | ALPHA: (8) implies: % 20.35/3.49 | (9) plus(n1, pv5) = all_76_1 % 20.35/3.49 | (10) minus(all_76_1, n1) = all_76_0 % 20.35/3.49 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(z_defuse, v0, % 20.35/3.49 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] % 20.35/3.49 | : ? [v5: any] : ? [v6: any] : ? [v7: $i] : (a_select3(u_defuse, % 20.35/3.49 | v0, v1) = v7 & leq(v1, pv5) = v6 & leq(v0, n2) = v5 & leq(n0, % 20.35/3.49 | v1) = v4 & leq(n0, v0) = v3 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = % 20.35/3.49 | 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v7 = use & v2 = use)))) % 20.35/3.49 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 20.35/3.49 | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = v2 & % 20.35/3.49 | leq(v1, all_76_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, % 20.35/3.49 | v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) | ~ % 20.35/3.49 | (v2 = use))) % 20.35/3.49 | % 20.35/3.49 | DELTA: instantiating (12) with fresh symbols all_79_0, all_79_1, all_79_2, % 20.35/3.49 | all_79_3 gives: % 20.35/3.49 | (13) a_select3(z_defuse, all_79_3, all_79_2) = all_79_0 & % 20.35/3.49 | a_select3(u_defuse, all_79_3, all_79_2) = all_79_1 & leq(all_79_2, % 20.35/3.49 | all_76_0) = 0 & leq(all_79_3, n2) = 0 & leq(n0, all_79_2) = 0 & % 20.35/3.49 | leq(n0, all_79_3) = 0 & $i(all_79_0) & $i(all_79_1) & $i(all_79_2) & % 20.35/3.49 | $i(all_79_3) & ( ~ (all_79_0 = use) | ~ (all_79_1 = use)) % 20.35/3.49 | % 20.35/3.49 | ALPHA: (13) implies: % 20.35/3.50 | (14) $i(all_79_3) % 20.35/3.50 | (15) $i(all_79_2) % 20.35/3.50 | (16) leq(n0, all_79_3) = 0 % 20.35/3.50 | (17) leq(n0, all_79_2) = 0 % 20.35/3.50 | (18) leq(all_79_3, n2) = 0 % 20.35/3.50 | (19) leq(all_79_2, all_76_0) = 0 % 20.35/3.50 | (20) a_select3(u_defuse, all_79_3, all_79_2) = all_79_1 % 20.35/3.50 | (21) a_select3(z_defuse, all_79_3, all_79_2) = all_79_0 % 20.35/3.50 | (22) ~ (all_79_0 = use) | ~ (all_79_1 = use) % 20.35/3.50 | % 20.35/3.50 | GROUND_INST: instantiating (11) with all_79_3, all_79_2, all_79_0, simplifying % 20.35/3.50 | with (14), (15), (21) gives: % 20.35/3.50 | (23) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 20.43/3.50 | $i] : (a_select3(u_defuse, all_79_3, all_79_2) = v4 & leq(all_79_2, % 20.43/3.50 | pv5) = v3 & leq(all_79_3, n2) = v2 & leq(n0, all_79_2) = v1 & % 20.43/3.50 | leq(n0, all_79_3) = v0 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ % 20.43/3.50 | (v1 = 0) | ~ (v0 = 0) | (v4 = use & all_79_0 = use))) % 20.43/3.50 | % 20.43/3.50 | GROUND_INST: instantiating (1) with pv5, all_76_1, simplifying with (3), (9) % 20.43/3.50 | gives: % 20.43/3.50 | (24) succ(pv5) = all_76_1 & $i(all_76_1) % 20.43/3.50 | % 20.43/3.50 | ALPHA: (24) implies: % 20.43/3.50 | (25) $i(all_76_1) % 20.43/3.50 | (26) succ(pv5) = all_76_1 % 20.43/3.50 | % 20.43/3.50 | GROUND_INST: instantiating (2) with all_76_1, all_76_0, simplifying with (10), % 20.43/3.50 | (25) gives: % 20.43/3.50 | (27) pred(all_76_1) = all_76_0 & $i(all_76_0) % 20.43/3.50 | % 20.43/3.50 | ALPHA: (27) implies: % 20.43/3.50 | (28) pred(all_76_1) = all_76_0 % 20.43/3.50 | % 20.43/3.50 | DELTA: instantiating (23) with fresh symbols all_103_0, all_103_1, all_103_2, % 20.43/3.50 | all_103_3, all_103_4 gives: % 20.43/3.50 | (29) a_select3(u_defuse, all_79_3, all_79_2) = all_103_0 & leq(all_79_2, % 20.43/3.50 | pv5) = all_103_1 & leq(all_79_3, n2) = all_103_2 & leq(n0, all_79_2) % 20.43/3.50 | = all_103_3 & leq(n0, all_79_3) = all_103_4 & $i(all_103_0) & ( ~ % 20.43/3.50 | (all_103_1 = 0) | ~ (all_103_2 = 0) | ~ (all_103_3 = 0) | ~ % 20.43/3.50 | (all_103_4 = 0) | (all_103_0 = use & all_79_0 = use)) % 20.43/3.50 | % 20.43/3.50 | ALPHA: (29) implies: % 20.43/3.50 | (30) leq(n0, all_79_3) = all_103_4 % 20.43/3.50 | (31) leq(n0, all_79_2) = all_103_3 % 20.43/3.50 | (32) leq(all_79_3, n2) = all_103_2 % 20.43/3.50 | (33) leq(all_79_2, pv5) = all_103_1 % 20.43/3.50 | (34) a_select3(u_defuse, all_79_3, all_79_2) = all_103_0 % 20.43/3.50 | (35) ~ (all_103_1 = 0) | ~ (all_103_2 = 0) | ~ (all_103_3 = 0) | ~ % 20.43/3.50 | (all_103_4 = 0) | (all_103_0 = use & all_79_0 = use) % 20.43/3.50 | % 20.43/3.50 | GROUND_INST: instantiating (6) with 0, all_103_4, all_79_3, n0, simplifying % 20.43/3.50 | with (16), (30) gives: % 20.43/3.50 | (36) all_103_4 = 0 % 20.43/3.50 | % 20.43/3.50 | GROUND_INST: instantiating (6) with 0, all_103_3, all_79_2, n0, simplifying % 20.43/3.50 | with (17), (31) gives: % 20.43/3.50 | (37) all_103_3 = 0 % 20.43/3.50 | % 20.43/3.50 | GROUND_INST: instantiating (6) with 0, all_103_2, n2, all_79_3, simplifying % 20.43/3.50 | with (18), (32) gives: % 20.43/3.50 | (38) all_103_2 = 0 % 20.43/3.50 | % 20.43/3.50 | GROUND_INST: instantiating (7) with all_79_1, all_103_0, all_79_2, all_79_3, % 20.43/3.50 | u_defuse, simplifying with (20), (34) gives: % 20.43/3.50 | (39) all_103_0 = all_79_1 % 20.43/3.50 | % 20.43/3.50 | GROUND_INST: instantiating (pred_succ) with pv5, all_76_1, simplifying with % 20.43/3.50 | (3), (26) gives: % 20.43/3.50 | (40) pred(all_76_1) = pv5 % 20.43/3.50 | % 20.43/3.50 | GROUND_INST: instantiating (5) with all_76_0, pv5, all_76_1, simplifying with % 20.43/3.50 | (28), (40) gives: % 20.43/3.50 | (41) all_76_0 = pv5 % 20.43/3.50 | % 20.43/3.50 | REDUCE: (19), (41) imply: % 20.43/3.50 | (42) leq(all_79_2, pv5) = 0 % 20.43/3.50 | % 20.43/3.50 | GROUND_INST: instantiating (6) with all_103_1, 0, pv5, all_79_2, simplifying % 20.43/3.51 | with (33), (42) gives: % 20.43/3.51 | (43) all_103_1 = 0 % 20.43/3.51 | % 20.43/3.51 | BETA: splitting (35) gives: % 20.43/3.51 | % 20.43/3.51 | Case 1: % 20.43/3.51 | | % 20.43/3.51 | | (44) ~ (all_103_1 = 0) % 20.43/3.51 | | % 20.43/3.51 | | REDUCE: (43), (44) imply: % 20.43/3.51 | | (45) $false % 20.43/3.51 | | % 20.43/3.51 | | CLOSE: (45) is inconsistent. % 20.43/3.51 | | % 20.43/3.51 | Case 2: % 20.43/3.51 | | % 20.43/3.51 | | (46) ~ (all_103_2 = 0) | ~ (all_103_3 = 0) | ~ (all_103_4 = 0) | % 20.43/3.51 | | (all_103_0 = use & all_79_0 = use) % 20.43/3.51 | | % 20.43/3.51 | | BETA: splitting (46) gives: % 20.43/3.51 | | % 20.43/3.51 | | Case 1: % 20.43/3.51 | | | % 20.43/3.51 | | | (47) ~ (all_103_2 = 0) % 20.43/3.51 | | | % 20.43/3.51 | | | REDUCE: (38), (47) imply: % 20.43/3.51 | | | (48) $false % 20.43/3.51 | | | % 20.43/3.51 | | | CLOSE: (48) is inconsistent. % 20.43/3.51 | | | % 20.43/3.51 | | Case 2: % 20.43/3.51 | | | % 20.43/3.51 | | | (49) ~ (all_103_3 = 0) | ~ (all_103_4 = 0) | (all_103_0 = use & % 20.43/3.51 | | | all_79_0 = use) % 20.43/3.51 | | | % 20.43/3.51 | | | BETA: splitting (49) gives: % 20.43/3.51 | | | % 20.43/3.51 | | | Case 1: % 20.43/3.51 | | | | % 20.43/3.51 | | | | (50) ~ (all_103_3 = 0) % 20.43/3.51 | | | | % 20.43/3.51 | | | | REDUCE: (37), (50) imply: % 20.43/3.51 | | | | (51) $false % 20.43/3.51 | | | | % 20.43/3.51 | | | | CLOSE: (51) is inconsistent. % 20.43/3.51 | | | | % 20.43/3.51 | | | Case 2: % 20.43/3.51 | | | | % 20.43/3.51 | | | | (52) ~ (all_103_4 = 0) | (all_103_0 = use & all_79_0 = use) % 20.43/3.51 | | | | % 20.43/3.51 | | | | BETA: splitting (52) gives: % 20.43/3.51 | | | | % 20.43/3.51 | | | | Case 1: % 20.43/3.51 | | | | | % 20.43/3.51 | | | | | (53) ~ (all_103_4 = 0) % 20.43/3.51 | | | | | % 20.43/3.51 | | | | | REDUCE: (36), (53) imply: % 20.43/3.51 | | | | | (54) $false % 20.43/3.51 | | | | | % 20.43/3.51 | | | | | CLOSE: (54) is inconsistent. % 20.43/3.51 | | | | | % 20.43/3.51 | | | | Case 2: % 20.43/3.51 | | | | | % 20.43/3.51 | | | | | (55) all_103_0 = use & all_79_0 = use % 20.43/3.51 | | | | | % 20.43/3.51 | | | | | ALPHA: (55) implies: % 20.43/3.51 | | | | | (56) all_79_0 = use % 20.43/3.51 | | | | | (57) all_103_0 = use % 20.43/3.51 | | | | | % 20.43/3.51 | | | | | COMBINE_EQS: (39), (57) imply: % 20.43/3.51 | | | | | (58) all_79_1 = use % 20.43/3.51 | | | | | % 20.43/3.51 | | | | | BETA: splitting (22) gives: % 20.43/3.51 | | | | | % 20.43/3.51 | | | | | Case 1: % 20.43/3.51 | | | | | | % 20.43/3.51 | | | | | | (59) ~ (all_79_0 = use) % 20.43/3.51 | | | | | | % 20.43/3.51 | | | | | | REDUCE: (56), (59) imply: % 20.43/3.51 | | | | | | (60) $false % 20.43/3.51 | | | | | | % 20.43/3.51 | | | | | | CLOSE: (60) is inconsistent. % 20.43/3.51 | | | | | | % 20.43/3.51 | | | | | Case 2: % 20.43/3.51 | | | | | | % 20.43/3.51 | | | | | | (61) ~ (all_79_1 = use) % 20.43/3.51 | | | | | | % 20.43/3.51 | | | | | | REDUCE: (58), (61) imply: % 20.43/3.51 | | | | | | (62) $false % 20.43/3.51 | | | | | | % 20.43/3.51 | | | | | | CLOSE: (62) is inconsistent. % 20.43/3.51 | | | | | | % 20.43/3.51 | | | | | End of split % 20.43/3.51 | | | | | % 20.43/3.51 | | | | End of split % 20.43/3.51 | | | | % 20.43/3.51 | | | End of split % 20.43/3.51 | | | % 20.43/3.51 | | End of split % 20.43/3.51 | | % 20.43/3.51 | End of split % 20.43/3.51 | % 20.43/3.51 End of proof % 20.43/3.51 % SZS output end Proof for theBenchmark % 20.43/3.51 % 20.43/3.51 2902ms %------------------------------------------------------------------------------