%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV203+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 : n002.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 22:55:20 EDT 2023 % Result : Theorem 22.21s 3.69s % Output : Proof 30.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV203+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n002.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 04:57:35 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.07/1.34 Prover 1: Preprocessing ... % 4.07/1.34 Prover 4: Preprocessing ... % 4.07/1.37 Prover 2: Preprocessing ... % 4.07/1.37 Prover 0: Preprocessing ... % 4.07/1.37 Prover 3: Preprocessing ... % 4.07/1.38 Prover 5: Preprocessing ... % 4.07/1.38 Prover 6: Preprocessing ... % 11.24/2.22 Prover 1: Warning: ignoring some quantifiers % 11.24/2.27 Prover 4: Warning: ignoring some quantifiers % 11.71/2.29 Prover 3: Warning: ignoring some quantifiers % 11.71/2.31 Prover 1: Constructing countermodel ... % 11.71/2.32 Prover 3: Constructing countermodel ... % 11.71/2.34 Prover 6: Proving ... % 11.71/2.35 Prover 4: Constructing countermodel ... % 12.33/2.37 Prover 0: Proving ... % 12.43/2.41 Prover 5: Proving ... % 13.46/2.60 Prover 2: Proving ... % 22.21/3.69 Prover 0: proved (3071ms) % 22.21/3.69 % 22.21/3.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.21/3.69 % 22.21/3.69 Prover 3: stopped % 22.21/3.69 Prover 6: stopped % 22.21/3.69 Prover 2: stopped % 22.55/3.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.55/3.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.55/3.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.55/3.73 Prover 5: stopped % 22.55/3.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.55/3.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.11/3.97 Prover 11: Preprocessing ... % 24.11/3.98 Prover 13: Preprocessing ... % 24.11/3.98 Prover 10: Preprocessing ... % 24.11/3.99 Prover 8: Preprocessing ... % 24.11/3.99 Prover 7: Preprocessing ... % 25.93/4.20 Prover 10: Warning: ignoring some quantifiers % 25.93/4.20 Prover 7: Warning: ignoring some quantifiers % 25.93/4.21 Prover 10: Constructing countermodel ... % 25.93/4.23 Prover 7: Constructing countermodel ... % 26.61/4.26 Prover 8: Warning: ignoring some quantifiers % 26.92/4.29 Prover 11: Warning: ignoring some quantifiers % 26.92/4.29 Prover 8: Constructing countermodel ... % 26.92/4.31 Prover 11: Constructing countermodel ... % 26.92/4.33 Prover 13: Warning: ignoring some quantifiers % 27.36/4.35 Prover 13: Constructing countermodel ... % 29.89/4.68 Prover 10: Found proof (size 38) % 29.89/4.68 Prover 10: proved (984ms) % 29.89/4.68 Prover 8: stopped % 29.89/4.68 Prover 13: stopped % 29.89/4.68 Prover 7: stopped % 29.89/4.68 Prover 4: stopped % 29.89/4.68 Prover 11: stopped % 29.89/4.68 Prover 1: stopped % 29.89/4.69 % 29.89/4.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.89/4.69 % 29.89/4.69 % SZS output start Proof for theBenchmark % 29.89/4.69 Assumptions after simplification: % 29.89/4.69 --------------------------------- % 29.89/4.70 % 29.89/4.70 (finite_domain_2) % 29.89/4.70 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 29.89/4.70 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0)) % 29.89/4.70 % 29.89/4.70 (leq_gt2) % 29.89/4.70 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 29.89/4.70 | gt(v1, v0)) % 29.89/4.70 % 29.89/4.70 (leq_gt_pred) % 29.89/4.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ % 29.89/4.72 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.89/4.72 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 29.89/4.72 v2)) % 29.89/4.72 % 29.89/4.72 (quaternion_ds1_inuse_0014) % 30.19/4.73 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) & % 30.19/4.73 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & % 30.19/4.73 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) % 30.19/4.73 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) & % 30.19/4.73 a_select3(z_defuse, v1, v2) = v3 & a_select3(u_defuse, n2, n0) = use & % 30.19/4.73 a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) = use & % 30.19/4.73 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4) % 30.19/4.73 = use & a_select2(xinit_noise_defuse, n3) = use & % 30.19/4.73 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1) % 30.19/4.73 = use & a_select2(xinit_noise_defuse, n0) = use & % 30.19/4.73 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) = % 30.19/4.73 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 30.19/4.73 n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 30.19/4.73 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use & % 30.19/4.73 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use & % 30.19/4.73 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use & % 30.19/4.73 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use & % 30.19/4.73 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use & % 30.19/4.73 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 30.19/4.73 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & $i(v3) & $i(v2) & $i(v1) % 30.19/4.73 & $i(v0) & leq(v2, pv5) & leq(v1, n2) & leq(pv5, n998) & leq(n0, v2) & % 30.19/4.73 leq(n0, v1) & leq(n0, pv5) & gt(pv5, n0) & ! [v4: $i] : ! [v5: $i] : ! % 30.19/4.73 [v6: $i] : (v6 = use | ~ (a_select3(z_defuse, v4, v5) = v6) | ~ $i(v5) | % 30.19/4.73 ~ $i(v4) | ~ leq(v5, v0) | ~ leq(v4, n2) | ~ leq(n0, v5) | ~ leq(n0, % 30.19/4.73 v4)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = use | ~ % 30.19/4.73 (a_select3(u_defuse, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ leq(v5, % 30.19/4.73 v0) | ~ leq(v4, n2) | ~ leq(n0, v5) | ~ leq(n0, v4)) & ( ~ (v2 = pv5) % 30.19/4.73 | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5) | ~ (v1 % 30.19/4.73 = n0))) % 30.19/4.73 % 30.19/4.73 Further assumptions not needed in the proof: % 30.19/4.73 -------------------------------------------- % 30.19/4.73 const_array1_select, const_array2_select, defuse, finite_domain_0, % 30.19/4.73 finite_domain_1, finite_domain_3, finite_domain_4, finite_domain_5, % 30.19/4.73 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, % 30.19/4.73 gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, % 30.19/4.73 gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, % 30.19/4.73 gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, % 30.19/4.73 gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, % 30.19/4.73 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 30.19/4.73 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 30.19/4.73 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 30.19/4.73 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 30.19/4.73 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 30.19/4.73 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 30.19/4.73 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 30.19/4.73 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 30.19/4.73 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 30.19/4.73 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 30.19/4.73 % 30.19/4.73 Those formulas are unsatisfiable: % 30.19/4.73 --------------------------------- % 30.19/4.73 % 30.19/4.73 Begin of proof % 30.19/4.73 | % 30.19/4.73 | ALPHA: (leq_gt_pred) implies: % 30.19/4.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 30.19/4.73 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 30.19/4.73 | % 30.19/4.73 | ALPHA: (finite_domain_2) implies: % 30.19/4.74 | (2) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) % 30.19/4.74 | | ~ leq(n0, v0)) % 30.19/4.74 | % 30.19/4.74 | ALPHA: (quaternion_ds1_inuse_0014) implies: % 30.19/4.74 | (3) $i(pv5) % 30.19/4.74 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) % 30.19/4.74 | & a_select3(z_defuse, v1, v2) = v3 & a_select3(u_defuse, n2, n0) = % 30.19/4.74 | use & a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) % 30.19/4.74 | = use & a_select2(xinit_noise_defuse, n5) = use & % 30.19/4.74 | a_select2(xinit_noise_defuse, n4) = use & % 30.19/4.74 | a_select2(xinit_noise_defuse, n3) = use & % 30.19/4.74 | a_select2(xinit_noise_defuse, n2) = use & % 30.19/4.74 | a_select2(xinit_noise_defuse, n1) = use & % 30.19/4.74 | a_select2(xinit_noise_defuse, n0) = use & % 30.19/4.74 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 30.19/4.74 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 30.19/4.74 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 30.19/4.74 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 30.19/4.74 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use % 30.19/4.74 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = % 30.19/4.74 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) % 30.19/4.74 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, % 30.19/4.74 | n1) = use & a_select2(sigma_defuse, n0) = use & % 30.19/4.74 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 30.19/4.74 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & $i(v3) & $i(v2) & % 30.19/4.74 | $i(v1) & $i(v0) & leq(v2, pv5) & leq(v1, n2) & leq(pv5, n998) & % 30.19/4.74 | leq(n0, v2) & leq(n0, v1) & leq(n0, pv5) & gt(pv5, n0) & ! [v4: $i] % 30.19/4.74 | : ! [v5: $i] : ! [v6: $i] : (v6 = use | ~ (a_select3(z_defuse, v4, % 30.19/4.74 | v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ leq(v5, v0) | ~ leq(v4, % 30.19/4.74 | n2) | ~ leq(n0, v5) | ~ leq(n0, v4)) & ! [v4: $i] : ! [v5: % 30.19/4.74 | $i] : ! [v6: $i] : (v6 = use | ~ (a_select3(u_defuse, v4, v5) = % 30.19/4.74 | v6) | ~ $i(v5) | ~ $i(v4) | ~ leq(v5, v0) | ~ leq(v4, n2) | % 30.19/4.74 | ~ leq(n0, v5) | ~ leq(n0, v4)) & ( ~ (v2 = pv5) | ~ (v1 = n2)) & % 30.19/4.74 | ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5) | ~ (v1 = n0))) % 30.19/4.74 | % 30.19/4.74 | DELTA: instantiating (4) with fresh symbols all_71_0, all_71_1, all_71_2, % 30.19/4.74 | all_71_3 gives: % 30.19/4.75 | (5) ~ (all_71_0 = use) & a_select3(z_defuse, all_71_2, all_71_1) = % 30.19/4.75 | all_71_0 & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, % 30.19/4.75 | n0) = use & a_select3(u_defuse, n0, n0) = use & % 30.19/4.75 | a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, % 30.19/4.75 | n4) = use & a_select2(xinit_noise_defuse, n3) = use & % 30.19/4.75 | a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, % 30.19/4.75 | n1) = use & a_select2(xinit_noise_defuse, n0) = use & % 30.19/4.75 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 30.19/4.75 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 30.19/4.75 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 30.19/4.75 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 30.19/4.75 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use & % 30.19/4.75 | a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use & % 30.19/4.75 | a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use & % 30.19/4.75 | a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use & % 30.19/4.75 | a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use & % 30.19/4.75 | a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use & % 30.19/4.75 | pred(pv5) = all_71_3 & $i(all_71_0) & $i(all_71_1) & $i(all_71_2) & % 30.19/4.75 | $i(all_71_3) & leq(all_71_1, pv5) & leq(all_71_2, n2) & leq(pv5, n998) % 30.19/4.75 | & leq(n0, all_71_1) & leq(n0, all_71_2) & leq(n0, pv5) & gt(pv5, n0) & % 30.19/4.75 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~ % 30.19/4.75 | (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.19/4.75 | leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 30.19/4.75 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~ % 30.19/4.75 | (a_select3(u_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.19/4.75 | leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 30.19/4.75 | & ( ~ (all_71_1 = pv5) | ~ (all_71_2 = n2)) & ( ~ (all_71_1 = pv5) | % 30.19/4.75 | ~ (all_71_2 = n1)) & ( ~ (all_71_1 = pv5) | ~ (all_71_2 = n0)) % 30.19/4.75 | % 30.19/4.75 | ALPHA: (5) implies: % 30.19/4.75 | (6) ~ (all_71_0 = use) % 30.19/4.75 | (7) leq(n0, all_71_2) % 30.19/4.75 | (8) leq(n0, all_71_1) % 30.19/4.75 | (9) leq(all_71_2, n2) % 30.19/4.75 | (10) leq(all_71_1, pv5) % 30.19/4.75 | (11) $i(all_71_2) % 30.19/4.75 | (12) $i(all_71_1) % 30.19/4.75 | (13) pred(pv5) = all_71_3 % 30.19/4.75 | (14) a_select3(z_defuse, all_71_2, all_71_1) = all_71_0 % 30.19/4.75 | (15) ~ (all_71_1 = pv5) | ~ (all_71_2 = n0) % 30.19/4.75 | (16) ~ (all_71_1 = pv5) | ~ (all_71_2 = n1) % 30.19/4.75 | (17) ~ (all_71_1 = pv5) | ~ (all_71_2 = n2) % 30.19/4.75 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~ % 30.19/4.75 | (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.19/4.75 | leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, % 30.19/4.75 | v0)) % 30.19/4.75 | % 30.19/4.75 | GROUND_INST: instantiating (2) with all_71_2, simplifying with (7), (9), (11) % 30.19/4.75 | gives: % 30.19/4.75 | (19) all_71_2 = n2 | all_71_2 = n1 | all_71_2 = n0 % 30.19/4.75 | % 30.19/4.75 | GROUND_INST: instantiating (leq_gt2) with all_71_1, pv5, simplifying with (3), % 30.19/4.75 | (10), (12) gives: % 30.19/4.75 | (20) all_71_1 = pv5 | gt(pv5, all_71_1) % 30.19/4.75 | % 30.19/4.75 | BETA: splitting (15) gives: % 30.19/4.75 | % 30.19/4.75 | Case 1: % 30.19/4.75 | | % 30.19/4.75 | | (21) ~ (all_71_2 = n0) % 30.19/4.75 | | % 30.19/4.75 | | BETA: splitting (17) gives: % 30.19/4.75 | | % 30.19/4.75 | | Case 1: % 30.19/4.75 | | | % 30.19/4.75 | | | (22) ~ (all_71_1 = pv5) % 30.19/4.75 | | | % 30.30/4.75 | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11), (12), (13), (14), (18), % 30.30/4.75 | | | (20), (22) are inconsistent by sub-proof #1. % 30.30/4.75 | | | % 30.30/4.75 | | Case 2: % 30.30/4.75 | | | % 30.30/4.75 | | | (23) all_71_1 = pv5 % 30.30/4.75 | | | (24) ~ (all_71_2 = n2) % 30.30/4.75 | | | % 30.30/4.75 | | | BETA: splitting (16) gives: % 30.30/4.75 | | | % 30.30/4.75 | | | Case 1: % 30.30/4.75 | | | | % 30.30/4.76 | | | | (25) ~ (all_71_1 = pv5) % 30.30/4.76 | | | | % 30.30/4.76 | | | | REDUCE: (23), (25) imply: % 30.30/4.76 | | | | (26) $false % 30.30/4.76 | | | | % 30.30/4.76 | | | | CLOSE: (26) is inconsistent. % 30.30/4.76 | | | | % 30.30/4.76 | | | Case 2: % 30.30/4.76 | | | | % 30.30/4.76 | | | | (27) ~ (all_71_2 = n1) % 30.30/4.76 | | | | % 30.30/4.76 | | | | BETA: splitting (19) gives: % 30.30/4.76 | | | | % 30.30/4.76 | | | | Case 1: % 30.30/4.76 | | | | | % 30.30/4.76 | | | | | (28) all_71_2 = n0 % 30.30/4.76 | | | | | % 30.30/4.76 | | | | | REDUCE: (21), (28) imply: % 30.30/4.76 | | | | | (29) $false % 30.30/4.76 | | | | | % 30.30/4.76 | | | | | CLOSE: (29) is inconsistent. % 30.30/4.76 | | | | | % 30.30/4.76 | | | | Case 2: % 30.30/4.76 | | | | | % 30.30/4.76 | | | | | (30) all_71_2 = n2 | all_71_2 = n1 % 30.30/4.76 | | | | | % 30.30/4.76 | | | | | BETA: splitting (30) gives: % 30.30/4.76 | | | | | % 30.30/4.76 | | | | | Case 1: % 30.30/4.76 | | | | | | % 30.30/4.76 | | | | | | (31) all_71_2 = n2 % 30.30/4.76 | | | | | | % 30.30/4.76 | | | | | | REDUCE: (24), (31) imply: % 30.30/4.76 | | | | | | (32) $false % 30.30/4.76 | | | | | | % 30.30/4.76 | | | | | | CLOSE: (32) is inconsistent. % 30.30/4.76 | | | | | | % 30.30/4.76 | | | | | Case 2: % 30.30/4.76 | | | | | | % 30.30/4.76 | | | | | | (33) all_71_2 = n1 % 30.30/4.76 | | | | | | % 30.30/4.76 | | | | | | REDUCE: (27), (33) imply: % 30.30/4.76 | | | | | | (34) $false % 30.30/4.76 | | | | | | % 30.30/4.76 | | | | | | CLOSE: (34) is inconsistent. % 30.30/4.76 | | | | | | % 30.30/4.76 | | | | | End of split % 30.30/4.76 | | | | | % 30.30/4.76 | | | | End of split % 30.30/4.76 | | | | % 30.30/4.76 | | | End of split % 30.30/4.76 | | | % 30.30/4.76 | | End of split % 30.30/4.76 | | % 30.30/4.76 | Case 2: % 30.30/4.76 | | % 30.30/4.76 | | (35) ~ (all_71_1 = pv5) % 30.30/4.76 | | % 30.30/4.76 | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11), (12), (13), (14), (18), (20), % 30.30/4.76 | | (35) are inconsistent by sub-proof #1. % 30.30/4.76 | | % 30.30/4.76 | End of split % 30.30/4.76 | % 30.30/4.76 End of proof % 30.30/4.76 % 30.30/4.76 Sub-proof #1 shows that the following formulas are inconsistent: % 30.30/4.76 ---------------------------------------------------------------- % 30.30/4.76 (1) leq(all_71_2, n2) % 30.30/4.76 (2) leq(n0, all_71_1) % 30.30/4.76 (3) $i(pv5) % 30.30/4.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 30.30/4.76 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 30.30/4.76 (5) a_select3(z_defuse, all_71_2, all_71_1) = all_71_0 % 30.30/4.76 (6) leq(n0, all_71_2) % 30.30/4.76 (7) pred(pv5) = all_71_3 % 30.30/4.76 (8) ~ (all_71_1 = pv5) % 30.30/4.76 (9) $i(all_71_1) % 30.30/4.76 (10) ~ (all_71_0 = use) % 30.30/4.76 (11) $i(all_71_2) % 30.30/4.76 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~ % 30.30/4.76 (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.30/4.76 leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 30.30/4.76 (13) all_71_1 = pv5 | gt(pv5, all_71_1) % 30.30/4.76 % 30.30/4.76 Begin of proof % 30.30/4.76 | % 30.30/4.76 | BETA: splitting (13) gives: % 30.30/4.76 | % 30.30/4.76 | Case 1: % 30.30/4.76 | | % 30.30/4.76 | | (14) gt(pv5, all_71_1) % 30.30/4.76 | | % 30.30/4.76 | | GROUND_INST: instantiating (4) with all_71_1, pv5, all_71_3, simplifying % 30.30/4.76 | | with (3), (7), (9), (14) gives: % 30.30/4.76 | | (15) leq(all_71_1, all_71_3) % 30.30/4.76 | | % 30.30/4.76 | | GROUND_INST: instantiating (12) with all_71_2, all_71_1, all_71_0, % 30.30/4.76 | | simplifying with (1), (2), (5), (6), (9), (11), (15) gives: % 30.30/4.76 | | (16) all_71_0 = use % 30.30/4.76 | | % 30.30/4.76 | | REDUCE: (10), (16) imply: % 30.30/4.76 | | (17) $false % 30.30/4.76 | | % 30.30/4.76 | | CLOSE: (17) is inconsistent. % 30.30/4.76 | | % 30.30/4.76 | Case 2: % 30.30/4.76 | | % 30.30/4.76 | | (18) all_71_1 = pv5 % 30.30/4.76 | | % 30.30/4.76 | | REDUCE: (8), (18) imply: % 30.30/4.76 | | (19) $false % 30.30/4.76 | | % 30.30/4.76 | | CLOSE: (19) is inconsistent. % 30.30/4.76 | | % 30.30/4.76 | End of split % 30.30/4.76 | % 30.30/4.76 End of proof % 30.30/4.76 % SZS output end Proof for theBenchmark % 30.30/4.76 % 30.30/4.76 4166ms %------------------------------------------------------------------------------