%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV202+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 : n021.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 32.11s 5.22s % Output : Proof 43.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWV202+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n021.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 08:04:29 EDT 2023 % 0.14/0.35 % CPUTime : % 0.42/0.63 ________ _____ % 0.42/0.63 ___ __ \_________(_)________________________________ % 0.42/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.42/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.42/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.42/0.63 % 0.42/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.42/0.63 (2023-06-19) % 0.42/0.63 % 0.42/0.63 (c) Philipp Rümmer, 2009-2023 % 0.42/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.42/0.63 Amanda Stjerna. % 0.42/0.63 Free software under BSD-3-Clause. % 0.42/0.63 % 0.42/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.42/0.63 % 0.42/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.42/0.64 Running up to 7 provers in parallel. % 0.42/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.42/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.42/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.42/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.42/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.42/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.42/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.35/1.62 Prover 1: Preprocessing ... % 5.35/1.63 Prover 4: Preprocessing ... % 5.95/1.67 Prover 2: Preprocessing ... % 5.95/1.67 Prover 5: Preprocessing ... % 5.95/1.67 Prover 6: Preprocessing ... % 5.95/1.68 Prover 0: Preprocessing ... % 5.95/1.69 Prover 3: Preprocessing ... % 15.18/2.96 Prover 1: Warning: ignoring some quantifiers % 15.82/3.04 Prover 6: Proving ... % 15.82/3.04 Prover 3: Warning: ignoring some quantifiers % 16.43/3.09 Prover 1: Constructing countermodel ... % 16.43/3.10 Prover 3: Constructing countermodel ... % 16.43/3.17 Prover 4: Warning: ignoring some quantifiers % 16.43/3.23 Prover 0: Proving ... % 17.32/3.29 Prover 4: Constructing countermodel ... % 18.13/3.40 Prover 5: Proving ... % 18.13/3.40 Prover 2: Proving ... % 32.11/5.21 Prover 0: proved (4517ms) % 32.11/5.22 % 32.11/5.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 32.11/5.22 % 32.11/5.22 Prover 3: stopped % 32.11/5.22 Prover 5: stopped % 32.49/5.23 Prover 2: stopped % 32.49/5.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 32.49/5.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 32.49/5.23 Prover 6: stopped % 32.49/5.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 32.49/5.24 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 32.49/5.24 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 34.14/5.47 Prover 8: Preprocessing ... % 34.14/5.49 Prover 11: Preprocessing ... % 34.51/5.53 Prover 10: Preprocessing ... % 34.92/5.61 Prover 13: Preprocessing ... % 34.92/5.61 Prover 7: Preprocessing ... % 36.79/5.86 Prover 10: Warning: ignoring some quantifiers % 36.79/5.86 Prover 8: Warning: ignoring some quantifiers % 36.79/5.89 Prover 8: Constructing countermodel ... % 36.79/5.89 Prover 10: Constructing countermodel ... % 37.27/6.01 Prover 7: Warning: ignoring some quantifiers % 38.88/6.07 Prover 7: Constructing countermodel ... % 38.88/6.07 Prover 11: Warning: ignoring some quantifiers % 38.88/6.12 Prover 11: Constructing countermodel ... % 39.45/6.16 Prover 13: Warning: ignoring some quantifiers % 40.05/6.24 Prover 13: Constructing countermodel ... % 41.94/6.67 Prover 10: Found proof (size 38) % 42.44/6.67 Prover 10: proved (1441ms) % 42.44/6.67 Prover 7: stopped % 42.44/6.67 Prover 13: stopped % 42.44/6.67 Prover 8: stopped % 42.44/6.67 Prover 4: stopped % 42.44/6.67 Prover 11: stopped % 42.44/6.68 Prover 1: stopped % 42.44/6.68 % 42.44/6.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 42.44/6.68 % 42.44/6.69 % SZS output start Proof for theBenchmark % 42.44/6.70 Assumptions after simplification: % 42.44/6.70 --------------------------------- % 42.44/6.70 % 42.44/6.70 (finite_domain_2) % 43.60/6.71 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 43.60/6.71 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0)) % 43.60/6.71 % 43.60/6.71 (leq_gt2) % 43.60/6.71 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 43.60/6.71 | gt(v1, v0)) % 43.60/6.71 % 43.60/6.71 (leq_gt_pred) % 43.60/6.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ % 43.60/6.74 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 43.60/6.74 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 43.60/6.74 v2)) % 43.60/6.74 % 43.60/6.74 (quaternion_ds1_inuse_0013) % 43.60/6.76 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) & % 43.60/6.76 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & % 43.60/6.76 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) % 43.60/6.76 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) & % 43.60/6.76 a_select3(u_defuse, v1, v2) = v3 & a_select3(u_defuse, n2, n0) = use & % 43.60/6.76 a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) = use & % 43.60/6.76 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4) % 43.60/6.76 = use & a_select2(xinit_noise_defuse, n3) = use & % 43.60/6.76 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1) % 43.60/6.76 = use & a_select2(xinit_noise_defuse, n0) = use & % 43.60/6.76 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) = % 43.60/6.76 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 43.60/6.76 n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 43.60/6.76 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use & % 43.60/6.76 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use & % 43.60/6.76 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use & % 43.60/6.76 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use & % 43.60/6.76 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use & % 43.60/6.76 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 43.60/6.76 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & $i(v3) & $i(v2) & $i(v1) % 43.60/6.76 & $i(v0) & leq(v2, pv5) & leq(v1, n2) & leq(pv5, n998) & leq(n0, v2) & % 43.60/6.76 leq(n0, v1) & leq(n0, pv5) & gt(pv5, n0) & ! [v4: $i] : ! [v5: $i] : ! % 43.60/6.76 [v6: $i] : (v6 = use | ~ (a_select3(z_defuse, v4, v5) = v6) | ~ $i(v5) | % 43.60/6.76 ~ $i(v4) | ~ leq(v5, v0) | ~ leq(v4, n2) | ~ leq(n0, v5) | ~ leq(n0, % 43.60/6.76 v4)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = use | ~ % 43.60/6.76 (a_select3(u_defuse, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ leq(v5, % 43.60/6.76 v0) | ~ leq(v4, n2) | ~ leq(n0, v5) | ~ leq(n0, v4)) & ( ~ (v2 = pv5) % 43.60/6.76 | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5) | ~ (v1 % 43.60/6.76 = n0))) % 43.60/6.76 % 43.60/6.76 Further assumptions not needed in the proof: % 43.60/6.76 -------------------------------------------- % 43.60/6.76 const_array1_select, const_array2_select, defuse, finite_domain_0, % 43.60/6.76 finite_domain_1, finite_domain_3, finite_domain_4, finite_domain_5, % 43.60/6.76 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, % 43.60/6.76 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, % 43.60/6.76 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, % 43.60/6.76 gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, % 43.60/6.76 gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, % 43.60/6.76 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 43.60/6.76 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 43.60/6.76 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 43.60/6.76 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 43.60/6.76 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 43.60/6.76 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 43.60/6.76 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 43.60/6.76 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 43.60/6.76 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 43.60/6.76 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 43.60/6.76 % 43.60/6.76 Those formulas are unsatisfiable: % 43.60/6.76 --------------------------------- % 43.60/6.76 % 43.60/6.76 Begin of proof % 43.60/6.76 | % 43.60/6.76 | ALPHA: (leq_gt_pred) implies: % 43.60/6.77 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 43.60/6.77 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 43.60/6.77 | % 43.60/6.77 | ALPHA: (finite_domain_2) implies: % 43.60/6.77 | (2) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) % 43.60/6.77 | | ~ leq(n0, v0)) % 43.60/6.77 | % 43.60/6.77 | ALPHA: (quaternion_ds1_inuse_0013) implies: % 43.60/6.77 | (3) $i(pv5) % 43.96/6.78 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) % 43.96/6.78 | & a_select3(u_defuse, v1, v2) = v3 & a_select3(u_defuse, n2, n0) = % 43.96/6.78 | use & a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) % 43.96/6.78 | = use & a_select2(xinit_noise_defuse, n5) = use & % 43.96/6.78 | a_select2(xinit_noise_defuse, n4) = use & % 43.96/6.78 | a_select2(xinit_noise_defuse, n3) = use & % 43.96/6.78 | a_select2(xinit_noise_defuse, n2) = use & % 43.96/6.78 | a_select2(xinit_noise_defuse, n1) = use & % 43.96/6.78 | a_select2(xinit_noise_defuse, n0) = use & % 43.96/6.78 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 43.96/6.78 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 43.96/6.78 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 43.96/6.78 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 43.96/6.78 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use % 43.96/6.78 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = % 43.96/6.78 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) % 43.96/6.78 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, % 43.96/6.78 | n1) = use & a_select2(sigma_defuse, n0) = use & % 43.96/6.78 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 43.96/6.78 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & $i(v3) & $i(v2) & % 43.96/6.78 | $i(v1) & $i(v0) & leq(v2, pv5) & leq(v1, n2) & leq(pv5, n998) & % 43.96/6.78 | leq(n0, v2) & leq(n0, v1) & leq(n0, pv5) & gt(pv5, n0) & ! [v4: $i] % 43.96/6.78 | : ! [v5: $i] : ! [v6: $i] : (v6 = use | ~ (a_select3(z_defuse, v4, % 43.96/6.78 | v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ leq(v5, v0) | ~ leq(v4, % 43.96/6.78 | n2) | ~ leq(n0, v5) | ~ leq(n0, v4)) & ! [v4: $i] : ! [v5: % 43.96/6.78 | $i] : ! [v6: $i] : (v6 = use | ~ (a_select3(u_defuse, v4, v5) = % 43.96/6.78 | v6) | ~ $i(v5) | ~ $i(v4) | ~ leq(v5, v0) | ~ leq(v4, n2) | % 43.96/6.78 | ~ leq(n0, v5) | ~ leq(n0, v4)) & ( ~ (v2 = pv5) | ~ (v1 = n2)) & % 43.96/6.78 | ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5) | ~ (v1 = n0))) % 43.96/6.78 | % 43.96/6.78 | DELTA: instantiating (4) with fresh symbols all_71_0, all_71_1, all_71_2, % 43.96/6.78 | all_71_3 gives: % 43.96/6.79 | (5) ~ (all_71_0 = use) & a_select3(u_defuse, all_71_2, all_71_1) = % 43.96/6.79 | all_71_0 & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, % 43.96/6.79 | n0) = use & a_select3(u_defuse, n0, n0) = use & % 43.96/6.79 | a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, % 43.96/6.79 | n4) = use & a_select2(xinit_noise_defuse, n3) = use & % 43.96/6.79 | a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, % 43.96/6.79 | n1) = use & a_select2(xinit_noise_defuse, n0) = use & % 43.96/6.79 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 43.96/6.79 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 43.96/6.79 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 43.96/6.79 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 43.96/6.79 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use & % 43.96/6.79 | a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use & % 43.96/6.79 | a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use & % 43.96/6.79 | a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use & % 43.96/6.79 | a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use & % 43.96/6.79 | a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use & % 43.96/6.79 | pred(pv5) = all_71_3 & $i(all_71_0) & $i(all_71_1) & $i(all_71_2) & % 43.96/6.79 | $i(all_71_3) & leq(all_71_1, pv5) & leq(all_71_2, n2) & leq(pv5, n998) % 43.96/6.79 | & leq(n0, all_71_1) & leq(n0, all_71_2) & leq(n0, pv5) & gt(pv5, n0) & % 43.96/6.79 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~ % 43.96/6.79 | (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 43.96/6.79 | leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 43.96/6.79 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~ % 43.96/6.79 | (a_select3(u_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 43.96/6.79 | leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 43.96/6.79 | & ( ~ (all_71_1 = pv5) | ~ (all_71_2 = n2)) & ( ~ (all_71_1 = pv5) | % 43.96/6.79 | ~ (all_71_2 = n1)) & ( ~ (all_71_1 = pv5) | ~ (all_71_2 = n0)) % 43.96/6.79 | % 43.96/6.79 | ALPHA: (5) implies: % 43.96/6.79 | (6) ~ (all_71_0 = use) % 43.96/6.79 | (7) leq(n0, all_71_2) % 43.96/6.79 | (8) leq(n0, all_71_1) % 43.96/6.79 | (9) leq(all_71_2, n2) % 43.96/6.79 | (10) leq(all_71_1, pv5) % 43.96/6.79 | (11) $i(all_71_2) % 43.96/6.79 | (12) $i(all_71_1) % 43.96/6.79 | (13) pred(pv5) = all_71_3 % 43.96/6.79 | (14) a_select3(u_defuse, all_71_2, all_71_1) = all_71_0 % 43.96/6.79 | (15) ~ (all_71_1 = pv5) | ~ (all_71_2 = n0) % 43.96/6.79 | (16) ~ (all_71_1 = pv5) | ~ (all_71_2 = n1) % 43.96/6.79 | (17) ~ (all_71_1 = pv5) | ~ (all_71_2 = n2) % 43.96/6.79 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~ % 43.96/6.79 | (a_select3(u_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 43.96/6.79 | leq(v1, all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, % 43.96/6.79 | v0)) % 43.96/6.79 | % 43.96/6.79 | GROUND_INST: instantiating (2) with all_71_2, simplifying with (7), (9), (11) % 43.96/6.79 | gives: % 43.96/6.79 | (19) all_71_2 = n2 | all_71_2 = n1 | all_71_2 = n0 % 43.96/6.79 | % 43.96/6.80 | GROUND_INST: instantiating (leq_gt2) with all_71_1, pv5, simplifying with (3), % 43.96/6.80 | (10), (12) gives: % 43.96/6.80 | (20) all_71_1 = pv5 | gt(pv5, all_71_1) % 43.96/6.80 | % 43.96/6.80 | BETA: splitting (15) gives: % 43.96/6.80 | % 43.96/6.80 | Case 1: % 43.96/6.80 | | % 43.96/6.80 | | (21) ~ (all_71_2 = n0) % 43.96/6.80 | | % 43.96/6.80 | | BETA: splitting (17) gives: % 43.96/6.80 | | % 43.96/6.80 | | Case 1: % 43.96/6.80 | | | % 43.96/6.80 | | | (22) ~ (all_71_1 = pv5) % 43.96/6.80 | | | % 43.96/6.80 | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11), (12), (13), (14), (18), % 43.96/6.80 | | | (20), (22) are inconsistent by sub-proof #1. % 43.96/6.80 | | | % 43.96/6.80 | | Case 2: % 43.96/6.80 | | | % 43.96/6.80 | | | (23) all_71_1 = pv5 % 43.96/6.80 | | | (24) ~ (all_71_2 = n2) % 43.96/6.80 | | | % 43.96/6.80 | | | BETA: splitting (16) gives: % 43.96/6.80 | | | % 43.96/6.80 | | | Case 1: % 43.96/6.80 | | | | % 43.96/6.80 | | | | (25) ~ (all_71_1 = pv5) % 43.96/6.80 | | | | % 43.96/6.80 | | | | REDUCE: (23), (25) imply: % 43.96/6.80 | | | | (26) $false % 43.96/6.80 | | | | % 43.96/6.80 | | | | CLOSE: (26) is inconsistent. % 43.96/6.80 | | | | % 43.96/6.80 | | | Case 2: % 43.96/6.80 | | | | % 43.96/6.80 | | | | (27) ~ (all_71_2 = n1) % 43.96/6.80 | | | | % 43.96/6.80 | | | | BETA: splitting (19) gives: % 43.96/6.80 | | | | % 43.96/6.80 | | | | Case 1: % 43.96/6.80 | | | | | % 43.96/6.80 | | | | | (28) all_71_2 = n0 % 43.96/6.80 | | | | | % 43.96/6.80 | | | | | REDUCE: (21), (28) imply: % 43.96/6.80 | | | | | (29) $false % 43.96/6.80 | | | | | % 43.96/6.80 | | | | | CLOSE: (29) is inconsistent. % 43.96/6.80 | | | | | % 43.96/6.80 | | | | Case 2: % 43.96/6.80 | | | | | % 43.96/6.81 | | | | | (30) all_71_2 = n2 | all_71_2 = n1 % 43.96/6.81 | | | | | % 43.96/6.81 | | | | | BETA: splitting (30) gives: % 43.96/6.81 | | | | | % 43.96/6.81 | | | | | Case 1: % 43.96/6.81 | | | | | | % 43.96/6.81 | | | | | | (31) all_71_2 = n2 % 43.96/6.81 | | | | | | % 43.96/6.81 | | | | | | REDUCE: (24), (31) imply: % 43.96/6.81 | | | | | | (32) $false % 43.96/6.81 | | | | | | % 43.96/6.81 | | | | | | CLOSE: (32) is inconsistent. % 43.96/6.81 | | | | | | % 43.96/6.81 | | | | | Case 2: % 43.96/6.81 | | | | | | % 43.96/6.81 | | | | | | (33) all_71_2 = n1 % 43.96/6.81 | | | | | | % 43.96/6.81 | | | | | | REDUCE: (27), (33) imply: % 43.96/6.81 | | | | | | (34) $false % 43.96/6.81 | | | | | | % 43.96/6.81 | | | | | | CLOSE: (34) is inconsistent. % 43.96/6.81 | | | | | | % 43.96/6.81 | | | | | End of split % 43.96/6.81 | | | | | % 43.96/6.81 | | | | End of split % 43.96/6.81 | | | | % 43.96/6.81 | | | End of split % 43.96/6.81 | | | % 43.96/6.81 | | End of split % 43.96/6.81 | | % 43.96/6.81 | Case 2: % 43.96/6.81 | | % 43.96/6.81 | | (35) ~ (all_71_1 = pv5) % 43.96/6.81 | | % 43.96/6.81 | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11), (12), (13), (14), (18), (20), % 43.96/6.81 | | (35) are inconsistent by sub-proof #1. % 43.96/6.81 | | % 43.96/6.81 | End of split % 43.96/6.81 | % 43.96/6.81 End of proof % 43.96/6.81 % 43.96/6.81 Sub-proof #1 shows that the following formulas are inconsistent: % 43.96/6.81 ---------------------------------------------------------------- % 43.96/6.81 (1) pred(pv5) = all_71_3 % 43.96/6.81 (2) ~ (all_71_0 = use) % 43.96/6.81 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~ % 43.96/6.81 (a_select3(u_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, % 43.96/6.81 all_71_3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 43.96/6.81 (4) leq(n0, all_71_1) % 43.96/6.81 (5) $i(all_71_2) % 43.96/6.81 (6) $i(all_71_1) % 43.96/6.81 (7) leq(n0, all_71_2) % 43.96/6.81 (8) all_71_1 = pv5 | gt(pv5, all_71_1) % 43.96/6.81 (9) ~ (all_71_1 = pv5) % 43.96/6.81 (10) a_select3(u_defuse, all_71_2, all_71_1) = all_71_0 % 43.96/6.81 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 43.96/6.81 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 43.96/6.81 (12) $i(pv5) % 43.96/6.81 (13) leq(all_71_2, n2) % 43.96/6.81 % 43.96/6.81 Begin of proof % 43.96/6.81 | % 43.96/6.81 | BETA: splitting (8) gives: % 43.96/6.81 | % 43.96/6.81 | Case 1: % 43.96/6.81 | | % 43.96/6.81 | | (14) gt(pv5, all_71_1) % 43.96/6.82 | | % 43.96/6.82 | | GROUND_INST: instantiating (11) with all_71_1, pv5, all_71_3, simplifying % 43.96/6.82 | | with (1), (6), (12), (14) gives: % 43.96/6.82 | | (15) leq(all_71_1, all_71_3) % 43.96/6.82 | | % 43.96/6.82 | | GROUND_INST: instantiating (3) with all_71_2, all_71_1, all_71_0, % 43.96/6.82 | | simplifying with (4), (5), (6), (7), (10), (13), (15) gives: % 43.96/6.82 | | (16) all_71_0 = use % 43.96/6.82 | | % 43.96/6.82 | | REDUCE: (2), (16) imply: % 43.96/6.82 | | (17) $false % 43.96/6.82 | | % 43.96/6.82 | | CLOSE: (17) is inconsistent. % 43.96/6.82 | | % 43.96/6.82 | Case 2: % 43.96/6.82 | | % 43.96/6.82 | | (18) all_71_1 = pv5 % 43.96/6.82 | | % 43.96/6.82 | | REDUCE: (9), (18) imply: % 43.96/6.82 | | (19) $false % 43.96/6.82 | | % 43.96/6.82 | | CLOSE: (19) is inconsistent. % 43.96/6.82 | | % 43.96/6.82 | End of split % 43.96/6.82 | % 43.96/6.82 End of proof % 43.96/6.82 % SZS output end Proof for theBenchmark % 43.96/6.82 % 43.96/6.82 6190ms %------------------------------------------------------------------------------