%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV092+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 : n015.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 22:54:52 EDT 2023 % Result : Theorem 22.49s 3.95s % Output : Proof 27.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWV092+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n015.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Tue Aug 29 04:19:10 EDT 2023 % 0.11/0.32 % CPUTime : % 0.17/0.61 ________ _____ % 0.17/0.61 ___ __ \_________(_)________________________________ % 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.61 % 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.61 (2023-06-19) % 0.17/0.61 % 0.17/0.61 (c) Philipp Rümmer, 2009-2023 % 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.61 Amanda Stjerna. % 0.17/0.61 Free software under BSD-3-Clause. % 0.17/0.61 % 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.61 % 0.17/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.62 Running up to 7 provers in parallel. % 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.70/1.60 Prover 1: Preprocessing ... % 5.70/1.62 Prover 4: Preprocessing ... % 5.84/1.67 Prover 0: Preprocessing ... % 5.84/1.67 Prover 3: Preprocessing ... % 5.84/1.67 Prover 5: Preprocessing ... % 5.84/1.67 Prover 2: Preprocessing ... % 5.84/1.68 Prover 6: Preprocessing ... % 14.13/2.85 Prover 1: Warning: ignoring some quantifiers % 14.52/2.96 Prover 3: Warning: ignoring some quantifiers % 14.52/2.97 Prover 4: Warning: ignoring some quantifiers % 15.90/3.01 Prover 3: Constructing countermodel ... % 15.99/3.03 Prover 6: Proving ... % 15.99/3.04 Prover 1: Constructing countermodel ... % 16.66/3.13 Prover 4: Constructing countermodel ... % 17.17/3.27 Prover 5: Proving ... % 18.09/3.36 Prover 0: Proving ... % 18.09/3.36 Prover 2: Proving ... % 22.49/3.95 Prover 3: proved (3302ms) % 22.49/3.95 % 22.49/3.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.49/3.95 % 22.49/3.95 Prover 0: stopped % 22.49/3.95 Prover 2: stopped % 22.49/3.96 Prover 5: stopped % 22.49/3.97 Prover 6: stopped % 22.49/3.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.49/3.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.49/3.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.49/3.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.49/3.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.07/4.23 Prover 1: Found proof (size 30) % 24.07/4.24 Prover 1: proved (3608ms) % 24.07/4.24 Prover 7: Preprocessing ... % 24.07/4.25 Prover 10: Preprocessing ... % 24.07/4.25 Prover 8: Preprocessing ... % 24.07/4.26 Prover 4: stopped % 24.07/4.26 Prover 13: Preprocessing ... % 24.07/4.28 Prover 11: Preprocessing ... % 24.84/4.40 Prover 13: stopped % 24.84/4.41 Prover 10: stopped % 24.84/4.41 Prover 7: stopped % 24.84/4.42 Prover 11: stopped % 26.42/4.55 Prover 8: Warning: ignoring some quantifiers % 26.49/4.58 Prover 8: Constructing countermodel ... % 26.74/4.62 Prover 8: stopped % 26.74/4.62 % 26.74/4.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 26.74/4.62 % 26.74/4.62 % SZS output start Proof for theBenchmark % 26.74/4.63 Assumptions after simplification: % 26.74/4.63 --------------------------------- % 26.74/4.63 % 26.74/4.63 (finite_domain_0) % 26.88/4.68 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 26.88/4.68 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 26.88/4.68 % 26.88/4.68 (gt_3_tptp_minus_1) % 26.88/4.68 gt(n3, tptp_minus_1) = 0 & $i(n3) & $i(tptp_minus_1) % 26.88/4.68 % 26.88/4.68 (irreflexivity_gt) % 26.88/4.68 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 26.88/4.68 % 26.88/4.68 (leq_gt1) % 26.88/4.68 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 26.88/4.68 leq(v0, v1) = 0) % 26.88/4.68 % 26.88/4.68 (leq_gt_pred) % 26.88/4.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.88/4.68 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 26.88/4.68 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 26.88/4.68 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 26.88/4.68 | gt(v1, v0) = 0) % 26.88/4.68 % 26.88/4.68 (pred_minus_1) % 26.88/4.69 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 26.88/4.69 (pred(v0) = v1 & $i(v1))) % 26.88/4.69 % 26.88/4.69 (pred_succ) % 26.88/4.69 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 26.88/4.69 % 26.88/4.69 (quaternion_ds1_inuse_0004) % 26.88/4.70 $i(z_defuse) & $i(xinit_noise_defuse) & $i(xinit_mean_defuse) & % 26.88/4.70 $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & $i(rho_defuse) & $i(use) % 26.88/4.70 & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ? [v0: $i] : % 26.88/4.70 (minus(n0, n1) = v0 & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, % 26.88/4.70 n1, n0) = use & a_select3(u_defuse, n0, n0) = use & % 26.88/4.70 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4) % 26.88/4.70 = use & a_select2(xinit_noise_defuse, n3) = use & % 26.88/4.70 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1) % 26.88/4.70 = use & a_select2(xinit_noise_defuse, n0) = use & % 26.88/4.70 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) = % 26.88/4.70 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 26.88/4.70 n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 26.88/4.70 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use & % 26.88/4.70 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use & % 26.88/4.70 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use & % 26.88/4.70 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use & % 26.88/4.70 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use & % 26.88/4.70 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 26.88/4.70 a_select2(rho_defuse, n0) = use & $i(v0) & ? [v1: $i] : ? [v2: $i] : ? % 26.88/4.70 [v3: $i] : ? [v4: $i] : (a_select3(z_defuse, v1, v2) = v4 & % 26.88/4.70 a_select3(u_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) = 0 & % 26.88/4.70 leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & ( % 26.88/4.70 ~ (v4 = use) | ~ (v3 = use)))) % 26.88/4.70 % 26.88/4.70 (succ_tptp_minus_1) % 26.88/4.70 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 26.88/4.70 % 26.88/4.70 (function-axioms) % 26.88/4.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.88/4.71 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 26.88/4.71 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.88/4.71 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 26.88/4.71 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 26.88/4.71 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 26.88/4.71 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.88/4.71 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 26.88/4.71 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 26.88/4.71 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 26.88/4.71 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 26.88/4.71 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 26.88/4.71 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 26.88/4.71 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 26.88/4.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 26.88/4.71 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.88/4.71 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 26.88/4.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 26.88/4.71 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 26.88/4.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 26.88/4.71 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 26.88/4.71 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 26.88/4.71 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 26.88/4.71 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 26.88/4.71 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.88/4.71 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 26.88/4.71 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 26.88/4.71 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 26.88/4.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.88/4.71 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 26.88/4.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.88/4.71 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 26.88/4.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.88/4.71 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 26.88/4.71 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 26.88/4.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 26.88/4.71 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 26.88/4.71 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.88/4.71 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 26.88/4.71 % 26.88/4.71 Further assumptions not needed in the proof: % 26.88/4.71 -------------------------------------------- % 26.88/4.71 const_array1_select, const_array2_select, defuse, finite_domain_1, % 26.88/4.71 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 26.88/4.71 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, % 26.88/4.71 gt_3_0, gt_3_1, gt_3_2, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, % 26.88/4.71 gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, leq_geq, % 26.88/4.71 leq_gt2, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, % 26.88/4.71 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 26.88/4.71 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 26.88/4.71 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 26.88/4.71 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, % 26.88/4.71 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, % 26.88/4.71 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, % 26.88/4.71 successor_1, successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 26.88/4.71 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 26.88/4.71 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 26.88/4.71 % 26.88/4.71 Those formulas are unsatisfiable: % 26.88/4.71 --------------------------------- % 26.88/4.71 % 26.88/4.71 Begin of proof % 26.88/4.72 | % 26.88/4.72 | ALPHA: (leq_gt_pred) implies: % 26.88/4.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 26.88/4.72 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 26.88/4.72 | % 26.88/4.72 | ALPHA: (succ_tptp_minus_1) implies: % 26.88/4.72 | (2) succ(tptp_minus_1) = n0 % 26.88/4.72 | % 26.88/4.72 | ALPHA: (pred_minus_1) implies: % 26.88/4.72 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 26.88/4.72 | (pred(v0) = v1 & $i(v1))) % 26.88/4.72 | % 26.88/4.72 | ALPHA: (gt_3_tptp_minus_1) implies: % 26.88/4.72 | (4) $i(tptp_minus_1) % 26.88/4.72 | % 26.88/4.72 | ALPHA: (finite_domain_0) implies: % 26.88/4.72 | (5) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 26.88/4.72 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 26.88/4.72 | % 26.88/4.72 | ALPHA: (quaternion_ds1_inuse_0004) implies: % 26.88/4.72 | (6) $i(n0) % 26.88/4.73 | (7) ? [v0: $i] : (minus(n0, n1) = v0 & a_select3(u_defuse, n2, n0) = use & % 26.88/4.73 | a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) = use % 26.88/4.73 | & a_select2(xinit_noise_defuse, n5) = use & % 26.88/4.73 | a_select2(xinit_noise_defuse, n4) = use & % 26.88/4.73 | a_select2(xinit_noise_defuse, n3) = use & % 26.88/4.73 | a_select2(xinit_noise_defuse, n2) = use & % 26.88/4.73 | a_select2(xinit_noise_defuse, n1) = use & % 26.88/4.73 | a_select2(xinit_noise_defuse, n0) = use & % 26.88/4.73 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, % 26.88/4.73 | n4) = use & a_select2(xinit_mean_defuse, n3) = use & % 26.88/4.73 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 26.88/4.73 | n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 26.88/4.73 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use % 26.88/4.73 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = % 26.88/4.73 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) % 26.88/4.73 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, % 26.88/4.73 | n1) = use & a_select2(sigma_defuse, n0) = use & % 26.88/4.73 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 26.88/4.73 | a_select2(rho_defuse, n0) = use & $i(v0) & ? [v1: $i] : ? [v2: $i] % 26.88/4.73 | : ? [v3: $i] : ? [v4: $i] : (a_select3(z_defuse, v1, v2) = v4 & % 26.88/4.73 | a_select3(u_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) = % 26.88/4.73 | 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & % 26.88/4.73 | $i(v1) & ( ~ (v4 = use) | ~ (v3 = use)))) % 26.88/4.73 | % 26.88/4.73 | ALPHA: (function-axioms) implies: % 26.88/4.73 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) % 26.88/4.73 | | ~ (pred(v2) = v0)) % 26.88/4.73 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.88/4.73 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 26.88/4.73 | % 27.28/4.73 | DELTA: instantiating (7) with fresh symbol all_74_0 gives: % 27.28/4.73 | (10) minus(n0, n1) = all_74_0 & a_select3(u_defuse, n2, n0) = use & % 27.28/4.73 | a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) = use % 27.28/4.73 | & a_select2(xinit_noise_defuse, n5) = use & % 27.28/4.73 | a_select2(xinit_noise_defuse, n4) = use & % 27.28/4.73 | a_select2(xinit_noise_defuse, n3) = use & % 27.28/4.73 | a_select2(xinit_noise_defuse, n2) = use & % 27.28/4.73 | a_select2(xinit_noise_defuse, n1) = use & % 27.28/4.73 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse, % 27.28/4.73 | n5) = use & a_select2(xinit_mean_defuse, n4) = use & % 27.28/4.73 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 27.28/4.73 | n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 27.28/4.73 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = % 27.28/4.73 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) % 27.28/4.73 | = use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, % 27.28/4.73 | n4) = use & a_select2(sigma_defuse, n3) = use & % 27.28/4.73 | a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use % 27.28/4.73 | & a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use % 27.28/4.73 | & a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use & % 27.28/4.73 | $i(all_74_0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 27.28/4.73 | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = v2 & % 27.28/4.73 | leq(v1, all_74_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, % 27.28/4.73 | v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) | ~ % 27.28/4.73 | (v2 = use))) % 27.28/4.73 | % 27.28/4.73 | ALPHA: (10) implies: % 27.28/4.74 | (11) minus(n0, n1) = all_74_0 % 27.28/4.74 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 27.28/4.74 | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = v2 & % 27.28/4.74 | leq(v1, all_74_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, % 27.28/4.74 | v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) | ~ % 27.28/4.74 | (v2 = use))) % 27.28/4.74 | % 27.28/4.74 | DELTA: instantiating (12) with fresh symbols all_78_0, all_78_1, all_78_2, % 27.28/4.74 | all_78_3 gives: % 27.28/4.74 | (13) a_select3(z_defuse, all_78_3, all_78_2) = all_78_0 & % 27.28/4.74 | a_select3(u_defuse, all_78_3, all_78_2) = all_78_1 & leq(all_78_2, % 27.28/4.74 | all_74_0) = 0 & leq(all_78_3, n2) = 0 & leq(n0, all_78_2) = 0 & % 27.28/4.74 | leq(n0, all_78_3) = 0 & $i(all_78_0) & $i(all_78_1) & $i(all_78_2) & % 27.28/4.74 | $i(all_78_3) & ( ~ (all_78_0 = use) | ~ (all_78_1 = use)) % 27.28/4.74 | % 27.28/4.74 | ALPHA: (13) implies: % 27.28/4.74 | (14) $i(all_78_2) % 27.28/4.74 | (15) leq(n0, all_78_2) = 0 % 27.28/4.74 | (16) leq(all_78_2, all_74_0) = 0 % 27.28/4.74 | % 27.28/4.74 | GROUND_INST: instantiating (5) with all_78_2, simplifying with (14), (15) % 27.28/4.74 | gives: % 27.28/4.74 | (17) all_78_2 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_78_2, n0) = v0) % 27.28/4.74 | % 27.28/4.74 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with % 27.28/4.74 | (2), (4) gives: % 27.28/4.74 | (18) pred(n0) = tptp_minus_1 % 27.28/4.74 | % 27.28/4.74 | GROUND_INST: instantiating (3) with n0, all_74_0, simplifying with (6), (11) % 27.28/4.74 | gives: % 27.28/4.74 | (19) pred(n0) = all_74_0 & $i(all_74_0) % 27.28/4.74 | % 27.28/4.74 | ALPHA: (19) implies: % 27.28/4.74 | (20) pred(n0) = all_74_0 % 27.28/4.74 | % 27.28/4.74 | GROUND_INST: instantiating (8) with tptp_minus_1, all_74_0, n0, simplifying % 27.28/4.74 | with (18), (20) gives: % 27.28/4.74 | (21) all_74_0 = tptp_minus_1 % 27.28/4.74 | % 27.28/4.74 | REDUCE: (16), (21) imply: % 27.28/4.74 | (22) leq(all_78_2, tptp_minus_1) = 0 % 27.28/4.74 | % 27.28/4.75 | GROUND_INST: instantiating (1) with all_78_2, n0, tptp_minus_1, simplifying % 27.28/4.75 | with (6), (14), (18), (22) gives: % 27.28/4.75 | (23) gt(n0, all_78_2) = 0 % 27.28/4.75 | % 27.28/4.75 | GROUND_INST: instantiating (leq_gt1) with all_78_2, n0, simplifying with (6), % 27.28/4.75 | (14), (23) gives: % 27.28/4.75 | (24) leq(all_78_2, n0) = 0 % 27.28/4.75 | % 27.28/4.75 | BETA: splitting (17) gives: % 27.28/4.75 | % 27.28/4.75 | Case 1: % 27.28/4.75 | | % 27.28/4.75 | | (25) all_78_2 = n0 % 27.28/4.75 | | % 27.28/4.75 | | REDUCE: (23), (25) imply: % 27.28/4.75 | | (26) gt(n0, n0) = 0 % 27.28/4.75 | | % 27.28/4.75 | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with (6), % 27.28/4.75 | | (26) gives: % 27.28/4.75 | | (27) $false % 27.28/4.75 | | % 27.28/4.75 | | CLOSE: (27) is inconsistent. % 27.28/4.75 | | % 27.28/4.75 | Case 2: % 27.28/4.75 | | % 27.28/4.75 | | (28) ? [v0: int] : ( ~ (v0 = 0) & leq(all_78_2, n0) = v0) % 27.28/4.75 | | % 27.28/4.75 | | DELTA: instantiating (28) with fresh symbol all_122_0 gives: % 27.28/4.75 | | (29) ~ (all_122_0 = 0) & leq(all_78_2, n0) = all_122_0 % 27.28/4.75 | | % 27.28/4.75 | | ALPHA: (29) implies: % 27.28/4.75 | | (30) ~ (all_122_0 = 0) % 27.28/4.75 | | (31) leq(all_78_2, n0) = all_122_0 % 27.28/4.75 | | % 27.28/4.75 | | GROUND_INST: instantiating (9) with 0, all_122_0, n0, all_78_2, simplifying % 27.28/4.75 | | with (24), (31) gives: % 27.28/4.75 | | (32) all_122_0 = 0 % 27.28/4.75 | | % 27.28/4.75 | | REDUCE: (30), (32) imply: % 27.28/4.75 | | (33) $false % 27.28/4.75 | | % 27.28/4.75 | | CLOSE: (33) is inconsistent. % 27.28/4.75 | | % 27.28/4.75 | End of split % 27.28/4.75 | % 27.28/4.75 End of proof % 27.28/4.75 % SZS output end Proof for theBenchmark % 27.28/4.75 % 27.28/4.75 4144ms %------------------------------------------------------------------------------