%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV221+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 : n003.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 22:55:24 EDT 2023 % Result : Theorem 14.77s 2.68s % Output : Proof 19.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWV221+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 08:06:55 EDT 2023 % 0.13/0.34 % 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 ... % 0.64/0.61 Running up to 7 provers in parallel. % 0.64/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.64/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.64/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.64/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.64/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.64/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.64/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.48/1.30 Prover 4: Preprocessing ... % 4.48/1.30 Prover 1: Preprocessing ... % 4.86/1.34 Prover 3: Preprocessing ... % 4.86/1.34 Prover 2: Preprocessing ... % 4.86/1.34 Prover 5: Preprocessing ... % 4.86/1.34 Prover 0: Preprocessing ... % 4.86/1.34 Prover 6: Preprocessing ... % 11.58/2.26 Prover 1: Warning: ignoring some quantifiers % 11.58/2.29 Prover 3: Warning: ignoring some quantifiers % 11.58/2.31 Prover 4: Warning: ignoring some quantifiers % 12.25/2.32 Prover 6: Proving ... % 12.25/2.33 Prover 3: Constructing countermodel ... % 12.25/2.33 Prover 1: Constructing countermodel ... % 12.25/2.38 Prover 4: Constructing countermodel ... % 12.73/2.46 Prover 0: Proving ... % 12.73/2.47 Prover 5: Proving ... % 14.04/2.57 Prover 2: Proving ... % 14.77/2.68 Prover 3: proved (2056ms) % 14.77/2.68 % 14.77/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.77/2.68 % 14.77/2.68 Prover 2: stopped % 14.77/2.68 Prover 6: stopped % 14.77/2.68 Prover 5: stopped % 14.77/2.69 Prover 0: stopped % 14.77/2.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.77/2.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.77/2.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.77/2.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.77/2.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.37/2.93 Prover 10: Preprocessing ... % 16.89/2.95 Prover 7: Preprocessing ... % 16.89/2.95 Prover 1: Found proof (size 30) % 16.89/2.95 Prover 1: proved (2335ms) % 16.89/2.96 Prover 4: stopped % 17.10/2.97 Prover 11: Preprocessing ... % 17.10/2.99 Prover 8: Preprocessing ... % 17.10/2.99 Prover 13: Preprocessing ... % 17.10/3.03 Prover 10: stopped % 17.10/3.04 Prover 7: stopped % 18.10/3.12 Prover 11: stopped % 18.10/3.13 Prover 13: stopped % 18.47/3.20 Prover 8: Warning: ignoring some quantifiers % 18.47/3.21 Prover 8: Constructing countermodel ... % 18.47/3.23 Prover 8: stopped % 18.47/3.23 % 18.47/3.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.47/3.23 % 18.47/3.24 % SZS output start Proof for theBenchmark % 18.47/3.24 Assumptions after simplification: % 18.47/3.24 --------------------------------- % 18.47/3.24 % 18.47/3.24 (quaternion_ds1_symm_0401) % 18.92/3.28 $i(id_ds1_filter) & $i(pminus_ds1_filter) & $i(r_ds1_filter) & % 18.92/3.28 $i(q_ds1_filter) & $i(pv58) & $i(n998) & $i(pv57) & $i(pv5) & $i(n5) & $i(n2) % 18.92/3.28 & $i(n0) & ? [v0: $i] : (pred(pv57) = v0 & leq(pv58, n5) = 0 & leq(pv57, n5) % 18.92/3.28 = 0 & leq(pv5, n998) = 0 & leq(n0, pv57) = 0 & leq(n0, pv5) = 0 & gt(pv58, % 18.92/3.28 pv57) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.92/3.28 (a_select3(pminus_ds1_filter, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? % 18.92/3.28 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : % 18.92/3.28 (a_select3(pminus_ds1_filter, v2, v1) = v8 & leq(v2, n5) = v7 & leq(v1, % 18.92/3.28 n5) = v6 & leq(n0, v2) = v5 & leq(n0, v1) = v4 & $i(v8) & ( ~ (v7 = 0) % 18.92/3.28 | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = v3))) & ! [v1: $i] : % 18.92/3.28 ! [v2: $i] : ! [v3: $i] : ( ~ (a_select3(r_ds1_filter, v1, v2) = v3) | ~ % 18.92/3.28 $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: % 18.92/3.28 any] : ? [v8: $i] : (a_select3(r_ds1_filter, v2, v1) = v8 & leq(v2, n2) % 18.92/3.28 = v7 & leq(v1, n2) = v6 & leq(n0, v2) = v5 & leq(n0, v1) = v4 & $i(v8) & % 18.92/3.28 ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = v3))) & ! % 18.92/3.28 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (a_select3(q_ds1_filter, v1, v2) % 18.92/3.28 = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: any] : ? [v6: % 18.92/3.28 any] : ? [v7: any] : ? [v8: $i] : (a_select3(q_ds1_filter, v2, v1) = % 18.92/3.28 v8 & leq(v2, n5) = v7 & leq(v1, n5) = v6 & leq(n0, v2) = v5 & leq(n0, % 18.92/3.28 v1) = v4 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 % 18.92/3.28 = 0) | v8 = v3))) & ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, n5) = % 18.92/3.28 0) | ~ (gt(pv57, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? % 18.92/3.28 [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 18.92/3.28 (a_select3(id_ds1_filter, v2, v1) = v7 & a_select3(id_ds1_filter, v1, v2) % 18.92/3.28 = v6 & leq(v1, n5) = v5 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v7) & % 18.92/3.28 $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = v6))) & ! [v1: % 18.92/3.28 $i] : ( ~ (leq(v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & % 18.92/3.28 leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] : ( ~ % 18.92/3.28 (a_select3(id_ds1_filter, v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 18.92/3.28 [v5: any] : ? [v6: $i] : (a_select3(id_ds1_filter, v2, v1) = v6 & % 18.92/3.28 leq(v2, n5) = v5 & leq(n0, v2) = v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = % 18.92/3.28 0) | v6 = v3)))) & ! [v1: $i] : ( ~ (gt(pv58, v1) = 0) | ~ % 18.92/3.28 $i(v1) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 18.92/3.28 (a_select3(id_ds1_filter, v1, pv57) = v5 & a_select3(id_ds1_filter, pv57, % 18.92/3.28 v1) = v4 & leq(v1, n5) = v3 & leq(n0, v1) = v2 & $i(v5) & $i(v4) & ( ~ % 18.92/3.28 (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & ? [v1: $i] : (leq(v1, v0) = 0 & % 18.92/3.28 leq(n0, v1) = 0 & $i(v1) & ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ % 18.92/3.28 (v4 = v3) & ~ (v1 = pv57) & a_select3(id_ds1_filter, v2, v1) = v4 & % 18.92/3.28 a_select3(id_ds1_filter, v1, v2) = v3 & leq(v2, n5) = 0 & leq(n0, v2) = % 18.92/3.28 0 & $i(v4) & $i(v3) & $i(v2)))) % 18.92/3.28 % 18.92/3.28 (function-axioms) % 18.92/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.92/3.29 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 18.92/3.29 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.92/3.29 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 18.92/3.29 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.92/3.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 18.92/3.29 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.92/3.29 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 18.92/3.29 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.92/3.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 18.92/3.29 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.92/3.29 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 18.92/3.29 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 18.92/3.29 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 18.92/3.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 19.06/3.29 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.06/3.29 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 19.06/3.29 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.06/3.29 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 19.06/3.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 19.06/3.29 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.06/3.29 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 19.06/3.29 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.06/3.29 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 19.06/3.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.06/3.29 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 19.06/3.29 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.06/3.29 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.06/3.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.06/3.29 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.06/3.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.06/3.29 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.06/3.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.06/3.29 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.06/3.29 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 19.06/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 19.06/3.29 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.06/3.29 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.06/3.29 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 19.06/3.29 % 19.06/3.29 Further assumptions not needed in the proof: % 19.06/3.29 -------------------------------------------- % 19.06/3.29 const_array1_select, const_array2_select, defuse, finite_domain_0, % 19.06/3.29 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 19.06/3.29 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, % 19.06/3.29 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, % 19.06/3.29 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, % 19.06/3.29 gt_5_tptp_minus_1, gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5, % 19.06/3.29 gt_998_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2, % 19.06/3.29 leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, % 19.06/3.29 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 19.06/3.29 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.06/3.29 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 19.06/3.29 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 19.06/3.29 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 19.06/3.29 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 19.06/3.29 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2, % 19.06/3.29 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float, % 19.06/3.29 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 19.06/3.29 uniform_int_rand_ranges_lo % 19.06/3.29 % 19.06/3.29 Those formulas are unsatisfiable: % 19.06/3.29 --------------------------------- % 19.06/3.29 % 19.06/3.29 Begin of proof % 19.06/3.29 | % 19.06/3.30 | ALPHA: (quaternion_ds1_symm_0401) implies: % 19.06/3.30 | (1) ? [v0: $i] : (pred(pv57) = v0 & leq(pv58, n5) = 0 & leq(pv57, n5) = 0 % 19.06/3.30 | & leq(pv5, n998) = 0 & leq(n0, pv57) = 0 & leq(n0, pv5) = 0 & % 19.06/3.30 | gt(pv58, pv57) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.06/3.30 | : ( ~ (a_select3(pminus_ds1_filter, v1, v2) = v3) | ~ $i(v2) | ~ % 19.06/3.30 | $i(v1) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] % 19.06/3.30 | : ? [v8: $i] : (a_select3(pminus_ds1_filter, v2, v1) = v8 & % 19.06/3.30 | leq(v2, n5) = v7 & leq(v1, n5) = v6 & leq(n0, v2) = v5 & leq(n0, % 19.06/3.30 | v1) = v4 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | % 19.06/3.30 | ~ (v4 = 0) | v8 = v3))) & ! [v1: $i] : ! [v2: $i] : ! [v3: % 19.06/3.30 | $i] : ( ~ (a_select3(r_ds1_filter, v1, v2) = v3) | ~ $i(v2) | ~ % 19.06/3.30 | $i(v1) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] % 19.06/3.30 | : ? [v8: $i] : (a_select3(r_ds1_filter, v2, v1) = v8 & leq(v2, n2) % 19.06/3.30 | = v7 & leq(v1, n2) = v6 & leq(n0, v2) = v5 & leq(n0, v1) = v4 & % 19.06/3.30 | $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | % 19.06/3.30 | v8 = v3))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 19.06/3.30 | (a_select3(q_ds1_filter, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? % 19.06/3.30 | [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 19.06/3.30 | $i] : (a_select3(q_ds1_filter, v2, v1) = v8 & leq(v2, n5) = v7 & % 19.06/3.30 | leq(v1, n5) = v6 & leq(n0, v2) = v5 & leq(n0, v1) = v4 & $i(v8) & % 19.06/3.30 | ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = % 19.06/3.30 | v3))) & ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, n5) = 0) | ~ % 19.06/3.30 | (gt(pv57, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 19.06/3.30 | any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 19.06/3.30 | (a_select3(id_ds1_filter, v2, v1) = v7 & a_select3(id_ds1_filter, % 19.06/3.30 | v1, v2) = v6 & leq(v1, n5) = v5 & leq(n0, v2) = v4 & leq(n0, % 19.06/3.30 | v1) = v3 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ % 19.06/3.30 | (v3 = 0) | v7 = v6))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) | % 19.06/3.30 | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! % 19.06/3.30 | [v2: $i] : ! [v3: $i] : ( ~ (a_select3(id_ds1_filter, v1, v2) = % 19.06/3.30 | v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : % 19.06/3.30 | (a_select3(id_ds1_filter, v2, v1) = v6 & leq(v2, n5) = v5 & % 19.06/3.30 | leq(n0, v2) = v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = % 19.06/3.30 | v3)))) & ! [v1: $i] : ( ~ (gt(pv58, v1) = 0) | ~ $i(v1) | % 19.06/3.30 | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 19.06/3.30 | (a_select3(id_ds1_filter, v1, pv57) = v5 & a_select3(id_ds1_filter, % 19.06/3.30 | pv57, v1) = v4 & leq(v1, n5) = v3 & leq(n0, v1) = v2 & $i(v5) & % 19.06/3.30 | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = v4))) & ? [v1: $i] : % 19.06/3.30 | (leq(v1, v0) = 0 & leq(n0, v1) = 0 & $i(v1) & ? [v2: $i] : ? [v3: % 19.06/3.30 | $i] : ? [v4: $i] : ( ~ (v4 = v3) & ~ (v1 = pv57) & % 19.06/3.30 | a_select3(id_ds1_filter, v2, v1) = v4 & a_select3(id_ds1_filter, % 19.06/3.30 | v1, v2) = v3 & leq(v2, n5) = 0 & leq(n0, v2) = 0 & $i(v4) & % 19.06/3.30 | $i(v3) & $i(v2)))) % 19.06/3.30 | % 19.06/3.30 | ALPHA: (function-axioms) implies: % 19.06/3.30 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.06/3.30 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 19.06/3.31 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.06/3.31 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 19.06/3.31 | = v0)) % 19.06/3.31 | % 19.06/3.31 | DELTA: instantiating (1) with fresh symbol all_76_0 gives: % 19.06/3.31 | (4) pred(pv57) = all_76_0 & leq(pv58, n5) = 0 & leq(pv57, n5) = 0 & % 19.06/3.31 | leq(pv5, n998) = 0 & leq(n0, pv57) = 0 & leq(n0, pv5) = 0 & gt(pv58, % 19.06/3.31 | pv57) = 0 & $i(all_76_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.06/3.31 | ( ~ (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 19.06/3.31 | | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: % 19.06/3.31 | $i] : (a_select3(pminus_ds1_filter, v1, v0) = v7 & leq(v1, n5) = v6 % 19.06/3.31 | & leq(v0, n5) = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3 & $i(v7) & % 19.06/3.31 | ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = v2))) % 19.06/3.31 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 19.06/3.31 | (a_select3(r_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 19.06/3.31 | [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] % 19.06/3.31 | : (a_select3(r_ds1_filter, v1, v0) = v7 & leq(v1, n2) = v6 & leq(v0, % 19.06/3.31 | n2) = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3 & $i(v7) & ( ~ (v6 % 19.06/3.31 | = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = v2))) & % 19.06/3.31 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 19.06/3.31 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 19.06/3.31 | any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] : % 19.06/3.31 | (a_select3(q_ds1_filter, v1, v0) = v7 & leq(v1, n5) = v6 & leq(v0, % 19.06/3.31 | n5) = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3 & $i(v7) & ( ~ (v6 % 19.06/3.31 | = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = v2))) & % 19.06/3.31 | ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, n5) = 0) | ~ (gt(pv57, v0) = % 19.06/3.31 | 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: % 19.06/3.31 | any] : ? [v5: $i] : ? [v6: $i] : (a_select3(id_ds1_filter, v1, % 19.06/3.31 | v0) = v6 & a_select3(id_ds1_filter, v0, v1) = v5 & leq(v0, n5) = % 19.06/3.31 | v4 & leq(n0, v1) = v3 & leq(n0, v0) = v2 & $i(v6) & $i(v5) & ( ~ % 19.06/3.31 | (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v6 = v5))) & ! [v0: $i] : % 19.06/3.31 | ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 19.06/3.31 | leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : ( ~ % 19.06/3.31 | (a_select3(id_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ? [v3: any] % 19.06/3.31 | : ? [v4: any] : ? [v5: $i] : (a_select3(id_ds1_filter, v1, v0) = % 19.06/3.31 | v5 & leq(v1, n5) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) % 19.06/3.31 | | ~ (v3 = 0) | v5 = v2)))) & ! [v0: $i] : ( ~ (gt(pv58, v0) = % 19.06/3.31 | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? % 19.06/3.31 | [v4: $i] : (a_select3(id_ds1_filter, v0, pv57) = v4 & % 19.06/3.31 | a_select3(id_ds1_filter, pv57, v0) = v3 & leq(v0, n5) = v2 & % 19.06/3.31 | leq(n0, v0) = v1 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | % 19.06/3.31 | v4 = v3))) & ? [v0: $i] : (leq(v0, all_76_0) = 0 & leq(n0, v0) = % 19.06/3.31 | 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) % 19.06/3.31 | & ~ (v0 = pv57) & a_select3(id_ds1_filter, v1, v0) = v3 & % 19.06/3.31 | a_select3(id_ds1_filter, v0, v1) = v2 & leq(v1, n5) = 0 & leq(n0, % 19.06/3.31 | v1) = 0 & $i(v3) & $i(v2) & $i(v1))) % 19.06/3.31 | % 19.06/3.31 | ALPHA: (4) implies: % 19.06/3.32 | (5) ! [v0: $i] : ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0) | ? [v1: int] : % 19.06/3.32 | ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : ( ~ % 19.06/3.32 | (a_select3(id_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ? [v3: any] % 19.06/3.32 | : ? [v4: any] : ? [v5: $i] : (a_select3(id_ds1_filter, v1, v0) = % 19.06/3.32 | v5 & leq(v1, n5) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) % 19.06/3.32 | | ~ (v3 = 0) | v5 = v2)))) % 19.06/3.32 | (6) ? [v0: $i] : (leq(v0, all_76_0) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 19.06/3.32 | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & ~ (v0 = pv57) % 19.06/3.32 | & a_select3(id_ds1_filter, v1, v0) = v3 & a_select3(id_ds1_filter, % 19.06/3.32 | v0, v1) = v2 & leq(v1, n5) = 0 & leq(n0, v1) = 0 & $i(v3) & % 19.06/3.32 | $i(v2) & $i(v1))) % 19.06/3.32 | % 19.06/3.32 | DELTA: instantiating (6) with fresh symbol all_79_0 gives: % 19.06/3.32 | (7) leq(all_79_0, all_76_0) = 0 & leq(n0, all_79_0) = 0 & $i(all_79_0) & ? % 19.06/3.32 | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & ~ (all_79_0 = % 19.06/3.32 | pv57) & a_select3(id_ds1_filter, v0, all_79_0) = v2 & % 19.06/3.32 | a_select3(id_ds1_filter, all_79_0, v0) = v1 & leq(v0, n5) = 0 & % 19.06/3.32 | leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 19.06/3.32 | % 19.06/3.32 | ALPHA: (7) implies: % 19.06/3.32 | (8) $i(all_79_0) % 19.06/3.32 | (9) leq(n0, all_79_0) = 0 % 19.06/3.32 | (10) leq(all_79_0, all_76_0) = 0 % 19.06/3.32 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & ~ (all_79_0 % 19.06/3.32 | = pv57) & a_select3(id_ds1_filter, v0, all_79_0) = v2 & % 19.06/3.32 | a_select3(id_ds1_filter, all_79_0, v0) = v1 & leq(v0, n5) = 0 & % 19.06/3.32 | leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 19.06/3.32 | % 19.06/3.32 | DELTA: instantiating (11) with fresh symbols all_81_0, all_81_1, all_81_2 % 19.06/3.32 | gives: % 19.06/3.32 | (12) ~ (all_81_0 = all_81_1) & ~ (all_79_0 = pv57) & % 19.06/3.32 | a_select3(id_ds1_filter, all_81_2, all_79_0) = all_81_0 & % 19.06/3.32 | a_select3(id_ds1_filter, all_79_0, all_81_2) = all_81_1 & % 19.06/3.32 | leq(all_81_2, n5) = 0 & leq(n0, all_81_2) = 0 & $i(all_81_0) & % 19.06/3.32 | $i(all_81_1) & $i(all_81_2) % 19.06/3.32 | % 19.06/3.32 | ALPHA: (12) implies: % 19.06/3.32 | (13) ~ (all_81_0 = all_81_1) % 19.06/3.32 | (14) $i(all_81_2) % 19.06/3.32 | (15) leq(n0, all_81_2) = 0 % 19.06/3.32 | (16) leq(all_81_2, n5) = 0 % 19.06/3.32 | (17) a_select3(id_ds1_filter, all_79_0, all_81_2) = all_81_1 % 19.06/3.32 | (18) a_select3(id_ds1_filter, all_81_2, all_79_0) = all_81_0 % 19.06/3.32 | % 19.21/3.32 | GROUND_INST: instantiating (5) with all_79_0, simplifying with (8), (10) % 19.21/3.32 | gives: % 19.21/3.32 | (19) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_79_0) = v0) | ! [v0: $i] : % 19.21/3.32 | ! [v1: $i] : ( ~ (a_select3(id_ds1_filter, all_79_0, v0) = v1) | ~ % 19.21/3.32 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 19.21/3.32 | (a_select3(id_ds1_filter, v0, all_79_0) = v4 & leq(v0, n5) = v3 & % 19.21/3.32 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = % 19.21/3.32 | v1))) % 19.21/3.32 | % 19.21/3.32 | BETA: splitting (19) gives: % 19.21/3.32 | % 19.21/3.32 | Case 1: % 19.21/3.32 | | % 19.21/3.32 | | (20) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_79_0) = v0) % 19.21/3.32 | | % 19.21/3.32 | | DELTA: instantiating (20) with fresh symbol all_110_0 gives: % 19.21/3.32 | | (21) ~ (all_110_0 = 0) & leq(n0, all_79_0) = all_110_0 % 19.21/3.32 | | % 19.21/3.32 | | ALPHA: (21) implies: % 19.21/3.32 | | (22) ~ (all_110_0 = 0) % 19.21/3.33 | | (23) leq(n0, all_79_0) = all_110_0 % 19.21/3.33 | | % 19.21/3.33 | | GROUND_INST: instantiating (2) with 0, all_110_0, all_79_0, n0, simplifying % 19.21/3.33 | | with (9), (23) gives: % 19.21/3.33 | | (24) all_110_0 = 0 % 19.21/3.33 | | % 19.22/3.33 | | REDUCE: (22), (24) imply: % 19.22/3.33 | | (25) $false % 19.22/3.33 | | % 19.22/3.33 | | CLOSE: (25) is inconsistent. % 19.22/3.33 | | % 19.22/3.33 | Case 2: % 19.22/3.33 | | % 19.22/3.33 | | (26) ! [v0: $i] : ! [v1: $i] : ( ~ (a_select3(id_ds1_filter, all_79_0, % 19.22/3.33 | | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: % 19.22/3.33 | | $i] : (a_select3(id_ds1_filter, v0, all_79_0) = v4 & leq(v0, n5) % 19.22/3.33 | | = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | % 19.22/3.33 | | v4 = v1))) % 19.22/3.33 | | % 19.22/3.33 | | GROUND_INST: instantiating (26) with all_81_2, all_81_1, simplifying with % 19.22/3.33 | | (14), (17) gives: % 19.22/3.33 | | (27) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 19.22/3.33 | | (a_select3(id_ds1_filter, all_81_2, all_79_0) = v2 & leq(all_81_2, % 19.22/3.33 | | n5) = v1 & leq(n0, all_81_2) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ % 19.22/3.33 | | (v0 = 0) | v2 = all_81_1)) % 19.22/3.33 | | % 19.22/3.33 | | DELTA: instantiating (27) with fresh symbols all_111_0, all_111_1, all_111_2 % 19.22/3.33 | | gives: % 19.22/3.33 | | (28) a_select3(id_ds1_filter, all_81_2, all_79_0) = all_111_0 & % 19.22/3.33 | | leq(all_81_2, n5) = all_111_1 & leq(n0, all_81_2) = all_111_2 & % 19.22/3.33 | | $i(all_111_0) & ( ~ (all_111_1 = 0) | ~ (all_111_2 = 0) | all_111_0 % 19.22/3.33 | | = all_81_1) % 19.22/3.33 | | % 19.22/3.33 | | ALPHA: (28) implies: % 19.22/3.33 | | (29) leq(n0, all_81_2) = all_111_2 % 19.22/3.33 | | (30) leq(all_81_2, n5) = all_111_1 % 19.22/3.33 | | (31) a_select3(id_ds1_filter, all_81_2, all_79_0) = all_111_0 % 19.22/3.33 | | (32) ~ (all_111_1 = 0) | ~ (all_111_2 = 0) | all_111_0 = all_81_1 % 19.22/3.33 | | % 19.22/3.33 | | GROUND_INST: instantiating (2) with 0, all_111_2, all_81_2, n0, simplifying % 19.22/3.33 | | with (15), (29) gives: % 19.22/3.33 | | (33) all_111_2 = 0 % 19.22/3.33 | | % 19.22/3.33 | | GROUND_INST: instantiating (2) with 0, all_111_1, n5, all_81_2, simplifying % 19.22/3.33 | | with (16), (30) gives: % 19.22/3.33 | | (34) all_111_1 = 0 % 19.22/3.33 | | % 19.22/3.33 | | GROUND_INST: instantiating (3) with all_81_0, all_111_0, all_79_0, all_81_2, % 19.22/3.33 | | id_ds1_filter, simplifying with (18), (31) gives: % 19.22/3.33 | | (35) all_111_0 = all_81_0 % 19.22/3.33 | | % 19.22/3.33 | | BETA: splitting (32) gives: % 19.22/3.33 | | % 19.22/3.33 | | Case 1: % 19.22/3.33 | | | % 19.22/3.33 | | | (36) ~ (all_111_1 = 0) % 19.22/3.33 | | | % 19.22/3.33 | | | REDUCE: (34), (36) imply: % 19.22/3.33 | | | (37) $false % 19.22/3.33 | | | % 19.22/3.33 | | | CLOSE: (37) is inconsistent. % 19.22/3.33 | | | % 19.22/3.33 | | Case 2: % 19.22/3.33 | | | % 19.22/3.33 | | | (38) ~ (all_111_2 = 0) | all_111_0 = all_81_1 % 19.22/3.33 | | | % 19.22/3.33 | | | BETA: splitting (38) gives: % 19.22/3.33 | | | % 19.22/3.33 | | | Case 1: % 19.22/3.33 | | | | % 19.22/3.33 | | | | (39) ~ (all_111_2 = 0) % 19.22/3.33 | | | | % 19.22/3.33 | | | | REDUCE: (33), (39) imply: % 19.22/3.33 | | | | (40) $false % 19.22/3.33 | | | | % 19.22/3.33 | | | | CLOSE: (40) is inconsistent. % 19.22/3.33 | | | | % 19.22/3.33 | | | Case 2: % 19.22/3.33 | | | | % 19.22/3.33 | | | | (41) all_111_0 = all_81_1 % 19.22/3.33 | | | | % 19.22/3.33 | | | | COMBINE_EQS: (35), (41) imply: % 19.22/3.33 | | | | (42) all_81_0 = all_81_1 % 19.22/3.33 | | | | % 19.22/3.33 | | | | REDUCE: (13), (42) imply: % 19.22/3.34 | | | | (43) $false % 19.22/3.34 | | | | % 19.22/3.34 | | | | CLOSE: (43) is inconsistent. % 19.22/3.34 | | | | % 19.22/3.34 | | | End of split % 19.22/3.34 | | | % 19.22/3.34 | | End of split % 19.22/3.34 | | % 19.22/3.34 | End of split % 19.22/3.34 | % 19.22/3.34 End of proof % 19.22/3.34 % SZS output end Proof for theBenchmark % 19.22/3.34 % 19.22/3.34 2735ms %------------------------------------------------------------------------------