%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MSC010+1 : TPTP v8.1.2. Released v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.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 09:26:45 EDT 2023 % Result : Theorem 8.38s 1.89s % Output : Proof 13.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : MSC010+1 : TPTP v8.1.2. Released v3.1.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n023.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Aug 24 14:02:27 EDT 2023 % 0.13/0.35 % CPUTime : % 0.62/0.61 ________ _____ % 0.62/0.61 ___ __ \_________(_)________________________________ % 0.62/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.62/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.62/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.62/0.61 % 0.62/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.62/0.61 (2023-06-19) % 0.62/0.61 % 0.62/0.61 (c) Philipp Rümmer, 2009-2023 % 0.62/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.62/0.61 Amanda Stjerna. % 0.62/0.61 Free software under BSD-3-Clause. % 0.62/0.61 % 0.62/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.62/0.61 % 0.62/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.62/0.62 Running up to 7 provers in parallel. % 0.72/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.10/1.11 Prover 4: Preprocessing ... % 3.10/1.11 Prover 1: Preprocessing ... % 3.10/1.15 Prover 5: Preprocessing ... % 3.10/1.15 Prover 6: Preprocessing ... % 3.10/1.15 Prover 3: Preprocessing ... % 3.10/1.15 Prover 2: Preprocessing ... % 3.10/1.15 Prover 0: Preprocessing ... % 6.28/1.57 Prover 3: Constructing countermodel ... % 6.28/1.57 Prover 1: Constructing countermodel ... % 6.28/1.58 Prover 2: Proving ... % 6.28/1.58 Prover 6: Proving ... % 6.28/1.59 Prover 5: Constructing countermodel ... % 6.87/1.61 Prover 4: Constructing countermodel ... % 6.87/1.62 Prover 0: Proving ... % 8.38/1.89 Prover 3: proved (1245ms) % 8.38/1.89 % 8.38/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.38/1.89 % 8.38/1.89 Prover 5: stopped % 8.38/1.89 Prover 0: stopped % 8.38/1.89 Prover 2: stopped % 8.91/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.91/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.91/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.91/1.90 Prover 6: stopped % 8.91/1.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.91/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.41/2.00 Prover 7: Preprocessing ... % 9.41/2.01 Prover 13: Preprocessing ... % 9.41/2.02 Prover 11: Preprocessing ... % 9.41/2.02 Prover 8: Preprocessing ... % 9.41/2.03 Prover 10: Preprocessing ... % 10.35/2.12 Prover 7: Constructing countermodel ... % 10.55/2.13 Prover 10: Constructing countermodel ... % 10.55/2.18 Prover 13: Constructing countermodel ... % 10.55/2.18 Prover 11: Constructing countermodel ... % 10.55/2.20 Prover 8: Warning: ignoring some quantifiers % 10.55/2.21 Prover 8: Constructing countermodel ... % 11.78/2.36 Prover 10: Found proof (size 86) % 11.78/2.36 Prover 10: proved (464ms) % 11.78/2.36 Prover 1: stopped % 11.78/2.36 Prover 8: stopped % 11.78/2.36 Prover 7: stopped % 11.78/2.36 Prover 13: stopped % 11.78/2.37 Prover 4: stopped % 11.78/2.37 Prover 11: stopped % 11.78/2.37 % 11.78/2.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.78/2.37 % 11.78/2.37 % SZS output start Proof for theBenchmark % 11.78/2.38 Assumptions after simplification: % 11.78/2.38 --------------------------------- % 11.78/2.38 % 11.78/2.38 (n1) % 12.60/2.41 $i(id_ds1_filter_init) & $i(pminus_ds1_filter_init) & % 12.60/2.41 $i(xhatmin_ds1_filter_init) & $i(r_ds1_filter_init) & $i(q_ds1_filter_init) & % 12.60/2.41 $i(dv_ds1_filter_init) & $i(phi_ds1_filter_init) & $i(init) & % 12.60/2.41 $i(h_ds1_filter_init) & $i(n2) & $i(n5) & $i(n998) & $i(pv5) & $i(n0) & % 12.60/2.41 $i(pv63) & $i(pv64) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 12.60/2.41 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 12.60/2.41 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 12.60/2.41 $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 12.60/2.41 $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: % 12.60/2.41 $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: % 12.60/2.41 $i] : ? [v30: $i] : ($i(v29) & $i(v28) & $i(v26) & $i(v25) & $i(v23) & % 12.60/2.41 $i(v22) & $i(v20) & $i(v19) & $i(v17) & $i(v16) & $i(v14) & $i(v13) & % 12.60/2.41 $i(v11) & $i(v10) & $i(v8) & $i(v7) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & % 12.60/2.41 (pv63 = pv64 | ~ leq(pv5, n998) | ~ leq(n0, pv5) | ~ leq(n0, pv63) | ~ % 12.60/2.41 leq(n0, pv64) | ~ leq(pv63, n5) | ~ leq(pv64, n5) | ! [v31: $i] : ! % 12.60/2.41 [v32: $i] : (v32 = init | v31 = pv64 | ~ (a_select3(id_ds1_filter_init, % 12.60/2.41 pv63, v31) = v32) | ~ $i(v31) | ~ leq(v31, n5) | ~ leq(v31, pv64) % 12.60/2.41 | ~ leq(n0, v31)) | (v7 = pv63 & ~ (v9 = init) & % 12.60/2.41 a_select3(id_ds1_filter_init, pv63, v8) = v9 & $i(v9) & gt(pv64, v8) & % 12.60/2.41 leq(v8, n5) & leq(n0, v8)) | ( ~ (v30 = init) & % 12.60/2.41 a_select3(h_ds1_filter_init, v28, v29) = v30 & $i(v30) & leq(v29, n5) & % 12.60/2.41 leq(v28, n2) & leq(n0, v29) & leq(n0, v28)) | ( ~ (v27 = init) & % 12.60/2.41 a_select3(phi_ds1_filter_init, v25, v26) = v27 & $i(v27) & leq(v26, n5) % 12.60/2.41 & leq(v25, n5) & leq(n0, v26) & leq(n0, v25)) | ( ~ (v24 = init) & % 12.60/2.41 a_select3(dv_ds1_filter_init, v22, v23) = v24 & $i(v24) & leq(v23, n0) & % 12.60/2.41 leq(v22, n5) & leq(n0, v23) & leq(n0, v22)) | ( ~ (v21 = init) & % 12.60/2.41 a_select3(q_ds1_filter_init, v19, v20) = v21 & $i(v21) & leq(v20, n5) & % 12.60/2.41 leq(v19, n5) & leq(n0, v20) & leq(n0, v19)) | ( ~ (v18 = init) & % 12.60/2.41 a_select3(r_ds1_filter_init, v16, v17) = v18 & $i(v18) & leq(v17, n2) & % 12.60/2.41 leq(v16, n2) & leq(n0, v17) & leq(n0, v16)) | ( ~ (v15 = init) & % 12.60/2.41 a_select3(xhatmin_ds1_filter_init, v13, v14) = v15 & $i(v15) & leq(v14, % 12.60/2.41 n0) & leq(v13, n5) & leq(n0, v14) & leq(n0, v13)) | ( ~ (v12 = init) & % 12.60/2.41 a_select3(pminus_ds1_filter_init, v10, v11) = v12 & $i(v12) & leq(v11, % 12.60/2.41 n5) & leq(v10, n5) & leq(n0, v11) & leq(n0, v10)) | ( ~ (v6 = init) & % 12.60/2.41 a_select3(id_ds1_filter_init, v4, v5) = v6 & $i(v6) & gt(pv63, v4) & % 12.60/2.41 leq(v5, n5) & leq(v4, n5) & leq(n0, v5) & leq(n0, v4)) | ( ~ (v3 = init) % 12.60/2.41 & pred(pv63) = v0 & a_select3(id_ds1_filter_init, v1, v2) = v3 & $i(v3) % 12.60/2.41 & $i(v0) & leq(v2, n5) & leq(v1, v0) & leq(n0, v2) & leq(n0, v1)))) % 12.60/2.41 % 12.60/2.41 (n91) % 12.60/2.42 $i(id_ds1_filter_init) & $i(pminus_ds1_filter_init) & % 12.60/2.42 $i(xhatmin_ds1_filter_init) & $i(r_ds1_filter_init) & $i(q_ds1_filter_init) & % 12.60/2.42 $i(dv_ds1_filter_init) & $i(phi_ds1_filter_init) & $i(init) & % 12.60/2.42 $i(h_ds1_filter_init) & $i(n2) & $i(n5) & $i(n998) & $i(pv5) & $i(n0) & % 12.60/2.42 $i(pv63) & $i(pv64) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 12.60/2.42 init) & ~ (v1 = pv64) & ~ (pv63 = pv64) & pred(pv63) = v0 & % 12.60/2.42 a_select3(id_ds1_filter_init, pv63, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & % 12.60/2.42 leq(v1, n5) & leq(v1, pv64) & leq(pv5, n998) & leq(n0, v1) & leq(n0, pv5) & % 12.60/2.42 leq(n0, pv63) & leq(n0, pv64) & leq(pv63, n5) & leq(pv64, n5) & ! [v3: $i] % 12.60/2.42 : ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ (a_select3(id_ds1_filter_init, % 12.60/2.42 v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ gt(pv63, v3) | ~ leq(v4, % 12.60/2.42 n5) | ~ leq(v3, n5) | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: $i] : % 12.60/2.42 ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ (a_select3(id_ds1_filter_init, % 12.60/2.42 v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ leq(v4, n5) | ~ leq(v3, % 12.60/2.42 v0) | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : ! % 12.60/2.42 [v5: $i] : (v5 = init | ~ (a_select3(pminus_ds1_filter_init, v3, v4) = v5) % 12.60/2.42 | ~ $i(v4) | ~ $i(v3) | ~ leq(v4, n5) | ~ leq(v3, n5) | ~ leq(n0, v4) % 12.60/2.42 | ~ leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init | % 12.60/2.42 ~ (a_select3(xhatmin_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ % 12.60/2.42 $i(v3) | ~ leq(v4, n0) | ~ leq(v3, n5) | ~ leq(n0, v4) | ~ leq(n0, % 12.60/2.42 v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ % 12.60/2.42 (a_select3(r_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 12.60/2.42 leq(v4, n2) | ~ leq(v3, n2) | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: % 12.60/2.42 $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ % 12.60/2.42 (a_select3(q_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 12.60/2.42 leq(v4, n5) | ~ leq(v3, n5) | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: % 12.60/2.42 $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ % 12.60/2.42 (a_select3(dv_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 12.60/2.42 leq(v4, n0) | ~ leq(v3, n5) | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: % 12.60/2.42 $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ % 12.60/2.42 (a_select3(phi_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 12.60/2.42 leq(v4, n5) | ~ leq(v3, n5) | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: % 12.60/2.42 $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ % 12.60/2.42 (a_select3(h_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 12.60/2.42 leq(v4, n5) | ~ leq(v3, n2) | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: % 12.60/2.42 $i] : ! [v4: $i] : (v4 = init | ~ (a_select3(id_ds1_filter_init, pv63, % 12.60/2.42 v3) = v4) | ~ $i(v3) | ~ gt(pv64, v3) | ~ leq(v3, n5) | ~ leq(n0, % 12.60/2.42 v3))) % 12.60/2.42 % 12.60/2.42 (function-axioms) % 12.60/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 12.60/2.42 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! % 12.60/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ % 12.60/2.42 (pred(v2) = v0)) % 12.60/2.42 % 12.60/2.42 Those formulas are unsatisfiable: % 12.60/2.42 --------------------------------- % 12.60/2.42 % 12.60/2.42 Begin of proof % 12.60/2.42 | % 12.60/2.42 | ALPHA: (n1) implies: % 12.60/2.43 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.60/2.43 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 12.60/2.43 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 12.60/2.43 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 12.60/2.43 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 12.60/2.43 | [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : % 12.60/2.43 | ? [v29: $i] : ? [v30: $i] : ($i(v29) & $i(v28) & $i(v26) & $i(v25) & % 12.60/2.43 | $i(v23) & $i(v22) & $i(v20) & $i(v19) & $i(v17) & $i(v16) & $i(v14) & % 12.60/2.43 | $i(v13) & $i(v11) & $i(v10) & $i(v8) & $i(v7) & $i(v5) & $i(v4) & % 12.60/2.43 | $i(v2) & $i(v1) & (pv63 = pv64 | ~ leq(pv5, n998) | ~ leq(n0, pv5) % 12.60/2.43 | | ~ leq(n0, pv63) | ~ leq(n0, pv64) | ~ leq(pv63, n5) | ~ % 12.60/2.43 | leq(pv64, n5) | ! [v31: $i] : ! [v32: $i] : (v32 = init | v31 = % 12.60/2.43 | pv64 | ~ (a_select3(id_ds1_filter_init, pv63, v31) = v32) | ~ % 12.60/2.43 | $i(v31) | ~ leq(v31, n5) | ~ leq(v31, pv64) | ~ leq(n0, v31)) % 12.60/2.43 | | (v7 = pv63 & ~ (v9 = init) & a_select3(id_ds1_filter_init, pv63, % 12.60/2.43 | v8) = v9 & $i(v9) & gt(pv64, v8) & leq(v8, n5) & leq(n0, v8)) | % 12.60/2.43 | ( ~ (v30 = init) & a_select3(h_ds1_filter_init, v28, v29) = v30 & % 12.60/2.43 | $i(v30) & leq(v29, n5) & leq(v28, n2) & leq(n0, v29) & leq(n0, % 12.60/2.43 | v28)) | ( ~ (v27 = init) & a_select3(phi_ds1_filter_init, v25, % 12.60/2.43 | v26) = v27 & $i(v27) & leq(v26, n5) & leq(v25, n5) & leq(n0, % 12.60/2.43 | v26) & leq(n0, v25)) | ( ~ (v24 = init) & % 12.60/2.43 | a_select3(dv_ds1_filter_init, v22, v23) = v24 & $i(v24) & % 12.60/2.43 | leq(v23, n0) & leq(v22, n5) & leq(n0, v23) & leq(n0, v22)) | ( ~ % 12.60/2.43 | (v21 = init) & a_select3(q_ds1_filter_init, v19, v20) = v21 & % 12.60/2.43 | $i(v21) & leq(v20, n5) & leq(v19, n5) & leq(n0, v20) & leq(n0, % 12.60/2.43 | v19)) | ( ~ (v18 = init) & a_select3(r_ds1_filter_init, v16, % 12.60/2.43 | v17) = v18 & $i(v18) & leq(v17, n2) & leq(v16, n2) & leq(n0, % 12.60/2.43 | v17) & leq(n0, v16)) | ( ~ (v15 = init) & % 12.60/2.43 | a_select3(xhatmin_ds1_filter_init, v13, v14) = v15 & $i(v15) & % 12.60/2.43 | leq(v14, n0) & leq(v13, n5) & leq(n0, v14) & leq(n0, v13)) | ( ~ % 12.60/2.43 | (v12 = init) & a_select3(pminus_ds1_filter_init, v10, v11) = v12 % 12.60/2.43 | & $i(v12) & leq(v11, n5) & leq(v10, n5) & leq(n0, v11) & leq(n0, % 12.60/2.43 | v10)) | ( ~ (v6 = init) & a_select3(id_ds1_filter_init, v4, v5) % 12.60/2.43 | = v6 & $i(v6) & gt(pv63, v4) & leq(v5, n5) & leq(v4, n5) & % 12.60/2.43 | leq(n0, v5) & leq(n0, v4)) | ( ~ (v3 = init) & pred(pv63) = v0 & % 12.60/2.43 | a_select3(id_ds1_filter_init, v1, v2) = v3 & $i(v3) & $i(v0) & % 12.60/2.43 | leq(v2, n5) & leq(v1, v0) & leq(n0, v2) & leq(n0, v1)))) % 12.60/2.43 | % 12.60/2.43 | ALPHA: (n91) implies: % 12.60/2.43 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & ~ (v1 = % 12.60/2.43 | pv64) & ~ (pv63 = pv64) & pred(pv63) = v0 & % 12.60/2.43 | a_select3(id_ds1_filter_init, pv63, v1) = v2 & $i(v2) & $i(v1) & % 12.60/2.43 | $i(v0) & leq(v1, n5) & leq(v1, pv64) & leq(pv5, n998) & leq(n0, v1) & % 12.60/2.43 | leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv63, n5) & % 12.60/2.43 | leq(pv64, n5) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init % 12.60/2.43 | | ~ (a_select3(id_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ % 12.60/2.43 | $i(v3) | ~ gt(pv63, v3) | ~ leq(v4, n5) | ~ leq(v3, n5) | ~ % 12.60/2.43 | leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 12.60/2.43 | $i] : (v5 = init | ~ (a_select3(id_ds1_filter_init, v3, v4) = v5) % 12.60/2.43 | | ~ $i(v4) | ~ $i(v3) | ~ leq(v4, n5) | ~ leq(v3, v0) | ~ % 12.60/2.43 | leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 12.60/2.43 | $i] : (v5 = init | ~ (a_select3(pminus_ds1_filter_init, v3, v4) = % 12.60/2.43 | v5) | ~ $i(v4) | ~ $i(v3) | ~ leq(v4, n5) | ~ leq(v3, n5) | % 12.60/2.43 | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : ! % 12.60/2.43 | [v5: $i] : (v5 = init | ~ (a_select3(xhatmin_ds1_filter_init, v3, % 12.60/2.43 | v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ leq(v4, n0) | ~ leq(v3, % 12.60/2.43 | n5) | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: $i] : ! [v4: % 12.60/2.43 | $i] : ! [v5: $i] : (v5 = init | ~ (a_select3(r_ds1_filter_init, % 12.60/2.43 | v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ leq(v4, n2) | ~ % 12.60/2.43 | leq(v3, n2) | ~ leq(n0, v4) | ~ leq(n0, v3)) & ! [v3: $i] : ! % 12.60/2.43 | [v4: $i] : ! [v5: $i] : (v5 = init | ~ % 12.60/2.43 | (a_select3(q_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) % 12.60/2.43 | | ~ leq(v4, n5) | ~ leq(v3, n5) | ~ leq(n0, v4) | ~ leq(n0, % 12.60/2.43 | v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ % 12.60/2.43 | (a_select3(dv_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ % 12.60/2.43 | $i(v3) | ~ leq(v4, n0) | ~ leq(v3, n5) | ~ leq(n0, v4) | ~ % 12.60/2.43 | leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init % 12.60/2.43 | | ~ (a_select3(phi_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ % 12.60/2.43 | $i(v3) | ~ leq(v4, n5) | ~ leq(v3, n5) | ~ leq(n0, v4) | ~ % 12.60/2.44 | leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init % 12.60/2.44 | | ~ (a_select3(h_ds1_filter_init, v3, v4) = v5) | ~ $i(v4) | ~ % 12.60/2.44 | $i(v3) | ~ leq(v4, n5) | ~ leq(v3, n2) | ~ leq(n0, v4) | ~ % 12.60/2.44 | leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = init | ~ % 12.60/2.44 | (a_select3(id_ds1_filter_init, pv63, v3) = v4) | ~ $i(v3) | ~ % 12.60/2.44 | gt(pv64, v3) | ~ leq(v3, n5) | ~ leq(n0, v3))) % 12.60/2.44 | % 12.60/2.44 | ALPHA: (function-axioms) implies: % 12.60/2.44 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) % 12.60/2.44 | | ~ (pred(v2) = v0)) % 12.60/2.44 | % 12.60/2.44 | DELTA: instantiating (2) with fresh symbols all_4_0, all_4_1, all_4_2 gives: % 12.60/2.44 | (4) ~ (all_4_0 = init) & ~ (all_4_1 = pv64) & ~ (pv63 = pv64) & % 12.60/2.44 | pred(pv63) = all_4_2 & a_select3(id_ds1_filter_init, pv63, all_4_1) = % 12.60/2.44 | all_4_0 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & leq(all_4_1, n5) & % 12.60/2.44 | leq(all_4_1, pv64) & leq(pv5, n998) & leq(n0, all_4_1) & leq(n0, pv5) & % 12.60/2.44 | leq(n0, pv63) & leq(n0, pv64) & leq(pv63, n5) & leq(pv64, n5) & ! [v0: % 12.60/2.44 | $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.44 | (a_select3(id_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 12.60/2.44 | | ~ gt(pv63, v0) | ~ leq(v1, n5) | ~ leq(v0, n5) | ~ leq(n0, v1) % 12.60/2.44 | | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = % 12.60/2.44 | init | ~ (a_select3(id_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | % 12.60/2.44 | ~ $i(v0) | ~ leq(v1, n5) | ~ leq(v0, all_4_2) | ~ leq(n0, v1) | ~ % 12.60/2.44 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | % 12.60/2.44 | ~ (a_select3(pminus_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.44 | $i(v0) | ~ leq(v1, n5) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ % 12.60/2.44 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | % 12.60/2.44 | ~ (a_select3(xhatmin_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.44 | $i(v0) | ~ leq(v1, n0) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ % 12.60/2.44 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | % 12.60/2.44 | ~ (a_select3(r_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.44 | $i(v0) | ~ leq(v1, n2) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ % 12.60/2.44 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | % 12.60/2.44 | ~ (a_select3(q_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.44 | $i(v0) | ~ leq(v1, n5) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ % 12.60/2.44 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | % 12.60/2.44 | ~ (a_select3(dv_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.44 | $i(v0) | ~ leq(v1, n0) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ % 12.60/2.44 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | % 12.60/2.44 | ~ (a_select3(phi_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.44 | $i(v0) | ~ leq(v1, n5) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ % 12.60/2.44 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | % 12.60/2.44 | ~ (a_select3(h_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.44 | $i(v0) | ~ leq(v1, n5) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ % 12.60/2.44 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 12.60/2.44 | (a_select3(id_ds1_filter_init, pv63, v0) = v1) | ~ $i(v0) | ~ % 12.60/2.44 | gt(pv64, v0) | ~ leq(v0, n5) | ~ leq(n0, v0)) % 12.60/2.44 | % 12.60/2.44 | ALPHA: (4) implies: % 12.60/2.44 | (5) ~ (pv63 = pv64) % 12.60/2.44 | (6) ~ (all_4_1 = pv64) % 12.60/2.44 | (7) ~ (all_4_0 = init) % 12.60/2.44 | (8) leq(pv64, n5) % 12.60/2.44 | (9) leq(pv63, n5) % 12.60/2.44 | (10) leq(n0, pv64) % 12.60/2.44 | (11) leq(n0, pv63) % 12.60/2.44 | (12) leq(n0, pv5) % 12.60/2.44 | (13) leq(n0, all_4_1) % 12.60/2.44 | (14) leq(pv5, n998) % 12.60/2.44 | (15) leq(all_4_1, pv64) % 12.60/2.44 | (16) leq(all_4_1, n5) % 12.60/2.44 | (17) $i(all_4_1) % 12.60/2.44 | (18) a_select3(id_ds1_filter_init, pv63, all_4_1) = all_4_0 % 12.60/2.44 | (19) pred(pv63) = all_4_2 % 12.60/2.45 | (20) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 12.60/2.45 | (a_select3(id_ds1_filter_init, pv63, v0) = v1) | ~ $i(v0) | ~ % 12.60/2.45 | gt(pv64, v0) | ~ leq(v0, n5) | ~ leq(n0, v0)) % 12.60/2.45 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.45 | (a_select3(h_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 12.60/2.45 | | ~ leq(v1, n5) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 12.60/2.45 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.45 | (a_select3(phi_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.45 | $i(v0) | ~ leq(v1, n5) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ % 12.60/2.45 | leq(n0, v0)) % 12.60/2.45 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.45 | (a_select3(dv_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 12.60/2.45 | | ~ leq(v1, n0) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 12.60/2.45 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.45 | (a_select3(q_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 12.60/2.45 | | ~ leq(v1, n5) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 12.60/2.45 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.45 | (a_select3(r_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 12.60/2.45 | | ~ leq(v1, n2) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 12.60/2.45 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.45 | (a_select3(xhatmin_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.45 | $i(v0) | ~ leq(v1, n0) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ % 12.60/2.45 | leq(n0, v0)) % 12.60/2.45 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.45 | (a_select3(pminus_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ % 12.60/2.45 | $i(v0) | ~ leq(v1, n5) | ~ leq(v0, n5) | ~ leq(n0, v1) | ~ % 12.60/2.45 | leq(n0, v0)) % 12.60/2.45 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.45 | (a_select3(id_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 12.60/2.45 | | ~ leq(v1, n5) | ~ leq(v0, all_4_2) | ~ leq(n0, v1) | ~ leq(n0, % 12.60/2.45 | v0)) % 12.60/2.45 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 12.60/2.45 | (a_select3(id_ds1_filter_init, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 12.60/2.45 | | ~ gt(pv63, v0) | ~ leq(v1, n5) | ~ leq(v0, n5) | ~ leq(n0, v1) % 12.60/2.45 | | ~ leq(n0, v0)) % 12.60/2.45 | % 12.60/2.45 | DELTA: instantiating (1) with fresh symbols all_7_0, all_7_1, all_7_2, % 12.60/2.45 | all_7_3, all_7_4, all_7_5, all_7_6, all_7_7, all_7_8, all_7_9, % 12.60/2.45 | all_7_10, all_7_11, all_7_12, all_7_13, all_7_14, all_7_15, all_7_16, % 12.60/2.45 | all_7_17, all_7_18, all_7_19, all_7_20, all_7_21, all_7_22, all_7_23, % 12.60/2.45 | all_7_24, all_7_25, all_7_26, all_7_27, all_7_28, all_7_29, all_7_30 % 12.60/2.45 | gives: % 12.60/2.46 | (30) $i(all_7_1) & $i(all_7_2) & $i(all_7_4) & $i(all_7_5) & $i(all_7_7) & % 12.60/2.46 | $i(all_7_8) & $i(all_7_10) & $i(all_7_11) & $i(all_7_13) & % 12.60/2.46 | $i(all_7_14) & $i(all_7_16) & $i(all_7_17) & $i(all_7_19) & % 12.60/2.46 | $i(all_7_20) & $i(all_7_22) & $i(all_7_23) & $i(all_7_25) & % 12.60/2.46 | $i(all_7_26) & $i(all_7_28) & $i(all_7_29) & (pv63 = pv64 | ~ % 12.60/2.46 | leq(pv5, n998) | ~ leq(n0, pv5) | ~ leq(n0, pv63) | ~ leq(n0, % 12.60/2.46 | pv64) | ~ leq(pv63, n5) | ~ leq(pv64, n5) | ! [v0: $i] : ! % 12.60/2.46 | [v1: $i] : (v1 = init | v0 = pv64 | ~ % 12.60/2.46 | (a_select3(id_ds1_filter_init, pv63, v0) = v1) | ~ $i(v0) | ~ % 12.60/2.46 | leq(v0, n5) | ~ leq(v0, pv64) | ~ leq(n0, v0)) | (all_7_23 = % 12.60/2.46 | pv63 & ~ (all_7_21 = init) & a_select3(id_ds1_filter_init, pv63, % 12.60/2.46 | all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) & % 12.60/2.46 | leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0 = init) & % 12.60/2.46 | a_select3(h_ds1_filter_init, all_7_2, all_7_1) = all_7_0 & % 12.60/2.46 | $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0, % 12.60/2.46 | all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 = init) & % 12.60/2.46 | a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = all_7_3 & % 12.60/2.46 | $i(all_7_3) & leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0, % 12.60/2.46 | all_7_4) & leq(n0, all_7_5)) | ( ~ (all_7_6 = init) & % 12.60/2.46 | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = all_7_6 & % 12.60/2.46 | $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) & leq(n0, % 12.60/2.46 | all_7_7) & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) & % 12.60/2.46 | a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 & % 12.60/2.46 | $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0, % 12.60/2.46 | all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init) & % 12.60/2.46 | a_select3(r_ds1_filter_init, all_7_14, all_7_13) = all_7_12 & % 12.60/2.46 | $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0, % 12.60/2.46 | all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 = init) & % 12.60/2.46 | a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) = all_7_15 % 12.60/2.46 | & $i(all_7_15) & leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, % 12.60/2.46 | all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 = init) & % 12.60/2.46 | a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = all_7_18 & % 12.60/2.46 | $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0, % 12.60/2.46 | all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 = init) & % 12.60/2.46 | a_select3(id_ds1_filter_init, all_7_26, all_7_25) = all_7_24 & % 12.60/2.46 | $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25, n5) & % 12.60/2.46 | leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~ % 12.60/2.46 | (all_7_27 = init) & pred(pv63) = all_7_30 & % 12.60/2.46 | a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 & % 12.60/2.46 | $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29, % 12.60/2.46 | all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29))) % 12.60/2.46 | % 12.60/2.46 | ALPHA: (30) implies: % 12.60/2.46 | (31) $i(all_7_29) % 12.60/2.46 | (32) $i(all_7_28) % 12.60/2.46 | (33) $i(all_7_26) % 12.60/2.46 | (34) $i(all_7_25) % 12.60/2.46 | (35) $i(all_7_22) % 12.60/2.46 | (36) $i(all_7_20) % 12.60/2.46 | (37) $i(all_7_19) % 12.60/2.46 | (38) $i(all_7_17) % 12.60/2.46 | (39) $i(all_7_16) % 12.60/2.46 | (40) $i(all_7_14) % 12.60/2.46 | (41) $i(all_7_13) % 12.60/2.46 | (42) $i(all_7_11) % 12.60/2.46 | (43) $i(all_7_10) % 12.60/2.46 | (44) $i(all_7_8) % 12.60/2.46 | (45) $i(all_7_7) % 12.60/2.46 | (46) $i(all_7_5) % 12.60/2.46 | (47) $i(all_7_4) % 12.60/2.46 | (48) $i(all_7_2) % 12.60/2.46 | (49) $i(all_7_1) % 12.60/2.46 | (50) pv63 = pv64 | ~ leq(pv5, n998) | ~ leq(n0, pv5) | ~ leq(n0, pv63) | % 12.60/2.46 | ~ leq(n0, pv64) | ~ leq(pv63, n5) | ~ leq(pv64, n5) | ! [v0: $i] : % 12.60/2.46 | ! [v1: $i] : (v1 = init | v0 = pv64 | ~ % 12.60/2.46 | (a_select3(id_ds1_filter_init, pv63, v0) = v1) | ~ $i(v0) | ~ % 12.60/2.46 | leq(v0, n5) | ~ leq(v0, pv64) | ~ leq(n0, v0)) | (all_7_23 = pv63 % 12.60/2.46 | & ~ (all_7_21 = init) & a_select3(id_ds1_filter_init, pv63, % 12.60/2.46 | all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) & % 12.60/2.46 | leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0 = init) & % 12.60/2.46 | a_select3(h_ds1_filter_init, all_7_2, all_7_1) = all_7_0 & % 12.60/2.46 | $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0, all_7_1) % 12.60/2.46 | & leq(n0, all_7_2)) | ( ~ (all_7_3 = init) & % 12.60/2.46 | a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = all_7_3 & % 12.60/2.46 | $i(all_7_3) & leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0, all_7_4) % 12.60/2.46 | & leq(n0, all_7_5)) | ( ~ (all_7_6 = init) & % 12.60/2.46 | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = all_7_6 & % 12.60/2.46 | $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) & leq(n0, all_7_7) % 12.60/2.46 | & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) & % 12.60/2.46 | a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 & % 12.60/2.46 | $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0, % 12.60/2.46 | all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init) & % 12.60/2.46 | a_select3(r_ds1_filter_init, all_7_14, all_7_13) = all_7_12 & % 12.60/2.46 | $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0, % 12.60/2.46 | all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 = init) & % 12.60/2.46 | a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) = all_7_15 & % 12.60/2.46 | $i(all_7_15) & leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, % 12.60/2.46 | all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 = init) & % 12.60/2.46 | a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = all_7_18 & % 12.60/2.46 | $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0, % 12.60/2.46 | all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 = init) & % 12.60/2.46 | a_select3(id_ds1_filter_init, all_7_26, all_7_25) = all_7_24 & % 12.60/2.46 | $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25, n5) & % 12.60/2.46 | leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~ % 12.60/2.46 | (all_7_27 = init) & pred(pv63) = all_7_30 & % 12.60/2.46 | a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 & % 12.60/2.46 | $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29, % 12.60/2.46 | all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29)) % 12.60/2.46 | % 12.60/2.46 | BETA: splitting (50) gives: % 12.60/2.46 | % 12.60/2.46 | Case 1: % 12.60/2.46 | | % 12.60/2.46 | | (51) ~ leq(pv5, n998) % 12.60/2.46 | | % 12.60/2.46 | | PRED_UNIFY: (14), (51) imply: % 12.60/2.46 | | (52) $false % 12.60/2.47 | | % 12.60/2.47 | | CLOSE: (52) is inconsistent. % 12.60/2.47 | | % 12.60/2.47 | Case 2: % 12.60/2.47 | | % 12.60/2.47 | | (53) pv63 = pv64 | ~ leq(n0, pv5) | ~ leq(n0, pv63) | ~ leq(n0, pv64) % 12.60/2.47 | | | ~ leq(pv63, n5) | ~ leq(pv64, n5) | ! [v0: $i] : ! [v1: $i] : % 12.60/2.47 | | (v1 = init | v0 = pv64 | ~ (a_select3(id_ds1_filter_init, pv63, v0) % 12.60/2.47 | | = v1) | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(v0, pv64) | ~ % 12.60/2.47 | | leq(n0, v0)) | (all_7_23 = pv63 & ~ (all_7_21 = init) & % 12.60/2.47 | | a_select3(id_ds1_filter_init, pv63, all_7_22) = all_7_21 & % 12.60/2.47 | | $i(all_7_21) & gt(pv64, all_7_22) & leq(all_7_22, n5) & leq(n0, % 12.60/2.47 | | all_7_22)) | ( ~ (all_7_0 = init) & a_select3(h_ds1_filter_init, % 12.60/2.47 | | all_7_2, all_7_1) = all_7_0 & $i(all_7_0) & leq(all_7_1, n5) & % 12.60/2.47 | | leq(all_7_2, n2) & leq(n0, all_7_1) & leq(n0, all_7_2)) | ( ~ % 12.60/2.47 | | (all_7_3 = init) & a_select3(phi_ds1_filter_init, all_7_5, % 12.60/2.47 | | all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4, n5) & % 12.60/2.47 | | leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0, all_7_5)) | ( ~ % 12.60/2.47 | | (all_7_6 = init) & a_select3(dv_ds1_filter_init, all_7_8, all_7_7) % 12.60/2.47 | | = all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) & % 12.60/2.47 | | leq(n0, all_7_7) & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) & % 12.60/2.47 | | a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 & % 12.60/2.47 | | $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0, % 12.60/2.47 | | all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init) & % 12.60/2.47 | | a_select3(r_ds1_filter_init, all_7_14, all_7_13) = all_7_12 & % 12.60/2.47 | | $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0, % 12.60/2.47 | | all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 = init) & % 12.60/2.47 | | a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) = all_7_15 % 12.60/2.47 | | & $i(all_7_15) & leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, % 12.60/2.47 | | all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 = init) & % 12.60/2.47 | | a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = all_7_18 & % 12.60/2.47 | | $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0, % 12.60/2.47 | | all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 = init) & % 12.60/2.47 | | a_select3(id_ds1_filter_init, all_7_26, all_7_25) = all_7_24 & % 12.60/2.47 | | $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25, n5) & % 12.60/2.47 | | leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~ % 12.60/2.47 | | (all_7_27 = init) & pred(pv63) = all_7_30 & % 12.60/2.47 | | a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 & % 12.60/2.47 | | $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29, % 12.60/2.47 | | all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29)) % 12.60/2.47 | | % 12.60/2.47 | | BETA: splitting (53) gives: % 12.60/2.47 | | % 12.60/2.47 | | Case 1: % 12.60/2.47 | | | % 12.60/2.47 | | | (54) ~ leq(n0, pv5) % 12.60/2.47 | | | % 12.60/2.47 | | | PRED_UNIFY: (12), (54) imply: % 12.60/2.47 | | | (55) $false % 12.60/2.47 | | | % 12.60/2.47 | | | CLOSE: (55) is inconsistent. % 12.60/2.47 | | | % 12.60/2.47 | | Case 2: % 12.60/2.47 | | | % 12.60/2.47 | | | (56) pv63 = pv64 | ~ leq(n0, pv63) | ~ leq(n0, pv64) | ~ leq(pv63, % 12.60/2.47 | | | n5) | ~ leq(pv64, n5) | ! [v0: $i] : ! [v1: $i] : (v1 = init % 12.60/2.47 | | | | v0 = pv64 | ~ (a_select3(id_ds1_filter_init, pv63, v0) = v1) % 12.60/2.47 | | | | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(v0, pv64) | ~ leq(n0, % 12.60/2.47 | | | v0)) | (all_7_23 = pv63 & ~ (all_7_21 = init) & % 12.60/2.47 | | | a_select3(id_ds1_filter_init, pv63, all_7_22) = all_7_21 & % 12.60/2.47 | | | $i(all_7_21) & gt(pv64, all_7_22) & leq(all_7_22, n5) & leq(n0, % 12.60/2.47 | | | all_7_22)) | ( ~ (all_7_0 = init) & % 12.60/2.47 | | | a_select3(h_ds1_filter_init, all_7_2, all_7_1) = all_7_0 & % 12.60/2.47 | | | $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0, % 12.60/2.47 | | | all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 = init) & % 12.60/2.47 | | | a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = all_7_3 & % 12.60/2.47 | | | $i(all_7_3) & leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0, % 12.60/2.47 | | | all_7_4) & leq(n0, all_7_5)) | ( ~ (all_7_6 = init) & % 12.60/2.47 | | | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = all_7_6 & % 12.60/2.47 | | | $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) & leq(n0, % 12.60/2.47 | | | all_7_7) & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) & % 12.60/2.47 | | | a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 & % 12.60/2.47 | | | $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0, % 12.60/2.47 | | | all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init) & % 12.60/2.47 | | | a_select3(r_ds1_filter_init, all_7_14, all_7_13) = all_7_12 & % 12.60/2.47 | | | $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0, % 12.60/2.47 | | | all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 = init) & % 12.60/2.47 | | | a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) = % 12.60/2.47 | | | all_7_15 & $i(all_7_15) & leq(all_7_16, n0) & leq(all_7_17, n5) % 12.60/2.47 | | | & leq(n0, all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 = init) % 12.60/2.47 | | | & a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = % 12.60/2.47 | | | all_7_18 & $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, n5) % 12.60/2.47 | | | & leq(n0, all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 = init) % 12.60/2.47 | | | & a_select3(id_ds1_filter_init, all_7_26, all_7_25) = all_7_24 & % 12.60/2.47 | | | $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25, n5) & % 12.60/2.47 | | | leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~ % 12.60/2.47 | | | (all_7_27 = init) & pred(pv63) = all_7_30 & % 12.60/2.47 | | | a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 & % 12.60/2.47 | | | $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29, % 12.60/2.47 | | | all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29)) % 12.60/2.47 | | | % 12.60/2.47 | | | BETA: splitting (56) gives: % 12.60/2.47 | | | % 12.60/2.47 | | | Case 1: % 12.60/2.47 | | | | % 12.60/2.47 | | | | (57) ~ leq(n0, pv63) % 12.60/2.47 | | | | % 12.60/2.47 | | | | PRED_UNIFY: (11), (57) imply: % 12.60/2.47 | | | | (58) $false % 12.60/2.47 | | | | % 12.60/2.47 | | | | CLOSE: (58) is inconsistent. % 12.60/2.47 | | | | % 12.60/2.47 | | | Case 2: % 12.60/2.47 | | | | % 12.60/2.48 | | | | (59) pv63 = pv64 | ~ leq(n0, pv64) | ~ leq(pv63, n5) | ~ leq(pv64, % 12.60/2.48 | | | | n5) | ! [v0: $i] : ! [v1: $i] : (v1 = init | v0 = pv64 | ~ % 12.60/2.48 | | | | (a_select3(id_ds1_filter_init, pv63, v0) = v1) | ~ $i(v0) | % 12.60/2.48 | | | | ~ leq(v0, n5) | ~ leq(v0, pv64) | ~ leq(n0, v0)) | (all_7_23 % 12.60/2.48 | | | | = pv63 & ~ (all_7_21 = init) & a_select3(id_ds1_filter_init, % 12.60/2.48 | | | | pv63, all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64, % 12.60/2.48 | | | | all_7_22) & leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ % 12.60/2.48 | | | | (all_7_0 = init) & a_select3(h_ds1_filter_init, all_7_2, % 12.60/2.48 | | | | all_7_1) = all_7_0 & $i(all_7_0) & leq(all_7_1, n5) & % 12.60/2.48 | | | | leq(all_7_2, n2) & leq(n0, all_7_1) & leq(n0, all_7_2)) | ( ~ % 12.60/2.48 | | | | (all_7_3 = init) & a_select3(phi_ds1_filter_init, all_7_5, % 12.60/2.48 | | | | all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4, n5) & % 12.60/2.48 | | | | leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0, all_7_5)) | ( ~ % 12.60/2.48 | | | | (all_7_6 = init) & a_select3(dv_ds1_filter_init, all_7_8, % 12.60/2.48 | | | | all_7_7) = all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & % 12.60/2.48 | | | | leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0, all_7_8)) | ( ~ % 12.60/2.48 | | | | (all_7_9 = init) & a_select3(q_ds1_filter_init, all_7_11, % 12.60/2.48 | | | | all_7_10) = all_7_9 & $i(all_7_9) & leq(all_7_10, n5) & % 12.60/2.48 | | | | leq(all_7_11, n5) & leq(n0, all_7_10) & leq(n0, all_7_11)) | ( % 12.60/2.48 | | | | ~ (all_7_12 = init) & a_select3(r_ds1_filter_init, all_7_14, % 12.60/2.48 | | | | all_7_13) = all_7_12 & $i(all_7_12) & leq(all_7_13, n2) & % 12.60/2.48 | | | | leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0, all_7_14)) | ( % 12.60/2.48 | | | | ~ (all_7_15 = init) & a_select3(xhatmin_ds1_filter_init, % 12.60/2.48 | | | | all_7_17, all_7_16) = all_7_15 & $i(all_7_15) & % 12.60/2.48 | | | | leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, all_7_16) & % 12.60/2.48 | | | | leq(n0, all_7_17)) | ( ~ (all_7_18 = init) & % 12.60/2.48 | | | | a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = % 12.60/2.48 | | | | all_7_18 & $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, % 12.60/2.48 | | | | n5) & leq(n0, all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 % 12.60/2.48 | | | | = init) & a_select3(id_ds1_filter_init, all_7_26, all_7_25) % 12.60/2.48 | | | | = all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25, % 12.60/2.48 | | | | n5) & leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, % 12.60/2.48 | | | | all_7_26)) | ( ~ (all_7_27 = init) & pred(pv63) = all_7_30 & % 12.60/2.48 | | | | a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 & % 12.60/2.48 | | | | $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) & % 12.60/2.48 | | | | leq(all_7_29, all_7_30) & leq(n0, all_7_28) & leq(n0, % 12.60/2.48 | | | | all_7_29)) % 12.60/2.48 | | | | % 12.60/2.48 | | | | BETA: splitting (59) gives: % 12.60/2.48 | | | | % 12.60/2.48 | | | | Case 1: % 12.60/2.48 | | | | | % 12.60/2.48 | | | | | (60) ~ leq(n0, pv64) % 12.60/2.48 | | | | | % 12.60/2.48 | | | | | PRED_UNIFY: (10), (60) imply: % 12.60/2.48 | | | | | (61) $false % 12.60/2.48 | | | | | % 12.60/2.48 | | | | | CLOSE: (61) is inconsistent. % 12.60/2.48 | | | | | % 12.60/2.48 | | | | Case 2: % 12.60/2.48 | | | | | % 12.60/2.48 | | | | | (62) pv63 = pv64 | ~ leq(pv63, n5) | ~ leq(pv64, n5) | ! [v0: % 12.60/2.48 | | | | | $i] : ! [v1: $i] : (v1 = init | v0 = pv64 | ~ % 12.60/2.48 | | | | | (a_select3(id_ds1_filter_init, pv63, v0) = v1) | ~ $i(v0) | % 12.60/2.48 | | | | | ~ leq(v0, n5) | ~ leq(v0, pv64) | ~ leq(n0, v0)) | % 12.60/2.48 | | | | | (all_7_23 = pv63 & ~ (all_7_21 = init) & % 12.60/2.48 | | | | | a_select3(id_ds1_filter_init, pv63, all_7_22) = all_7_21 & % 12.60/2.48 | | | | | $i(all_7_21) & gt(pv64, all_7_22) & leq(all_7_22, n5) & % 12.60/2.48 | | | | | leq(n0, all_7_22)) | ( ~ (all_7_0 = init) & % 12.60/2.48 | | | | | a_select3(h_ds1_filter_init, all_7_2, all_7_1) = all_7_0 & % 12.60/2.48 | | | | | $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0, % 12.60/2.48 | | | | | all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 = init) & % 12.60/2.48 | | | | | a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = all_7_3 & % 12.60/2.48 | | | | | $i(all_7_3) & leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0, % 12.60/2.48 | | | | | all_7_4) & leq(n0, all_7_5)) | ( ~ (all_7_6 = init) & % 12.60/2.48 | | | | | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = all_7_6 & % 12.60/2.48 | | | | | $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) & leq(n0, % 12.60/2.48 | | | | | all_7_7) & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) & % 12.60/2.48 | | | | | a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 & % 12.60/2.48 | | | | | $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & % 12.60/2.48 | | | | | leq(n0, all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = % 12.60/2.48 | | | | | init) & a_select3(r_ds1_filter_init, all_7_14, all_7_13) = % 12.60/2.48 | | | | | all_7_12 & $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14, % 12.60/2.48 | | | | | n2) & leq(n0, all_7_13) & leq(n0, all_7_14)) | ( ~ % 12.60/2.48 | | | | | (all_7_15 = init) & a_select3(xhatmin_ds1_filter_init, % 12.60/2.48 | | | | | all_7_17, all_7_16) = all_7_15 & $i(all_7_15) & % 12.60/2.48 | | | | | leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, all_7_16) & % 12.60/2.48 | | | | | leq(n0, all_7_17)) | ( ~ (all_7_18 = init) & % 12.60/2.48 | | | | | a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = % 12.60/2.48 | | | | | all_7_18 & $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, % 12.60/2.48 | | | | | n5) & leq(n0, all_7_19) & leq(n0, all_7_20)) | ( ~ % 12.60/2.48 | | | | | (all_7_24 = init) & a_select3(id_ds1_filter_init, all_7_26, % 12.60/2.48 | | | | | all_7_25) = all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) & % 12.60/2.48 | | | | | leq(all_7_25, n5) & leq(all_7_26, n5) & leq(n0, all_7_25) & % 12.60/2.48 | | | | | leq(n0, all_7_26)) | ( ~ (all_7_27 = init) & pred(pv63) = % 12.60/2.48 | | | | | all_7_30 & a_select3(id_ds1_filter_init, all_7_29, all_7_28) % 12.60/2.48 | | | | | = all_7_27 & $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) % 12.60/2.48 | | | | | & leq(all_7_29, all_7_30) & leq(n0, all_7_28) & leq(n0, % 12.60/2.48 | | | | | all_7_29)) % 12.60/2.48 | | | | | % 12.60/2.48 | | | | | BETA: splitting (62) gives: % 12.60/2.48 | | | | | % 12.60/2.48 | | | | | Case 1: % 12.60/2.48 | | | | | | % 12.60/2.48 | | | | | | (63) ~ leq(pv63, n5) % 12.60/2.48 | | | | | | % 12.60/2.48 | | | | | | PRED_UNIFY: (9), (63) imply: % 12.60/2.48 | | | | | | (64) $false % 12.60/2.48 | | | | | | % 12.60/2.48 | | | | | | CLOSE: (64) is inconsistent. % 12.60/2.48 | | | | | | % 12.60/2.48 | | | | | Case 2: % 12.60/2.48 | | | | | | % 12.60/2.48 | | | | | | (65) pv63 = pv64 | ~ leq(pv64, n5) | ! [v0: $i] : ! [v1: $i] : % 12.60/2.48 | | | | | | (v1 = init | v0 = pv64 | ~ (a_select3(id_ds1_filter_init, % 12.60/2.48 | | | | | | pv63, v0) = v1) | ~ $i(v0) | ~ leq(v0, n5) | ~ % 12.60/2.48 | | | | | | leq(v0, pv64) | ~ leq(n0, v0)) | (all_7_23 = pv63 & ~ % 12.60/2.48 | | | | | | (all_7_21 = init) & a_select3(id_ds1_filter_init, pv63, % 12.60/2.48 | | | | | | all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) % 12.60/2.48 | | | | | | & leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0 = % 12.60/2.48 | | | | | | init) & a_select3(h_ds1_filter_init, all_7_2, all_7_1) = % 12.60/2.48 | | | | | | all_7_0 & $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2, % 12.60/2.48 | | | | | | n2) & leq(n0, all_7_1) & leq(n0, all_7_2)) | ( ~ % 12.60/2.48 | | | | | | (all_7_3 = init) & a_select3(phi_ds1_filter_init, all_7_5, % 12.60/2.48 | | | | | | all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4, n5) & % 12.60/2.48 | | | | | | leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0, all_7_5)) | % 12.60/2.48 | | | | | | ( ~ (all_7_6 = init) & a_select3(dv_ds1_filter_init, % 12.60/2.48 | | | | | | all_7_8, all_7_7) = all_7_6 & $i(all_7_6) & leq(all_7_7, % 12.60/2.48 | | | | | | n0) & leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0, % 12.60/2.48 | | | | | | all_7_8)) | ( ~ (all_7_9 = init) & % 12.60/2.48 | | | | | | a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 % 12.60/2.48 | | | | | | & $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & % 12.60/2.48 | | | | | | leq(n0, all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = % 12.60/2.48 | | | | | | init) & a_select3(r_ds1_filter_init, all_7_14, all_7_13) % 12.60/2.48 | | | | | | = all_7_12 & $i(all_7_12) & leq(all_7_13, n2) & % 12.60/2.48 | | | | | | leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0, all_7_14)) % 12.60/2.48 | | | | | | | ( ~ (all_7_15 = init) & a_select3(xhatmin_ds1_filter_init, % 12.60/2.48 | | | | | | all_7_17, all_7_16) = all_7_15 & $i(all_7_15) & % 12.60/2.48 | | | | | | leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, all_7_16) % 12.60/2.48 | | | | | | & leq(n0, all_7_17)) | ( ~ (all_7_18 = init) & % 12.60/2.48 | | | | | | a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = % 12.60/2.48 | | | | | | all_7_18 & $i(all_7_18) & leq(all_7_19, n5) & % 12.60/2.48 | | | | | | leq(all_7_20, n5) & leq(n0, all_7_19) & leq(n0, all_7_20)) % 12.60/2.48 | | | | | | | ( ~ (all_7_24 = init) & a_select3(id_ds1_filter_init, % 12.60/2.48 | | | | | | all_7_26, all_7_25) = all_7_24 & $i(all_7_24) & gt(pv63, % 12.60/2.48 | | | | | | all_7_26) & leq(all_7_25, n5) & leq(all_7_26, n5) & % 12.60/2.48 | | | | | | leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~ (all_7_27 = % 12.60/2.48 | | | | | | init) & pred(pv63) = all_7_30 & % 12.60/2.48 | | | | | | a_select3(id_ds1_filter_init, all_7_29, all_7_28) = % 12.60/2.48 | | | | | | all_7_27 & $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) % 12.60/2.48 | | | | | | & leq(all_7_29, all_7_30) & leq(n0, all_7_28) & leq(n0, % 12.60/2.48 | | | | | | all_7_29)) % 12.60/2.48 | | | | | | % 12.60/2.48 | | | | | | BETA: splitting (65) gives: % 12.60/2.48 | | | | | | % 12.60/2.48 | | | | | | Case 1: % 12.60/2.48 | | | | | | | % 12.60/2.48 | | | | | | | (66) ~ leq(pv64, n5) % 12.60/2.48 | | | | | | | % 12.60/2.48 | | | | | | | PRED_UNIFY: (8), (66) imply: % 12.60/2.48 | | | | | | | (67) $false % 12.60/2.48 | | | | | | | % 12.60/2.48 | | | | | | | CLOSE: (67) is inconsistent. % 12.60/2.48 | | | | | | | % 12.60/2.48 | | | | | | Case 2: % 12.60/2.48 | | | | | | | % 12.60/2.49 | | | | | | | (68) pv63 = pv64 | ! [v0: $i] : ! [v1: $i] : (v1 = init | v0 % 12.60/2.49 | | | | | | | = pv64 | ~ (a_select3(id_ds1_filter_init, pv63, v0) = % 12.60/2.49 | | | | | | | v1) | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(v0, pv64) | % 12.60/2.49 | | | | | | | ~ leq(n0, v0)) | (all_7_23 = pv63 & ~ (all_7_21 = init) % 12.60/2.49 | | | | | | | & a_select3(id_ds1_filter_init, pv63, all_7_22) = % 12.60/2.49 | | | | | | | all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) & % 12.60/2.49 | | | | | | | leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0 = % 12.60/2.49 | | | | | | | init) & a_select3(h_ds1_filter_init, all_7_2, all_7_1) % 12.60/2.49 | | | | | | | = all_7_0 & $i(all_7_0) & leq(all_7_1, n5) & % 12.60/2.49 | | | | | | | leq(all_7_2, n2) & leq(n0, all_7_1) & leq(n0, all_7_2)) % 12.60/2.49 | | | | | | | | ( ~ (all_7_3 = init) & a_select3(phi_ds1_filter_init, % 12.60/2.49 | | | | | | | all_7_5, all_7_4) = all_7_3 & $i(all_7_3) & % 12.60/2.49 | | | | | | | leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0, all_7_4) & % 12.60/2.49 | | | | | | | leq(n0, all_7_5)) | ( ~ (all_7_6 = init) & % 12.60/2.49 | | | | | | | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = % 12.60/2.49 | | | | | | | all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, % 12.60/2.49 | | | | | | | n5) & leq(n0, all_7_7) & leq(n0, all_7_8)) | ( ~ % 12.60/2.49 | | | | | | | (all_7_9 = init) & a_select3(q_ds1_filter_init, % 12.60/2.49 | | | | | | | all_7_11, all_7_10) = all_7_9 & $i(all_7_9) & % 12.60/2.49 | | | | | | | leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0, % 12.60/2.49 | | | | | | | all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init) % 12.60/2.49 | | | | | | | & a_select3(r_ds1_filter_init, all_7_14, all_7_13) = % 12.60/2.49 | | | | | | | all_7_12 & $i(all_7_12) & leq(all_7_13, n2) & % 12.60/2.49 | | | | | | | leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0, % 12.60/2.49 | | | | | | | all_7_14)) | ( ~ (all_7_15 = init) & % 12.60/2.49 | | | | | | | a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) = % 12.60/2.49 | | | | | | | all_7_15 & $i(all_7_15) & leq(all_7_16, n0) & % 12.60/2.49 | | | | | | | leq(all_7_17, n5) & leq(n0, all_7_16) & leq(n0, % 12.60/2.49 | | | | | | | all_7_17)) | ( ~ (all_7_18 = init) & % 12.60/2.49 | | | | | | | a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = % 12.60/2.49 | | | | | | | all_7_18 & $i(all_7_18) & leq(all_7_19, n5) & % 12.60/2.49 | | | | | | | leq(all_7_20, n5) & leq(n0, all_7_19) & leq(n0, % 12.60/2.49 | | | | | | | all_7_20)) | ( ~ (all_7_24 = init) & % 12.60/2.49 | | | | | | | a_select3(id_ds1_filter_init, all_7_26, all_7_25) = % 12.60/2.49 | | | | | | | all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) & % 12.60/2.49 | | | | | | | leq(all_7_25, n5) & leq(all_7_26, n5) & leq(n0, % 12.60/2.49 | | | | | | | all_7_25) & leq(n0, all_7_26)) | ( ~ (all_7_27 = init) % 12.60/2.49 | | | | | | | & pred(pv63) = all_7_30 & a_select3(id_ds1_filter_init, % 12.60/2.49 | | | | | | | all_7_29, all_7_28) = all_7_27 & $i(all_7_27) & % 12.60/2.49 | | | | | | | $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29, % 12.60/2.49 | | | | | | | all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29)) % 12.60/2.49 | | | | | | | % 12.60/2.49 | | | | | | | BETA: splitting (68) gives: % 12.60/2.49 | | | | | | | % 12.60/2.49 | | | | | | | Case 1: % 12.60/2.49 | | | | | | | | % 12.60/2.49 | | | | | | | | (69) pv63 = pv64 % 12.60/2.49 | | | | | | | | % 12.60/2.49 | | | | | | | | REDUCE: (5), (69) imply: % 12.60/2.49 | | | | | | | | (70) $false % 12.60/2.49 | | | | | | | | % 12.60/2.49 | | | | | | | | CLOSE: (70) is inconsistent. % 12.60/2.49 | | | | | | | | % 12.60/2.49 | | | | | | | Case 2: % 12.60/2.49 | | | | | | | | % 12.60/2.49 | | | | | | | | (71) ! [v0: $i] : ! [v1: $i] : (v1 = init | v0 = pv64 | ~ % 12.60/2.49 | | | | | | | | (a_select3(id_ds1_filter_init, pv63, v0) = v1) | ~ % 12.60/2.49 | | | | | | | | $i(v0) | ~ leq(v0, n5) | ~ leq(v0, pv64) | ~ % 12.60/2.49 | | | | | | | | leq(n0, v0)) | (all_7_23 = pv63 & ~ (all_7_21 = init) % 12.60/2.49 | | | | | | | | & a_select3(id_ds1_filter_init, pv63, all_7_22) = % 12.60/2.49 | | | | | | | | all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) & % 12.60/2.49 | | | | | | | | leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0 % 12.60/2.49 | | | | | | | | = init) & a_select3(h_ds1_filter_init, all_7_2, % 12.60/2.49 | | | | | | | | all_7_1) = all_7_0 & $i(all_7_0) & leq(all_7_1, n5) % 12.60/2.49 | | | | | | | | & leq(all_7_2, n2) & leq(n0, all_7_1) & leq(n0, % 12.60/2.49 | | | | | | | | all_7_2)) | ( ~ (all_7_3 = init) & % 12.60/2.49 | | | | | | | | a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = % 12.60/2.49 | | | | | | | | all_7_3 & $i(all_7_3) & leq(all_7_4, n5) & % 12.60/2.49 | | | | | | | | leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0, % 12.60/2.49 | | | | | | | | all_7_5)) | ( ~ (all_7_6 = init) & % 12.60/2.49 | | | | | | | | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = % 12.60/2.49 | | | | | | | | all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & % 12.60/2.49 | | | | | | | | leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0, % 12.60/2.49 | | | | | | | | all_7_8)) | ( ~ (all_7_9 = init) & % 12.60/2.49 | | | | | | | | a_select3(q_ds1_filter_init, all_7_11, all_7_10) = % 12.60/2.49 | | | | | | | | all_7_9 & $i(all_7_9) & leq(all_7_10, n5) & % 12.60/2.49 | | | | | | | | leq(all_7_11, n5) & leq(n0, all_7_10) & leq(n0, % 12.60/2.49 | | | | | | | | all_7_11)) | ( ~ (all_7_12 = init) & % 12.60/2.49 | | | | | | | | a_select3(r_ds1_filter_init, all_7_14, all_7_13) = % 12.60/2.49 | | | | | | | | all_7_12 & $i(all_7_12) & leq(all_7_13, n2) & % 12.60/2.49 | | | | | | | | leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0, % 12.60/2.49 | | | | | | | | all_7_14)) | ( ~ (all_7_15 = init) & % 12.60/2.49 | | | | | | | | a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) % 12.60/2.49 | | | | | | | | = all_7_15 & $i(all_7_15) & leq(all_7_16, n0) & % 12.60/2.49 | | | | | | | | leq(all_7_17, n5) & leq(n0, all_7_16) & leq(n0, % 12.60/2.49 | | | | | | | | all_7_17)) | ( ~ (all_7_18 = init) & % 12.60/2.49 | | | | | | | | a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) % 12.60/2.49 | | | | | | | | = all_7_18 & $i(all_7_18) & leq(all_7_19, n5) & % 12.60/2.49 | | | | | | | | leq(all_7_20, n5) & leq(n0, all_7_19) & leq(n0, % 12.60/2.49 | | | | | | | | all_7_20)) | ( ~ (all_7_24 = init) & % 12.60/2.49 | | | | | | | | a_select3(id_ds1_filter_init, all_7_26, all_7_25) = % 12.60/2.49 | | | | | | | | all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) & % 12.60/2.49 | | | | | | | | leq(all_7_25, n5) & leq(all_7_26, n5) & leq(n0, % 12.60/2.49 | | | | | | | | all_7_25) & leq(n0, all_7_26)) | ( ~ (all_7_27 = % 12.60/2.49 | | | | | | | | init) & pred(pv63) = all_7_30 & % 12.60/2.49 | | | | | | | | a_select3(id_ds1_filter_init, all_7_29, all_7_28) = % 12.60/2.49 | | | | | | | | all_7_27 & $i(all_7_27) & $i(all_7_30) & leq(all_7_28, % 12.60/2.49 | | | | | | | | n5) & leq(all_7_29, all_7_30) & leq(n0, all_7_28) & % 12.60/2.49 | | | | | | | | leq(n0, all_7_29)) % 12.60/2.49 | | | | | | | | % 12.60/2.49 | | | | | | | | BETA: splitting (71) gives: % 12.60/2.49 | | | | | | | | % 12.60/2.49 | | | | | | | | Case 1: % 12.60/2.49 | | | | | | | | | % 12.60/2.49 | | | | | | | | | (72) ! [v0: $i] : ! [v1: $i] : (v1 = init | v0 = pv64 | % 12.60/2.49 | | | | | | | | | ~ (a_select3(id_ds1_filter_init, pv63, v0) = v1) | % 12.60/2.49 | | | | | | | | | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(v0, pv64) | ~ % 12.60/2.49 | | | | | | | | | leq(n0, v0)) | (all_7_23 = pv63 & ~ (all_7_21 = % 12.60/2.49 | | | | | | | | | init) & a_select3(id_ds1_filter_init, pv63, % 12.60/2.49 | | | | | | | | | all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64, % 12.60/2.49 | | | | | | | | | all_7_22) & leq(all_7_22, n5) & leq(n0, all_7_22)) % 12.60/2.49 | | | | | | | | | | ( ~ (all_7_0 = init) & a_select3(h_ds1_filter_init, % 12.60/2.49 | | | | | | | | | all_7_2, all_7_1) = all_7_0 & $i(all_7_0) & % 12.60/2.49 | | | | | | | | | leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0, % 12.60/2.49 | | | | | | | | | all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 = % 12.60/2.49 | | | | | | | | | init) & a_select3(phi_ds1_filter_init, all_7_5, % 12.60/2.49 | | | | | | | | | all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4, % 12.60/2.49 | | | | | | | | | n5) & leq(all_7_5, n5) & leq(n0, all_7_4) & % 12.60/2.49 | | | | | | | | | leq(n0, all_7_5)) | ( ~ (all_7_6 = init) & % 12.60/2.49 | | | | | | | | | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = % 12.60/2.49 | | | | | | | | | all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & % 12.60/2.49 | | | | | | | | | leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0, % 12.60/2.49 | | | | | | | | | all_7_8)) % 12.60/2.49 | | | | | | | | | % 12.60/2.49 | | | | | | | | | BETA: splitting (72) gives: % 12.60/2.49 | | | | | | | | | % 12.60/2.49 | | | | | | | | | Case 1: % 12.60/2.49 | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | (73) ! [v0: $i] : ! [v1: $i] : (v1 = init | v0 = pv64 | % 12.60/2.49 | | | | | | | | | | ~ (a_select3(id_ds1_filter_init, pv63, v0) = v1) % 12.60/2.49 | | | | | | | | | | | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(v0, pv64) | % 12.60/2.49 | | | | | | | | | | ~ leq(n0, v0)) | (all_7_23 = pv63 & ~ (all_7_21 = % 12.60/2.49 | | | | | | | | | | init) & a_select3(id_ds1_filter_init, pv63, % 12.60/2.49 | | | | | | | | | | all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64, % 12.60/2.49 | | | | | | | | | | all_7_22) & leq(all_7_22, n5) & leq(n0, % 12.60/2.49 | | | | | | | | | | all_7_22)) % 12.60/2.49 | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | BETA: splitting (73) gives: % 12.60/2.49 | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | Case 1: % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | (74) ! [v0: $i] : ! [v1: $i] : (v1 = init | v0 = pv64 % 12.60/2.49 | | | | | | | | | | | | ~ (a_select3(id_ds1_filter_init, pv63, v0) = % 12.60/2.49 | | | | | | | | | | | v1) | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(v0, % 12.60/2.49 | | | | | | | | | | | pv64) | ~ leq(n0, v0)) % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | GROUND_INST: instantiating (74) with all_4_1, all_4_0, % 12.60/2.49 | | | | | | | | | | | simplifying with (13), (15), (16), (17), (18) % 12.60/2.49 | | | | | | | | | | | gives: % 12.60/2.49 | | | | | | | | | | | (75) all_4_0 = init | all_4_1 = pv64 % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | BETA: splitting (75) gives: % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | Case 1: % 12.60/2.49 | | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | | (76) all_4_0 = init % 12.60/2.49 | | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | | REDUCE: (7), (76) imply: % 12.60/2.49 | | | | | | | | | | | | (77) $false % 12.60/2.49 | | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | | CLOSE: (77) is inconsistent. % 12.60/2.49 | | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | Case 2: % 12.60/2.49 | | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | | (78) all_4_1 = pv64 % 12.60/2.49 | | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | | REDUCE: (6), (78) imply: % 12.60/2.49 | | | | | | | | | | | | (79) $false % 12.60/2.49 | | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | | CLOSE: (79) is inconsistent. % 12.60/2.49 | | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | End of split % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | Case 2: % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | (80) all_7_23 = pv63 & ~ (all_7_21 = init) & % 12.60/2.49 | | | | | | | | | | | a_select3(id_ds1_filter_init, pv63, all_7_22) = % 12.60/2.49 | | | | | | | | | | | all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) & % 12.60/2.49 | | | | | | | | | | | leq(all_7_22, n5) & leq(n0, all_7_22) % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | ALPHA: (80) implies: % 12.60/2.49 | | | | | | | | | | | (81) ~ (all_7_21 = init) % 12.60/2.49 | | | | | | | | | | | (82) leq(n0, all_7_22) % 12.60/2.49 | | | | | | | | | | | (83) leq(all_7_22, n5) % 12.60/2.49 | | | | | | | | | | | (84) gt(pv64, all_7_22) % 12.60/2.49 | | | | | | | | | | | (85) a_select3(id_ds1_filter_init, pv63, all_7_22) = % 12.60/2.49 | | | | | | | | | | | all_7_21 % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_7_22, all_7_21, % 12.60/2.49 | | | | | | | | | | | simplifying with (35), (82), (83), (84), (85) % 12.60/2.49 | | | | | | | | | | | gives: % 12.60/2.49 | | | | | | | | | | | (86) all_7_21 = init % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | REDUCE: (81), (86) imply: % 12.60/2.49 | | | | | | | | | | | (87) $false % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | | CLOSE: (87) is inconsistent. % 12.60/2.49 | | | | | | | | | | | % 12.60/2.49 | | | | | | | | | | End of split % 12.60/2.49 | | | | | | | | | | % 12.60/2.49 | | | | | | | | | Case 2: % 12.60/2.49 | | | | | | | | | | % 12.60/2.50 | | | | | | | | | | (88) ( ~ (all_7_0 = init) & a_select3(h_ds1_filter_init, % 12.60/2.50 | | | | | | | | | | all_7_2, all_7_1) = all_7_0 & $i(all_7_0) & % 12.60/2.50 | | | | | | | | | | leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0, % 12.60/2.50 | | | | | | | | | | all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 = % 12.60/2.50 | | | | | | | | | | init) & a_select3(phi_ds1_filter_init, all_7_5, % 12.60/2.50 | | | | | | | | | | all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4, % 12.60/2.50 | | | | | | | | | | n5) & leq(all_7_5, n5) & leq(n0, all_7_4) & % 12.60/2.50 | | | | | | | | | | leq(n0, all_7_5)) | ( ~ (all_7_6 = init) & % 12.60/2.50 | | | | | | | | | | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = % 12.60/2.50 | | | | | | | | | | all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & % 12.60/2.50 | | | | | | | | | | leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0, % 12.60/2.50 | | | | | | | | | | all_7_8)) % 12.60/2.50 | | | | | | | | | | % 12.60/2.50 | | | | | | | | | | BETA: splitting (88) gives: % 12.60/2.50 | | | | | | | | | | % 12.60/2.50 | | | | | | | | | | Case 1: % 12.60/2.50 | | | | | | | | | | | % 12.60/2.50 | | | | | | | | | | | (89) ~ (all_7_0 = init) & a_select3(h_ds1_filter_init, % 12.60/2.50 | | | | | | | | | | | all_7_2, all_7_1) = all_7_0 & $i(all_7_0) & % 12.60/2.50 | | | | | | | | | | | leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0, % 12.60/2.50 | | | | | | | | | | | all_7_1) & leq(n0, all_7_2) % 12.60/2.50 | | | | | | | | | | | % 12.60/2.50 | | | | | | | | | | | ALPHA: (89) implies: % 12.60/2.50 | | | | | | | | | | | (90) ~ (all_7_0 = init) % 12.60/2.50 | | | | | | | | | | | (91) leq(n0, all_7_2) % 12.60/2.50 | | | | | | | | | | | (92) leq(n0, all_7_1) % 12.60/2.50 | | | | | | | | | | | (93) leq(all_7_2, n2) % 12.60/2.50 | | | | | | | | | | | (94) leq(all_7_1, n5) % 12.60/2.50 | | | | | | | | | | | (95) a_select3(h_ds1_filter_init, all_7_2, all_7_1) = % 12.60/2.50 | | | | | | | | | | | all_7_0 % 12.60/2.50 | | | | | | | | | | | % 12.60/2.50 | | | | | | | | | | | GROUND_INST: instantiating (21) with all_7_2, all_7_1, all_7_0, % 12.60/2.50 | | | | | | | | | | | simplifying with (48), (49), (91), (92), (93), % 12.60/2.50 | | | | | | | | | | | (94), (95) gives: % 13.02/2.50 | | | | | | | | | | | (96) all_7_0 = init % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | REDUCE: (90), (96) imply: % 13.02/2.50 | | | | | | | | | | | (97) $false % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | CLOSE: (97) is inconsistent. % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | Case 2: % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | (98) ( ~ (all_7_3 = init) & % 13.02/2.50 | | | | | | | | | | | a_select3(phi_ds1_filter_init, all_7_5, all_7_4) % 13.02/2.50 | | | | | | | | | | | = all_7_3 & $i(all_7_3) & leq(all_7_4, n5) & % 13.02/2.50 | | | | | | | | | | | leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0, % 13.02/2.50 | | | | | | | | | | | all_7_5)) | ( ~ (all_7_6 = init) & % 13.02/2.50 | | | | | | | | | | | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) % 13.02/2.50 | | | | | | | | | | | = all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & % 13.02/2.50 | | | | | | | | | | | leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0, % 13.02/2.50 | | | | | | | | | | | all_7_8)) % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | BETA: splitting (98) gives: % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | Case 1: % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | (99) ~ (all_7_3 = init) & % 13.02/2.50 | | | | | | | | | | | | a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = % 13.02/2.50 | | | | | | | | | | | | all_7_3 & $i(all_7_3) & leq(all_7_4, n5) & % 13.02/2.50 | | | | | | | | | | | | leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0, % 13.02/2.50 | | | | | | | | | | | | all_7_5) % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | ALPHA: (99) implies: % 13.02/2.50 | | | | | | | | | | | | (100) ~ (all_7_3 = init) % 13.02/2.50 | | | | | | | | | | | | (101) leq(n0, all_7_5) % 13.02/2.50 | | | | | | | | | | | | (102) leq(n0, all_7_4) % 13.02/2.50 | | | | | | | | | | | | (103) leq(all_7_5, n5) % 13.02/2.50 | | | | | | | | | | | | (104) leq(all_7_4, n5) % 13.02/2.50 | | | | | | | | | | | | (105) a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = % 13.02/2.50 | | | | | | | | | | | | all_7_3 % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_7_5, all_7_4, all_7_3, % 13.02/2.50 | | | | | | | | | | | | simplifying with (46), (47), (101), (102), (103), % 13.02/2.50 | | | | | | | | | | | | (104), (105) gives: % 13.02/2.50 | | | | | | | | | | | | (106) all_7_3 = init % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | REDUCE: (100), (106) imply: % 13.02/2.50 | | | | | | | | | | | | (107) $false % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | CLOSE: (107) is inconsistent. % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | Case 2: % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | (108) ~ (all_7_6 = init) & % 13.02/2.50 | | | | | | | | | | | | a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = % 13.02/2.50 | | | | | | | | | | | | all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & % 13.02/2.50 | | | | | | | | | | | | leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0, % 13.02/2.50 | | | | | | | | | | | | all_7_8) % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | ALPHA: (108) implies: % 13.02/2.50 | | | | | | | | | | | | (109) ~ (all_7_6 = init) % 13.02/2.50 | | | | | | | | | | | | (110) leq(n0, all_7_8) % 13.02/2.50 | | | | | | | | | | | | (111) leq(n0, all_7_7) % 13.02/2.50 | | | | | | | | | | | | (112) leq(all_7_8, n5) % 13.02/2.50 | | | | | | | | | | | | (113) leq(all_7_7, n0) % 13.02/2.50 | | | | | | | | | | | | (114) a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = % 13.02/2.50 | | | | | | | | | | | | all_7_6 % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_7_8, all_7_7, all_7_6, % 13.02/2.50 | | | | | | | | | | | | simplifying with (44), (45), (110), (111), (112), % 13.02/2.50 | | | | | | | | | | | | (113), (114) gives: % 13.02/2.50 | | | | | | | | | | | | (115) all_7_6 = init % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | REDUCE: (109), (115) imply: % 13.02/2.50 | | | | | | | | | | | | (116) $false % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | CLOSE: (116) is inconsistent. % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | End of split % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | End of split % 13.02/2.50 | | | | | | | | | | % 13.02/2.50 | | | | | | | | | End of split % 13.02/2.50 | | | | | | | | | % 13.02/2.50 | | | | | | | | Case 2: % 13.02/2.50 | | | | | | | | | % 13.02/2.50 | | | | | | | | | (117) ( ~ (all_7_9 = init) & a_select3(q_ds1_filter_init, % 13.02/2.50 | | | | | | | | | all_7_11, all_7_10) = all_7_9 & $i(all_7_9) & % 13.02/2.50 | | | | | | | | | leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0, % 13.02/2.50 | | | | | | | | | all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = % 13.02/2.50 | | | | | | | | | init) & a_select3(r_ds1_filter_init, all_7_14, % 13.02/2.50 | | | | | | | | | all_7_13) = all_7_12 & $i(all_7_12) & % 13.02/2.50 | | | | | | | | | leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0, % 13.02/2.50 | | | | | | | | | all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 = % 13.02/2.50 | | | | | | | | | init) & a_select3(xhatmin_ds1_filter_init, % 13.02/2.50 | | | | | | | | | all_7_17, all_7_16) = all_7_15 & $i(all_7_15) & % 13.02/2.50 | | | | | | | | | leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, % 13.02/2.50 | | | | | | | | | all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 = % 13.02/2.50 | | | | | | | | | init) & a_select3(pminus_ds1_filter_init, % 13.02/2.50 | | | | | | | | | all_7_20, all_7_19) = all_7_18 & $i(all_7_18) & % 13.02/2.50 | | | | | | | | | leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0, % 13.02/2.50 | | | | | | | | | all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 = % 13.02/2.50 | | | | | | | | | init) & a_select3(id_ds1_filter_init, all_7_26, % 13.02/2.50 | | | | | | | | | all_7_25) = all_7_24 & $i(all_7_24) & gt(pv63, % 13.02/2.50 | | | | | | | | | all_7_26) & leq(all_7_25, n5) & leq(all_7_26, n5) % 13.02/2.50 | | | | | | | | | & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~ % 13.02/2.50 | | | | | | | | | (all_7_27 = init) & pred(pv63) = all_7_30 & % 13.02/2.50 | | | | | | | | | a_select3(id_ds1_filter_init, all_7_29, all_7_28) = % 13.02/2.50 | | | | | | | | | all_7_27 & $i(all_7_27) & $i(all_7_30) & % 13.02/2.50 | | | | | | | | | leq(all_7_28, n5) & leq(all_7_29, all_7_30) & % 13.02/2.50 | | | | | | | | | leq(n0, all_7_28) & leq(n0, all_7_29)) % 13.02/2.50 | | | | | | | | | % 13.02/2.50 | | | | | | | | | BETA: splitting (117) gives: % 13.02/2.50 | | | | | | | | | % 13.02/2.50 | | | | | | | | | Case 1: % 13.02/2.50 | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | (118) ( ~ (all_7_9 = init) & a_select3(q_ds1_filter_init, % 13.02/2.50 | | | | | | | | | | all_7_11, all_7_10) = all_7_9 & $i(all_7_9) & % 13.02/2.50 | | | | | | | | | | leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0, % 13.02/2.50 | | | | | | | | | | all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 % 13.02/2.50 | | | | | | | | | | = init) & a_select3(r_ds1_filter_init, % 13.02/2.50 | | | | | | | | | | all_7_14, all_7_13) = all_7_12 & $i(all_7_12) & % 13.02/2.50 | | | | | | | | | | leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0, % 13.02/2.50 | | | | | | | | | | all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 % 13.02/2.50 | | | | | | | | | | = init) & a_select3(xhatmin_ds1_filter_init, % 13.02/2.50 | | | | | | | | | | all_7_17, all_7_16) = all_7_15 & $i(all_7_15) & % 13.02/2.50 | | | | | | | | | | leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, % 13.02/2.50 | | | | | | | | | | all_7_16) & leq(n0, all_7_17)) % 13.02/2.50 | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | BETA: splitting (118) gives: % 13.02/2.50 | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | Case 1: % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | (119) ~ (all_7_9 = init) & a_select3(q_ds1_filter_init, % 13.02/2.50 | | | | | | | | | | | all_7_11, all_7_10) = all_7_9 & $i(all_7_9) & % 13.02/2.50 | | | | | | | | | | | leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0, % 13.02/2.50 | | | | | | | | | | | all_7_10) & leq(n0, all_7_11) % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | ALPHA: (119) implies: % 13.02/2.50 | | | | | | | | | | | (120) ~ (all_7_9 = init) % 13.02/2.50 | | | | | | | | | | | (121) leq(n0, all_7_11) % 13.02/2.50 | | | | | | | | | | | (122) leq(n0, all_7_10) % 13.02/2.50 | | | | | | | | | | | (123) leq(all_7_11, n5) % 13.02/2.50 | | | | | | | | | | | (124) leq(all_7_10, n5) % 13.02/2.50 | | | | | | | | | | | (125) a_select3(q_ds1_filter_init, all_7_11, all_7_10) = % 13.02/2.50 | | | | | | | | | | | all_7_9 % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_7_11, all_7_10, % 13.02/2.50 | | | | | | | | | | | all_7_9, simplifying with (42), (43), (121), % 13.02/2.50 | | | | | | | | | | | (122), (123), (124), (125) gives: % 13.02/2.50 | | | | | | | | | | | (126) all_7_9 = init % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | REDUCE: (120), (126) imply: % 13.02/2.50 | | | | | | | | | | | (127) $false % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | CLOSE: (127) is inconsistent. % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | Case 2: % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | (128) ( ~ (all_7_12 = init) & % 13.02/2.50 | | | | | | | | | | | a_select3(r_ds1_filter_init, all_7_14, all_7_13) % 13.02/2.50 | | | | | | | | | | | = all_7_12 & $i(all_7_12) & leq(all_7_13, n2) & % 13.02/2.50 | | | | | | | | | | | leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0, % 13.02/2.50 | | | | | | | | | | | all_7_14)) | ( ~ (all_7_15 = init) & % 13.02/2.50 | | | | | | | | | | | a_select3(xhatmin_ds1_filter_init, all_7_17, % 13.02/2.50 | | | | | | | | | | | all_7_16) = all_7_15 & $i(all_7_15) & % 13.02/2.50 | | | | | | | | | | | leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, % 13.02/2.50 | | | | | | | | | | | all_7_16) & leq(n0, all_7_17)) % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | BETA: splitting (128) gives: % 13.02/2.50 | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | Case 1: % 13.02/2.50 | | | | | | | | | | | | % 13.02/2.50 | | | | | | | | | | | | (129) ~ (all_7_12 = init) & % 13.02/2.50 | | | | | | | | | | | | a_select3(r_ds1_filter_init, all_7_14, all_7_13) = % 13.02/2.50 | | | | | | | | | | | | all_7_12 & $i(all_7_12) & leq(all_7_13, n2) & % 13.02/2.50 | | | | | | | | | | | | leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0, % 13.02/2.50 | | | | | | | | | | | | all_7_14) % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | ALPHA: (129) implies: % 13.02/2.51 | | | | | | | | | | | | (130) ~ (all_7_12 = init) % 13.02/2.51 | | | | | | | | | | | | (131) leq(n0, all_7_14) % 13.02/2.51 | | | | | | | | | | | | (132) leq(n0, all_7_13) % 13.02/2.51 | | | | | | | | | | | | (133) leq(all_7_14, n2) % 13.02/2.51 | | | | | | | | | | | | (134) leq(all_7_13, n2) % 13.02/2.51 | | | | | | | | | | | | (135) a_select3(r_ds1_filter_init, all_7_14, all_7_13) = % 13.02/2.51 | | | | | | | | | | | | all_7_12 % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_7_14, all_7_13, % 13.02/2.51 | | | | | | | | | | | | all_7_12, simplifying with (40), (41), (131), % 13.02/2.51 | | | | | | | | | | | | (132), (133), (134), (135) gives: % 13.02/2.51 | | | | | | | | | | | | (136) all_7_12 = init % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | REDUCE: (130), (136) imply: % 13.02/2.51 | | | | | | | | | | | | (137) $false % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | CLOSE: (137) is inconsistent. % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | Case 2: % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | (138) ~ (all_7_15 = init) & % 13.02/2.51 | | | | | | | | | | | | a_select3(xhatmin_ds1_filter_init, all_7_17, % 13.02/2.51 | | | | | | | | | | | | all_7_16) = all_7_15 & $i(all_7_15) & % 13.02/2.51 | | | | | | | | | | | | leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, % 13.02/2.51 | | | | | | | | | | | | all_7_16) & leq(n0, all_7_17) % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | ALPHA: (138) implies: % 13.02/2.51 | | | | | | | | | | | | (139) ~ (all_7_15 = init) % 13.02/2.51 | | | | | | | | | | | | (140) leq(n0, all_7_17) % 13.02/2.51 | | | | | | | | | | | | (141) leq(n0, all_7_16) % 13.02/2.51 | | | | | | | | | | | | (142) leq(all_7_17, n5) % 13.02/2.51 | | | | | | | | | | | | (143) leq(all_7_16, n0) % 13.02/2.51 | | | | | | | | | | | | (144) a_select3(xhatmin_ds1_filter_init, all_7_17, % 13.02/2.51 | | | | | | | | | | | | all_7_16) = all_7_15 % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_7_17, all_7_16, % 13.02/2.51 | | | | | | | | | | | | all_7_15, simplifying with (38), (39), (140), % 13.02/2.51 | | | | | | | | | | | | (141), (142), (143), (144) gives: % 13.02/2.51 | | | | | | | | | | | | (145) all_7_15 = init % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | REDUCE: (139), (145) imply: % 13.02/2.51 | | | | | | | | | | | | (146) $false % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | CLOSE: (146) is inconsistent. % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | End of split % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | End of split % 13.02/2.51 | | | | | | | | | | % 13.02/2.51 | | | | | | | | | Case 2: % 13.02/2.51 | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | (147) ( ~ (all_7_18 = init) & % 13.02/2.51 | | | | | | | | | | a_select3(pminus_ds1_filter_init, all_7_20, % 13.02/2.51 | | | | | | | | | | all_7_19) = all_7_18 & $i(all_7_18) & % 13.02/2.51 | | | | | | | | | | leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0, % 13.02/2.51 | | | | | | | | | | all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 % 13.02/2.51 | | | | | | | | | | = init) & a_select3(id_ds1_filter_init, % 13.02/2.51 | | | | | | | | | | all_7_26, all_7_25) = all_7_24 & $i(all_7_24) & % 13.02/2.51 | | | | | | | | | | gt(pv63, all_7_26) & leq(all_7_25, n5) & % 13.02/2.51 | | | | | | | | | | leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, % 13.02/2.51 | | | | | | | | | | all_7_26)) | ( ~ (all_7_27 = init) & pred(pv63) % 13.02/2.51 | | | | | | | | | | = all_7_30 & a_select3(id_ds1_filter_init, % 13.02/2.51 | | | | | | | | | | all_7_29, all_7_28) = all_7_27 & $i(all_7_27) & % 13.02/2.51 | | | | | | | | | | $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29, % 13.02/2.51 | | | | | | | | | | all_7_30) & leq(n0, all_7_28) & leq(n0, % 13.02/2.51 | | | | | | | | | | all_7_29)) % 13.02/2.51 | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | BETA: splitting (147) gives: % 13.02/2.51 | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | Case 1: % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | (148) ~ (all_7_18 = init) & % 13.02/2.51 | | | | | | | | | | | a_select3(pminus_ds1_filter_init, all_7_20, % 13.02/2.51 | | | | | | | | | | | all_7_19) = all_7_18 & $i(all_7_18) & % 13.02/2.51 | | | | | | | | | | | leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0, % 13.02/2.51 | | | | | | | | | | | all_7_19) & leq(n0, all_7_20) % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | ALPHA: (148) implies: % 13.02/2.51 | | | | | | | | | | | (149) ~ (all_7_18 = init) % 13.02/2.51 | | | | | | | | | | | (150) leq(n0, all_7_20) % 13.02/2.51 | | | | | | | | | | | (151) leq(n0, all_7_19) % 13.02/2.51 | | | | | | | | | | | (152) leq(all_7_20, n5) % 13.02/2.51 | | | | | | | | | | | (153) leq(all_7_19, n5) % 13.02/2.51 | | | | | | | | | | | (154) a_select3(pminus_ds1_filter_init, all_7_20, % 13.02/2.51 | | | | | | | | | | | all_7_19) = all_7_18 % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | GROUND_INST: instantiating (27) with all_7_20, all_7_19, % 13.02/2.51 | | | | | | | | | | | all_7_18, simplifying with (36), (37), (150), % 13.02/2.51 | | | | | | | | | | | (151), (152), (153), (154) gives: % 13.02/2.51 | | | | | | | | | | | (155) all_7_18 = init % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | REDUCE: (149), (155) imply: % 13.02/2.51 | | | | | | | | | | | (156) $false % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | CLOSE: (156) is inconsistent. % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | Case 2: % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | (157) ( ~ (all_7_24 = init) & % 13.02/2.51 | | | | | | | | | | | a_select3(id_ds1_filter_init, all_7_26, % 13.02/2.51 | | | | | | | | | | | all_7_25) = all_7_24 & $i(all_7_24) & gt(pv63, % 13.02/2.51 | | | | | | | | | | | all_7_26) & leq(all_7_25, n5) & leq(all_7_26, % 13.02/2.51 | | | | | | | | | | | n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) | % 13.02/2.51 | | | | | | | | | | | ( ~ (all_7_27 = init) & pred(pv63) = all_7_30 & % 13.02/2.51 | | | | | | | | | | | a_select3(id_ds1_filter_init, all_7_29, % 13.02/2.51 | | | | | | | | | | | all_7_28) = all_7_27 & $i(all_7_27) & % 13.02/2.51 | | | | | | | | | | | $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29, % 13.02/2.51 | | | | | | | | | | | all_7_30) & leq(n0, all_7_28) & leq(n0, % 13.02/2.51 | | | | | | | | | | | all_7_29)) % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | BETA: splitting (157) gives: % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | Case 1: % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | (158) ~ (all_7_24 = init) & % 13.02/2.51 | | | | | | | | | | | | a_select3(id_ds1_filter_init, all_7_26, all_7_25) % 13.02/2.51 | | | | | | | | | | | | = all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) & % 13.02/2.51 | | | | | | | | | | | | leq(all_7_25, n5) & leq(all_7_26, n5) & leq(n0, % 13.02/2.51 | | | | | | | | | | | | all_7_25) & leq(n0, all_7_26) % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | ALPHA: (158) implies: % 13.02/2.51 | | | | | | | | | | | | (159) ~ (all_7_24 = init) % 13.02/2.51 | | | | | | | | | | | | (160) leq(n0, all_7_26) % 13.02/2.51 | | | | | | | | | | | | (161) leq(n0, all_7_25) % 13.02/2.51 | | | | | | | | | | | | (162) leq(all_7_26, n5) % 13.02/2.51 | | | | | | | | | | | | (163) leq(all_7_25, n5) % 13.02/2.51 | | | | | | | | | | | | (164) gt(pv63, all_7_26) % 13.02/2.51 | | | | | | | | | | | | (165) a_select3(id_ds1_filter_init, all_7_26, all_7_25) % 13.02/2.51 | | | | | | | | | | | | = all_7_24 % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_7_26, all_7_25, % 13.02/2.51 | | | | | | | | | | | | all_7_24, simplifying with (33), (34), (160), % 13.02/2.51 | | | | | | | | | | | | (161), (162), (163), (164), (165) gives: % 13.02/2.51 | | | | | | | | | | | | (166) all_7_24 = init % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | REDUCE: (159), (166) imply: % 13.02/2.51 | | | | | | | | | | | | (167) $false % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | Case 2: % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | (168) ~ (all_7_27 = init) & pred(pv63) = all_7_30 & % 13.02/2.51 | | | | | | | | | | | | a_select3(id_ds1_filter_init, all_7_29, all_7_28) % 13.02/2.51 | | | | | | | | | | | | = all_7_27 & $i(all_7_27) & $i(all_7_30) & % 13.02/2.51 | | | | | | | | | | | | leq(all_7_28, n5) & leq(all_7_29, all_7_30) & % 13.02/2.51 | | | | | | | | | | | | leq(n0, all_7_28) & leq(n0, all_7_29) % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | ALPHA: (168) implies: % 13.02/2.51 | | | | | | | | | | | | (169) ~ (all_7_27 = init) % 13.02/2.51 | | | | | | | | | | | | (170) leq(n0, all_7_29) % 13.02/2.51 | | | | | | | | | | | | (171) leq(n0, all_7_28) % 13.02/2.51 | | | | | | | | | | | | (172) leq(all_7_29, all_7_30) % 13.02/2.51 | | | | | | | | | | | | (173) leq(all_7_28, n5) % 13.02/2.51 | | | | | | | | | | | | (174) a_select3(id_ds1_filter_init, all_7_29, all_7_28) % 13.02/2.51 | | | | | | | | | | | | = all_7_27 % 13.02/2.51 | | | | | | | | | | | | (175) pred(pv63) = all_7_30 % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_4_2, all_7_30, pv63, % 13.02/2.51 | | | | | | | | | | | | simplifying with (19), (175) gives: % 13.02/2.51 | | | | | | | | | | | | (176) all_7_30 = all_4_2 % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | REDUCE: (172), (176) imply: % 13.02/2.51 | | | | | | | | | | | | (177) leq(all_7_29, all_4_2) % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_7_29, all_7_28, % 13.02/2.51 | | | | | | | | | | | | all_7_27, simplifying with (31), (32), (170), % 13.02/2.51 | | | | | | | | | | | | (171), (173), (174), (177) gives: % 13.02/2.51 | | | | | | | | | | | | (178) all_7_27 = init % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | REDUCE: (169), (178) imply: % 13.02/2.51 | | | | | | | | | | | | (179) $false % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 13.02/2.51 | | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | | End of split % 13.02/2.51 | | | | | | | | | | | % 13.02/2.51 | | | | | | | | | | End of split % 13.02/2.51 | | | | | | | | | | % 13.02/2.51 | | | | | | | | | End of split % 13.02/2.51 | | | | | | | | | % 13.02/2.51 | | | | | | | | End of split % 13.02/2.51 | | | | | | | | % 13.02/2.51 | | | | | | | End of split % 13.02/2.51 | | | | | | | % 13.02/2.51 | | | | | | End of split % 13.02/2.51 | | | | | | % 13.02/2.51 | | | | | End of split % 13.02/2.51 | | | | | % 13.02/2.51 | | | | End of split % 13.02/2.51 | | | | % 13.02/2.51 | | | End of split % 13.02/2.51 | | | % 13.02/2.51 | | End of split % 13.02/2.51 | | % 13.02/2.51 | End of split % 13.02/2.51 | % 13.02/2.51 End of proof % 13.02/2.51 % SZS output end Proof for theBenchmark % 13.02/2.51 % 13.02/2.51 1902ms %------------------------------------------------------------------------------