%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL658+1.010 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:54:33 PM UTC 2026 % Result : Theorem 151.26s 20.23s % Output : Proof 152.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL658+1.010 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.36 % Computer : n001.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 16:59:17 UTC 2026 % 0.09/0.36 % CPUTime : % 0.12/0.38 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.63/0.76 ________ _____ % 0.63/0.76 ___ __ \_________(_)________________________________ % 0.63/0.76 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.63/0.76 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.63/0.76 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.63/0.76 % 0.63/0.76 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.63/0.76 (2023-06-19) % 0.63/0.76 % 0.63/0.76 (c) Philipp Rümmer, 2009-2023 % 0.63/0.76 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.63/0.76 Amanda Stjerna. % 0.63/0.76 Free software under BSD-3-Clause. % 0.63/0.76 % 0.63/0.76 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.63/0.76 % 0.63/0.76 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.63/0.79 Running up to 7 provers in parallel. % 0.83/0.81 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.83/0.81 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.83/0.81 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.83/0.81 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.83/0.81 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.83/0.81 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.83/0.81 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 8.37/2.14 Prover 1: Preprocessing ... % 8.37/2.16 Prover 0: Preprocessing ... % 9.18/2.22 Prover 5: Preprocessing ... % 9.18/2.27 Prover 4: Preprocessing ... % 9.18/2.28 Prover 3: Preprocessing ... % 10.69/2.40 Prover 6: Preprocessing ... % 10.69/2.48 Prover 2: Preprocessing ... % 17.76/3.30 Prover 2: Proving ... % 17.76/3.34 Prover 5: Proving ... % 23.36/4.17 Prover 6: Proving ... % 25.72/4.36 Prover 3: Constructing countermodel ... % 27.23/4.53 Prover 1: Constructing countermodel ... % 34.40/5.44 Prover 4: Constructing countermodel ... % 35.87/5.61 Prover 0: Proving ... % 86.92/12.07 Prover 2: stopped % 86.92/12.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 88.82/12.34 Prover 7: Preprocessing ... % 89.57/12.42 Prover 7: Warning: ignoring some quantifiers % 89.57/12.44 Prover 7: Constructing countermodel ... % 103.10/14.14 Prover 5: stopped % 103.10/14.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 106.15/14.54 Prover 8: Preprocessing ... % 110.18/15.12 Prover 8: Warning: ignoring some quantifiers % 110.18/15.16 Prover 8: Constructing countermodel ... % 118.87/16.16 Prover 1: stopped % 118.87/16.16 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 121.99/16.56 Prover 9: Preprocessing ... % 125.17/16.91 Prover 9: Constructing countermodel ... % 133.80/18.05 Prover 6: stopped % 133.80/18.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 136.20/18.44 Prover 10: Preprocessing ... % 137.79/18.53 Prover 10: Warning: ignoring some quantifiers % 137.79/18.54 Prover 10: Constructing countermodel ... % 151.26/20.20 Prover 10: Found proof (size 49) % 151.26/20.21 Prover 10: proved (2141ms) % 151.26/20.21 Prover 7: stopped % 151.26/20.22 Prover 0: stopped % 151.26/20.22 Prover 9: stopped % 151.26/20.22 Prover 3: stopped % 151.26/20.23 Prover 4: stopped % 151.26/20.23 Prover 8: stopped % 151.26/20.23 % 151.26/20.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 151.26/20.23 % 151.26/20.24 % SZS output start Proof for theBenchmark % 151.26/20.25 Assumptions after simplification: % 151.26/20.25 --------------------------------- % 151.26/20.25 % 151.26/20.25 (main) % 151.78/20.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 151.78/20.33 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v8) & $i(v7) & $i(v6) & % 151.78/20.33 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & r1(v6, v8) & r1(v6, % 151.78/20.33 v7) & r1(v5, v6) & r1(v4, v5) & r1(v3, v4) & r1(v2, v3) & r1(v1, v2) & % 151.78/20.33 r1(v0, v1) & ~ p1(v8) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! % 151.78/20.33 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! % 151.78/20.33 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ( ~ $i(v19) | ~ $i(v18) | ~ % 151.78/20.33 $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | % 151.78/20.33 ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v18, v19) | ~ r1(v17, v18) | % 151.78/20.33 ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ % 151.78/20.33 r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ % 151.78/20.33 r1(v0, v9) | p1(v19) | ? [v20: $i] : ($i(v20) & r1(v17, v20) & ~ % 151.78/20.33 p1(v20))) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : % 151.78/20.33 ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! % 151.78/20.33 [v18: $i] : ( ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) % 151.78/20.33 | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ % 151.78/20.33 r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ % 151.78/20.33 r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ % 151.78/20.34 r1(v9, v10) | ~ r1(v0, v9) | p1(v18) | ? [v19: $i] : ($i(v19) & r1(v16, % 151.78/20.34 v19) & ~ p1(v19))) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! % 151.78/20.34 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! % 151.78/20.34 [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) % 151.78/20.34 | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v16, v17) | ~ % 151.78/20.34 r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ % 151.78/20.34 r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v17) % 151.78/20.34 | ? [v18: $i] : ($i(v18) & r1(v15, v18) & ~ p1(v18))) & ! [v9: $i] : ! % 151.78/20.34 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! % 151.78/20.34 [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ % 151.78/20.34 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ p1(v14) | % 151.78/20.34 ~ r1(v14, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ % 151.78/20.34 r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v16) % 151.78/20.34 | ? [v17: $i] : ? [v18: $i] : ($i(v18) & $i(v17) & ((p1(v17) & r1(v17, % 151.78/20.34 v18) & r1(v15, v17) & ~ p1(v18)) | (p1(v17) & r1(v17, v18) & % 151.78/20.34 r1(v14, v17) & ~ p1(v18) & ! [v19: $i] : ! [v20: $i] : ! [v21: % 151.78/20.34 $i] : ( ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ p1(v20) | ~ % 151.78/20.34 r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v17, v19) | p1(v21) | % 151.78/20.34 p1(v19)) & ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ % 151.78/20.34 $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ p1(v20) | ~ r1(v20, v21) | % 151.78/20.34 ~ r1(v19, v20) | ~ r1(v17, v19) | p1(v21) | ? [v22: $i] : % 151.78/20.34 ($i(v22) & r1(v19, v22) & ~ p1(v22))))))) & ! [v9: $i] : ! % 151.78/20.34 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! % 151.78/20.34 [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ % 151.78/20.34 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v15, % 151.78/20.34 v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, % 151.78/20.34 v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v16) | ? % 151.78/20.34 [v17: $i] : ? [v18: $i] : ($i(v18) & $i(v17) & ((p1(v17) & r1(v17, v18) & % 151.78/20.34 r1(v16, v17) & ~ p1(v18)) | (r1(v14, v17) & ~ p1(v17) & ! [v19: % 151.78/20.34 $i] : ! [v20: $i] : ( ~ $i(v20) | ~ $i(v19) | ~ p1(v19) | ~ % 151.78/20.34 r1(v19, v20) | ~ r1(v17, v19) | p1(v20)))))) & ! [v9: $i] : ! % 151.78/20.34 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! % 151.78/20.34 [v15: $i] : ( ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) % 151.78/20.34 | ~ $i(v10) | ~ $i(v9) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, % 151.78/20.34 v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, % 151.78/20.34 v9) | p1(v15) | ? [v16: $i] : ($i(v16) & r1(v13, v16) & ~ p1(v16))) & % 151.78/20.34 ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! % 151.78/20.34 [v14: $i] : ! [v15: $i] : ( ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ % 151.78/20.34 $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v14, v15) | ~ % 151.78/20.34 r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ % 151.78/20.34 r1(v9, v10) | ~ r1(v0, v9) | p1(v14) | ? [v16: $i] : ($i(v16) & % 151.78/20.35 ((r1(v15, v16) & ~ p1(v16)) | (r1(v14, v16) & ~ p1(v16) & ! [v17: $i] % 151.78/20.35 : ! [v18: $i] : ( ~ $i(v18) | ~ $i(v17) | ~ p1(v17) | ~ r1(v17, % 151.78/20.35 v18) | ~ r1(v16, v17) | p1(v18)))))) & ! [v9: $i] : ! [v10: % 151.78/20.35 $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~ % 151.78/20.35 $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | % 151.78/20.35 ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ % 151.78/20.35 r1(v9, v10) | ~ r1(v0, v9) | p1(v14) | ? [v15: $i] : ($i(v15) & r1(v12, % 151.78/20.35 v15) & ~ p1(v15))) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! % 151.78/20.35 [v12: $i] : ! [v13: $i] : ( ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ % 151.78/20.35 $i(v10) | ~ $i(v9) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) % 151.78/20.35 | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v13) | ? [v14: $i] : ($i(v14) & % 151.78/20.35 r1(v11, v14) & ~ p1(v14))) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] % 151.78/20.35 : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ % 151.78/20.35 r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v12) % 151.78/20.35 | ? [v13: $i] : ($i(v13) & r1(v10, v13) & ~ p1(v13))) & ! [v9: $i] : ! % 151.78/20.35 [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v10, % 151.78/20.35 v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v11) | ? [v12: $i] : % 151.78/20.35 ($i(v12) & r1(v9, v12) & ~ p1(v12))) & ! [v9: $i] : ( ~ $i(v9) | ~ % 151.78/20.35 r1(v7, v9) | p1(v9)) & ! [v9: $i] : ( ~ $i(v9) | ~ r1(v6, v9) | p1(v9) | % 151.78/20.35 ? [v10: $i] : ? [v11: $i] : ($i(v11) & $i(v10) & p1(v10) & r1(v10, v11) % 151.78/20.35 & r1(v9, v10) & ~ p1(v11)))) % 151.78/20.35 % 151.78/20.35 Further assumptions not needed in the proof: % 151.78/20.35 -------------------------------------------- % 151.78/20.35 reflexivity % 151.78/20.35 % 151.78/20.35 Those formulas are unsatisfiable: % 151.78/20.35 --------------------------------- % 151.78/20.35 % 151.78/20.35 Begin of proof % 151.78/20.35 | % 151.78/20.35 | DELTA: instantiating (main) with fresh symbols all_3_0, all_3_1, all_3_2, % 151.78/20.35 | all_3_3, all_3_4, all_3_5, all_3_6, all_3_7, all_3_8 gives: % 152.28/20.40 | (1) $i(all_3_0) & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & $i(all_3_4) & % 152.28/20.40 | $i(all_3_5) & $i(all_3_6) & $i(all_3_7) & $i(all_3_8) & r1(all_3_2, % 152.28/20.40 | all_3_0) & r1(all_3_2, all_3_1) & r1(all_3_3, all_3_2) & r1(all_3_4, % 152.28/20.40 | all_3_3) & r1(all_3_5, all_3_4) & r1(all_3_6, all_3_5) & r1(all_3_7, % 152.28/20.40 | all_3_6) & r1(all_3_8, all_3_7) & ~ p1(all_3_0) & ! [v0: $i] : ! % 152.28/20.40 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 152.28/20.40 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 152.28/20.40 | $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | % 152.28/20.41 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v9, % 152.28/20.41 | v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, % 152.28/20.41 | v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) % 152.28/20.41 | | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v10) | ? [v11: $i] : % 152.28/20.41 | ($i(v11) & r1(v8, v11) & ~ p1(v11))) & ! [v0: $i] : ! [v1: $i] : % 152.28/20.41 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 152.28/20.41 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ % 152.28/20.41 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 152.28/20.41 | ~ $i(v1) | ~ $i(v0) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) % 152.28/20.41 | | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ % 152.28/20.41 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v9) | ? [v10: % 152.28/20.41 | $i] : ($i(v10) & r1(v7, v10) & ~ p1(v10))) & ! [v0: $i] : ! [v1: % 152.28/20.41 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 152.28/20.41 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) % 152.28/20.41 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 152.28/20.41 | $i(v0) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, % 152.28/20.41 | v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) % 152.28/20.41 | | ~ r1(all_3_8, v0) | p1(v8) | ? [v9: $i] : ($i(v9) & r1(v6, v9) & % 152.28/20.41 | ~ p1(v9))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 152.28/20.41 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | % 152.28/20.41 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 152.28/20.41 | | ~ $i(v0) | ~ p1(v5) | ~ r1(v5, v7) | ~ r1(v5, v6) | ~ r1(v4, % 152.28/20.41 | v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) % 152.28/20.41 | | ~ r1(all_3_8, v0) | p1(v7) | ? [v8: $i] : ? [v9: $i] : ($i(v9) & % 152.28/20.41 | $i(v8) & ((p1(v8) & r1(v8, v9) & r1(v6, v8) & ~ p1(v9)) | (p1(v8) % 152.28/20.41 | & r1(v8, v9) & r1(v5, v8) & ~ p1(v9) & ! [v10: $i] : ! [v11: % 152.28/20.41 | $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | % 152.28/20.41 | ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, % 152.28/20.41 | v10) | p1(v12) | p1(v10)) & ! [v10: $i] : ! [v11: $i] : % 152.28/20.41 | ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ % 152.28/20.41 | p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, v10) % 152.28/20.41 | | p1(v12) | ? [v13: $i] : ($i(v13) & r1(v10, v13) & ~ % 152.28/20.41 | p1(v13))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 152.28/20.41 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 152.28/20.41 | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 152.28/20.41 | | ~ $i(v1) | ~ $i(v0) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, % 152.28/20.41 | v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) % 152.28/20.41 | | ~ r1(all_3_8, v0) | p1(v7) | ? [v8: $i] : ? [v9: $i] : ($i(v9) & % 152.28/20.41 | $i(v8) & ((p1(v8) & r1(v8, v9) & r1(v7, v8) & ~ p1(v9)) | (r1(v5, % 152.28/20.41 | v8) & ~ p1(v8) & ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | % 152.28/20.41 | ~ $i(v10) | ~ p1(v10) | ~ r1(v10, v11) | ~ r1(v8, v10) | % 152.28/20.41 | p1(v11)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 152.28/20.41 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 152.28/20.41 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 152.28/20.41 | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ % 152.28/20.41 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v6) | ? [v7: % 152.28/20.41 | $i] : ($i(v7) & r1(v4, v7) & ~ p1(v7))) & ! [v0: $i] : ! [v1: % 152.28/20.41 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 152.28/20.41 | $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 152.28/20.41 | $i(v1) | ~ $i(v0) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | % 152.28/20.41 | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | % 152.28/20.41 | p1(v5) | ? [v7: $i] : ($i(v7) & ((r1(v6, v7) & ~ p1(v7)) | (r1(v5, % 152.28/20.41 | v7) & ~ p1(v7) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ % 152.28/20.41 | $i(v8) | ~ p1(v8) | ~ r1(v8, v9) | ~ r1(v7, v8) | % 152.28/20.41 | p1(v9)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 152.28/20.41 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ % 152.28/20.41 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v4, v5) | ~ % 152.28/20.41 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 152.28/20.41 | r1(all_3_8, v0) | p1(v5) | ? [v6: $i] : ($i(v6) & r1(v3, v6) & ~ % 152.28/20.41 | p1(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 152.28/20.41 | ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 152.28/20.41 | | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 152.28/20.41 | r1(all_3_8, v0) | p1(v4) | ? [v5: $i] : ($i(v5) & r1(v2, v5) & ~ % 152.28/20.41 | p1(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 152.28/20.41 | ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ % 152.28/20.41 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v3) | ? [v4: % 152.28/20.41 | $i] : ($i(v4) & r1(v1, v4) & ~ p1(v4))) & ! [v0: $i] : ! [v1: % 152.28/20.41 | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, % 152.28/20.41 | v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v2) | ? [v3: $i] : % 152.28/20.41 | ($i(v3) & r1(v0, v3) & ~ p1(v3))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 152.28/20.41 | r1(all_3_1, v0) | p1(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, % 152.28/20.41 | v0) | p1(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & % 152.28/20.41 | p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ p1(v2))) % 152.28/20.42 | % 152.28/20.42 | ALPHA: (1) implies: % 152.28/20.42 | (2) ~ p1(all_3_0) % 152.28/20.42 | (3) r1(all_3_8, all_3_7) % 152.28/20.42 | (4) r1(all_3_7, all_3_6) % 152.28/20.42 | (5) r1(all_3_6, all_3_5) % 152.28/20.42 | (6) r1(all_3_5, all_3_4) % 152.28/20.42 | (7) r1(all_3_4, all_3_3) % 152.28/20.42 | (8) r1(all_3_3, all_3_2) % 152.28/20.42 | (9) r1(all_3_2, all_3_1) % 152.28/20.42 | (10) r1(all_3_2, all_3_0) % 152.28/20.42 | (11) $i(all_3_7) % 152.28/20.42 | (12) $i(all_3_6) % 152.28/20.42 | (13) $i(all_3_5) % 152.28/20.42 | (14) $i(all_3_4) % 152.28/20.42 | (15) $i(all_3_3) % 152.28/20.42 | (16) $i(all_3_2) % 152.28/20.42 | (17) $i(all_3_1) % 152.28/20.42 | (18) $i(all_3_0) % 152.28/20.43 | (19) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, v0) | p1(v0) | ? [v1: $i] : % 152.28/20.43 | ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & r1(v0, v1) & % 152.28/20.43 | ~ p1(v2))) % 152.28/20.43 | (20) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_1, v0) | p1(v0)) % 152.28/20.43 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 152.28/20.43 | ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 152.28/20.43 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v5, v6) | ~ % 152.28/20.43 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 152.28/20.43 | r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v5) | ? [v7: $i] : ($i(v7) & % 152.28/20.43 | ((r1(v6, v7) & ~ p1(v7)) | (r1(v5, v7) & ~ p1(v7) & ! [v8: $i] % 152.28/20.43 | : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p1(v8) | ~ r1(v8, % 152.28/20.43 | v9) | ~ r1(v7, v8) | p1(v9)))))) % 152.28/20.44 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 152.28/20.44 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ % 152.28/20.44 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 152.28/20.44 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ % 152.28/20.44 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | % 152.28/20.44 | p1(v7) | ? [v8: $i] : ? [v9: $i] : ($i(v9) & $i(v8) & ((p1(v8) & % 152.28/20.44 | r1(v8, v9) & r1(v7, v8) & ~ p1(v9)) | (r1(v5, v8) & ~ p1(v8) % 152.28/20.44 | & ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ % 152.28/20.44 | p1(v10) | ~ r1(v10, v11) | ~ r1(v8, v10) | p1(v11)))))) % 152.28/20.45 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 152.28/20.45 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ % 152.28/20.45 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 152.28/20.45 | ~ p1(v5) | ~ r1(v5, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ % 152.28/20.45 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 152.28/20.45 | r1(all_3_8, v0) | p1(v7) | ? [v8: $i] : ? [v9: $i] : ($i(v9) & % 152.28/20.45 | $i(v8) & ((p1(v8) & r1(v8, v9) & r1(v6, v8) & ~ p1(v9)) | (p1(v8) % 152.28/20.45 | & r1(v8, v9) & r1(v5, v8) & ~ p1(v9) & ! [v10: $i] : ! % 152.28/20.45 | [v11: $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ % 152.28/20.45 | $i(v10) | ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | % 152.28/20.45 | ~ r1(v8, v10) | p1(v12) | p1(v10)) & ! [v10: $i] : ! [v11: % 152.28/20.45 | $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | % 152.28/20.45 | ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, % 152.28/20.45 | v10) | p1(v12) | ? [v13: $i] : ($i(v13) & r1(v10, v13) & % 152.28/20.45 | ~ p1(v13))))))) % 152.28/20.46 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 152.28/20.46 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ % 152.28/20.46 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 152.28/20.46 | ~ $i(v1) | ~ $i(v0) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, % 152.28/20.46 | v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, % 152.28/20.46 | v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v8) | ? [v9: $i] : % 152.28/20.46 | ($i(v9) & r1(v6, v9) & ~ p1(v9))) % 152.28/20.46 | % 152.28/20.46 | GROUND_INST: instantiating (21) with all_3_7, all_3_6, all_3_5, all_3_4, % 152.28/20.46 | all_3_3, all_3_2, all_3_1, simplifying with (3), (4), (5), (6), % 152.28/20.46 | (7), (8), (9), (11), (12), (13), (14), (15), (16), (17) gives: % 152.28/20.46 | (25) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) | % 152.28/20.46 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 152.28/20.46 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) % 152.28/20.46 | | p1(v2))))) % 152.28/20.46 | % 152.28/20.47 | GROUND_INST: instantiating (21) with all_3_7, all_3_6, all_3_5, all_3_4, % 152.28/20.47 | all_3_3, all_3_2, all_3_0, simplifying with (3), (4), (5), (6), % 152.28/20.47 | (7), (8), (10), (11), (12), (13), (14), (15), (16), (18) gives: % 152.28/20.47 | (26) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_0, v0) & ~ p1(v0)) | % 152.28/20.47 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 152.28/20.47 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) % 152.28/20.47 | | p1(v2))))) % 152.28/20.47 | % 152.28/20.47 | BETA: splitting (26) gives: % 152.28/20.47 | % 152.28/20.47 | Case 1: % 152.28/20.47 | | % 152.28/20.47 | | (27) p1(all_3_2) % 152.28/20.47 | | % 152.28/20.48 | | GROUND_INST: instantiating (23) with all_3_7, all_3_6, all_3_5, all_3_4, % 152.28/20.48 | | all_3_3, all_3_2, all_3_1, all_3_0, simplifying with (2), (3), % 152.28/20.48 | | (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 152.28/20.48 | | (15), (16), (17), (18), (27) gives: % 152.28/20.48 | | (28) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, v1) % 152.28/20.48 | | & r1(all_3_1, v0) & ~ p1(v1)) | (p1(v0) & r1(v0, v1) & % 152.28/20.48 | | r1(all_3_2, v0) & ~ p1(v1) & ! [v2: $i] : ! [v3: $i] : ! % 152.28/20.48 | | [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ % 152.28/20.48 | | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | % 152.28/20.48 | | p1(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 152.28/20.48 | | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ r1(v3, v4) | % 152.28/20.48 | | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5: $i] : % 152.28/20.48 | | ($i(v5) & r1(v2, v5) & ~ p1(v5)))))) % 152.28/20.48 | | % 152.28/20.48 | | DELTA: instantiating (28) with fresh symbols all_66_0, all_66_1 gives: % 152.28/20.48 | | (29) $i(all_66_0) & $i(all_66_1) & ((p1(all_66_1) & r1(all_66_1, % 152.28/20.48 | | all_66_0) & r1(all_3_1, all_66_1) & ~ p1(all_66_0)) | % 152.28/20.48 | | (p1(all_66_1) & r1(all_66_1, all_66_0) & r1(all_3_2, all_66_1) & % 152.28/20.48 | | ~ p1(all_66_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 152.28/20.48 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | % 152.28/20.49 | | ~ r1(v0, v1) | ~ r1(all_66_1, v0) | p1(v2) | p1(v0)) & ! % 152.28/20.49 | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | % 152.28/20.49 | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 152.28/20.49 | | r1(all_66_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3) % 152.28/20.49 | | & ~ p1(v3))))) % 152.28/20.49 | | % 152.28/20.49 | | ALPHA: (29) implies: % 152.28/20.49 | | (30) $i(all_66_1) % 152.28/20.49 | | (31) $i(all_66_0) % 152.28/20.49 | | (32) (p1(all_66_1) & r1(all_66_1, all_66_0) & r1(all_3_1, all_66_1) & ~ % 152.28/20.49 | | p1(all_66_0)) | (p1(all_66_1) & r1(all_66_1, all_66_0) & % 152.28/20.49 | | r1(all_3_2, all_66_1) & ~ p1(all_66_0) & ! [v0: $i] : ! [v1: % 152.28/20.49 | | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 152.28/20.49 | | p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_66_1, v0) | % 152.28/20.49 | | p1(v2) | p1(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 152.28/20.49 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ % 152.28/20.49 | | r1(v0, v1) | ~ r1(all_66_1, v0) | p1(v2) | ? [v3: $i] : % 152.28/20.49 | | ($i(v3) & r1(v0, v3) & ~ p1(v3)))) % 152.28/20.49 | | % 152.28/20.49 | | BETA: splitting (32) gives: % 152.28/20.49 | | % 152.28/20.49 | | Case 1: % 152.28/20.49 | | | % 152.28/20.49 | | | (33) p1(all_66_1) & r1(all_66_1, all_66_0) & r1(all_3_1, all_66_1) & ~ % 152.28/20.49 | | | p1(all_66_0) % 152.28/20.49 | | | % 152.28/20.49 | | | ALPHA: (33) implies: % 152.28/20.49 | | | (34) ~ p1(all_66_0) % 152.28/20.49 | | | (35) r1(all_3_1, all_66_1) % 152.28/20.49 | | | (36) r1(all_66_1, all_66_0) % 152.28/20.49 | | | % 152.28/20.50 | | | GROUND_INST: instantiating (24) with all_3_7, all_3_6, all_3_5, all_3_4, % 152.28/20.50 | | | all_3_3, all_3_2, all_3_1, all_66_1, all_66_0, simplifying % 152.28/20.50 | | | with (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 152.28/20.50 | | | (14), (15), (16), (17), (30), (31), (34), (35), (36) gives: % 152.28/20.50 | | | (37) ? [v0: $i] : ($i(v0) & r1(all_3_1, v0) & ~ p1(v0)) % 152.28/20.50 | | | % 152.28/20.50 | | | DELTA: instantiating (37) with fresh symbol all_140_0 gives: % 152.28/20.50 | | | (38) $i(all_140_0) & r1(all_3_1, all_140_0) & ~ p1(all_140_0) % 152.28/20.50 | | | % 152.28/20.50 | | | ALPHA: (38) implies: % 152.76/20.50 | | | (39) ~ p1(all_140_0) % 152.76/20.50 | | | (40) r1(all_3_1, all_140_0) % 152.76/20.50 | | | (41) $i(all_140_0) % 152.76/20.50 | | | % 152.76/20.50 | | | GROUND_INST: instantiating (20) with all_140_0, simplifying with (39), % 152.76/20.50 | | | (40), (41) gives: % 152.76/20.50 | | | (42) $false % 152.76/20.50 | | | % 152.76/20.50 | | | CLOSE: (42) is inconsistent. % 152.76/20.50 | | | % 152.76/20.50 | | Case 2: % 152.76/20.50 | | | % 152.76/20.50 | | | (43) p1(all_66_1) & r1(all_66_1, all_66_0) & r1(all_3_2, all_66_1) & ~ % 152.76/20.51 | | | p1(all_66_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 152.76/20.51 | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ % 152.76/20.51 | | | r1(v0, v1) | ~ r1(all_66_1, v0) | p1(v2) | p1(v0)) & ! [v0: % 152.76/20.51 | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 152.76/20.51 | | | $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 152.76/20.51 | | | r1(all_66_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3) & % 152.76/20.51 | | | ~ p1(v3))) % 152.76/20.51 | | | % 152.76/20.51 | | | ALPHA: (43) implies: % 152.76/20.51 | | | (44) ~ p1(all_66_0) % 152.76/20.51 | | | (45) r1(all_3_2, all_66_1) % 152.76/20.51 | | | (46) r1(all_66_1, all_66_0) % 152.76/20.51 | | | (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | % 152.76/20.51 | | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 152.76/20.51 | | | r1(all_66_1, v0) | p1(v2) | p1(v0)) % 152.76/20.51 | | | % 152.76/20.51 | | | GROUND_INST: instantiating (22) with all_3_7, all_3_6, all_3_5, all_3_4, % 152.76/20.51 | | | all_3_3, all_3_2, all_66_1, all_66_0, simplifying with (3), % 152.76/20.51 | | | (4), (5), (6), (7), (8), (11), (12), (13), (14), (15), (16), % 152.76/20.51 | | | (30), (31), (44), (45), (46) gives: % 152.76/20.51 | | | (48) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, % 152.76/20.51 | | | v1) & r1(all_66_0, v0) & ~ p1(v1)) | (r1(all_3_2, v0) & % 152.76/20.51 | | | ~ p1(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 152.76/20.51 | | | $i(v2) | ~ p1(v2) | ~ r1(v2, v3) | ~ r1(v0, v2) | % 152.76/20.51 | | | p1(v3))))) % 152.76/20.51 | | | % 152.76/20.51 | | | DELTA: instantiating (48) with fresh symbols all_141_0, all_141_1 gives: % 152.76/20.52 | | | (49) $i(all_141_0) & $i(all_141_1) & ((p1(all_141_1) & r1(all_141_1, % 152.76/20.52 | | | all_141_0) & r1(all_66_0, all_141_1) & ~ p1(all_141_0)) | % 152.76/20.52 | | | (r1(all_3_2, all_141_1) & ~ p1(all_141_1) & ! [v0: $i] : ! % 152.76/20.52 | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) % 152.76/20.52 | | | | ~ r1(all_141_1, v0) | p1(v1)))) % 152.76/20.52 | | | % 152.76/20.52 | | | ALPHA: (49) implies: % 152.76/20.52 | | | (50) $i(all_141_1) % 152.76/20.52 | | | (51) $i(all_141_0) % 152.76/20.52 | | | (52) (p1(all_141_1) & r1(all_141_1, all_141_0) & r1(all_66_0, % 152.76/20.52 | | | all_141_1) & ~ p1(all_141_0)) | (r1(all_3_2, all_141_1) & ~ % 152.76/20.52 | | | p1(all_141_1) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 152.76/20.52 | | | $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_141_1, v0) | % 152.76/20.52 | | | p1(v1))) % 152.76/20.52 | | | % 152.76/20.52 | | | BETA: splitting (52) gives: % 152.76/20.52 | | | % 152.76/20.52 | | | Case 1: % 152.76/20.52 | | | | % 152.76/20.52 | | | | (53) p1(all_141_1) & r1(all_141_1, all_141_0) & r1(all_66_0, % 152.76/20.52 | | | | all_141_1) & ~ p1(all_141_0) % 152.76/20.52 | | | | % 152.76/20.52 | | | | ALPHA: (53) implies: % 152.76/20.52 | | | | (54) ~ p1(all_141_0) % 152.76/20.52 | | | | (55) r1(all_66_0, all_141_1) % 152.76/20.52 | | | | (56) r1(all_141_1, all_141_0) % 152.76/20.52 | | | | (57) p1(all_141_1) % 152.76/20.52 | | | | % 152.76/20.52 | | | | GROUND_INST: instantiating (47) with all_66_0, all_141_1, all_141_0, % 152.76/20.52 | | | | simplifying with (31), (44), (46), (50), (51), (54), (55), % 152.76/20.52 | | | | (56), (57) gives: % 152.76/20.52 | | | | (58) $false % 152.76/20.52 | | | | % 152.76/20.52 | | | | CLOSE: (58) is inconsistent. % 152.76/20.52 | | | | % 152.76/20.52 | | | Case 2: % 152.76/20.52 | | | | % 152.76/20.52 | | | | (59) r1(all_3_2, all_141_1) & ~ p1(all_141_1) & ! [v0: $i] : ! % 152.76/20.52 | | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | % 152.76/20.52 | | | | ~ r1(all_141_1, v0) | p1(v1)) % 152.76/20.52 | | | | % 152.76/20.52 | | | | ALPHA: (59) implies: % 152.76/20.53 | | | | (60) ~ p1(all_141_1) % 152.76/20.53 | | | | (61) r1(all_3_2, all_141_1) % 152.76/20.53 | | | | (62) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | % 152.76/20.53 | | | | ~ r1(v0, v1) | ~ r1(all_141_1, v0) | p1(v1)) % 152.76/20.53 | | | | % 152.76/20.53 | | | | GROUND_INST: instantiating (19) with all_141_1, simplifying with (50), % 152.76/20.53 | | | | (60), (61) gives: % 152.76/20.53 | | | | (63) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0, % 152.76/20.53 | | | | v1) & r1(all_141_1, v0) & ~ p1(v1)) % 152.76/20.53 | | | | % 152.76/20.53 | | | | DELTA: instantiating (63) with fresh symbols all_205_0, all_205_1 gives: % 152.76/20.53 | | | | (64) $i(all_205_0) & $i(all_205_1) & p1(all_205_1) & r1(all_205_1, % 152.76/20.53 | | | | all_205_0) & r1(all_141_1, all_205_1) & ~ p1(all_205_0) % 152.76/20.53 | | | | % 152.76/20.53 | | | | ALPHA: (64) implies: % 152.76/20.53 | | | | (65) ~ p1(all_205_0) % 152.76/20.53 | | | | (66) r1(all_141_1, all_205_1) % 152.76/20.53 | | | | (67) r1(all_205_1, all_205_0) % 152.76/20.53 | | | | (68) p1(all_205_1) % 152.76/20.53 | | | | (69) $i(all_205_1) % 152.76/20.53 | | | | (70) $i(all_205_0) % 152.76/20.53 | | | | % 152.76/20.53 | | | | GROUND_INST: instantiating (62) with all_205_1, all_205_0, simplifying % 152.76/20.53 | | | | with (65), (66), (67), (68), (69), (70) gives: % 152.76/20.53 | | | | (71) $false % 152.76/20.53 | | | | % 152.76/20.53 | | | | CLOSE: (71) is inconsistent. % 152.76/20.53 | | | | % 152.76/20.53 | | | End of split % 152.76/20.53 | | | % 152.76/20.53 | | End of split % 152.76/20.53 | | % 152.76/20.53 | Case 2: % 152.76/20.53 | | % 152.76/20.53 | | (72) ~ p1(all_3_2) % 152.76/20.53 | | % 152.76/20.53 | | BETA: splitting (25) gives: % 152.76/20.53 | | % 152.76/20.53 | | Case 1: % 152.76/20.53 | | | % 152.76/20.53 | | | (73) p1(all_3_2) % 152.76/20.53 | | | % 152.76/20.53 | | | PRED_UNIFY: (72), (73) imply: % 152.76/20.53 | | | (74) $false % 152.76/20.53 | | | % 152.76/20.53 | | | CLOSE: (74) is inconsistent. % 152.76/20.53 | | | % 152.76/20.53 | | Case 2: % 152.76/20.53 | | | % 152.76/20.54 | | | (75) ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) | % 152.76/20.54 | | | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 152.76/20.54 | | | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, % 152.76/20.54 | | | v1) | p1(v2))))) % 152.76/20.54 | | | % 152.76/20.54 | | | DELTA: instantiating (75) with fresh symbol all_72_0 gives: % 152.76/20.54 | | | (76) $i(all_72_0) & ((r1(all_3_1, all_72_0) & ~ p1(all_72_0)) | % 152.76/20.54 | | | (r1(all_3_2, all_72_0) & ~ p1(all_72_0) & ! [v0: $i] : ! [v1: % 152.76/20.54 | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | % 152.76/20.54 | | | ~ r1(all_72_0, v0) | p1(v1)))) % 152.76/20.54 | | | % 152.76/20.54 | | | ALPHA: (76) implies: % 152.76/20.54 | | | (77) $i(all_72_0) % 152.76/20.54 | | | (78) (r1(all_3_1, all_72_0) & ~ p1(all_72_0)) | (r1(all_3_2, all_72_0) % 152.76/20.54 | | | & ~ p1(all_72_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 152.76/20.54 | | | $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_72_0, v0) | % 152.76/20.54 | | | p1(v1))) % 152.76/20.54 | | | % 152.76/20.54 | | | BETA: splitting (78) gives: % 152.76/20.54 | | | % 152.76/20.54 | | | Case 1: % 152.76/20.54 | | | | % 152.76/20.54 | | | | (79) r1(all_3_1, all_72_0) & ~ p1(all_72_0) % 152.76/20.54 | | | | % 152.76/20.54 | | | | ALPHA: (79) implies: % 152.76/20.54 | | | | (80) ~ p1(all_72_0) % 152.76/20.54 | | | | (81) r1(all_3_1, all_72_0) % 152.76/20.54 | | | | % 152.76/20.54 | | | | GROUND_INST: instantiating (20) with all_72_0, simplifying with (77), % 152.76/20.54 | | | | (80), (81) gives: % 152.76/20.54 | | | | (82) $false % 152.76/20.54 | | | | % 152.76/20.54 | | | | CLOSE: (82) is inconsistent. % 152.76/20.54 | | | | % 152.76/20.54 | | | Case 2: % 152.76/20.54 | | | | % 152.76/20.54 | | | | (83) r1(all_3_2, all_72_0) & ~ p1(all_72_0) & ! [v0: $i] : ! [v1: % 152.76/20.54 | | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ % 152.76/20.54 | | | | r1(all_72_0, v0) | p1(v1)) % 152.76/20.54 | | | | % 152.76/20.54 | | | | ALPHA: (83) implies: % 152.76/20.55 | | | | (84) ~ p1(all_72_0) % 152.76/20.55 | | | | (85) r1(all_3_2, all_72_0) % 152.76/20.55 | | | | (86) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | % 152.76/20.55 | | | | ~ r1(v0, v1) | ~ r1(all_72_0, v0) | p1(v1)) % 152.76/20.55 | | | | % 152.76/20.55 | | | | GROUND_INST: instantiating (19) with all_72_0, simplifying with (77), % 152.76/20.55 | | | | (84), (85) gives: % 152.76/20.55 | | | | (87) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0, % 152.76/20.55 | | | | v1) & r1(all_72_0, v0) & ~ p1(v1)) % 152.76/20.55 | | | | % 152.76/20.55 | | | | DELTA: instantiating (87) with fresh symbols all_178_0, all_178_1 gives: % 152.76/20.55 | | | | (88) $i(all_178_0) & $i(all_178_1) & p1(all_178_1) & r1(all_178_1, % 152.76/20.55 | | | | all_178_0) & r1(all_72_0, all_178_1) & ~ p1(all_178_0) % 152.76/20.55 | | | | % 152.76/20.55 | | | | ALPHA: (88) implies: % 152.76/20.55 | | | | (89) ~ p1(all_178_0) % 152.76/20.55 | | | | (90) r1(all_72_0, all_178_1) % 152.76/20.55 | | | | (91) r1(all_178_1, all_178_0) % 152.76/20.55 | | | | (92) p1(all_178_1) % 152.76/20.55 | | | | (93) $i(all_178_1) % 152.76/20.55 | | | | (94) $i(all_178_0) % 152.76/20.55 | | | | % 152.76/20.55 | | | | GROUND_INST: instantiating (86) with all_178_1, all_178_0, simplifying % 152.76/20.55 | | | | with (89), (90), (91), (92), (93), (94) gives: % 152.76/20.55 | | | | (95) $false % 152.76/20.55 | | | | % 152.76/20.55 | | | | CLOSE: (95) is inconsistent. % 152.76/20.55 | | | | % 152.76/20.55 | | | End of split % 152.76/20.55 | | | % 152.76/20.55 | | End of split % 152.76/20.55 | | % 152.76/20.55 | End of split % 152.76/20.55 | % 152.76/20.55 End of proof % 152.76/20.55 % SZS output end Proof for theBenchmark % 152.76/20.55 % 152.76/20.55 19790ms %------------------------------------------------------------------------------