%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL642+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n031.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 12:54:26 PM UTC 2026 % Result : Theorem 139.58s 18.47s % Output : Proof 141.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL642+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.35 % Computer : n031.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 12:07:55 UTC 2026 % 0.09/0.35 % CPUTime : % 0.09/0.37 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. % 0.46/0.59 ________ _____ % 0.46/0.59 ___ __ \_________(_)________________________________ % 0.46/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.46/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.46/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.46/0.59 % 0.46/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.46/0.59 (2023-06-19) % 0.46/0.59 % 0.46/0.59 (c) Philipp Rümmer, 2009-2023 % 0.46/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.46/0.59 Amanda Stjerna. % 0.46/0.59 Free software under BSD-3-Clause. % 0.46/0.59 % 0.46/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.46/0.59 % 0.46/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.46/0.60 Running up to 7 provers in parallel. % 0.46/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.46/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.46/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.46/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.46/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.46/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.46/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.04/1.30 Prover 4: Preprocessing ... % 5.04/1.30 Prover 1: Preprocessing ... % 5.04/1.35 Prover 0: Preprocessing ... % 5.04/1.35 Prover 3: Preprocessing ... % 5.04/1.35 Prover 6: Preprocessing ... % 5.04/1.35 Prover 2: Preprocessing ... % 5.83/1.46 Prover 5: Preprocessing ... % 9.77/1.95 Prover 5: Constructing countermodel ... % 9.77/2.01 Prover 2: Constructing countermodel ... % 12.11/2.23 Prover 3: Constructing countermodel ... % 12.90/2.35 Prover 1: Constructing countermodel ... % 12.90/2.38 Prover 6: Proving ... % 63.10/8.78 Prover 0: Proving ... % 64.60/8.94 Prover 4: Constructing countermodel ... % 77.90/10.66 Prover 2: stopped % 77.90/10.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 78.72/10.71 Prover 7: Preprocessing ... % 78.72/10.75 Prover 7: Constructing countermodel ... % 104.05/13.94 Prover 5: stopped % 104.05/13.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 105.32/14.10 Prover 8: Preprocessing ... % 106.16/14.19 Prover 8: Warning: ignoring some quantifiers % 106.16/14.19 Prover 8: Constructing countermodel ... % 119.85/15.96 Prover 1: stopped % 119.85/15.97 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 120.90/16.09 Prover 9: Preprocessing ... % 122.14/16.28 Prover 9: Constructing countermodel ... % 134.88/17.86 Prover 6: stopped % 134.88/17.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 135.70/17.99 Prover 10: Preprocessing ... % 135.70/18.02 Prover 10: Constructing countermodel ... % 139.58/18.41 Prover 10: Found proof (size 50) % 139.58/18.41 Prover 10: proved (546ms) % 139.58/18.41 Prover 9: stopped % 139.58/18.41 Prover 0: stopped % 139.58/18.41 Prover 3: stopped % 139.58/18.41 Prover 8: stopped % 139.58/18.41 Prover 4: stopped % 139.58/18.47 Prover 7: stopped % 139.58/18.47 % 139.58/18.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 139.58/18.47 % 139.58/18.48 % SZS output start Proof for theBenchmark % 139.58/18.48 Assumptions after simplification: % 139.58/18.48 --------------------------------- % 139.58/18.48 % 139.58/18.48 (main) % 140.05/18.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 140.05/18.56 $i] : ? [v6: $i] : ($i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 140.05/18.56 $i(v0) & r1(v0, v6) & r1(v0, v5) & r1(v0, v4) & ~ p1(v4) & ~ p2(v5) & ~ % 140.05/18.56 p3(v6) & ! [v7: $i] : ( ~ $i(v7) | ~ r1(v0, v7) | p1(v7) | ? [v8: $i] : % 140.05/18.56 ? [v9: $i] : ($i(v9) & $i(v8) & p1(v8) & r1(v8, v9) & r1(v7, v8) & ~ % 140.05/18.56 p1(v9))) & ! [v7: $i] : ( ~ $i(v7) | ~ r1(v0, v7) | p2(v7) | ? [v8: % 140.05/18.56 $i] : ? [v9: $i] : ($i(v9) & $i(v8) & p2(v8) & r1(v8, v9) & r1(v7, v8) % 140.05/18.56 & ~ p2(v9))) & ! [v7: $i] : ( ~ $i(v7) | ~ r1(v0, v7) | p2(v7) | ? % 140.05/18.56 [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p2(v8) & ! [v9: $i] : ! [v10: $i] : % 140.05/18.56 ( ~ $i(v10) | ~ $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v8, v9) | % 140.05/18.56 p2(v10)))) & ! [v7: $i] : ( ~ $i(v7) | ~ r1(v0, v7) | p3(v7) | ? % 140.05/18.56 [v8: $i] : ? [v9: $i] : ($i(v9) & $i(v8) & p3(v8) & r1(v8, v9) & r1(v7, % 140.05/18.56 v8) & ~ p3(v9))) & ((r1(v0, v1) & ! [v7: $i] : ! [v8: $i] : ! [v9: % 140.05/18.56 $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 140.05/18.56 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) % 140.05/18.56 | ~ $i(v7) | ~ p2(v8) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ % 140.05/18.56 r1(v8, v9) | ~ r1(v7, v11) | ~ r1(v7, v10) | ~ r1(v7, v8) | ~ % 140.05/18.56 r1(v1, v7) | p2(v13) | p2(v10) | p2(v9) | ? [v14: $i] : ? [v15: $i] % 140.05/18.56 : ($i(v15) & $i(v14) & ((p2(v14) & r1(v14, v15) & r1(v13, v14) & ~ % 140.05/18.56 p2(v15)) | (p2(v14) & r1(v14, v15) & r1(v10, v14) & ~ p2(v15)) % 140.05/18.56 | (r1(v11, v14) & ~ p2(v14) & ! [v16: $i] : ! [v17: $i] : ( ~ % 140.05/18.56 $i(v17) | ~ $i(v16) | ~ p2(v16) | ~ r1(v16, v17) | ~ % 140.05/18.56 r1(v14, v16) | p2(v17)))))) & ! [v7: $i] : ! [v8: $i] : ! % 140.05/18.56 [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ $i(v12) | ~ % 140.05/18.56 $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ p2(v8) | % 140.05/18.56 ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, v9) | ~ r1(v7, v10) | % 140.05/18.56 ~ r1(v7, v8) | ~ r1(v1, v7) | p2(v12) | p2(v9) | ? [v13: $i] : ? % 140.05/18.56 [v14: $i] : ($i(v14) & $i(v13) & ((p2(v13) & r1(v13, v14) & r1(v12, % 140.05/18.56 v13) & ~ p2(v14)) | (r1(v13, v14) & r1(v7, v13) & ~ p2(v14) % 140.05/18.56 & ! [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~ % 140.05/18.56 p2(v15) | ~ r1(v15, v16) | ~ r1(v14, v15) | p2(v16))) | % 140.05/18.56 (r1(v10, v13) & ~ p2(v13) & ! [v15: $i] : ! [v16: $i] : ( ~ % 140.05/18.56 $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v15, v16) | ~ % 140.05/18.57 r1(v13, v15) | p2(v16)))))) & ! [v7: $i] : ! [v8: $i] : ! % 140.05/18.57 [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ % 140.05/18.57 $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v7, % 140.05/18.57 v11) | ~ r1(v7, v10) | ~ r1(v7, v8) | ~ r1(v1, v7) | p2(v11) | % 140.05/18.57 p2(v10) | p2(v9) | ? [v12: $i] : ? [v13: $i] : ($i(v13) & $i(v12) & % 140.05/18.57 ((p2(v12) & r1(v12, v13) & r1(v11, v12) & ~ p2(v13)) | (p2(v12) & % 140.05/18.57 r1(v12, v13) & r1(v10, v12) & ~ p2(v13))))) & ! [v7: $i] : ! % 140.05/18.57 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ % 140.05/18.57 $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ r1(v10, % 140.05/18.57 v11) | ~ r1(v9, v10) | ~ r1(v7, v9) | ~ r1(v7, v8) | ~ r1(v1, % 140.05/18.57 v7) | p2(v11) | p2(v8) | ? [v12: $i] : ? [v13: $i] : ($i(v13) & % 140.05/18.57 $i(v12) & ((p2(v12) & r1(v12, v13) & r1(v11, v12) & ~ p2(v13)) | % 140.05/18.57 (p2(v12) & r1(v12, v13) & r1(v8, v12) & ~ p2(v13)) | (r1(v9, v12) % 140.05/18.57 & ~ p2(v12) & ! [v14: $i] : ! [v15: $i] : ( ~ $i(v15) | ~ % 140.05/18.57 $i(v14) | ~ p2(v14) | ~ r1(v14, v15) | ~ r1(v12, v14) | % 140.05/18.57 p2(v15)))))) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 140.05/18.57 [v10: $i] : ( ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ p2(v8) % 140.05/18.57 | ~ r1(v8, v9) | ~ r1(v7, v10) | ~ r1(v7, v8) | ~ r1(v1, v7) | % 140.05/18.57 p2(v10) | p2(v9) | ? [v11: $i] : ? [v12: $i] : ($i(v12) & $i(v11) & % 140.05/18.57 ((p2(v11) & r1(v11, v12) & r1(v10, v11) & ~ p2(v12)) | (r1(v11, % 140.05/18.57 v12) & r1(v7, v11) & ~ p2(v12) & ! [v13: $i] : ! [v14: $i] % 140.05/18.57 : ( ~ $i(v14) | ~ $i(v13) | ~ p2(v13) | ~ r1(v13, v14) | ~ % 140.05/18.57 r1(v12, v13) | p2(v14)))))) & ! [v7: $i] : ! [v8: $i] : ! % 140.05/18.57 [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ % 140.05/18.57 $i(v7) | ~ p2(v7) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | % 140.05/18.57 ~ r1(v1, v7) | p2(v10) | ? [v11: $i] : ? [v12: $i] : ($i(v12) & % 140.05/18.57 $i(v11) & ((p2(v11) & r1(v11, v12) & r1(v10, v11) & ~ p2(v12)) | % 140.05/18.57 (r1(v11, v12) & r1(v7, v11) & ~ p2(v12) & ! [v13: $i] : ! [v14: % 140.05/18.57 $i] : ( ~ $i(v14) | ~ $i(v13) | ~ p2(v13) | ~ r1(v13, v14) % 140.05/18.57 | ~ r1(v12, v13) | p2(v14))) | (r1(v8, v11) & ~ p2(v11) & ! % 140.05/18.57 [v13: $i] : ! [v14: $i] : ( ~ $i(v14) | ~ $i(v13) | ~ p2(v13) % 140.05/18.57 | ~ r1(v13, v14) | ~ r1(v11, v13) | p2(v14)))))) & ! [v7: % 140.05/18.57 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | % 140.05/18.57 ~ p2(v7) | ~ r1(v7, v9) | ~ r1(v7, v8) | ~ r1(v1, v7) | p2(v9) | % 140.05/18.57 p2(v8) | ? [v10: $i] : ? [v11: $i] : ($i(v11) & $i(v10) & ((p2(v10) % 140.05/18.57 & r1(v10, v11) & r1(v9, v10) & ~ p2(v11)) | (p2(v10) & r1(v10, % 140.05/18.57 v11) & r1(v8, v10) & ~ p2(v11))))) & ! [v7: $i] : ! [v8: % 140.05/18.57 $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ r1(v7, v8) | ~ r1(v1, % 140.05/18.57 v7) | p2(v8) | ? [v9: $i] : ? [v10: $i] : ($i(v10) & $i(v9) & % 140.05/18.57 ((p2(v9) & r1(v9, v10) & r1(v8, v9) & ~ p2(v10)) | (r1(v9, v10) & % 140.05/18.57 r1(v7, v9) & ~ p2(v10) & ! [v11: $i] : ! [v12: $i] : ( ~ % 140.05/18.57 $i(v12) | ~ $i(v11) | ~ p2(v11) | ~ r1(v11, v12) | ~ % 140.05/18.57 r1(v10, v11) | p2(v12)))))) & ((r1(v2, v3) & r1(v1, v2) & ~ % 140.05/18.57 p2(v3) & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ % 140.05/18.57 p2(v7) | ~ r1(v7, v8) | ~ r1(v3, v7) | p2(v8)) & ! [v7: $i] : ( % 140.05/18.57 ~ $i(v7) | ~ r1(v1, v7) | p2(v7) | ? [v8: $i] : ? [v9: $i] : % 140.05/18.57 ($i(v9) & $i(v8) & p2(v8) & r1(v8, v9) & r1(v7, v8) & ~ p2(v9)))) % 140.05/18.57 | ( ~ p2(v1) & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ % 140.05/18.57 p2(v7) | ~ r1(v7, v8) | ~ r1(v1, v7) | p2(v8))))) | ((p2(v0) | % 140.05/18.57 (p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2))) & ( ! [v7: $i] : ! % 140.05/18.57 [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ r1(v7, v8) | ~ r1(v0, v7) | % 140.05/18.57 p2(v8) | ? [v9: $i] : ? [v10: $i] : ($i(v10) & $i(v9) & p2(v9) & % 140.05/18.57 r1(v9, v10) & r1(v8, v9) & ~ p2(v10))) | (r1(v0, v3) & ~ p2(v3) % 140.05/18.57 & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | % 140.05/18.57 ~ r1(v7, v8) | ~ r1(v3, v7) | p2(v8))))))) % 140.05/18.57 % 140.05/18.57 Those formulas are unsatisfiable: % 140.05/18.57 --------------------------------- % 140.05/18.57 % 140.05/18.57 Begin of proof % 140.05/18.57 | % 140.05/18.58 | DELTA: instantiating (main) with fresh symbols all_2_0, all_2_1, all_2_2, % 140.05/18.58 | all_2_3, all_2_4, all_2_5, all_2_6 gives: % 140.54/18.62 | (1) $i(all_2_0) & $i(all_2_1) & $i(all_2_2) & $i(all_2_3) & $i(all_2_4) & % 140.54/18.62 | $i(all_2_5) & $i(all_2_6) & r1(all_2_6, all_2_0) & r1(all_2_6, all_2_1) % 140.54/18.62 | & r1(all_2_6, all_2_2) & ~ p1(all_2_2) & ~ p2(all_2_1) & ~ % 140.54/18.62 | p3(all_2_0) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) | p1(v0) | % 140.54/18.62 | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & % 140.54/18.62 | r1(v0, v1) & ~ p1(v2))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 140.54/18.62 | r1(all_2_6, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & % 140.54/18.62 | $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2))) & ! [v0: % 140.54/18.62 | $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) | p2(v0) | ? [v1: $i] : % 140.54/18.62 | ($i(v1) & r1(v0, v1) & ~ p2(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ % 140.54/18.62 | $i(v3) | ~ $i(v2) | ~ p2(v2) | ~ r1(v2, v3) | ~ r1(v1, v2) | % 140.54/18.62 | p2(v3)))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) | % 140.54/18.62 | p3(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p3(v1) & % 140.54/18.62 | r1(v1, v2) & r1(v0, v1) & ~ p3(v2))) & ((r1(all_2_6, all_2_5) & ! % 140.54/18.62 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 140.54/18.62 | ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 140.54/18.62 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ % 140.54/18.62 | r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ % 140.54/18.62 | r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v6) | p2(v3) % 140.54/18.63 | | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) & $i(v7) & % 140.54/18.63 | ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) | (p2(v7) & % 140.54/18.63 | r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) & ~ % 140.54/18.63 | p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ % 140.54/18.63 | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) | % 140.54/18.63 | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 140.54/18.63 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | % 140.54/18.63 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ % 140.54/18.63 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ % 140.54/18.63 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : % 140.54/18.63 | ? [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, % 140.54/18.63 | v6) & ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & % 140.54/18.63 | ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ % 140.54/18.63 | p2(v8) | ~ r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | % 140.54/18.63 | (r1(v3, v6) & ~ p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ % 140.54/18.63 | $i(v9) | ~ $i(v8) | ~ p2(v8) | ~ r1(v8, v9) | ~ % 140.54/18.63 | r1(v6, v8) | p2(v9)))))) & ! [v0: $i] : ! [v1: $i] : ! % 140.54/18.63 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 140.54/18.63 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ % 140.54/18.63 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 140.54/18.63 | p2(v4) | p2(v3) | p2(v2) | ? [v5: $i] : ? [v6: $i] : ($i(v6) & % 140.54/18.63 | $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4, v5) & ~ p2(v6)) | % 140.54/18.63 | (p2(v5) & r1(v5, v6) & r1(v3, v5) & ~ p2(v6))))) & ! [v0: % 140.54/18.63 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 140.54/18.63 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 140.54/18.63 | p2(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | ~ % 140.54/18.63 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v1) | ? [v5: $i] : % 140.54/18.63 | ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4, % 140.54/18.63 | v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v1, v5) & ~ % 140.54/18.63 | p2(v6)) | (r1(v2, v5) & ~ p2(v5) & ! [v7: $i] : ! [v8: % 140.54/18.63 | $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ r1(v7, v8) % 140.54/18.63 | | ~ r1(v5, v7) | p2(v8)))))) & ! [v0: $i] : ! [v1: $i] % 140.54/18.63 | : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 140.54/18.63 | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0, % 140.54/18.63 | v1) | ~ r1(all_2_5, v0) | p2(v3) | p2(v2) | ? [v4: $i] : ? % 140.54/18.63 | [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) % 140.54/18.63 | & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! % 140.54/18.63 | [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) % 140.54/18.63 | | ~ r1(v6, v7) | ~ r1(v5, v6) | p2(v7)))))) & ! [v0: % 140.54/18.63 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 140.54/18.63 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v2, v3) | ~ % 140.54/18.63 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | ? % 140.54/18.63 | [v4: $i] : ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) % 140.54/18.63 | & r1(v3, v4) & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ % 140.54/18.63 | p2(v5) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) % 140.54/18.63 | | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | p2(v7))) | % 140.54/18.63 | (r1(v1, v4) & ~ p2(v4) & ! [v6: $i] : ! [v7: $i] : ( ~ % 140.54/18.63 | $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | ~ % 140.54/18.63 | r1(v4, v6) | p2(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! % 140.54/18.63 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ % 140.54/18.63 | r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v2) | p2(v1) % 140.54/18.63 | | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p2(v3) & % 140.54/18.63 | r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) | (p2(v3) & r1(v3, v4) % 140.54/18.63 | & r1(v1, v3) & ~ p2(v4))))) & ! [v0: $i] : ! [v1: $i] : % 140.54/18.63 | ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, % 140.54/18.63 | v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & % 140.54/18.63 | ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) | (r1(v2, v3) & % 140.54/18.63 | r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 140.54/18.63 | $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) | ~ % 140.54/18.63 | r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) & % 140.54/18.63 | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: % 140.54/18.63 | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 140.54/18.63 | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 140.54/18.63 | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : % 140.54/18.63 | ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ % 140.54/18.63 | p2(v2)))) | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( % 140.54/18.63 | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 140.54/18.63 | r1(all_2_5, v0) | p2(v1))))) | ((p2(all_2_6) | (p2(all_2_5) & % 140.54/18.63 | r1(all_2_5, all_2_4) & r1(all_2_6, all_2_5) & ~ p2(all_2_4))) % 140.54/18.63 | & ( ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, % 140.54/18.63 | v1) | ~ r1(all_2_6, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] % 140.54/18.64 | : ($i(v3) & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ % 140.54/18.64 | p2(v3))) | (r1(all_2_6, all_2_3) & ~ p2(all_2_3) & ! [v0: % 140.54/18.64 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ % 140.54/18.64 | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)))))) % 140.54/18.64 | % 140.54/18.64 | ALPHA: (1) implies: % 140.54/18.64 | (2) ~ p2(all_2_1) % 140.54/18.64 | (3) r1(all_2_6, all_2_1) % 140.54/18.64 | (4) $i(all_2_5) % 140.54/18.64 | (5) $i(all_2_4) % 140.54/18.64 | (6) $i(all_2_3) % 140.54/18.64 | (7) $i(all_2_1) % 140.54/18.67 | (8) (r1(all_2_6, all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 140.54/18.67 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 140.54/18.67 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 140.54/18.67 | | ~ p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~ % 140.54/18.67 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 140.54/18.67 | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) & % 140.54/18.67 | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) | % 140.54/18.67 | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) & % 140.54/18.67 | ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ % 140.54/18.67 | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) | % 140.54/18.67 | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 140.54/18.67 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ % 140.54/18.67 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v4, % 140.54/18.67 | v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0, % 140.54/18.67 | v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : ? % 140.54/18.67 | [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, v6) & % 140.54/18.67 | ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & ! [v8: % 140.54/18.67 | $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p2(v8) | ~ % 140.54/18.67 | r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | (r1(v3, v6) & ~ % 140.54/18.67 | p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | % 140.54/18.67 | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v6, v8) | p2(v9)))))) & % 140.54/18.67 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 140.54/18.67 | ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 140.54/18.67 | p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, % 140.54/18.67 | v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? [v5: $i] % 140.54/18.67 | : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4, % 140.54/18.67 | v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, v5) & ~ % 140.54/18.67 | p2(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 140.54/18.67 | [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 140.54/18.67 | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ % 140.54/18.67 | r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v1) | % 140.54/18.67 | ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, % 140.54/18.67 | v6) & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & % 140.54/18.67 | r1(v1, v5) & ~ p2(v6)) | (r1(v2, v5) & ~ p2(v5) & ! [v7: % 140.54/18.67 | $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ % 140.54/18.67 | r1(v7, v8) | ~ r1(v5, v7) | p2(v8)))))) & ! [v0: $i] : ! % 140.54/18.67 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 140.54/18.67 | $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ % 140.54/18.67 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | p2(v2) | ? [v4: $i] : % 140.54/18.67 | ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) % 140.54/18.67 | & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: % 140.54/18.67 | $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ % 140.54/18.67 | r1(v6, v7) | ~ r1(v5, v6) | p2(v7)))))) & ! [v0: $i] : ! % 140.54/18.67 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 140.54/18.67 | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 140.54/18.67 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | ? [v4: $i] : ? [v5: % 140.54/18.67 | $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) & ~ % 140.54/18.67 | p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: $i] % 140.54/18.67 | : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ % 140.54/18.67 | r1(v6, v7) | ~ r1(v5, v6) | p2(v7))) | (r1(v1, v4) & ~ % 140.54/18.67 | p2(v4) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | % 140.54/18.67 | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v4, v6) | p2(v7)))))) & % 140.54/18.67 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 140.54/18.67 | $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, % 140.54/18.67 | v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] : ($i(v4) & % 140.54/18.67 | $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) | % 140.54/18.67 | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) & ! [v0: $i] % 140.54/18.67 | : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | % 140.54/18.67 | ~ r1(all_2_5, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & % 140.54/18.67 | $i(v2) & ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) | % 140.54/18.67 | (r1(v2, v3) & r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5: % 140.54/18.67 | $i] : ( ~ $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) | % 140.54/18.67 | ~ r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) & % 140.54/18.67 | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] % 140.54/18.67 | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 140.54/18.67 | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 140.54/18.68 | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) % 140.54/18.68 | & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2)))) | % 140.54/18.68 | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 140.54/18.68 | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 140.54/18.68 | p2(v1))))) | ((p2(all_2_6) | (p2(all_2_5) & r1(all_2_5, % 140.54/18.68 | all_2_4) & r1(all_2_6, all_2_5) & ~ p2(all_2_4))) & ( ! [v0: % 140.54/18.68 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 140.54/18.68 | r1(all_2_6, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & % 140.54/18.68 | $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) | % 140.54/18.68 | (r1(all_2_6, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] % 140.54/18.68 | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 140.54/18.68 | r1(all_2_3, v0) | p2(v1))))) % 140.54/18.68 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) | p2(v0) | ? [v1: $i] : % 140.54/18.68 | ($i(v1) & r1(v0, v1) & ~ p2(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ % 140.54/18.68 | $i(v3) | ~ $i(v2) | ~ p2(v2) | ~ r1(v2, v3) | ~ r1(v1, v2) | % 140.54/18.68 | p2(v3)))) % 140.54/18.68 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) | p2(v0) | ? [v1: $i] : % 140.54/18.68 | ? [v2: $i] : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & % 140.54/18.68 | ~ p2(v2))) % 140.54/18.68 | % 140.54/18.68 | GROUND_INST: instantiating (9) with all_2_1, simplifying with (2), (3), (7) % 140.54/18.68 | gives: % 140.54/18.68 | (11) ? [v0: $i] : ($i(v0) & r1(all_2_1, v0) & ~ p2(v0) & ! [v1: $i] : ! % 140.54/18.68 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ p2(v1) | ~ r1(v1, v2) | ~ % 140.54/18.68 | r1(v0, v1) | p2(v2))) % 140.54/18.68 | % 140.54/18.68 | DELTA: instantiating (11) with fresh symbol all_16_0 gives: % 140.54/18.68 | (12) $i(all_16_0) & r1(all_2_1, all_16_0) & ~ p2(all_16_0) & ! [v0: $i] : % 140.54/18.68 | ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 140.54/18.68 | r1(all_16_0, v0) | p2(v1)) % 140.54/18.68 | % 140.54/18.68 | ALPHA: (12) implies: % 140.54/18.68 | (13) ~ p2(all_16_0) % 140.54/18.68 | (14) r1(all_2_1, all_16_0) % 140.54/18.68 | (15) $i(all_16_0) % 140.54/18.69 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ % 140.54/18.69 | r1(v0, v1) | ~ r1(all_16_0, v0) | p2(v1)) % 140.54/18.69 | % 140.54/18.69 | BETA: splitting (8) gives: % 140.54/18.69 | % 140.54/18.69 | Case 1: % 140.54/18.69 | | % 141.04/18.71 | | (17) r1(all_2_6, all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 141.04/18.71 | | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 141.04/18.71 | | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 141.04/18.71 | | | ~ p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~ % 141.04/18.71 | | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 141.04/18.71 | | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) & % 141.04/18.71 | | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) | % 141.04/18.71 | | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) & % 141.04/18.71 | | ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ % 141.04/18.71 | | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) | % 141.04/18.71 | | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 141.04/18.71 | | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ % 141.04/18.71 | | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v4, % 141.04/18.71 | | v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0, % 141.04/18.71 | | v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : ? % 141.04/18.71 | | [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, v6) & % 141.04/18.71 | | ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & ! [v8: % 141.04/18.71 | | $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p2(v8) | % 141.04/18.71 | | ~ r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | (r1(v3, v6) & ~ % 141.04/18.71 | | p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) % 141.04/18.71 | | | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v6, v8) | p2(v9)))))) % 141.04/18.71 | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 141.04/18.71 | | $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 141.04/18.71 | | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ % 141.04/18.71 | | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? % 141.04/18.71 | | [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) % 141.04/18.71 | | & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, % 141.04/18.71 | | v5) & ~ p2(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 141.04/18.71 | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 141.04/18.71 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v3, v4) | ~ % 141.04/18.71 | | r1(v2, v3) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 141.04/18.71 | | p2(v4) | p2(v1) | ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & % 141.04/18.71 | | ((p2(v5) & r1(v5, v6) & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & % 141.04/18.71 | | r1(v5, v6) & r1(v1, v5) & ~ p2(v6)) | (r1(v2, v5) & ~ % 141.04/18.71 | | p2(v5) & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) % 141.04/18.71 | | | ~ p2(v7) | ~ r1(v7, v8) | ~ r1(v5, v7) | p2(v8)))))) % 141.04/18.71 | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) % 141.04/18.71 | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | % 141.04/18.71 | | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | % 141.04/18.71 | | p2(v2) | ? [v4: $i] : ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & % 141.04/18.71 | | r1(v4, v5) & r1(v3, v4) & ~ p2(v5)) | (r1(v4, v5) & r1(v0, % 141.04/18.71 | | v4) & ~ p2(v5) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | % 141.04/18.71 | | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | % 141.04/18.71 | | p2(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 141.04/18.71 | | [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 141.04/18.72 | | p2(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 141.04/18.72 | | r1(all_2_5, v0) | p2(v3) | ? [v4: $i] : ? [v5: $i] : ($i(v5) & % 141.04/18.72 | | $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) & ~ p2(v5)) | % 141.04/18.72 | | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: $i] : ! [v7: % 141.04/18.72 | | $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | % 141.04/18.72 | | ~ r1(v5, v6) | p2(v7))) | (r1(v1, v4) & ~ p2(v4) & ! % 141.04/18.72 | | [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) % 141.04/18.72 | | | ~ r1(v6, v7) | ~ r1(v4, v6) | p2(v7)))))) & ! [v0: % 141.04/18.72 | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 141.04/18.72 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ % 141.04/18.72 | | r1(all_2_5, v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] : % 141.04/18.72 | | ($i(v4) & $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) % 141.04/18.72 | | | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) & ! [v0: % 141.04/18.72 | | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, % 141.04/18.72 | | v1) | ~ r1(all_2_5, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : % 141.04/18.72 | | ($i(v3) & $i(v2) & ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) % 141.04/18.72 | | | (r1(v2, v3) & r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5: % 141.04/18.72 | | $i] : ( ~ $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) | % 141.04/18.72 | | ~ r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) & % 141.04/18.72 | | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: % 141.04/18.72 | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 141.04/18.72 | | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 141.04/18.72 | | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) % 141.04/18.72 | | & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2)))) | % 141.04/18.72 | | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 141.04/18.72 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 141.04/18.72 | | p2(v1)))) % 141.04/18.72 | | % 141.04/18.72 | | ALPHA: (17) implies: % 141.04/18.72 | | (18) r1(all_2_6, all_2_5) % 141.04/18.72 | | (19) (r1(all_2_4, all_2_3) & r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! % 141.04/18.72 | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ % 141.04/18.72 | | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ % 141.04/18.72 | | $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] % 141.04/18.72 | | : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ % 141.04/18.72 | | p2(v2)))) | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ % 141.04/18.72 | | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, % 141.04/18.72 | | v0) | p2(v1))) % 141.04/18.72 | | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | % 141.04/18.72 | | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ % 141.04/18.72 | | r1(all_2_5, v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] : % 141.04/18.72 | | ($i(v4) & $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) % 141.04/18.72 | | | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) % 141.04/18.73 | | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 141.04/18.73 | | : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 141.04/18.73 | | p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, % 141.04/18.73 | | v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? [v5: % 141.04/18.73 | | $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & % 141.04/18.73 | | r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, v5) % 141.04/18.73 | | & ~ p2(v6))))) % 141.04/18.73 | | % 141.04/18.73 | | GROUND_INST: instantiating (10) with all_2_5, simplifying with (4), (18) % 141.04/18.73 | | gives: % 141.04/18.73 | | (22) p2(all_2_5) | ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) % 141.04/18.73 | | & r1(v0, v1) & r1(all_2_5, v0) & ~ p2(v1)) % 141.04/18.73 | | % 141.04/18.73 | | BETA: splitting (19) gives: % 141.04/18.73 | | % 141.04/18.73 | | Case 1: % 141.04/18.73 | | | % 141.04/18.73 | | | (23) r1(all_2_4, all_2_3) & r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! % 141.04/18.73 | | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ % 141.04/18.73 | | | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ % 141.04/18.73 | | | $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] % 141.04/18.73 | | | : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ % 141.04/18.73 | | | p2(v2))) % 141.04/18.73 | | | % 141.04/18.73 | | | ALPHA: (23) implies: % 141.04/18.73 | | | (24) ~ p2(all_2_3) % 141.04/18.73 | | | (25) r1(all_2_5, all_2_4) % 141.04/18.73 | | | (26) r1(all_2_4, all_2_3) % 141.04/18.73 | | | (27) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: % 141.04/18.73 | | | $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & % 141.04/18.73 | | | r1(v0, v1) & ~ p2(v2))) % 141.04/18.73 | | | (28) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | % 141.04/18.73 | | | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) % 141.04/18.73 | | | % 141.04/18.73 | | | GROUND_INST: instantiating (27) with all_2_4, simplifying with (5), (25) % 141.04/18.73 | | | gives: % 141.04/18.74 | | | (29) p2(all_2_4) | ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & % 141.04/18.74 | | | p2(v0) & r1(v0, v1) & r1(all_2_4, v0) & ~ p2(v1)) % 141.04/18.74 | | | % 141.04/18.74 | | | BETA: splitting (29) gives: % 141.04/18.74 | | | % 141.04/18.74 | | | Case 1: % 141.04/18.74 | | | | % 141.04/18.74 | | | | (30) p2(all_2_4) % 141.04/18.74 | | | | % 141.04/18.74 | | | | GROUND_INST: instantiating (20) with all_2_4, all_2_3, all_2_3, % 141.04/18.74 | | | | simplifying with (5), (6), (24), (25), (26), (30) gives: % 141.04/18.74 | | | | (31) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, % 141.04/18.74 | | | | v1) & r1(all_2_3, v0) & ~ p2(v1)) % 141.04/18.74 | | | | % 141.04/18.74 | | | | DELTA: instantiating (31) with fresh symbols all_123_0, all_123_1 gives: % 141.04/18.74 | | | | (32) $i(all_123_0) & $i(all_123_1) & p2(all_123_1) & r1(all_123_1, % 141.04/18.74 | | | | all_123_0) & r1(all_2_3, all_123_1) & ~ p2(all_123_0) % 141.04/18.74 | | | | % 141.04/18.74 | | | | ALPHA: (32) implies: % 141.04/18.74 | | | | (33) ~ p2(all_123_0) % 141.04/18.74 | | | | (34) r1(all_2_3, all_123_1) % 141.04/18.74 | | | | (35) r1(all_123_1, all_123_0) % 141.04/18.74 | | | | (36) p2(all_123_1) % 141.04/18.74 | | | | (37) $i(all_123_1) % 141.04/18.74 | | | | (38) $i(all_123_0) % 141.04/18.74 | | | | % 141.04/18.74 | | | | GROUND_INST: instantiating (28) with all_123_1, all_123_0, simplifying % 141.04/18.74 | | | | with (33), (34), (35), (36), (37), (38) gives: % 141.04/18.74 | | | | (39) $false % 141.04/18.74 | | | | % 141.04/18.74 | | | | CLOSE: (39) is inconsistent. % 141.04/18.74 | | | | % 141.04/18.74 | | | Case 2: % 141.04/18.74 | | | | % 141.04/18.74 | | | | (40) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, % 141.04/18.75 | | | | v1) & r1(all_2_4, v0) & ~ p2(v1)) % 141.04/18.75 | | | | % 141.04/18.75 | | | | DELTA: instantiating (40) with fresh symbols all_118_0, all_118_1 gives: % 141.04/18.75 | | | | (41) $i(all_118_0) & $i(all_118_1) & p2(all_118_1) & r1(all_118_1, % 141.04/18.75 | | | | all_118_0) & r1(all_2_4, all_118_1) & ~ p2(all_118_0) % 141.04/18.75 | | | | % 141.04/18.75 | | | | ALPHA: (41) implies: % 141.04/18.75 | | | | (42) ~ p2(all_118_0) % 141.04/18.75 | | | | (43) r1(all_2_4, all_118_1) % 141.04/18.75 | | | | (44) r1(all_118_1, all_118_0) % 141.04/18.75 | | | | (45) p2(all_118_1) % 141.04/18.75 | | | | (46) $i(all_118_1) % 141.04/18.75 | | | | (47) $i(all_118_0) % 141.04/18.75 | | | | % 141.04/18.75 | | | | GROUND_INST: instantiating (21) with all_2_4, all_118_1, all_118_0, % 141.04/18.75 | | | | all_2_3, all_2_3, simplifying with (5), (6), (24), (25), % 141.04/18.75 | | | | (26), (42), (43), (44), (45), (46), (47) gives: % 141.04/18.75 | | | | (48) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, % 141.04/18.75 | | | | v1) & r1(all_2_3, v0) & ~ p2(v1)) % 141.04/18.75 | | | | % 141.04/18.75 | | | | DELTA: instantiating (48) with fresh symbols all_125_0, all_125_1 gives: % 141.04/18.75 | | | | (49) $i(all_125_0) & $i(all_125_1) & p2(all_125_1) & r1(all_125_1, % 141.04/18.75 | | | | all_125_0) & r1(all_2_3, all_125_1) & ~ p2(all_125_0) % 141.04/18.75 | | | | % 141.04/18.75 | | | | ALPHA: (49) implies: % 141.04/18.75 | | | | (50) ~ p2(all_125_0) % 141.04/18.75 | | | | (51) r1(all_2_3, all_125_1) % 141.04/18.75 | | | | (52) r1(all_125_1, all_125_0) % 141.04/18.75 | | | | (53) p2(all_125_1) % 141.04/18.75 | | | | (54) $i(all_125_1) % 141.04/18.75 | | | | (55) $i(all_125_0) % 141.04/18.75 | | | | % 141.04/18.75 | | | | GROUND_INST: instantiating (28) with all_125_1, all_125_0, simplifying % 141.04/18.75 | | | | with (50), (51), (52), (53), (54), (55) gives: % 141.04/18.75 | | | | (56) $false % 141.04/18.75 | | | | % 141.04/18.75 | | | | CLOSE: (56) is inconsistent. % 141.04/18.75 | | | | % 141.04/18.75 | | | End of split % 141.04/18.75 | | | % 141.04/18.75 | | Case 2: % 141.04/18.75 | | | % 141.04/18.76 | | | (57) ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 141.04/18.76 | | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 141.04/18.76 | | | p2(v1)) % 141.04/18.76 | | | % 141.04/18.76 | | | ALPHA: (57) implies: % 141.04/18.76 | | | (58) ~ p2(all_2_5) % 141.04/18.76 | | | (59) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | % 141.04/18.76 | | | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v1)) % 141.04/18.76 | | | % 141.04/18.76 | | | BETA: splitting (22) gives: % 141.04/18.76 | | | % 141.04/18.76 | | | Case 1: % 141.04/18.76 | | | | % 141.04/18.76 | | | | (60) p2(all_2_5) % 141.04/18.76 | | | | % 141.04/18.76 | | | | PRED_UNIFY: (58), (60) imply: % 141.04/18.76 | | | | (61) $false % 141.04/18.76 | | | | % 141.04/18.76 | | | | CLOSE: (61) is inconsistent. % 141.04/18.76 | | | | % 141.04/18.76 | | | Case 2: % 141.04/18.76 | | | | % 141.04/18.76 | | | | (62) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, % 141.04/18.76 | | | | v1) & r1(all_2_5, v0) & ~ p2(v1)) % 141.04/18.76 | | | | % 141.04/18.76 | | | | DELTA: instantiating (62) with fresh symbols all_92_0, all_92_1 gives: % 141.04/18.76 | | | | (63) $i(all_92_0) & $i(all_92_1) & p2(all_92_1) & r1(all_92_1, % 141.04/18.76 | | | | all_92_0) & r1(all_2_5, all_92_1) & ~ p2(all_92_0) % 141.04/18.76 | | | | % 141.04/18.76 | | | | ALPHA: (63) implies: % 141.04/18.76 | | | | (64) ~ p2(all_92_0) % 141.04/18.76 | | | | (65) r1(all_2_5, all_92_1) % 141.04/18.76 | | | | (66) r1(all_92_1, all_92_0) % 141.04/18.76 | | | | (67) p2(all_92_1) % 141.04/18.76 | | | | (68) $i(all_92_1) % 141.04/18.76 | | | | (69) $i(all_92_0) % 141.04/18.76 | | | | % 141.04/18.77 | | | | GROUND_INST: instantiating (59) with all_92_1, all_92_0, simplifying % 141.04/18.77 | | | | with (64), (65), (66), (67), (68), (69) gives: % 141.04/18.77 | | | | (70) $false % 141.04/18.77 | | | | % 141.04/18.77 | | | | CLOSE: (70) is inconsistent. % 141.04/18.77 | | | | % 141.04/18.77 | | | End of split % 141.04/18.77 | | | % 141.04/18.77 | | End of split % 141.04/18.77 | | % 141.04/18.77 | Case 2: % 141.04/18.77 | | % 141.04/18.77 | | (71) (p2(all_2_6) | (p2(all_2_5) & r1(all_2_5, all_2_4) & r1(all_2_6, % 141.04/18.77 | | all_2_5) & ~ p2(all_2_4))) & ( ! [v0: $i] : ! [v1: $i] : ( ~ % 141.04/18.77 | | $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_6, v0) | p2(v1) % 141.04/18.77 | | | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & p2(v2) & r1(v2, % 141.04/18.77 | | v3) & r1(v1, v2) & ~ p2(v3))) | (r1(all_2_6, all_2_3) & ~ % 141.04/18.77 | | p2(all_2_3) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) % 141.04/18.77 | | | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)))) % 141.04/18.77 | | % 141.04/18.77 | | ALPHA: (71) implies: % 141.04/18.77 | | (72) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | % 141.04/18.77 | | ~ r1(all_2_6, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) % 141.04/18.77 | | & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) | % 141.04/18.77 | | (r1(all_2_6, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] : % 141.04/18.77 | | ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 141.04/18.77 | | r1(all_2_3, v0) | p2(v1))) % 141.04/18.77 | | % 141.04/18.77 | | BETA: splitting (72) gives: % 141.04/18.77 | | % 141.04/18.77 | | Case 1: % 141.04/18.77 | | | % 141.04/18.77 | | | (73) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) % 141.04/18.77 | | | | ~ r1(all_2_6, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : % 141.04/18.77 | | | ($i(v3) & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ % 141.04/18.77 | | | p2(v3))) % 141.04/18.77 | | | % 141.04/18.77 | | | GROUND_INST: instantiating (73) with all_2_1, all_16_0, simplifying with % 141.04/18.77 | | | (3), (7), (13), (14), (15) gives: % 141.04/18.78 | | | (74) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, v1) % 141.04/18.78 | | | & r1(all_16_0, v0) & ~ p2(v1)) % 141.04/18.78 | | | % 141.04/18.78 | | | DELTA: instantiating (74) with fresh symbols all_91_0, all_91_1 gives: % 141.04/18.78 | | | (75) $i(all_91_0) & $i(all_91_1) & p2(all_91_1) & r1(all_91_1, % 141.04/18.78 | | | all_91_0) & r1(all_16_0, all_91_1) & ~ p2(all_91_0) % 141.04/18.78 | | | % 141.04/18.78 | | | ALPHA: (75) implies: % 141.04/18.78 | | | (76) ~ p2(all_91_0) % 141.04/18.78 | | | (77) r1(all_16_0, all_91_1) % 141.04/18.78 | | | (78) r1(all_91_1, all_91_0) % 141.04/18.78 | | | (79) p2(all_91_1) % 141.04/18.78 | | | (80) $i(all_91_1) % 141.04/18.78 | | | (81) $i(all_91_0) % 141.04/18.78 | | | % 141.04/18.78 | | | GROUND_INST: instantiating (16) with all_91_1, all_91_0, simplifying with % 141.04/18.78 | | | (76), (77), (78), (79), (80), (81) gives: % 141.04/18.78 | | | (82) $false % 141.04/18.78 | | | % 141.04/18.78 | | | CLOSE: (82) is inconsistent. % 141.04/18.78 | | | % 141.04/18.78 | | Case 2: % 141.04/18.78 | | | % 141.04/18.78 | | | (83) r1(all_2_6, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] % 141.04/18.78 | | | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 141.04/18.78 | | | r1(all_2_3, v0) | p2(v1)) % 141.04/18.78 | | | % 141.04/18.78 | | | ALPHA: (83) implies: % 141.04/18.78 | | | (84) ~ p2(all_2_3) % 141.04/18.78 | | | (85) r1(all_2_6, all_2_3) % 141.04/18.78 | | | (86) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | % 141.04/18.78 | | | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) % 141.04/18.78 | | | % 141.04/18.78 | | | GROUND_INST: instantiating (10) with all_2_3, simplifying with (6), (84), % 141.04/18.78 | | | (85) gives: % 141.04/18.78 | | | (87) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, v1) % 141.04/18.78 | | | & r1(all_2_3, v0) & ~ p2(v1)) % 141.04/18.78 | | | % 141.04/18.78 | | | DELTA: instantiating (87) with fresh symbols all_95_0, all_95_1 gives: % 141.04/18.78 | | | (88) $i(all_95_0) & $i(all_95_1) & p2(all_95_1) & r1(all_95_1, % 141.04/18.78 | | | all_95_0) & r1(all_2_3, all_95_1) & ~ p2(all_95_0) % 141.04/18.78 | | | % 141.04/18.78 | | | ALPHA: (88) implies: % 141.04/18.78 | | | (89) ~ p2(all_95_0) % 141.04/18.78 | | | (90) r1(all_2_3, all_95_1) % 141.04/18.78 | | | (91) r1(all_95_1, all_95_0) % 141.04/18.79 | | | (92) p2(all_95_1) % 141.04/18.79 | | | (93) $i(all_95_1) % 141.04/18.79 | | | (94) $i(all_95_0) % 141.04/18.79 | | | % 141.04/18.79 | | | GROUND_INST: instantiating (86) with all_95_1, all_95_0, simplifying with % 141.04/18.79 | | | (89), (90), (91), (92), (93), (94) gives: % 141.04/18.79 | | | (95) $false % 141.04/18.79 | | | % 141.04/18.79 | | | CLOSE: (95) is inconsistent. % 141.04/18.79 | | | % 141.04/18.79 | | End of split % 141.04/18.79 | | % 141.04/18.79 | End of split % 141.04/18.79 | % 141.04/18.79 End of proof % 141.04/18.79 % SZS output end Proof for theBenchmark % 141.04/18.79 % 141.04/18.79 18195ms %------------------------------------------------------------------------------