%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL658+1.015 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 145.82s 19.06s % Output : Proof 147.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL658+1.015 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.36 % Computer : n013.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Sat Sep 5 05:27:05 UTC 2026 % 0.11/0.36 % CPUTime : % 0.11/0.38 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. % 0.49/0.57 ________ _____ % 0.49/0.57 ___ __ \_________(_)________________________________ % 0.49/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.49/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.49/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.49/0.57 % 0.49/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.49/0.57 (2023-06-19) % 0.49/0.58 % 0.49/0.58 (c) Philipp Rümmer, 2009-2023 % 0.49/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.49/0.58 Amanda Stjerna. % 0.49/0.58 Free software under BSD-3-Clause. % 0.49/0.58 % 0.49/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.49/0.58 % 0.49/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.49/0.59 Running up to 7 provers in parallel. % 0.49/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.49/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.49/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.49/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.49/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.49/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.49/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 8.30/1.77 Prover 4: Preprocessing ... % 9.11/1.83 Prover 1: Preprocessing ... % 9.11/1.86 Prover 0: Preprocessing ... % 9.11/1.86 Prover 6: Preprocessing ... % 9.11/1.86 Prover 2: Preprocessing ... % 9.11/1.86 Prover 3: Preprocessing ... % 9.11/1.86 Prover 5: Preprocessing ... % 15.43/2.70 Prover 2: Proving ... % 17.80/2.96 Prover 5: Proving ... % 25.72/3.93 Prover 6: Proving ... % 26.73/4.06 Prover 3: Constructing countermodel ... % 26.73/4.08 Prover 1: Constructing countermodel ... % 27.57/4.20 Prover 0: Proving ... % 31.21/4.68 Prover 4: Constructing countermodel ... % 77.24/10.49 Prover 2: stopped % 78.06/10.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 80.45/10.89 Prover 7: Preprocessing ... % 81.23/10.97 Prover 7: Warning: ignoring some quantifiers % 81.23/10.99 Prover 7: Constructing countermodel ... % 105.06/13.93 Prover 5: stopped % 105.06/13.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 106.24/14.12 Prover 8: Preprocessing ... % 107.37/14.28 Prover 8: Warning: ignoring some quantifiers % 107.37/14.29 Prover 8: Constructing countermodel ... % 120.86/15.94 Prover 1: stopped % 120.86/15.95 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 122.65/16.13 Prover 9: Preprocessing ... % 125.59/16.53 Prover 9: Constructing countermodel ... % 135.87/17.84 Prover 6: stopped % 135.87/17.85 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 136.67/18.05 Prover 10: Preprocessing ... % 138.02/18.09 Prover 10: Warning: ignoring some quantifiers % 138.02/18.10 Prover 10: Constructing countermodel ... % 144.61/19.05 Prover 10: Found proof (size 50) % 144.61/19.05 Prover 10: proved (1209ms) % 144.61/19.06 Prover 7: stopped % 144.61/19.06 Prover 3: stopped % 145.82/19.06 Prover 8: stopped % 145.82/19.06 Prover 0: stopped % 145.82/19.06 Prover 9: stopped % 145.82/19.06 Prover 4: stopped % 145.82/19.06 % 145.82/19.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 145.82/19.06 % 145.82/19.07 % SZS output start Proof for theBenchmark % 145.82/19.07 Assumptions after simplification: % 145.82/19.07 --------------------------------- % 145.82/19.07 % 145.82/19.07 (main) % 145.82/19.16 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 145.82/19.16 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 145.82/19.16 ($i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 145.82/19.16 $i(v2) & $i(v1) & $i(v0) & r1(v8, v10) & r1(v8, v9) & r1(v7, v8) & r1(v6, % 145.82/19.16 v7) & r1(v5, v6) & r1(v4, v5) & r1(v3, v4) & r1(v2, v3) & r1(v1, v2) & % 145.82/19.16 r1(v0, v1) & ~ p1(v10) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! % 145.82/19.16 [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! % 146.34/19.16 [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! % 146.34/19.16 [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ $i(v26) | ~ $i(v25) | ~ % 146.34/19.16 $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | % 146.34/19.16 ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ % 146.34/19.16 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v25, v26) | ~ r1(v24, v25) | ~ % 146.34/19.16 r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~ % 146.34/19.16 r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ % 146.34/19.16 r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ % 146.34/19.16 r1(v11, v12) | ~ r1(v0, v11) | p1(v26) | ? [v27: $i] : ($i(v27) & % 146.34/19.16 r1(v24, v27) & ~ p1(v27))) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] % 146.34/19.16 : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : % 146.34/19.16 ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : % 146.34/19.16 ! [v24: $i] : ! [v25: $i] : ( ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~ % 146.34/19.16 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | % 146.34/19.16 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ % 146.34/19.16 $i(v11) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21, % 146.34/19.16 v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, % 146.34/19.16 v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, % 146.34/19.16 v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v25) | ? % 146.34/19.16 [v26: $i] : ($i(v26) & r1(v23, v26) & ~ p1(v26))) & ! [v11: $i] : ! % 146.34/19.16 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! % 146.34/19.16 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! % 146.34/19.16 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ $i(v24) | ~ $i(v23) | ~ % 146.34/19.16 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | % 146.34/19.16 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ % 146.34/19.16 $i(v11) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20, % 146.34/19.16 v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, % 146.34/19.16 v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, % 146.34/19.16 v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v24) | ? [v25: $i] : % 146.34/19.16 ($i(v25) & r1(v22, v25) & ~ p1(v25))) & ! [v11: $i] : ! [v12: $i] : ! % 146.34/19.16 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! % 146.34/19.16 [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! % 146.34/19.16 [v23: $i] : ( ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) % 146.34/19.16 | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ % 146.34/19.16 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v22, v23) | ~ r1(v21, v22) | ~ % 146.34/19.16 r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~ % 146.34/19.16 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ % 146.34/19.16 r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v23) | ? [v24: $i] : % 146.34/19.16 ($i(v24) & r1(v21, v24) & ~ p1(v24))) & ! [v11: $i] : ! [v12: $i] : ! % 146.34/19.16 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! % 146.34/19.16 [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ % 146.34/19.16 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | % 146.34/19.16 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ % 146.34/19.16 $i(v11) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, % 146.34/19.16 v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, % 146.34/19.16 v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, % 146.34/19.16 v11) | p1(v22) | ? [v23: $i] : ($i(v23) & r1(v20, v23) & ~ p1(v23))) & % 146.34/19.16 ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : % 146.34/19.16 ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! % 146.34/19.16 [v21: $i] : ( ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) % 146.34/19.16 | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ % 146.34/19.16 $i(v11) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, % 146.34/19.16 v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, % 146.34/19.16 v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v21) | ? % 146.34/19.16 [v22: $i] : ($i(v22) & r1(v19, v22) & ~ p1(v22))) & ! [v11: $i] : ! % 146.34/19.16 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! % 146.34/19.16 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ $i(v20) | ~ % 146.34/19.16 $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | % 146.34/19.16 ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ p1(v18) | ~ r1(v18, v20) | ~ % 146.34/19.16 r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ % 146.34/19.16 r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ % 146.34/19.16 r1(v0, v11) | p1(v20) | ? [v21: $i] : ? [v22: $i] : ($i(v22) & $i(v21) & % 146.34/19.16 ((p1(v21) & r1(v21, v22) & r1(v19, v21) & ~ p1(v22)) | (p1(v21) & % 146.34/19.16 r1(v21, v22) & r1(v18, v21) & ~ p1(v22) & ! [v23: $i] : ! [v24: % 146.34/19.17 $i] : ! [v25: $i] : ( ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~ % 146.34/19.17 p1(v24) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v21, v23) | % 146.34/19.17 p1(v25) | p1(v23)) & ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : % 146.34/19.17 ( ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~ p1(v24) | ~ r1(v24, v25) % 146.34/19.17 | ~ r1(v23, v24) | ~ r1(v21, v23) | p1(v25) | ? [v26: $i] : % 146.34/19.17 ($i(v26) & r1(v23, v26) & ~ p1(v26))))))) & ! [v11: $i] : ! % 146.34/19.17 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! % 146.34/19.17 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ $i(v20) | ~ % 146.34/19.17 $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | % 146.34/19.17 ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v19, v20) | ~ r1(v18, v19) | % 146.34/19.17 ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ % 146.34/19.17 r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | % 146.34/19.17 p1(v20) | ? [v21: $i] : ? [v22: $i] : ($i(v22) & $i(v21) & ((p1(v21) & % 146.34/19.17 r1(v21, v22) & r1(v20, v21) & ~ p1(v22)) | (r1(v18, v21) & ~ % 146.34/19.17 p1(v21) & ! [v23: $i] : ! [v24: $i] : ( ~ $i(v24) | ~ $i(v23) | % 146.34/19.17 ~ p1(v23) | ~ r1(v23, v24) | ~ r1(v21, v23) | p1(v24)))))) & ! % 146.34/19.17 [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! % 146.34/19.17 [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ( ~ $i(v19) | ~ % 146.34/19.17 $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | % 146.34/19.17 ~ $i(v12) | ~ $i(v11) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, % 146.34/19.17 v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, % 146.34/19.17 v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v19) | ? [v20: $i] : % 146.34/19.17 ($i(v20) & r1(v17, v20) & ~ p1(v20))) & ! [v11: $i] : ! [v12: $i] : ! % 146.34/19.17 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! % 146.34/19.17 [v18: $i] : ! [v19: $i] : ( ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ % 146.34/19.17 $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | % 146.34/19.17 ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ % 146.34/19.17 r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ % 146.34/19.17 r1(v0, v11) | p1(v18) | ? [v20: $i] : ($i(v20) & ((r1(v19, v20) & ~ % 146.34/19.17 p1(v20)) | (r1(v18, v20) & ~ p1(v20) & ! [v21: $i] : ! [v22: $i] % 146.34/19.17 : ( ~ $i(v22) | ~ $i(v21) | ~ p1(v21) | ~ r1(v21, v22) | ~ % 146.34/19.17 r1(v20, v21) | p1(v22)))))) & ! [v11: $i] : ! [v12: $i] : ! % 146.34/19.17 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! % 146.34/19.17 [v18: $i] : ( ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) % 146.34/19.17 | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v17, v18) | ~ r1(v16, v17) % 146.34/19.17 | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | % 146.34/19.17 ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v18) | ? [v19: $i] : ($i(v19) & % 146.34/19.17 r1(v16, v19) & ~ p1(v19))) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] % 146.34/19.17 : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | % 146.34/19.17 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) % 146.34/19.17 | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | % 146.34/19.17 ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v17) | ? [v18: $i] % 146.34/19.17 : ($i(v18) & r1(v15, v18) & ~ p1(v18))) & ! [v11: $i] : ! [v12: $i] : % 146.34/19.17 ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ % 146.34/19.17 $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v15, % 146.34/19.17 v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, % 146.34/19.17 v12) | ~ r1(v0, v11) | p1(v16) | ? [v17: $i] : ($i(v17) & r1(v14, v17) % 146.34/19.17 & ~ p1(v17))) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: % 146.34/19.17 $i] : ! [v15: $i] : ( ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | % 146.34/19.17 ~ $i(v11) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ % 146.34/19.17 r1(v11, v12) | ~ r1(v0, v11) | p1(v15) | ? [v16: $i] : ($i(v16) & % 146.34/19.17 r1(v13, v16) & ~ p1(v16))) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] % 146.34/19.17 : ! [v14: $i] : ( ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ % 146.34/19.17 r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | % 146.34/19.17 p1(v14) | ? [v15: $i] : ($i(v15) & r1(v12, v15) & ~ p1(v15))) & ! [v11: % 146.34/19.17 $i] : ! [v12: $i] : ! [v13: $i] : ( ~ $i(v13) | ~ $i(v12) | ~ $i(v11) % 146.34/19.17 | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v13) | ? [v14: % 146.34/19.17 $i] : ($i(v14) & r1(v11, v14) & ~ p1(v14))) & ! [v11: $i] : ( ~ % 146.34/19.17 $i(v11) | ~ r1(v9, v11) | p1(v11)) & ! [v11: $i] : ( ~ $i(v11) | ~ % 146.34/19.17 r1(v8, v11) | p1(v11) | ? [v12: $i] : ? [v13: $i] : ($i(v13) & $i(v12) & % 146.34/19.17 p1(v12) & r1(v12, v13) & r1(v11, v12) & ~ p1(v13)))) % 146.34/19.17 % 146.34/19.17 Further assumptions not needed in the proof: % 146.34/19.17 -------------------------------------------- % 146.34/19.17 reflexivity % 146.34/19.17 % 146.34/19.17 Those formulas are unsatisfiable: % 146.34/19.17 --------------------------------- % 146.34/19.17 % 146.34/19.17 Begin of proof % 146.34/19.17 | % 146.34/19.17 | DELTA: instantiating (main) with fresh symbols all_3_0, all_3_1, all_3_2, % 146.34/19.17 | all_3_3, all_3_4, all_3_5, all_3_6, all_3_7, all_3_8, all_3_9, all_3_10 % 146.34/19.17 | gives: % 146.52/19.23 | (1) $i(all_3_0) & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & $i(all_3_4) & % 146.52/19.23 | $i(all_3_5) & $i(all_3_6) & $i(all_3_7) & $i(all_3_8) & $i(all_3_9) & % 146.52/19.23 | $i(all_3_10) & r1(all_3_2, all_3_0) & r1(all_3_2, all_3_1) & % 146.52/19.23 | r1(all_3_3, all_3_2) & r1(all_3_4, all_3_3) & r1(all_3_5, all_3_4) & % 146.52/19.23 | r1(all_3_6, all_3_5) & r1(all_3_7, all_3_6) & r1(all_3_8, all_3_7) & % 146.52/19.23 | r1(all_3_9, all_3_8) & r1(all_3_10, all_3_9) & ~ p1(all_3_0) & ! [v0: % 146.52/19.23 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 146.52/19.23 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 146.52/19.23 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : % 146.52/19.23 | ! [v15: $i] : ( ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ % 146.52/19.23 | $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) % 146.52/19.23 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 146.52/19.23 | $i(v0) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ % 146.52/19.23 | r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ % 146.52/19.23 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ % 146.52/19.23 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 146.52/19.23 | r1(all_3_10, v0) | p1(v15) | ? [v16: $i] : ($i(v16) & r1(v13, v16) & % 146.52/19.23 | ~ p1(v16))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 146.52/19.23 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 146.52/19.23 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! % 146.52/19.23 | [v13: $i] : ! [v14: $i] : ( ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ % 146.52/19.24 | $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) % 146.52/19.24 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 146.52/19.24 | $i(v0) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ % 146.52/19.24 | r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ % 146.52/19.24 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ % 146.52/19.24 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | % 146.52/19.24 | p1(v14) | ? [v15: $i] : ($i(v15) & r1(v12, v15) & ~ p1(v15))) & ! % 146.52/19.24 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 146.52/19.24 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 146.52/19.24 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ $i(v13) | % 146.52/19.24 | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ % 146.52/19.24 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 146.52/19.24 | ~ $i(v1) | ~ $i(v0) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, % 146.52/19.24 | v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, % 146.52/19.24 | v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) % 146.52/19.24 | | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v13) | ? % 146.52/19.24 | [v14: $i] : ($i(v14) & r1(v11, v14) & ~ p1(v14))) & ! [v0: $i] : ! % 146.52/19.24 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 146.52/19.24 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 146.52/19.24 | [v11: $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ % 146.52/19.24 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 146.52/19.24 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v11, v12) | ~ % 146.52/19.24 | r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ % 146.52/19.24 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ % 146.52/19.24 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | % 146.52/19.24 | p1(v12) | ? [v13: $i] : ($i(v13) & r1(v10, v13) & ~ p1(v13))) & ! % 146.52/19.24 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 146.52/19.24 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 146.52/19.24 | [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ % 146.52/19.24 | $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 146.52/19.24 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v10, v11) | ~ r1(v9, v10) | % 146.52/19.24 | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ % 146.52/19.24 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 146.52/19.24 | r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v11) | ? [v12: $i] : ($i(v12) % 146.52/19.24 | & r1(v9, v12) & ~ p1(v12))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 146.52/19.24 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 146.52/19.24 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ % 146.52/19.24 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 146.52/19.24 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v9, v10) | ~ % 146.52/19.24 | r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ % 146.52/19.24 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 146.52/19.24 | r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v10) | ? [v11: $i] : ($i(v11) % 146.52/19.24 | & r1(v8, v11) & ~ p1(v11))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 146.52/19.24 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 146.52/19.24 | $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ $i(v7) % 146.52/19.24 | | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 146.52/19.24 | $i(v1) | ~ $i(v0) | ~ p1(v7) | ~ r1(v7, v9) | ~ r1(v7, v8) | ~ % 146.52/19.24 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ % 146.52/19.24 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | % 146.52/19.24 | p1(v9) | ? [v10: $i] : ? [v11: $i] : ($i(v11) & $i(v10) & ((p1(v10) % 146.52/19.24 | & r1(v10, v11) & r1(v8, v10) & ~ p1(v11)) | (p1(v10) & r1(v10, % 146.52/19.24 | v11) & r1(v7, v10) & ~ p1(v11) & ! [v12: $i] : ! [v13: $i] % 146.52/19.24 | : ! [v14: $i] : ( ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ % 146.52/19.24 | p1(v13) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v10, v12) % 146.52/19.24 | | p1(v14) | p1(v12)) & ! [v12: $i] : ! [v13: $i] : ! [v14: % 146.52/19.24 | $i] : ( ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ p1(v13) | ~ % 146.52/19.24 | r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v10, v12) | p1(v14) | % 146.52/19.24 | ? [v15: $i] : ($i(v15) & r1(v12, v15) & ~ p1(v15))))))) & ! % 146.52/19.24 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 146.52/19.24 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 146.52/19.24 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 146.52/19.24 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v8, v9) | ~ % 146.52/19.24 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ % 146.52/19.24 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 146.52/19.24 | r1(all_3_10, v0) | p1(v9) | ? [v10: $i] : ? [v11: $i] : ($i(v11) & % 146.52/19.24 | $i(v10) & ((p1(v10) & r1(v10, v11) & r1(v9, v10) & ~ p1(v11)) | % 146.52/19.24 | (r1(v7, v10) & ~ p1(v10) & ! [v12: $i] : ! [v13: $i] : ( ~ % 146.52/19.24 | $i(v13) | ~ $i(v12) | ~ p1(v12) | ~ r1(v12, v13) | ~ % 146.52/19.24 | r1(v10, v12) | p1(v13)))))) & ! [v0: $i] : ! [v1: $i] : ! % 146.52/19.24 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 146.52/19.24 | [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) % 146.52/19.24 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 146.52/19.24 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ % 146.52/19.24 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 146.52/19.24 | r1(all_3_10, v0) | p1(v8) | ? [v9: $i] : ($i(v9) & r1(v6, v9) & ~ % 146.52/19.24 | p1(v9))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 146.52/19.24 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( % 146.52/19.24 | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 146.52/19.24 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v7, v8) | ~ r1(v6, v7) | % 146.52/19.24 | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ % 146.52/19.24 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v7) | ? [v9: % 146.52/19.24 | $i] : ($i(v9) & ((r1(v8, v9) & ~ p1(v9)) | (r1(v7, v9) & ~ p1(v9) % 146.52/19.24 | & ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ % 146.52/19.24 | p1(v10) | ~ r1(v10, v11) | ~ r1(v9, v10) | p1(v11)))))) & % 146.52/19.24 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 146.52/19.24 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ % 146.52/19.24 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 146.52/19.24 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ % 146.52/19.24 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | % 146.52/19.24 | p1(v7) | ? [v8: $i] : ($i(v8) & r1(v5, v8) & ~ p1(v8))) & ! [v0: % 146.52/19.24 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 146.52/19.24 | $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 146.52/19.24 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ % 146.52/19.24 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 146.52/19.24 | r1(all_3_10, v0) | p1(v6) | ? [v7: $i] : ($i(v7) & r1(v4, v7) & ~ % 146.52/19.24 | p1(v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 146.52/19.24 | ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 146.52/19.24 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ % 146.52/19.24 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | % 146.52/19.24 | p1(v5) | ? [v6: $i] : ($i(v6) & r1(v3, v6) & ~ p1(v6))) & ! [v0: % 146.52/19.24 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 146.52/19.24 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v3, % 146.52/19.24 | v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 146.52/19.24 | r1(all_3_10, v0) | p1(v4) | ? [v5: $i] : ($i(v5) & r1(v2, v5) & ~ % 146.52/19.24 | p1(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 146.52/19.24 | ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ % 146.52/19.24 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v3) | ? [v4: % 146.52/19.24 | $i] : ($i(v4) & r1(v1, v4) & ~ p1(v4))) & ! [v0: $i] : ! [v1: % 146.52/19.24 | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, % 146.52/19.24 | v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v2) | ? [v3: $i] : % 146.52/19.24 | ($i(v3) & r1(v0, v3) & ~ p1(v3))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 146.52/19.24 | r1(all_3_1, v0) | p1(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, % 146.52/19.24 | v0) | p1(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & % 146.52/19.24 | p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ p1(v2))) % 146.52/19.24 | % 146.52/19.25 | ALPHA: (1) implies: % 146.52/19.25 | (2) ~ p1(all_3_0) % 146.52/19.25 | (3) r1(all_3_10, all_3_9) % 146.52/19.25 | (4) r1(all_3_9, all_3_8) % 146.52/19.25 | (5) r1(all_3_8, all_3_7) % 146.52/19.25 | (6) r1(all_3_7, all_3_6) % 146.52/19.25 | (7) r1(all_3_6, all_3_5) % 146.52/19.25 | (8) r1(all_3_5, all_3_4) % 146.52/19.25 | (9) r1(all_3_4, all_3_3) % 146.52/19.25 | (10) r1(all_3_3, all_3_2) % 146.52/19.25 | (11) r1(all_3_2, all_3_1) % 146.52/19.25 | (12) r1(all_3_2, all_3_0) % 146.52/19.25 | (13) $i(all_3_9) % 146.52/19.25 | (14) $i(all_3_8) % 146.52/19.25 | (15) $i(all_3_7) % 146.52/19.25 | (16) $i(all_3_6) % 146.52/19.25 | (17) $i(all_3_5) % 146.52/19.25 | (18) $i(all_3_4) % 146.52/19.25 | (19) $i(all_3_3) % 146.52/19.25 | (20) $i(all_3_2) % 146.52/19.25 | (21) $i(all_3_1) % 146.52/19.25 | (22) $i(all_3_0) % 146.52/19.25 | (23) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, v0) | p1(v0) | ? [v1: $i] : % 146.52/19.25 | ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & r1(v0, v1) & % 146.52/19.25 | ~ p1(v2))) % 146.52/19.25 | (24) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_1, v0) | p1(v0)) % 146.52/19.26 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 146.52/19.26 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ % 146.52/19.26 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 146.52/19.26 | ~ $i(v1) | ~ $i(v0) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, % 146.52/19.26 | v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, % 146.52/19.26 | v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v7) | ? [v9: $i] : % 146.52/19.26 | ($i(v9) & ((r1(v8, v9) & ~ p1(v9)) | (r1(v7, v9) & ~ p1(v9) & ! % 146.52/19.26 | [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ % 146.52/19.26 | p1(v10) | ~ r1(v10, v11) | ~ r1(v9, v10) | p1(v11)))))) % 146.52/19.26 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 146.52/19.26 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( % 146.52/19.26 | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) % 146.52/19.26 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v8, v9) | ~ % 146.52/19.26 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ % 146.52/19.26 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 146.52/19.26 | r1(all_3_10, v0) | p1(v9) | ? [v10: $i] : ? [v11: $i] : ($i(v11) & % 146.52/19.26 | $i(v10) & ((p1(v10) & r1(v10, v11) & r1(v9, v10) & ~ p1(v11)) | % 146.52/19.26 | (r1(v7, v10) & ~ p1(v10) & ! [v12: $i] : ! [v13: $i] : ( ~ % 146.52/19.26 | $i(v13) | ~ $i(v12) | ~ p1(v12) | ~ r1(v12, v13) | ~ % 146.52/19.26 | r1(v10, v12) | p1(v13)))))) % 146.52/19.27 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 146.52/19.27 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( % 146.52/19.27 | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) % 146.52/19.27 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v7) | ~ % 146.52/19.27 | r1(v7, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ % 146.52/19.27 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 146.52/19.27 | r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v9) | ? [v10: $i] : ? [v11: % 146.52/19.27 | $i] : ($i(v11) & $i(v10) & ((p1(v10) & r1(v10, v11) & r1(v8, v10) % 146.52/19.27 | & ~ p1(v11)) | (p1(v10) & r1(v10, v11) & r1(v7, v10) & ~ % 146.52/19.27 | p1(v11) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~ % 146.52/19.27 | $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ p1(v13) | ~ r1(v13, % 146.52/19.27 | v14) | ~ r1(v12, v13) | ~ r1(v10, v12) | p1(v14) | % 146.52/19.27 | p1(v12)) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~ % 146.52/19.27 | $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ p1(v13) | ~ r1(v13, % 146.52/19.27 | v14) | ~ r1(v12, v13) | ~ r1(v10, v12) | p1(v14) | ? % 146.52/19.27 | [v15: $i] : ($i(v15) & r1(v12, v15) & ~ p1(v15))))))) % 146.52/19.27 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 146.52/19.27 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 146.52/19.27 | ! [v10: $i] : ( ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ % 146.52/19.27 | $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 146.52/19.27 | ~ $i(v0) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ % 146.52/19.27 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ % 146.52/19.27 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | % 146.52/19.27 | p1(v10) | ? [v11: $i] : ($i(v11) & r1(v8, v11) & ~ p1(v11))) % 146.52/19.27 | % 146.52/19.27 | GROUND_INST: instantiating (25) with all_3_9, all_3_8, all_3_7, all_3_6, % 146.52/19.27 | all_3_5, all_3_4, all_3_3, all_3_2, all_3_1, simplifying with % 146.52/19.27 | (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), (15), % 146.52/19.27 | (16), (17), (18), (19), (20), (21) gives: % 146.52/19.28 | (29) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) | % 146.52/19.28 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 146.52/19.28 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) % 146.52/19.28 | | p1(v2))))) % 146.52/19.28 | % 146.52/19.28 | GROUND_INST: instantiating (25) with all_3_9, all_3_8, all_3_7, all_3_6, % 146.52/19.28 | all_3_5, all_3_4, all_3_3, all_3_2, all_3_0, simplifying with % 146.52/19.28 | (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), (15), % 146.52/19.28 | (16), (17), (18), (19), (20), (22) gives: % 146.52/19.28 | (30) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_0, v0) & ~ p1(v0)) | % 146.52/19.28 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 146.52/19.28 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) % 146.52/19.28 | | p1(v2))))) % 146.52/19.28 | % 146.52/19.28 | BETA: splitting (30) gives: % 146.52/19.28 | % 146.52/19.28 | Case 1: % 146.52/19.28 | | % 146.52/19.28 | | (31) p1(all_3_2) % 146.52/19.28 | | % 146.52/19.28 | | GROUND_INST: instantiating (27) with all_3_9, all_3_8, all_3_7, all_3_6, % 146.52/19.28 | | all_3_5, all_3_4, all_3_3, all_3_2, all_3_1, all_3_0, % 146.52/19.28 | | simplifying with (2), (3), (4), (5), (6), (7), (8), (9), (10), % 146.52/19.28 | | (11), (12), (13), (14), (15), (16), (17), (18), (19), (20), % 146.52/19.28 | | (21), (22), (31) gives: % 146.52/19.29 | | (32) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, v1) % 146.52/19.29 | | & r1(all_3_1, v0) & ~ p1(v1)) | (p1(v0) & r1(v0, v1) & % 146.52/19.29 | | r1(all_3_2, v0) & ~ p1(v1) & ! [v2: $i] : ! [v3: $i] : ! % 146.52/19.29 | | [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ % 146.52/19.29 | | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | % 146.52/19.29 | | p1(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 146.52/19.29 | | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ r1(v3, v4) | % 146.52/19.29 | | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5: $i] : % 146.52/19.29 | | ($i(v5) & r1(v2, v5) & ~ p1(v5)))))) % 146.52/19.29 | | % 146.52/19.29 | | DELTA: instantiating (32) with fresh symbols all_101_0, all_101_1 gives: % 146.52/19.29 | | (33) $i(all_101_0) & $i(all_101_1) & ((p1(all_101_1) & r1(all_101_1, % 146.52/19.29 | | all_101_0) & r1(all_3_1, all_101_1) & ~ p1(all_101_0)) | % 146.52/19.29 | | (p1(all_101_1) & r1(all_101_1, all_101_0) & r1(all_3_2, all_101_1) % 146.52/19.29 | | & ~ p1(all_101_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 146.52/19.29 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | % 146.52/19.29 | | ~ r1(v0, v1) | ~ r1(all_101_1, v0) | p1(v2) | p1(v0)) & ! % 146.52/19.29 | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | % 146.52/19.29 | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 146.52/19.29 | | r1(all_101_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, % 146.52/19.29 | | v3) & ~ p1(v3))))) % 146.52/19.29 | | % 146.52/19.29 | | ALPHA: (33) implies: % 146.52/19.29 | | (34) $i(all_101_1) % 146.52/19.29 | | (35) $i(all_101_0) % 146.52/19.29 | | (36) (p1(all_101_1) & r1(all_101_1, all_101_0) & r1(all_3_1, all_101_1) & % 146.52/19.29 | | ~ p1(all_101_0)) | (p1(all_101_1) & r1(all_101_1, all_101_0) & % 146.52/19.29 | | r1(all_3_2, all_101_1) & ~ p1(all_101_0) & ! [v0: $i] : ! [v1: % 146.52/19.29 | | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 146.52/19.29 | | p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_101_1, v0) | % 146.52/19.29 | | p1(v2) | p1(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 146.52/19.29 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ % 146.52/19.29 | | r1(v0, v1) | ~ r1(all_101_1, v0) | p1(v2) | ? [v3: $i] : % 146.52/19.29 | | ($i(v3) & r1(v0, v3) & ~ p1(v3)))) % 146.52/19.29 | | % 146.52/19.29 | | BETA: splitting (36) gives: % 146.52/19.29 | | % 146.52/19.29 | | Case 1: % 146.52/19.29 | | | % 146.52/19.29 | | | (37) p1(all_101_1) & r1(all_101_1, all_101_0) & r1(all_3_1, all_101_1) % 146.52/19.29 | | | & ~ p1(all_101_0) % 146.52/19.30 | | | % 146.52/19.30 | | | ALPHA: (37) implies: % 146.52/19.30 | | | (38) ~ p1(all_101_0) % 146.52/19.30 | | | (39) r1(all_3_1, all_101_1) % 146.52/19.30 | | | (40) r1(all_101_1, all_101_0) % 146.52/19.30 | | | % 147.00/19.30 | | | GROUND_INST: instantiating (28) with all_3_9, all_3_8, all_3_7, all_3_6, % 147.00/19.30 | | | all_3_5, all_3_4, all_3_3, all_3_2, all_3_1, all_101_1, % 147.00/19.30 | | | all_101_0, simplifying with (3), (4), (5), (6), (7), (8), % 147.00/19.30 | | | (9), (10), (11), (13), (14), (15), (16), (17), (18), (19), % 147.00/19.30 | | | (20), (21), (34), (35), (38), (39), (40) gives: % 147.00/19.30 | | | (41) ? [v0: $i] : ($i(v0) & r1(all_3_1, v0) & ~ p1(v0)) % 147.00/19.30 | | | % 147.00/19.30 | | | DELTA: instantiating (41) with fresh symbol all_164_0 gives: % 147.00/19.30 | | | (42) $i(all_164_0) & r1(all_3_1, all_164_0) & ~ p1(all_164_0) % 147.00/19.30 | | | % 147.00/19.30 | | | ALPHA: (42) implies: % 147.00/19.30 | | | (43) ~ p1(all_164_0) % 147.00/19.30 | | | (44) r1(all_3_1, all_164_0) % 147.00/19.30 | | | (45) $i(all_164_0) % 147.00/19.30 | | | % 147.00/19.30 | | | GROUND_INST: instantiating (24) with all_164_0, simplifying with (43), % 147.00/19.30 | | | (44), (45) gives: % 147.00/19.30 | | | (46) $false % 147.00/19.30 | | | % 147.00/19.30 | | | CLOSE: (46) is inconsistent. % 147.00/19.30 | | | % 147.00/19.30 | | Case 2: % 147.00/19.30 | | | % 147.00/19.31 | | | (47) p1(all_101_1) & r1(all_101_1, all_101_0) & r1(all_3_2, all_101_1) % 147.00/19.31 | | | & ~ p1(all_101_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 147.00/19.31 | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ % 147.00/19.31 | | | r1(v0, v1) | ~ r1(all_101_1, v0) | p1(v2) | p1(v0)) & ! [v0: % 147.00/19.31 | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 147.00/19.31 | | | $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 147.00/19.31 | | | r1(all_101_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3) % 147.00/19.31 | | | & ~ p1(v3))) % 147.00/19.31 | | | % 147.00/19.31 | | | ALPHA: (47) implies: % 147.00/19.31 | | | (48) ~ p1(all_101_0) % 147.00/19.31 | | | (49) r1(all_3_2, all_101_1) % 147.00/19.31 | | | (50) r1(all_101_1, all_101_0) % 147.00/19.31 | | | (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | % 147.00/19.31 | | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 147.00/19.31 | | | r1(all_101_1, v0) | p1(v2) | p1(v0)) % 147.00/19.31 | | | % 147.00/19.31 | | | GROUND_INST: instantiating (26) with all_3_9, all_3_8, all_3_7, all_3_6, % 147.00/19.31 | | | all_3_5, all_3_4, all_3_3, all_3_2, all_101_1, all_101_0, % 147.00/19.31 | | | simplifying with (3), (4), (5), (6), (7), (8), (9), (10), % 147.00/19.31 | | | (13), (14), (15), (16), (17), (18), (19), (20), (34), (35), % 147.00/19.31 | | | (48), (49), (50) gives: % 147.00/19.31 | | | (52) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, % 147.00/19.31 | | | v1) & r1(all_101_0, v0) & ~ p1(v1)) | (r1(all_3_2, v0) & % 147.00/19.31 | | | ~ p1(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 147.00/19.31 | | | $i(v2) | ~ p1(v2) | ~ r1(v2, v3) | ~ r1(v0, v2) | % 147.00/19.31 | | | p1(v3))))) % 147.00/19.31 | | | % 147.00/19.31 | | | DELTA: instantiating (52) with fresh symbols all_165_0, all_165_1 gives: % 147.00/19.31 | | | (53) $i(all_165_0) & $i(all_165_1) & ((p1(all_165_1) & r1(all_165_1, % 147.00/19.31 | | | all_165_0) & r1(all_101_0, all_165_1) & ~ p1(all_165_0)) | % 147.00/19.31 | | | (r1(all_3_2, all_165_1) & ~ p1(all_165_1) & ! [v0: $i] : ! % 147.00/19.31 | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) % 147.00/19.31 | | | | ~ r1(all_165_1, v0) | p1(v1)))) % 147.00/19.31 | | | % 147.00/19.31 | | | ALPHA: (53) implies: % 147.00/19.32 | | | (54) $i(all_165_1) % 147.00/19.32 | | | (55) $i(all_165_0) % 147.00/19.32 | | | (56) (p1(all_165_1) & r1(all_165_1, all_165_0) & r1(all_101_0, % 147.00/19.32 | | | all_165_1) & ~ p1(all_165_0)) | (r1(all_3_2, all_165_1) & ~ % 147.00/19.32 | | | p1(all_165_1) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 147.00/19.32 | | | $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_165_1, v0) | % 147.00/19.32 | | | p1(v1))) % 147.00/19.32 | | | % 147.00/19.32 | | | BETA: splitting (56) gives: % 147.00/19.32 | | | % 147.00/19.32 | | | Case 1: % 147.00/19.32 | | | | % 147.00/19.32 | | | | (57) p1(all_165_1) & r1(all_165_1, all_165_0) & r1(all_101_0, % 147.00/19.32 | | | | all_165_1) & ~ p1(all_165_0) % 147.00/19.32 | | | | % 147.00/19.32 | | | | ALPHA: (57) implies: % 147.00/19.32 | | | | (58) ~ p1(all_165_0) % 147.00/19.32 | | | | (59) r1(all_101_0, all_165_1) % 147.00/19.32 | | | | (60) r1(all_165_1, all_165_0) % 147.00/19.32 | | | | (61) p1(all_165_1) % 147.00/19.32 | | | | % 147.00/19.32 | | | | GROUND_INST: instantiating (51) with all_101_0, all_165_1, all_165_0, % 147.00/19.32 | | | | simplifying with (35), (48), (50), (54), (55), (58), (59), % 147.00/19.32 | | | | (60), (61) gives: % 147.00/19.32 | | | | (62) $false % 147.00/19.32 | | | | % 147.00/19.32 | | | | CLOSE: (62) is inconsistent. % 147.00/19.32 | | | | % 147.00/19.32 | | | Case 2: % 147.00/19.32 | | | | % 147.00/19.32 | | | | (63) r1(all_3_2, all_165_1) & ~ p1(all_165_1) & ! [v0: $i] : ! % 147.00/19.32 | | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | % 147.00/19.32 | | | | ~ r1(all_165_1, v0) | p1(v1)) % 147.00/19.32 | | | | % 147.00/19.32 | | | | ALPHA: (63) implies: % 147.00/19.32 | | | | (64) ~ p1(all_165_1) % 147.00/19.32 | | | | (65) r1(all_3_2, all_165_1) % 147.00/19.32 | | | | (66) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | % 147.00/19.32 | | | | ~ r1(v0, v1) | ~ r1(all_165_1, v0) | p1(v1)) % 147.00/19.32 | | | | % 147.00/19.32 | | | | GROUND_INST: instantiating (23) with all_165_1, simplifying with (54), % 147.00/19.32 | | | | (64), (65) gives: % 147.00/19.32 | | | | (67) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0, % 147.00/19.32 | | | | v1) & r1(all_165_1, v0) & ~ p1(v1)) % 147.00/19.32 | | | | % 147.00/19.32 | | | | DELTA: instantiating (67) with fresh symbols all_229_0, all_229_1 gives: % 147.00/19.33 | | | | (68) $i(all_229_0) & $i(all_229_1) & p1(all_229_1) & r1(all_229_1, % 147.00/19.33 | | | | all_229_0) & r1(all_165_1, all_229_1) & ~ p1(all_229_0) % 147.00/19.33 | | | | % 147.00/19.33 | | | | ALPHA: (68) implies: % 147.00/19.33 | | | | (69) ~ p1(all_229_0) % 147.00/19.33 | | | | (70) r1(all_165_1, all_229_1) % 147.00/19.33 | | | | (71) r1(all_229_1, all_229_0) % 147.00/19.33 | | | | (72) p1(all_229_1) % 147.00/19.33 | | | | (73) $i(all_229_1) % 147.00/19.33 | | | | (74) $i(all_229_0) % 147.00/19.33 | | | | % 147.00/19.33 | | | | GROUND_INST: instantiating (66) with all_229_1, all_229_0, simplifying % 147.00/19.33 | | | | with (69), (70), (71), (72), (73), (74) gives: % 147.00/19.33 | | | | (75) $false % 147.00/19.33 | | | | % 147.00/19.33 | | | | CLOSE: (75) is inconsistent. % 147.00/19.33 | | | | % 147.00/19.33 | | | End of split % 147.00/19.33 | | | % 147.00/19.33 | | End of split % 147.00/19.33 | | % 147.00/19.33 | Case 2: % 147.00/19.33 | | % 147.00/19.33 | | (76) ~ p1(all_3_2) % 147.00/19.33 | | % 147.00/19.33 | | BETA: splitting (29) gives: % 147.00/19.33 | | % 147.00/19.33 | | Case 1: % 147.00/19.33 | | | % 147.00/19.33 | | | (77) p1(all_3_2) % 147.00/19.33 | | | % 147.00/19.33 | | | PRED_UNIFY: (76), (77) imply: % 147.00/19.33 | | | (78) $false % 147.00/19.33 | | | % 147.00/19.33 | | | CLOSE: (78) is inconsistent. % 147.00/19.33 | | | % 147.00/19.33 | | Case 2: % 147.00/19.33 | | | % 147.00/19.33 | | | (79) ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) | % 147.00/19.33 | | | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 147.00/19.33 | | | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, % 147.00/19.33 | | | v1) | p1(v2))))) % 147.00/19.33 | | | % 147.00/19.33 | | | DELTA: instantiating (79) with fresh symbol all_107_0 gives: % 147.00/19.33 | | | (80) $i(all_107_0) & ((r1(all_3_1, all_107_0) & ~ p1(all_107_0)) | % 147.00/19.33 | | | (r1(all_3_2, all_107_0) & ~ p1(all_107_0) & ! [v0: $i] : ! % 147.00/19.33 | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) % 147.00/19.33 | | | | ~ r1(all_107_0, v0) | p1(v1)))) % 147.00/19.33 | | | % 147.00/19.33 | | | ALPHA: (80) implies: % 147.00/19.33 | | | (81) $i(all_107_0) % 147.00/19.33 | | | (82) (r1(all_3_1, all_107_0) & ~ p1(all_107_0)) | (r1(all_3_2, % 147.00/19.33 | | | all_107_0) & ~ p1(all_107_0) & ! [v0: $i] : ! [v1: $i] : ( % 147.00/19.33 | | | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ % 147.00/19.33 | | | r1(all_107_0, v0) | p1(v1))) % 147.00/19.33 | | | % 147.00/19.33 | | | BETA: splitting (82) gives: % 147.00/19.33 | | | % 147.00/19.33 | | | Case 1: % 147.00/19.33 | | | | % 147.00/19.33 | | | | (83) r1(all_3_1, all_107_0) & ~ p1(all_107_0) % 147.00/19.33 | | | | % 147.00/19.33 | | | | ALPHA: (83) implies: % 147.00/19.33 | | | | (84) ~ p1(all_107_0) % 147.00/19.34 | | | | (85) r1(all_3_1, all_107_0) % 147.00/19.34 | | | | % 147.00/19.34 | | | | GROUND_INST: instantiating (24) with all_107_0, simplifying with (81), % 147.00/19.34 | | | | (84), (85) gives: % 147.00/19.34 | | | | (86) $false % 147.00/19.34 | | | | % 147.00/19.34 | | | | CLOSE: (86) is inconsistent. % 147.00/19.34 | | | | % 147.00/19.34 | | | Case 2: % 147.00/19.34 | | | | % 147.00/19.34 | | | | (87) r1(all_3_2, all_107_0) & ~ p1(all_107_0) & ! [v0: $i] : ! % 147.00/19.34 | | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | % 147.00/19.34 | | | | ~ r1(all_107_0, v0) | p1(v1)) % 147.00/19.34 | | | | % 147.00/19.34 | | | | ALPHA: (87) implies: % 147.00/19.34 | | | | (88) ~ p1(all_107_0) % 147.00/19.34 | | | | (89) r1(all_3_2, all_107_0) % 147.00/19.34 | | | | (90) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | % 147.00/19.34 | | | | ~ r1(v0, v1) | ~ r1(all_107_0, v0) | p1(v1)) % 147.00/19.34 | | | | % 147.00/19.34 | | | | GROUND_INST: instantiating (23) with all_107_0, simplifying with (81), % 147.00/19.34 | | | | (88), (89) gives: % 147.00/19.34 | | | | (91) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0, % 147.00/19.34 | | | | v1) & r1(all_107_0, v0) & ~ p1(v1)) % 147.00/19.34 | | | | % 147.00/19.34 | | | | DELTA: instantiating (91) with fresh symbols all_213_0, all_213_1 gives: % 147.00/19.34 | | | | (92) $i(all_213_0) & $i(all_213_1) & p1(all_213_1) & r1(all_213_1, % 147.00/19.34 | | | | all_213_0) & r1(all_107_0, all_213_1) & ~ p1(all_213_0) % 147.00/19.34 | | | | % 147.00/19.34 | | | | ALPHA: (92) implies: % 147.00/19.34 | | | | (93) ~ p1(all_213_0) % 147.00/19.34 | | | | (94) r1(all_107_0, all_213_1) % 147.00/19.34 | | | | (95) r1(all_213_1, all_213_0) % 147.00/19.34 | | | | (96) p1(all_213_1) % 147.00/19.34 | | | | (97) $i(all_213_1) % 147.00/19.34 | | | | (98) $i(all_213_0) % 147.00/19.34 | | | | % 147.00/19.34 | | | | GROUND_INST: instantiating (90) with all_213_1, all_213_0, simplifying % 147.00/19.34 | | | | with (93), (94), (95), (96), (97), (98) gives: % 147.00/19.34 | | | | (99) $false % 147.00/19.34 | | | | % 147.00/19.34 | | | | CLOSE: (99) is inconsistent. % 147.00/19.34 | | | | % 147.00/19.34 | | | End of split % 147.00/19.34 | | | % 147.00/19.34 | | End of split % 147.00/19.34 | | % 147.00/19.34 | End of split % 147.00/19.34 | % 147.00/19.34 End of proof % 147.00/19.34 % SZS output end Proof for theBenchmark % 147.00/19.34 % 147.00/19.34 18767ms %------------------------------------------------------------------------------