%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL642+1.005 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 142.77s 18.94s % Output : Proof 144.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL642+1.005 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.35 % Computer : n026.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Sat Sep 5 04:54:10 UTC 2026 % 0.08/0.35 % CPUTime : % 0.12/0.37 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. % 0.52/0.57 ________ _____ % 0.52/0.57 ___ __ \_________(_)________________________________ % 0.52/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.57 % 0.52/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.57 (2023-06-19) % 0.52/0.57 % 0.52/0.57 (c) Philipp Rümmer, 2009-2023 % 0.52/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.57 Amanda Stjerna. % 0.52/0.57 Free software under BSD-3-Clause. % 0.52/0.57 % 0.52/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.57 % 0.52/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.52/0.58 Running up to 7 provers in parallel. % 0.52/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.20/1.37 Prover 1: Preprocessing ... % 5.98/1.43 Prover 4: Preprocessing ... % 5.98/1.45 Prover 0: Preprocessing ... % 5.98/1.45 Prover 3: Preprocessing ... % 5.98/1.45 Prover 2: Preprocessing ... % 5.98/1.45 Prover 5: Preprocessing ... % 5.98/1.45 Prover 6: Preprocessing ... % 11.21/2.12 Prover 2: Constructing countermodel ... % 12.24/2.20 Prover 5: Constructing countermodel ... % 15.41/2.67 Prover 1: Constructing countermodel ... % 15.41/2.68 Prover 6: Proving ... % 17.02/2.86 Prover 3: Constructing countermodel ... % 54.64/7.62 Prover 4: Constructing countermodel ... % 56.22/7.84 Prover 0: Proving ... % 90.67/12.27 Prover 2: stopped % 90.67/12.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 91.47/12.39 Prover 7: Preprocessing ... % 93.06/12.53 Prover 7: Constructing countermodel ... % 104.09/13.92 Prover 5: stopped % 104.09/13.92 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 ... % 107.16/14.34 Prover 8: Warning: ignoring some quantifiers % 107.16/14.35 Prover 8: Constructing countermodel ... % 119.79/15.94 Prover 1: stopped % 119.79/15.95 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 119.79/16.05 Prover 9: Preprocessing ... % 124.37/16.52 Prover 9: Constructing countermodel ... % 134.58/17.84 Prover 6: stopped % 134.58/17.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 135.38/17.98 Prover 10: Preprocessing ... % 136.80/18.10 Prover 10: Constructing countermodel ... % 141.56/18.78 Prover 10: Found proof (size 49) % 141.56/18.79 Prover 10: proved (948ms) % 141.56/18.79 Prover 3: stopped % 141.56/18.79 Prover 9: stopped % 141.56/18.79 Prover 4: stopped % 141.56/18.79 Prover 8: stopped % 142.34/18.81 Prover 0: stopped % 142.77/18.93 Prover 7: stopped % 142.77/18.93 % 142.77/18.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 142.77/18.94 % 142.77/18.94 % SZS output start Proof for theBenchmark % 142.77/18.94 Assumptions after simplification: % 142.77/18.94 --------------------------------- % 142.77/18.94 % 142.77/18.94 (main) % 143.37/19.06 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 143.37/19.06 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 143.37/19.06 ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ($i(v14) & $i(v13) % 143.37/19.06 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 143.37/19.06 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & r1(v0, v14) & r1(v0, v13) & % 143.37/19.06 r1(v0, v12) & ~ p1(v12) & ~ p2(v13) & ~ p3(v14) & ! [v15: $i] : ( ~ % 143.37/19.06 $i(v15) | ~ r1(v0, v15) | p1(v15) | ? [v16: $i] : ? [v17: $i] : % 143.37/19.06 ($i(v17) & $i(v16) & p1(v16) & r1(v16, v17) & r1(v15, v16) & ~ p1(v17))) % 143.37/19.06 & ! [v15: $i] : ( ~ $i(v15) | ~ r1(v0, v15) | p2(v15) | ? [v16: $i] : ? % 143.37/19.06 [v17: $i] : ($i(v17) & $i(v16) & p2(v16) & r1(v16, v17) & r1(v15, v16) & % 143.37/19.06 ~ p2(v17))) & ! [v15: $i] : ( ~ $i(v15) | ~ r1(v0, v15) | p2(v15) | ? % 143.37/19.06 [v16: $i] : ($i(v16) & r1(v15, v16) & ~ p2(v16) & ! [v17: $i] : ! [v18: % 143.37/19.06 $i] : ( ~ $i(v18) | ~ $i(v17) | ~ p2(v17) | ~ r1(v17, v18) | ~ % 143.37/19.06 r1(v16, v17) | p2(v18)))) & ! [v15: $i] : ( ~ $i(v15) | ~ r1(v0, % 143.37/19.06 v15) | p3(v15) | ? [v16: $i] : ? [v17: $i] : ($i(v17) & $i(v16) & % 143.37/19.06 p3(v16) & r1(v16, v17) & r1(v15, v16) & ~ p3(v17))) & (p4(v0) | p1(v0) % 143.37/19.06 | p2(v0) | p3(v0) | ! [v15: $i] : ( ~ $i(v15) | ~ r1(v0, v15)) | (r1(v7, % 143.37/19.06 v8) & r1(v0, v7) & ~ p4(v7) & ~ p1(v7) & ~ p2(v7) & ~ p3(v7) & ! % 143.37/19.06 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ % 143.37/19.06 $i(v15) | ~ p4(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v7, % 143.37/19.06 v15) | p4(v16) | p1(v16) | p2(v16) | p3(v16)) & ! [v15: $i] : ! % 143.37/19.06 [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ % 143.37/19.06 p1(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v7, v15) | p4(v16) % 143.37/19.06 | p1(v16) | p2(v16) | p3(v16)) & ! [v15: $i] : ! [v16: $i] : ! % 143.37/19.06 [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ % 143.37/19.06 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v7, v15) | p4(v16) | p1(v16) | % 143.37/19.06 p2(v16) | p3(v16)) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ % 143.37/19.06 $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p3(v15) | ~ r1(v16, v17) | ~ % 143.37/19.06 r1(v15, v16) | ~ r1(v7, v15) | p4(v16) | p1(v16) | p2(v16) | p3(v16)) % 143.37/19.06 & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) % 143.37/19.06 | ~ $i(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v7, v15) | % 143.37/19.06 p4(v16) | p1(v16) | p2(v16) | p3(v16) | ? [v18: $i] : ($i(v18) & % 143.37/19.06 r1(v15, v18))))) & (p1(v0) | p2(v0) | p3(v0) | ! [v15: $i] : ( ~ % 143.37/19.06 $i(v15) | ~ r1(v0, v15)) | (r1(v5, v6) & r1(v0, v5) & ~ p1(v5) & ~ % 143.37/19.06 p2(v5) & ~ p3(v5) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ % 143.37/19.06 $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p1(v15) | ~ r1(v16, v17) | ~ % 143.37/19.06 r1(v15, v16) | ~ r1(v5, v15) | p1(v16) | p2(v16) | p3(v16)) & ! % 143.37/19.06 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ % 143.37/19.06 $i(v15) | ~ p2(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v5, % 143.37/19.06 v15) | p1(v16) | p2(v16) | p3(v16)) & ! [v15: $i] : ! [v16: $i] : % 143.37/19.06 ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p3(v15) | ~ % 143.37/19.06 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v5, v15) | p1(v16) | p2(v16) | % 143.37/19.06 p3(v16)) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | % 143.37/19.06 ~ $i(v16) | ~ $i(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v5, % 143.37/19.06 v15) | p1(v16) | p2(v16) | p3(v16) | ? [v18: $i] : ($i(v18) & % 143.37/19.06 r1(v15, v18))))) & (p1(v0) | p2(v0) | ! [v15: $i] : ( ~ $i(v15) | % 143.37/19.06 ~ r1(v0, v15)) | (r1(v3, v4) & r1(v0, v3) & ~ p1(v3) & ~ p2(v3) & ! % 143.37/19.06 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ % 143.37/19.06 $i(v15) | ~ p1(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v3, % 143.37/19.06 v15) | p1(v16) | p2(v16)) & ! [v15: $i] : ! [v16: $i] : ! [v17: % 143.37/19.06 $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v16, % 143.37/19.06 v17) | ~ r1(v15, v16) | ~ r1(v3, v15) | p1(v16) | p2(v16)) & ! % 143.37/19.07 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ % 143.37/19.07 $i(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v3, v15) | p1(v16) % 143.37/19.07 | p2(v16) | ? [v18: $i] : ($i(v18) & r1(v15, v18))))) & (p1(v0) | ! % 143.37/19.07 [v15: $i] : ( ~ $i(v15) | ~ r1(v0, v15)) | (r1(v1, v2) & r1(v0, v1) & ~ % 143.37/19.07 p1(v1) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ % 143.37/19.07 $i(v16) | ~ $i(v15) | ~ p1(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) % 143.37/19.07 | ~ r1(v1, v15) | p1(v16)) & ! [v15: $i] : ! [v16: $i] : ! [v17: % 143.37/19.07 $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ r1(v16, v17) | ~ % 143.37/19.07 r1(v15, v16) | ~ r1(v1, v15) | p1(v16) | ? [v18: $i] : ($i(v18) & % 143.37/19.07 r1(v15, v18))))) & ((r1(v0, v9) & ! [v15: $i] : ! [v16: $i] : ! % 143.37/19.07 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : % 143.37/19.07 ( ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ % 143.37/19.07 $i(v16) | ~ $i(v15) | ~ p2(v16) | ~ r1(v20, v21) | ~ r1(v19, v20) % 143.37/19.07 | ~ r1(v16, v17) | ~ r1(v15, v19) | ~ r1(v15, v18) | ~ r1(v15, % 143.37/19.07 v16) | ~ r1(v9, v15) | p2(v21) | p2(v18) | p2(v17) | ? [v22: $i] : % 143.37/19.07 ? [v23: $i] : ($i(v23) & $i(v22) & ((p2(v22) & r1(v22, v23) & r1(v21, % 143.37/19.07 v22) & ~ p2(v23)) | (p2(v22) & r1(v22, v23) & r1(v18, v22) & % 143.37/19.07 ~ p2(v23)) | (r1(v19, v22) & ~ p2(v22) & ! [v24: $i] : ! % 143.37/19.07 [v25: $i] : ( ~ $i(v25) | ~ $i(v24) | ~ p2(v24) | ~ r1(v24, % 143.37/19.07 v25) | ~ r1(v22, v24) | p2(v25)))))) & ! [v15: $i] : ! % 143.37/19.07 [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : % 143.37/19.07 ( ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ % 143.37/19.07 $i(v15) | ~ p2(v16) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v16, % 143.37/19.07 v17) | ~ r1(v15, v18) | ~ r1(v15, v16) | ~ r1(v9, v15) | p2(v20) % 143.37/19.07 | p2(v17) | ? [v21: $i] : ? [v22: $i] : ($i(v22) & $i(v21) & % 143.37/19.07 ((p2(v21) & r1(v21, v22) & r1(v20, v21) & ~ p2(v22)) | (r1(v21, % 143.37/19.07 v22) & r1(v15, v21) & ~ p2(v22) & ! [v23: $i] : ! [v24: $i] % 143.37/19.07 : ( ~ $i(v24) | ~ $i(v23) | ~ p2(v23) | ~ r1(v23, v24) | ~ % 143.37/19.07 r1(v22, v23) | p2(v24))) | (r1(v18, v21) & ~ p2(v21) & ! % 143.37/19.07 [v23: $i] : ! [v24: $i] : ( ~ $i(v24) | ~ $i(v23) | ~ p2(v23) % 143.37/19.07 | ~ r1(v23, v24) | ~ r1(v21, v23) | p2(v24)))))) & ! [v15: % 143.37/19.07 $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ( ~ % 143.37/19.07 $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ % 143.37/19.07 p2(v16) | ~ r1(v16, v17) | ~ r1(v15, v19) | ~ r1(v15, v18) | ~ % 143.37/19.07 r1(v15, v16) | ~ r1(v9, v15) | p2(v19) | p2(v18) | p2(v17) | ? [v20: % 143.37/19.07 $i] : ? [v21: $i] : ($i(v21) & $i(v20) & ((p2(v20) & r1(v20, v21) & % 143.37/19.07 r1(v19, v20) & ~ p2(v21)) | (p2(v20) & r1(v20, v21) & r1(v18, % 143.37/19.07 v20) & ~ p2(v21))))) & ! [v15: $i] : ! [v16: $i] : ! [v17: % 143.37/19.07 $i] : ! [v18: $i] : ! [v19: $i] : ( ~ $i(v19) | ~ $i(v18) | ~ % 143.37/19.07 $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v18, v19) | ~ % 143.37/19.07 r1(v17, v18) | ~ r1(v15, v17) | ~ r1(v15, v16) | ~ r1(v9, v15) | % 143.37/19.07 p2(v19) | p2(v16) | ? [v20: $i] : ? [v21: $i] : ($i(v21) & $i(v20) & % 143.37/19.07 ((p2(v20) & r1(v20, v21) & r1(v19, v20) & ~ p2(v21)) | (p2(v20) & % 143.37/19.07 r1(v20, v21) & r1(v16, v20) & ~ p2(v21)) | (r1(v17, v20) & ~ % 143.37/19.07 p2(v20) & ! [v22: $i] : ! [v23: $i] : ( ~ $i(v23) | ~ $i(v22) % 143.37/19.07 | ~ p2(v22) | ~ r1(v22, v23) | ~ r1(v20, v22) | % 143.37/19.07 p2(v23)))))) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! % 143.37/19.07 [v18: $i] : ( ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ % 143.37/19.07 p2(v16) | ~ r1(v16, v17) | ~ r1(v15, v18) | ~ r1(v15, v16) | ~ % 143.37/19.07 r1(v9, v15) | p2(v18) | p2(v17) | ? [v19: $i] : ? [v20: $i] : % 143.37/19.07 ($i(v20) & $i(v19) & ((p2(v19) & r1(v19, v20) & r1(v18, v19) & ~ % 143.37/19.07 p2(v20)) | (r1(v19, v20) & r1(v15, v19) & ~ p2(v20) & ! [v21: % 143.37/19.07 $i] : ! [v22: $i] : ( ~ $i(v22) | ~ $i(v21) | ~ p2(v21) | % 143.37/19.07 ~ r1(v21, v22) | ~ r1(v20, v21) | p2(v22)))))) & ! [v15: $i] % 143.37/19.07 : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ( ~ $i(v18) | ~ $i(v17) % 143.37/19.07 | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v17, v18) | ~ r1(v16, % 143.37/19.07 v17) | ~ r1(v15, v16) | ~ r1(v9, v15) | p2(v18) | ? [v19: $i] : % 143.37/19.07 ? [v20: $i] : ($i(v20) & $i(v19) & ((p2(v19) & r1(v19, v20) & r1(v18, % 143.37/19.07 v19) & ~ p2(v20)) | (r1(v19, v20) & r1(v15, v19) & ~ p2(v20) % 143.37/19.07 & ! [v21: $i] : ! [v22: $i] : ( ~ $i(v22) | ~ $i(v21) | ~ % 143.37/19.07 p2(v21) | ~ r1(v21, v22) | ~ r1(v20, v21) | p2(v22))) | % 143.37/19.07 (r1(v16, v19) & ~ p2(v19) & ! [v21: $i] : ! [v22: $i] : ( ~ % 143.37/19.07 $i(v22) | ~ $i(v21) | ~ p2(v21) | ~ r1(v21, v22) | ~ % 143.37/19.07 r1(v19, v21) | p2(v22)))))) & ! [v15: $i] : ! [v16: $i] : ! % 143.37/19.08 [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ % 143.37/19.08 r1(v15, v17) | ~ r1(v15, v16) | ~ r1(v9, v15) | p2(v17) | p2(v16) | % 143.37/19.08 ? [v18: $i] : ? [v19: $i] : ($i(v19) & $i(v18) & ((p2(v18) & r1(v18, % 143.37/19.08 v19) & r1(v17, v18) & ~ p2(v19)) | (p2(v18) & r1(v18, v19) & % 143.37/19.08 r1(v16, v18) & ~ p2(v19))))) & ! [v15: $i] : ! [v16: $i] : ( % 143.37/19.08 ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v15, v16) | ~ r1(v9, v15) % 143.37/19.08 | p2(v16) | ? [v17: $i] : ? [v18: $i] : ($i(v18) & $i(v17) & % 143.37/19.08 ((p2(v17) & r1(v17, v18) & r1(v16, v17) & ~ p2(v18)) | (r1(v17, % 143.37/19.08 v18) & r1(v15, v17) & ~ p2(v18) & ! [v19: $i] : ! [v20: $i] % 143.37/19.08 : ( ~ $i(v20) | ~ $i(v19) | ~ p2(v19) | ~ r1(v19, v20) | ~ % 143.37/19.08 r1(v18, v19) | p2(v20)))))) & ((r1(v10, v11) & r1(v9, v10) & % 143.37/19.08 ~ p2(v11) & ! [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | % 143.37/19.08 ~ p2(v15) | ~ r1(v15, v16) | ~ r1(v11, v15) | p2(v16)) & ! % 143.37/19.08 [v15: $i] : ( ~ $i(v15) | ~ r1(v9, v15) | p2(v15) | ? [v16: $i] : % 143.37/19.08 ? [v17: $i] : ($i(v17) & $i(v16) & p2(v16) & r1(v16, v17) & % 143.37/19.08 r1(v15, v16) & ~ p2(v17)))) | ( ~ p2(v9) & ! [v15: $i] : ! % 143.37/19.08 [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v15, v16) % 143.37/19.08 | ~ r1(v9, v15) | p2(v16))))) | ((p2(v0) | (p2(v9) & r1(v9, v10) % 143.37/19.08 & r1(v0, v9) & ~ p2(v10))) & ( ! [v15: $i] : ! [v16: $i] : ( ~ % 143.37/19.08 $i(v16) | ~ $i(v15) | ~ r1(v15, v16) | ~ r1(v0, v15) | p2(v16) | % 143.37/19.08 ? [v17: $i] : ? [v18: $i] : ($i(v18) & $i(v17) & p2(v17) & r1(v17, % 143.37/19.08 v18) & r1(v16, v17) & ~ p2(v18))) | (r1(v0, v11) & ~ p2(v11) & % 143.37/19.08 ! [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~ p2(v15) % 143.37/19.08 | ~ r1(v15, v16) | ~ r1(v11, v15) | p2(v16))))))) % 143.37/19.08 % 143.37/19.08 Those formulas are unsatisfiable: % 143.37/19.08 --------------------------------- % 143.37/19.08 % 143.37/19.08 Begin of proof % 143.37/19.08 | % 143.37/19.08 | DELTA: instantiating (main) with fresh symbols all_2_0, all_2_1, all_2_2, % 143.37/19.08 | all_2_3, all_2_4, all_2_5, all_2_6, all_2_7, all_2_8, all_2_9, % 143.37/19.08 | all_2_10, all_2_11, all_2_12, all_2_13, all_2_14 gives: % 143.87/19.14 | (1) $i(all_2_0) & $i(all_2_1) & $i(all_2_2) & $i(all_2_3) & $i(all_2_4) & % 143.87/19.14 | $i(all_2_5) & $i(all_2_6) & $i(all_2_7) & $i(all_2_8) & $i(all_2_9) & % 143.87/19.14 | $i(all_2_10) & $i(all_2_11) & $i(all_2_12) & $i(all_2_13) & % 143.87/19.14 | $i(all_2_14) & r1(all_2_14, all_2_0) & r1(all_2_14, all_2_1) & % 143.87/19.14 | r1(all_2_14, all_2_2) & ~ p1(all_2_2) & ~ p2(all_2_1) & ~ % 143.87/19.14 | p3(all_2_0) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) | p1(v0) | % 143.87/19.14 | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & % 143.87/19.14 | r1(v0, v1) & ~ p1(v2))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 143.87/19.14 | r1(all_2_14, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & % 143.87/19.14 | $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2))) & ! [v0: % 143.87/19.14 | $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) | p2(v0) | ? [v1: $i] : % 143.87/19.14 | ($i(v1) & r1(v0, v1) & ~ p2(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ % 143.87/19.14 | $i(v3) | ~ $i(v2) | ~ p2(v2) | ~ r1(v2, v3) | ~ r1(v1, v2) | % 143.87/19.14 | p2(v3)))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) | % 143.87/19.14 | p3(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p3(v1) & % 143.87/19.14 | r1(v1, v2) & r1(v0, v1) & ~ p3(v2))) & (p4(all_2_14) | % 143.87/19.14 | p1(all_2_14) | p2(all_2_14) | p3(all_2_14) | ! [v0: $i] : ( ~ $i(v0) % 143.87/19.14 | | ~ r1(all_2_14, v0)) | (r1(all_2_7, all_2_6) & r1(all_2_14, % 143.87/19.14 | all_2_7) & ~ p4(all_2_7) & ~ p1(all_2_7) & ~ p2(all_2_7) & ~ % 143.87/19.15 | p3(all_2_7) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) % 143.87/19.15 | | ~ $i(v1) | ~ $i(v0) | ~ p4(v0) | ~ r1(v1, v2) | ~ r1(v0, % 143.87/19.15 | v1) | ~ r1(all_2_7, v0) | p4(v1) | p1(v1) | p2(v1) | p3(v1)) & % 143.87/19.15 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | % 143.87/19.15 | ~ $i(v0) | ~ p1(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 143.87/19.15 | r1(all_2_7, v0) | p4(v1) | p1(v1) | p2(v1) | p3(v1)) & ! [v0: % 143.87/19.15 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 143.87/19.15 | $i(v0) | ~ p2(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 143.87/19.15 | r1(all_2_7, v0) | p4(v1) | p1(v1) | p2(v1) | p3(v1)) & ! [v0: % 143.87/19.15 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 143.87/19.15 | $i(v0) | ~ p3(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 143.87/19.15 | r1(all_2_7, v0) | p4(v1) | p1(v1) | p2(v1) | p3(v1)) & ! [v0: % 143.87/19.15 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 143.87/19.15 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_7, v0) | % 143.87/19.15 | p4(v1) | p1(v1) | p2(v1) | p3(v1) | ? [v3: $i] : ($i(v3) & % 143.87/19.15 | r1(v0, v3))))) & (p1(all_2_14) | p2(all_2_14) | p3(all_2_14) | % 143.87/19.15 | ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0)) | (r1(all_2_9, % 143.87/19.15 | all_2_8) & r1(all_2_14, all_2_9) & ~ p1(all_2_9) & ~ % 143.87/19.15 | p2(all_2_9) & ~ p3(all_2_9) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 143.87/19.15 | $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v1, % 143.87/19.15 | v2) | ~ r1(v0, v1) | ~ r1(all_2_9, v0) | p1(v1) | p2(v1) | % 143.87/19.15 | p3(v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | % 143.87/19.15 | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) % 143.87/19.15 | | ~ r1(all_2_9, v0) | p1(v1) | p2(v1) | p3(v1)) & ! [v0: $i] : % 143.87/19.15 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 143.87/19.15 | p3(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_9, v0) | % 143.87/19.15 | p1(v1) | p2(v1) | p3(v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 143.87/19.15 | $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ % 143.87/19.15 | r1(v0, v1) | ~ r1(all_2_9, v0) | p1(v1) | p2(v1) | p3(v1) | ? % 143.87/19.15 | [v3: $i] : ($i(v3) & r1(v0, v3))))) & (p1(all_2_14) | % 143.87/19.15 | p2(all_2_14) | ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0)) | % 143.87/19.15 | (r1(all_2_11, all_2_10) & r1(all_2_14, all_2_11) & ~ p1(all_2_11) & % 143.87/19.15 | ~ p2(all_2_11) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 143.87/19.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v1, v2) | ~ % 143.87/19.15 | r1(v0, v1) | ~ r1(all_2_11, v0) | p1(v1) | p2(v1)) & ! [v0: $i] % 143.87/19.15 | : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 143.87/19.15 | ~ p2(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_11, v0) | % 143.87/19.15 | p1(v1) | p2(v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 143.87/19.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | % 143.87/19.15 | ~ r1(all_2_11, v0) | p1(v1) | p2(v1) | ? [v3: $i] : ($i(v3) & % 143.87/19.15 | r1(v0, v3))))) & (p1(all_2_14) | ! [v0: $i] : ( ~ $i(v0) | ~ % 143.87/19.15 | r1(all_2_14, v0)) | (r1(all_2_13, all_2_12) & r1(all_2_14, % 143.87/19.15 | all_2_13) & ~ p1(all_2_13) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 143.87/19.15 | $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v1, % 143.87/19.15 | v2) | ~ r1(v0, v1) | ~ r1(all_2_13, v0) | p1(v1)) & ! [v0: % 143.87/19.15 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 143.87/19.15 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_13, v0) | % 143.87/19.15 | p1(v1) | ? [v3: $i] : ($i(v3) & r1(v0, v3))))) & ((r1(all_2_14, % 143.87/19.15 | all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 143.87/19.15 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) % 143.87/19.15 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 143.87/19.15 | p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~ % 143.87/19.15 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 143.87/19.15 | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) & % 143.87/19.15 | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) | % 143.87/19.15 | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) % 143.87/19.15 | & ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ % 143.87/19.15 | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) | % 143.87/19.15 | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 143.87/19.15 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | % 143.87/19.16 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ % 143.87/19.16 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ % 143.87/19.16 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : % 143.87/19.16 | ? [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, % 143.87/19.16 | v6) & ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & % 143.87/19.16 | ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ % 143.87/19.16 | p2(v8) | ~ r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | % 143.87/19.16 | (r1(v3, v6) & ~ p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ % 143.87/19.16 | $i(v9) | ~ $i(v8) | ~ p2(v8) | ~ r1(v8, v9) | ~ % 143.87/19.16 | r1(v6, v8) | p2(v9)))))) & ! [v0: $i] : ! [v1: $i] : ! % 143.87/19.16 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 143.87/19.16 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ % 143.87/19.16 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 143.87/19.16 | p2(v4) | p2(v3) | p2(v2) | ? [v5: $i] : ? [v6: $i] : ($i(v6) & % 143.87/19.16 | $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4, v5) & ~ p2(v6)) | % 143.87/19.16 | (p2(v5) & r1(v5, v6) & r1(v3, v5) & ~ p2(v6))))) & ! [v0: % 143.87/19.16 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 143.87/19.16 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 143.87/19.16 | p2(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | ~ % 143.87/19.16 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v1) | ? [v5: $i] : % 143.87/19.16 | ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4, % 143.87/19.16 | v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v1, v5) & ~ % 143.87/19.16 | p2(v6)) | (r1(v2, v5) & ~ p2(v5) & ! [v7: $i] : ! [v8: % 143.87/19.16 | $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ r1(v7, v8) % 143.87/19.16 | | ~ r1(v5, v7) | p2(v8)))))) & ! [v0: $i] : ! [v1: $i] % 143.87/19.16 | : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 143.87/19.16 | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0, % 143.87/19.16 | v1) | ~ r1(all_2_5, v0) | p2(v3) | p2(v2) | ? [v4: $i] : ? % 143.87/19.16 | [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) % 143.87/19.16 | & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! % 143.87/19.16 | [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) % 143.87/19.16 | | ~ r1(v6, v7) | ~ r1(v5, v6) | p2(v7)))))) & ! [v0: % 143.87/19.16 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 143.87/19.16 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v2, v3) | ~ % 143.87/19.16 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | ? % 143.87/19.16 | [v4: $i] : ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) % 143.87/19.16 | & r1(v3, v4) & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ % 143.87/19.16 | p2(v5) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) % 143.87/19.16 | | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | p2(v7))) | % 143.87/19.16 | (r1(v1, v4) & ~ p2(v4) & ! [v6: $i] : ! [v7: $i] : ( ~ % 143.87/19.16 | $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | ~ % 143.87/19.16 | r1(v4, v6) | p2(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! % 143.87/19.16 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ % 143.87/19.16 | r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v2) | p2(v1) % 143.87/19.16 | | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p2(v3) & % 143.87/19.16 | r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) | (p2(v3) & r1(v3, v4) % 143.87/19.16 | & r1(v1, v3) & ~ p2(v4))))) & ! [v0: $i] : ! [v1: $i] : % 143.87/19.16 | ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, % 143.87/19.16 | v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & % 143.87/19.16 | ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) | (r1(v2, v3) & % 143.87/19.16 | r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 143.87/19.16 | $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) | ~ % 143.87/19.16 | r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) & % 143.87/19.16 | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: % 143.87/19.16 | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 143.87/19.16 | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 143.87/19.16 | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : % 143.87/19.16 | ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ % 143.87/19.16 | p2(v2)))) | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( % 143.87/19.17 | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 143.87/19.17 | r1(all_2_5, v0) | p2(v1))))) | ((p2(all_2_14) | (p2(all_2_5) % 143.87/19.17 | & r1(all_2_5, all_2_4) & r1(all_2_14, all_2_5) & ~ % 143.87/19.17 | p2(all_2_4))) & ( ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 143.87/19.17 | $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_14, v0) | p2(v1) | ? [v2: % 143.87/19.17 | $i] : ? [v3: $i] : ($i(v3) & $i(v2) & p2(v2) & r1(v2, v3) & % 143.87/19.17 | r1(v1, v2) & ~ p2(v3))) | (r1(all_2_14, all_2_3) & ~ % 143.87/19.17 | p2(all_2_3) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 143.87/19.17 | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | % 143.87/19.17 | p2(v1)))))) % 143.87/19.17 | % 143.87/19.17 | ALPHA: (1) implies: % 143.87/19.17 | (2) ~ p2(all_2_1) % 143.87/19.17 | (3) r1(all_2_14, all_2_1) % 143.87/19.17 | (4) $i(all_2_5) % 143.87/19.17 | (5) $i(all_2_4) % 143.87/19.17 | (6) $i(all_2_3) % 143.87/19.17 | (7) $i(all_2_1) % 144.20/19.21 | (8) (r1(all_2_14, all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 144.20/19.21 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 144.20/19.21 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 144.20/19.21 | | ~ p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~ % 144.20/19.21 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 144.20/19.21 | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) & % 144.20/19.21 | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) | % 144.20/19.21 | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) & % 144.20/19.21 | ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ % 144.20/19.21 | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) | % 144.20/19.21 | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 144.20/19.21 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ % 144.20/19.21 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v4, % 144.20/19.21 | v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0, % 144.20/19.21 | v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : ? % 144.20/19.21 | [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, v6) & % 144.20/19.21 | ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & ! [v8: % 144.20/19.21 | $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p2(v8) | ~ % 144.20/19.21 | r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | (r1(v3, v6) & ~ % 144.20/19.21 | p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | % 144.20/19.21 | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v6, v8) | p2(v9)))))) & % 144.20/19.21 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 144.20/19.21 | ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 144.20/19.21 | p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, % 144.20/19.21 | v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? [v5: $i] % 144.20/19.21 | : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4, % 144.20/19.21 | v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, v5) & ~ % 144.20/19.21 | p2(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 144.20/19.21 | [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 144.20/19.21 | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ % 144.20/19.21 | r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v1) | % 144.20/19.21 | ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, % 144.20/19.21 | v6) & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & % 144.20/19.21 | r1(v1, v5) & ~ p2(v6)) | (r1(v2, v5) & ~ p2(v5) & ! [v7: % 144.20/19.21 | $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ % 144.20/19.21 | r1(v7, v8) | ~ r1(v5, v7) | p2(v8)))))) & ! [v0: $i] : ! % 144.20/19.21 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 144.20/19.21 | $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ % 144.20/19.21 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | p2(v2) | ? [v4: $i] : % 144.20/19.21 | ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) % 144.20/19.21 | & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: % 144.20/19.21 | $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ % 144.20/19.21 | r1(v6, v7) | ~ r1(v5, v6) | p2(v7)))))) & ! [v0: $i] : ! % 144.20/19.21 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 144.20/19.21 | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 144.20/19.21 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | ? [v4: $i] : ? [v5: % 144.20/19.21 | $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) & ~ % 144.20/19.21 | p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: $i] % 144.20/19.21 | : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ % 144.20/19.21 | r1(v6, v7) | ~ r1(v5, v6) | p2(v7))) | (r1(v1, v4) & ~ % 144.20/19.21 | p2(v4) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | % 144.20/19.21 | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v4, v6) | p2(v7)))))) & % 144.20/19.21 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 144.20/19.21 | $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, % 144.20/19.21 | v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] : ($i(v4) & % 144.20/19.21 | $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) | % 144.20/19.21 | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) & ! [v0: $i] % 144.20/19.21 | : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | % 144.20/19.21 | ~ r1(all_2_5, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & % 144.20/19.21 | $i(v2) & ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) | % 144.20/19.21 | (r1(v2, v3) & r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5: % 144.20/19.21 | $i] : ( ~ $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) | % 144.20/19.21 | ~ r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) & % 144.20/19.21 | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] % 144.20/19.21 | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 144.20/19.21 | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 144.20/19.21 | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) % 144.20/19.21 | & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2)))) | % 144.20/19.21 | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 144.20/19.21 | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 144.20/19.21 | p2(v1))))) | ((p2(all_2_14) | (p2(all_2_5) & r1(all_2_5, % 144.20/19.21 | all_2_4) & r1(all_2_14, all_2_5) & ~ p2(all_2_4))) & ( ! [v0: % 144.20/19.21 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 144.20/19.21 | r1(all_2_14, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & % 144.20/19.21 | $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) | % 144.20/19.21 | (r1(all_2_14, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] % 144.20/19.21 | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 144.20/19.21 | r1(all_2_3, v0) | p2(v1))))) % 144.20/19.22 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) | p2(v0) | ? [v1: $i] : % 144.20/19.22 | ($i(v1) & r1(v0, v1) & ~ p2(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ % 144.20/19.22 | $i(v3) | ~ $i(v2) | ~ p2(v2) | ~ r1(v2, v3) | ~ r1(v1, v2) | % 144.20/19.22 | p2(v3)))) % 144.20/19.22 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) | p2(v0) | ? [v1: $i] % 144.20/19.22 | : ? [v2: $i] : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) % 144.20/19.22 | & ~ p2(v2))) % 144.20/19.22 | % 144.20/19.22 | GROUND_INST: instantiating (9) with all_2_1, simplifying with (2), (3), (7) % 144.20/19.22 | gives: % 144.20/19.22 | (11) ? [v0: $i] : ($i(v0) & r1(all_2_1, v0) & ~ p2(v0) & ! [v1: $i] : ! % 144.20/19.22 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ p2(v1) | ~ r1(v1, v2) | ~ % 144.20/19.22 | r1(v0, v1) | p2(v2))) % 144.20/19.22 | % 144.20/19.22 | DELTA: instantiating (11) with fresh symbol all_16_0 gives: % 144.20/19.22 | (12) $i(all_16_0) & r1(all_2_1, all_16_0) & ~ p2(all_16_0) & ! [v0: $i] : % 144.20/19.22 | ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 144.20/19.22 | r1(all_16_0, v0) | p2(v1)) % 144.20/19.22 | % 144.20/19.22 | ALPHA: (12) implies: % 144.20/19.22 | (13) ~ p2(all_16_0) % 144.20/19.22 | (14) r1(all_2_1, all_16_0) % 144.20/19.22 | (15) $i(all_16_0) % 144.20/19.22 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ % 144.20/19.22 | r1(v0, v1) | ~ r1(all_16_0, v0) | p2(v1)) % 144.20/19.22 | % 144.20/19.22 | BETA: splitting (8) gives: % 144.20/19.22 | % 144.20/19.22 | Case 1: % 144.20/19.22 | | % 144.20/19.24 | | (17) r1(all_2_14, all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 144.20/19.24 | | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 144.20/19.24 | | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 144.20/19.24 | | | ~ p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~ % 144.20/19.24 | | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 144.20/19.24 | | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) & % 144.20/19.24 | | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) | % 144.20/19.24 | | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) & % 144.20/19.24 | | ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ % 144.20/19.24 | | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) | % 144.20/19.24 | | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 144.20/19.24 | | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ % 144.20/19.24 | | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v4, % 144.20/19.24 | | v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0, % 144.20/19.24 | | v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : ? % 144.20/19.24 | | [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, v6) & % 144.20/19.24 | | ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & ! [v8: % 144.20/19.24 | | $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p2(v8) | % 144.20/19.24 | | ~ r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | (r1(v3, v6) & ~ % 144.20/19.24 | | p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) % 144.20/19.24 | | | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v6, v8) | p2(v9)))))) % 144.20/19.24 | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 144.20/19.24 | | $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 144.20/19.24 | | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ % 144.20/19.24 | | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? % 144.20/19.24 | | [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) % 144.20/19.24 | | & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, % 144.20/19.24 | | v5) & ~ p2(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 144.20/19.24 | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 144.20/19.24 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v3, v4) | ~ % 144.20/19.24 | | r1(v2, v3) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 144.20/19.24 | | p2(v4) | p2(v1) | ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & % 144.20/19.24 | | ((p2(v5) & r1(v5, v6) & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & % 144.20/19.24 | | r1(v5, v6) & r1(v1, v5) & ~ p2(v6)) | (r1(v2, v5) & ~ % 144.20/19.24 | | p2(v5) & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) % 144.20/19.24 | | | ~ p2(v7) | ~ r1(v7, v8) | ~ r1(v5, v7) | p2(v8)))))) % 144.20/19.24 | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) % 144.20/19.24 | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | % 144.20/19.24 | | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | % 144.20/19.24 | | p2(v2) | ? [v4: $i] : ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & % 144.20/19.24 | | r1(v4, v5) & r1(v3, v4) & ~ p2(v5)) | (r1(v4, v5) & r1(v0, % 144.20/19.24 | | v4) & ~ p2(v5) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | % 144.20/19.24 | | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | % 144.20/19.24 | | p2(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 144.20/19.24 | | [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 144.20/19.24 | | p2(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 144.20/19.24 | | r1(all_2_5, v0) | p2(v3) | ? [v4: $i] : ? [v5: $i] : ($i(v5) & % 144.20/19.24 | | $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) & ~ p2(v5)) | % 144.20/19.24 | | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: $i] : ! [v7: % 144.20/19.24 | | $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | % 144.20/19.24 | | ~ r1(v5, v6) | p2(v7))) | (r1(v1, v4) & ~ p2(v4) & ! % 144.20/19.24 | | [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) % 144.20/19.24 | | | ~ r1(v6, v7) | ~ r1(v4, v6) | p2(v7)))))) & ! [v0: % 144.20/19.24 | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 144.20/19.24 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ % 144.20/19.24 | | r1(all_2_5, v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] : % 144.20/19.24 | | ($i(v4) & $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) % 144.20/19.24 | | | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) & ! [v0: % 144.20/19.24 | | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, % 144.20/19.24 | | v1) | ~ r1(all_2_5, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : % 144.20/19.24 | | ($i(v3) & $i(v2) & ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) % 144.20/19.24 | | | (r1(v2, v3) & r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5: % 144.20/19.24 | | $i] : ( ~ $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) | % 144.20/19.24 | | ~ r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) & % 144.20/19.24 | | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: % 144.20/19.24 | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 144.20/19.24 | | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 144.20/19.24 | | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) % 144.20/19.24 | | & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2)))) | % 144.20/19.24 | | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 144.20/19.24 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 144.20/19.24 | | p2(v1)))) % 144.20/19.24 | | % 144.20/19.24 | | ALPHA: (17) implies: % 144.20/19.24 | | (18) r1(all_2_14, all_2_5) % 144.20/19.25 | | (19) (r1(all_2_4, all_2_3) & r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! % 144.20/19.25 | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ % 144.20/19.25 | | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ % 144.20/19.25 | | $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] % 144.20/19.25 | | : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ % 144.20/19.25 | | p2(v2)))) | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ % 144.20/19.25 | | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, % 144.20/19.25 | | v0) | p2(v1))) % 144.20/19.25 | | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | % 144.20/19.25 | | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ % 144.20/19.25 | | r1(all_2_5, v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] : % 144.20/19.25 | | ($i(v4) & $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) % 144.20/19.25 | | | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) % 144.20/19.25 | | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 144.20/19.25 | | : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 144.20/19.25 | | p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, % 144.20/19.25 | | v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? [v5: % 144.20/19.25 | | $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & % 144.20/19.25 | | r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, v5) % 144.20/19.25 | | & ~ p2(v6))))) % 144.20/19.25 | | % 144.20/19.25 | | GROUND_INST: instantiating (10) with all_2_5, simplifying with (4), (18) % 144.20/19.25 | | gives: % 144.20/19.25 | | (22) p2(all_2_5) | ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) % 144.20/19.25 | | & r1(v0, v1) & r1(all_2_5, v0) & ~ p2(v1)) % 144.20/19.25 | | % 144.20/19.25 | | BETA: splitting (19) gives: % 144.20/19.25 | | % 144.20/19.25 | | Case 1: % 144.20/19.25 | | | % 144.20/19.25 | | | (23) r1(all_2_4, all_2_3) & r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! % 144.20/19.25 | | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ % 144.20/19.25 | | | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ % 144.20/19.25 | | | $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] % 144.20/19.25 | | | : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ % 144.20/19.25 | | | p2(v2))) % 144.20/19.25 | | | % 144.20/19.25 | | | ALPHA: (23) implies: % 144.20/19.25 | | | (24) ~ p2(all_2_3) % 144.20/19.25 | | | (25) r1(all_2_5, all_2_4) % 144.20/19.25 | | | (26) r1(all_2_4, all_2_3) % 144.20/19.25 | | | (27) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: % 144.20/19.25 | | | $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & % 144.20/19.25 | | | r1(v0, v1) & ~ p2(v2))) % 144.20/19.26 | | | (28) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | % 144.20/19.26 | | | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) % 144.20/19.26 | | | % 144.20/19.26 | | | GROUND_INST: instantiating (27) with all_2_4, simplifying with (5), (25) % 144.20/19.26 | | | gives: % 144.20/19.26 | | | (29) p2(all_2_4) | ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & % 144.20/19.26 | | | p2(v0) & r1(v0, v1) & r1(all_2_4, v0) & ~ p2(v1)) % 144.20/19.26 | | | % 144.20/19.26 | | | BETA: splitting (29) gives: % 144.20/19.26 | | | % 144.20/19.26 | | | Case 1: % 144.20/19.26 | | | | % 144.20/19.26 | | | | (30) p2(all_2_4) % 144.20/19.26 | | | | % 144.20/19.26 | | | | GROUND_INST: instantiating (20) with all_2_4, all_2_3, all_2_3, % 144.20/19.26 | | | | simplifying with (5), (6), (24), (25), (26), (30) gives: % 144.20/19.26 | | | | (31) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, % 144.20/19.26 | | | | v1) & r1(all_2_3, v0) & ~ p2(v1)) % 144.20/19.26 | | | | % 144.20/19.26 | | | | DELTA: instantiating (31) with fresh symbols all_130_0, all_130_1 gives: % 144.20/19.26 | | | | (32) $i(all_130_0) & $i(all_130_1) & p2(all_130_1) & r1(all_130_1, % 144.20/19.26 | | | | all_130_0) & r1(all_2_3, all_130_1) & ~ p2(all_130_0) % 144.20/19.26 | | | | % 144.20/19.26 | | | | ALPHA: (32) implies: % 144.20/19.26 | | | | (33) ~ p2(all_130_0) % 144.20/19.26 | | | | (34) r1(all_2_3, all_130_1) % 144.20/19.26 | | | | (35) r1(all_130_1, all_130_0) % 144.20/19.26 | | | | (36) p2(all_130_1) % 144.20/19.26 | | | | (37) $i(all_130_1) % 144.20/19.26 | | | | (38) $i(all_130_0) % 144.20/19.26 | | | | % 144.20/19.26 | | | | GROUND_INST: instantiating (28) with all_130_1, all_130_0, simplifying % 144.20/19.26 | | | | with (33), (34), (35), (36), (37), (38) gives: % 144.20/19.26 | | | | (39) $false % 144.20/19.26 | | | | % 144.20/19.26 | | | | CLOSE: (39) is inconsistent. % 144.20/19.26 | | | | % 144.20/19.26 | | | Case 2: % 144.20/19.26 | | | | % 144.20/19.26 | | | | (40) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, % 144.20/19.26 | | | | v1) & r1(all_2_4, v0) & ~ p2(v1)) % 144.20/19.26 | | | | % 144.20/19.26 | | | | DELTA: instantiating (40) with fresh symbols all_125_0, all_125_1 gives: % 144.20/19.26 | | | | (41) $i(all_125_0) & $i(all_125_1) & p2(all_125_1) & r1(all_125_1, % 144.20/19.26 | | | | all_125_0) & r1(all_2_4, all_125_1) & ~ p2(all_125_0) % 144.20/19.26 | | | | % 144.20/19.26 | | | | ALPHA: (41) implies: % 144.20/19.26 | | | | (42) ~ p2(all_125_0) % 144.20/19.26 | | | | (43) r1(all_2_4, all_125_1) % 144.20/19.26 | | | | (44) r1(all_125_1, all_125_0) % 144.20/19.27 | | | | (45) p2(all_125_1) % 144.20/19.27 | | | | (46) $i(all_125_1) % 144.20/19.27 | | | | (47) $i(all_125_0) % 144.20/19.27 | | | | % 144.20/19.27 | | | | GROUND_INST: instantiating (21) with all_2_4, all_125_1, all_125_0, % 144.20/19.27 | | | | all_2_3, all_2_3, simplifying with (5), (6), (24), (25), % 144.20/19.27 | | | | (26), (42), (43), (44), (45), (46), (47) gives: % 144.20/19.27 | | | | (48) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, % 144.20/19.27 | | | | v1) & r1(all_2_3, v0) & ~ p2(v1)) % 144.20/19.27 | | | | % 144.20/19.27 | | | | DELTA: instantiating (48) with fresh symbols all_132_0, all_132_1 gives: % 144.20/19.27 | | | | (49) $i(all_132_0) & $i(all_132_1) & p2(all_132_1) & r1(all_132_1, % 144.20/19.27 | | | | all_132_0) & r1(all_2_3, all_132_1) & ~ p2(all_132_0) % 144.20/19.27 | | | | % 144.20/19.27 | | | | ALPHA: (49) implies: % 144.20/19.27 | | | | (50) ~ p2(all_132_0) % 144.20/19.27 | | | | (51) r1(all_2_3, all_132_1) % 144.20/19.27 | | | | (52) r1(all_132_1, all_132_0) % 144.20/19.27 | | | | (53) p2(all_132_1) % 144.20/19.27 | | | | (54) $i(all_132_1) % 144.20/19.27 | | | | (55) $i(all_132_0) % 144.20/19.27 | | | | % 144.20/19.27 | | | | GROUND_INST: instantiating (28) with all_132_1, all_132_0, simplifying % 144.20/19.27 | | | | with (50), (51), (52), (53), (54), (55) gives: % 144.20/19.27 | | | | (56) $false % 144.20/19.27 | | | | % 144.20/19.27 | | | | CLOSE: (56) is inconsistent. % 144.20/19.27 | | | | % 144.20/19.27 | | | End of split % 144.20/19.27 | | | % 144.20/19.27 | | Case 2: % 144.20/19.27 | | | % 144.20/19.27 | | | (57) ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 144.20/19.27 | | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | % 144.20/19.27 | | | p2(v1)) % 144.20/19.27 | | | % 144.20/19.27 | | | ALPHA: (57) implies: % 144.20/19.27 | | | (58) ~ p2(all_2_5) % 144.20/19.27 | | | (59) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | % 144.20/19.27 | | | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v1)) % 144.20/19.27 | | | % 144.20/19.27 | | | BETA: splitting (22) gives: % 144.20/19.27 | | | % 144.20/19.27 | | | Case 1: % 144.20/19.27 | | | | % 144.20/19.27 | | | | (60) p2(all_2_5) % 144.20/19.27 | | | | % 144.20/19.27 | | | | PRED_UNIFY: (58), (60) imply: % 144.20/19.27 | | | | (61) $false % 144.20/19.27 | | | | % 144.20/19.27 | | | | CLOSE: (61) is inconsistent. % 144.20/19.27 | | | | % 144.20/19.27 | | | Case 2: % 144.20/19.27 | | | | % 144.20/19.27 | | | | (62) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, % 144.20/19.27 | | | | v1) & r1(all_2_5, v0) & ~ p2(v1)) % 144.20/19.27 | | | | % 144.20/19.27 | | | | DELTA: instantiating (62) with fresh symbols all_101_0, all_101_1 gives: % 144.20/19.27 | | | | (63) $i(all_101_0) & $i(all_101_1) & p2(all_101_1) & r1(all_101_1, % 144.20/19.27 | | | | all_101_0) & r1(all_2_5, all_101_1) & ~ p2(all_101_0) % 144.20/19.27 | | | | % 144.20/19.27 | | | | ALPHA: (63) implies: % 144.20/19.27 | | | | (64) ~ p2(all_101_0) % 144.20/19.27 | | | | (65) r1(all_2_5, all_101_1) % 144.20/19.27 | | | | (66) r1(all_101_1, all_101_0) % 144.20/19.27 | | | | (67) p2(all_101_1) % 144.20/19.27 | | | | (68) $i(all_101_1) % 144.20/19.27 | | | | (69) $i(all_101_0) % 144.20/19.27 | | | | % 144.20/19.28 | | | | GROUND_INST: instantiating (59) with all_101_1, all_101_0, simplifying % 144.20/19.28 | | | | with (64), (65), (66), (67), (68), (69) gives: % 144.20/19.28 | | | | (70) $false % 144.20/19.28 | | | | % 144.20/19.28 | | | | CLOSE: (70) is inconsistent. % 144.20/19.28 | | | | % 144.20/19.28 | | | End of split % 144.20/19.28 | | | % 144.20/19.28 | | End of split % 144.20/19.28 | | % 144.20/19.28 | Case 2: % 144.20/19.28 | | % 144.20/19.28 | | (71) (p2(all_2_14) | (p2(all_2_5) & r1(all_2_5, all_2_4) & r1(all_2_14, % 144.20/19.28 | | all_2_5) & ~ p2(all_2_4))) & ( ! [v0: $i] : ! [v1: $i] : ( ~ % 144.20/19.28 | | $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_14, v0) | % 144.20/19.28 | | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & p2(v2) & % 144.20/19.28 | | r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) | (r1(all_2_14, all_2_3) % 144.20/19.28 | | & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 144.20/19.28 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | % 144.20/19.28 | | p2(v1)))) % 144.20/19.28 | | % 144.20/19.28 | | ALPHA: (71) implies: % 144.20/19.28 | | (72) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | % 144.20/19.28 | | ~ r1(all_2_14, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) % 144.20/19.28 | | & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) | % 144.20/19.28 | | (r1(all_2_14, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] % 144.20/19.28 | | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 144.20/19.28 | | r1(all_2_3, v0) | p2(v1))) % 144.20/19.28 | | % 144.20/19.28 | | BETA: splitting (72) gives: % 144.20/19.28 | | % 144.20/19.28 | | Case 1: % 144.20/19.28 | | | % 144.20/19.28 | | | (73) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) % 144.20/19.28 | | | | ~ r1(all_2_14, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : % 144.20/19.28 | | | ($i(v3) & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ % 144.20/19.28 | | | p2(v3))) % 144.20/19.28 | | | % 144.20/19.28 | | | GROUND_INST: instantiating (73) with all_2_1, all_16_0, simplifying with % 144.20/19.28 | | | (3), (7), (13), (14), (15) gives: % 144.20/19.28 | | | (74) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, v1) % 144.20/19.28 | | | & r1(all_16_0, v0) & ~ p2(v1)) % 144.20/19.28 | | | % 144.20/19.28 | | | DELTA: instantiating (74) with fresh symbols all_100_0, all_100_1 gives: % 144.20/19.28 | | | (75) $i(all_100_0) & $i(all_100_1) & p2(all_100_1) & r1(all_100_1, % 144.20/19.28 | | | all_100_0) & r1(all_16_0, all_100_1) & ~ p2(all_100_0) % 144.20/19.28 | | | % 144.20/19.28 | | | ALPHA: (75) implies: % 144.20/19.28 | | | (76) ~ p2(all_100_0) % 144.20/19.28 | | | (77) r1(all_16_0, all_100_1) % 144.20/19.28 | | | (78) r1(all_100_1, all_100_0) % 144.20/19.28 | | | (79) p2(all_100_1) % 144.20/19.28 | | | (80) $i(all_100_1) % 144.20/19.28 | | | (81) $i(all_100_0) % 144.20/19.28 | | | % 144.20/19.28 | | | GROUND_INST: instantiating (16) with all_100_1, all_100_0, simplifying % 144.20/19.28 | | | with (76), (77), (78), (79), (80), (81) gives: % 144.20/19.28 | | | (82) $false % 144.20/19.28 | | | % 144.20/19.28 | | | CLOSE: (82) is inconsistent. % 144.20/19.28 | | | % 144.20/19.28 | | Case 2: % 144.20/19.28 | | | % 144.20/19.29 | | | (83) r1(all_2_14, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] % 144.20/19.29 | | | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ % 144.20/19.29 | | | r1(all_2_3, v0) | p2(v1)) % 144.20/19.29 | | | % 144.20/19.29 | | | ALPHA: (83) implies: % 144.20/19.29 | | | (84) ~ p2(all_2_3) % 144.20/19.29 | | | (85) r1(all_2_14, all_2_3) % 144.20/19.29 | | | (86) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | % 144.20/19.29 | | | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) % 144.20/19.29 | | | % 144.20/19.29 | | | GROUND_INST: instantiating (10) with all_2_3, simplifying with (6), (84), % 144.20/19.29 | | | (85) gives: % 144.20/19.29 | | | (87) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, v1) % 144.20/19.29 | | | & r1(all_2_3, v0) & ~ p2(v1)) % 144.20/19.29 | | | % 144.20/19.29 | | | DELTA: instantiating (87) with fresh symbols all_104_0, all_104_1 gives: % 144.20/19.29 | | | (88) $i(all_104_0) & $i(all_104_1) & p2(all_104_1) & r1(all_104_1, % 144.20/19.29 | | | all_104_0) & r1(all_2_3, all_104_1) & ~ p2(all_104_0) % 144.20/19.29 | | | % 144.20/19.29 | | | ALPHA: (88) implies: % 144.20/19.29 | | | (89) ~ p2(all_104_0) % 144.20/19.29 | | | (90) r1(all_2_3, all_104_1) % 144.20/19.29 | | | (91) r1(all_104_1, all_104_0) % 144.20/19.29 | | | (92) p2(all_104_1) % 144.20/19.29 | | | (93) $i(all_104_1) % 144.20/19.29 | | | (94) $i(all_104_0) % 144.20/19.29 | | | % 144.20/19.29 | | | GROUND_INST: instantiating (86) with all_104_1, all_104_0, simplifying % 144.20/19.29 | | | with (89), (90), (91), (92), (93), (94) gives: % 144.20/19.29 | | | (95) $false % 144.20/19.29 | | | % 144.20/19.29 | | | CLOSE: (95) is inconsistent. % 144.20/19.29 | | | % 144.20/19.29 | | End of split % 144.20/19.29 | | % 144.20/19.29 | End of split % 144.20/19.29 | % 144.20/19.29 End of proof % 144.20/19.29 % SZS output end Proof for theBenchmark % 144.20/19.29 % 144.20/19.29 18719ms %------------------------------------------------------------------------------