%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG056+1 : TPTP v8.1.2. Released v2.7.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:36:02 EDT 2023 % Result : Theorem 15.06s 2.87s % Output : Proof 89.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG056+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n016.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Mon Aug 28 04:13:14 EDT 2023 % 0.17/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.55/1.69 Prover 1: Preprocessing ... % 6.55/1.70 Prover 4: Preprocessing ... % 7.33/1.74 Prover 0: Preprocessing ... % 7.33/1.74 Prover 2: Preprocessing ... % 7.33/1.74 Prover 6: Preprocessing ... % 7.33/1.74 Prover 5: Preprocessing ... % 7.33/1.74 Prover 3: Preprocessing ... % 11.05/2.30 Prover 4: Constructing countermodel ... % 11.05/2.30 Prover 1: Constructing countermodel ... % 11.05/2.31 Prover 2: Constructing countermodel ... % 11.05/2.31 Prover 3: Constructing countermodel ... % 12.25/2.38 Prover 6: Constructing countermodel ... % 12.82/2.45 Prover 0: Constructing countermodel ... % 15.06/2.86 Prover 6: proved (2237ms) % 15.06/2.87 % 15.06/2.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.06/2.87 % 15.06/2.88 Prover 0: stopped % 15.06/2.89 Prover 2: stopped % 15.06/2.89 Prover 3: stopped % 15.06/2.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.06/2.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.06/2.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.06/2.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.01/3.07 Prover 5: Constructing countermodel ... % 17.54/3.09 Prover 5: stopped % 17.54/3.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.21/3.18 Prover 11: Preprocessing ... % 18.41/3.21 Prover 7: Preprocessing ... % 18.71/3.24 Prover 8: Preprocessing ... % 18.71/3.26 Prover 10: Preprocessing ... % 19.29/3.32 Prover 13: Preprocessing ... % 19.29/3.33 Prover 8: Constructing countermodel ... % 19.81/3.44 Prover 7: Constructing countermodel ... % 20.52/3.48 Prover 11: Constructing countermodel ... % 20.71/3.56 Prover 13: Constructing countermodel ... % 20.71/3.59 Prover 10: Constructing countermodel ... % 63.29/9.13 Prover 13: stopped % 63.29/9.15 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 64.62/9.33 Prover 16: Preprocessing ... % 66.52/9.57 Prover 16: Constructing countermodel ... % 84.39/11.93 Prover 7: Found proof (size 74165) % 84.39/11.93 Prover 7: proved (9013ms) % 84.39/11.93 Prover 11: stopped % 84.39/11.93 Prover 4: stopped % 84.39/11.93 Prover 16: stopped % 84.39/11.93 Prover 8: stopped % 84.39/11.93 Prover 1: stopped % 84.39/11.93 Prover 10: stopped % 84.39/11.94 % 84.39/11.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 84.39/11.94 % 85.53/12.07 % SZS output start Proof for theBenchmark % 85.53/12.07 Assumptions after simplification: % 85.53/12.07 --------------------------------- % 85.53/12.07 % 85.53/12.07 (ax1) % 85.53/12.13 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 85.53/12.13 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 85.53/12.13 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 85.53/12.13 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 85.53/12.13 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 85.53/12.13 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 85.53/12.13 v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 85.53/12.13 v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, e4) = % 85.53/12.13 v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = % 85.53/12.13 v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 % 85.53/12.13 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 85.53/12.13 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 85.53/12.13 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 85.53/12.13 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 85.53/12.13 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | % 85.53/12.13 v24 = e2 | v24 = e1 | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = % 85.53/12.13 e1 | v23 = e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & % 85.53/12.13 (v21 = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 = % 85.53/12.13 e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 = e2 | % 85.53/12.13 v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1 | v18 = % 85.53/12.13 e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 = e0) & (v16 = e4 | % 85.53/12.13 v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & (v15 = e4 | v15 = e3 | v15 = % 85.53/12.13 e2 | v15 = e1 | v15 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1 | % 85.53/12.13 v14 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 % 85.53/12.13 = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | % 85.53/12.13 v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = % 85.53/12.13 e1 | v10 = e0) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = % 85.53/12.13 e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 % 85.53/12.13 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & % 85.53/12.13 (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e3 | v4 % 85.53/12.13 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = % 85.53/12.13 e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 = % 85.53/12.13 e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 % 85.53/12.13 | v0 = e0)) % 85.53/12.13 % 85.53/12.13 (ax2) % 85.53/12.13 op(unit, e4) = e4 & op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 % 85.53/12.13 & op(unit, e0) = e0 & op(e4, unit) = e4 & op(e3, unit) = e3 & op(e2, unit) = % 85.53/12.13 e2 & op(e1, unit) = e1 & op(e0, unit) = e0 & $i(unit) & $i(e4) & $i(e3) & % 85.53/12.13 $i(e2) & $i(e1) & $i(e0) & (unit = e4 | unit = e3 | unit = e2 | unit = e1 | % 85.53/12.13 unit = e0) % 85.53/12.13 % 85.53/12.13 (ax3) % 85.98/12.18 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 85.98/12.18 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 85.98/12.18 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 85.98/12.18 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 85.98/12.18 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 85.98/12.18 [v23: $i] : ? [v24: $i] : (((v24 = e4 & op(e4, e4) = e4) | (v23 = e4 & op(e4, % 85.98/12.18 e3) = e4) | (v20 = e4 & op(e4, e2) = e4) | (v15 = e4 & op(e4, e1) = % 85.98/12.18 e4) | (v8 = e4 & op(e4, e0) = e4)) & ((v24 = e4 & op(e4, e4) = e4) | % 85.98/12.18 (v22 = e4 & op(e3, e4) = e4) | (v18 = e4 & op(e2, e4) = e4) | (v12 = e4 & % 85.98/12.18 op(e1, e4) = e4) | (v4 = e4 & op(e0, e4) = e4)) & ((v24 = e3 & op(e4, % 85.98/12.18 e4) = e3) | (v23 = e3 & op(e4, e3) = e3) | (v20 = e3 & op(e4, e2) = % 85.98/12.18 e3) | (v15 = e3 & op(e4, e1) = e3) | (v8 = e3 & op(e4, e0) = e3)) & % 85.98/12.18 ((v24 = e3 & op(e4, e4) = e3) | (v22 = e3 & op(e3, e4) = e3) | (v18 = e3 & % 85.98/12.18 op(e2, e4) = e3) | (v12 = e3 & op(e1, e4) = e3) | (v4 = e3 & op(e0, e4) % 85.98/12.18 = e3)) & ((v24 = e2 & op(e4, e4) = e2) | (v23 = e2 & op(e4, e3) = e2) | % 85.98/12.18 (v20 = e2 & op(e4, e2) = e2) | (v15 = e2 & op(e4, e1) = e2) | (v8 = e2 & % 85.98/12.18 op(e4, e0) = e2)) & ((v24 = e2 & op(e4, e4) = e2) | (v22 = e2 & op(e3, % 85.98/12.18 e4) = e2) | (v18 = e2 & op(e2, e4) = e2) | (v12 = e2 & op(e1, e4) = % 85.98/12.18 e2) | (v4 = e2 & op(e0, e4) = e2)) & ((v24 = e1 & op(e4, e4) = e1) | % 85.98/12.18 (v23 = e1 & op(e4, e3) = e1) | (v20 = e1 & op(e4, e2) = e1) | (v15 = e1 & % 85.98/12.18 op(e4, e1) = e1) | (v8 = e1 & op(e4, e0) = e1)) & ((v24 = e1 & op(e4, % 85.98/12.18 e4) = e1) | (v22 = e1 & op(e3, e4) = e1) | (v18 = e1 & op(e2, e4) = % 85.98/12.18 e1) | (v12 = e1 & op(e1, e4) = e1) | (v4 = e1 & op(e0, e4) = e1)) & % 85.98/12.18 ((v24 = e0 & op(e4, e4) = e0) | (v23 = e0 & op(e4, e3) = e0) | (v20 = e0 & % 85.98/12.18 op(e4, e2) = e0) | (v15 = e0 & op(e4, e1) = e0) | (v8 = e0 & op(e4, e0) % 85.98/12.18 = e0)) & ((v24 = e0 & op(e4, e4) = e0) | (v22 = e0 & op(e3, e4) = e0) | % 85.98/12.18 (v18 = e0 & op(e2, e4) = e0) | (v12 = e0 & op(e1, e4) = e0) | (v4 = e0 & % 85.98/12.18 op(e0, e4) = e0)) & ((v23 = e4 & op(e4, e3) = e4) | (v21 = e4 & op(e3, % 85.98/12.18 e3) = e4) | (v17 = e4 & op(e2, e3) = e4) | (v11 = e4 & op(e1, e3) = % 85.98/12.18 e4) | (v3 = e4 & op(e0, e3) = e4)) & ((v23 = e3 & op(e4, e3) = e3) | % 85.98/12.18 (v21 = e3 & op(e3, e3) = e3) | (v17 = e3 & op(e2, e3) = e3) | (v11 = e3 & % 85.98/12.18 op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v23 = e2 & op(e4, % 85.98/12.18 e3) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v17 = e2 & op(e2, e3) = % 85.98/12.18 e2) | (v11 = e2 & op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & % 85.98/12.18 ((v23 = e1 & op(e4, e3) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v17 = e1 & % 85.98/12.18 op(e2, e3) = e1) | (v11 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) % 85.98/12.18 = e1)) & ((v23 = e0 & op(e4, e3) = e0) | (v21 = e0 & op(e3, e3) = e0) | % 85.98/12.18 (v17 = e0 & op(e2, e3) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v3 = e0 & % 85.98/12.18 op(e0, e3) = e0)) & ((v22 = e4 & op(e3, e4) = e4) | (v21 = e4 & op(e3, % 85.98/12.18 e3) = e4) | (v19 = e4 & op(e3, e2) = e4) | (v14 = e4 & op(e3, e1) = % 85.98/12.18 e4) | (v7 = e4 & op(e3, e0) = e4)) & ((v22 = e3 & op(e3, e4) = e3) | % 85.98/12.18 (v21 = e3 & op(e3, e3) = e3) | (v19 = e3 & op(e3, e2) = e3) | (v14 = e3 & % 85.98/12.18 op(e3, e1) = e3) | (v7 = e3 & op(e3, e0) = e3)) & ((v22 = e2 & op(e3, % 85.98/12.18 e4) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v19 = e2 & op(e3, e2) = % 85.98/12.18 e2) | (v14 = e2 & op(e3, e1) = e2) | (v7 = e2 & op(e3, e0) = e2)) & % 85.98/12.18 ((v22 = e1 & op(e3, e4) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v19 = e1 & % 85.98/12.18 op(e3, e2) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v7 = e1 & op(e3, e0) % 85.98/12.18 = e1)) & ((v22 = e0 & op(e3, e4) = e0) | (v21 = e0 & op(e3, e3) = e0) | % 85.98/12.18 (v19 = e0 & op(e3, e2) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v7 = e0 & % 85.98/12.18 op(e3, e0) = e0)) & ((v20 = e4 & op(e4, e2) = e4) | (v19 = e4 & op(e3, % 85.98/12.18 e2) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v10 = e4 & op(e1, e2) = % 85.98/12.18 e4) | (v2 = e4 & op(e0, e2) = e4)) & ((v20 = e3 & op(e4, e2) = e3) | % 85.98/12.18 (v19 = e3 & op(e3, e2) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v10 = e3 & % 85.98/12.18 op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v20 = e2 & op(e4, % 85.98/12.18 e2) = e2) | (v19 = e2 & op(e3, e2) = e2) | (v16 = e2 & op(e2, e2) = % 85.98/12.18 e2) | (v10 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & % 85.98/12.18 ((v20 = e1 & op(e4, e2) = e1) | (v19 = e1 & op(e3, e2) = e1) | (v16 = e1 & % 85.98/12.18 op(e2, e2) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) % 85.98/12.18 = e1)) & ((v20 = e0 & op(e4, e2) = e0) | (v19 = e0 & op(e3, e2) = e0) | % 85.98/12.18 (v16 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e1, e2) = e0) | (v2 = e0 & % 85.98/12.18 op(e0, e2) = e0)) & ((v18 = e4 & op(e2, e4) = e4) | (v17 = e4 & op(e2, % 85.98/12.18 e3) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v13 = e4 & op(e2, e1) = % 85.98/12.18 e4) | (v6 = e4 & op(e2, e0) = e4)) & ((v18 = e3 & op(e2, e4) = e3) | % 85.98/12.18 (v17 = e3 & op(e2, e3) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v13 = e3 & % 85.98/12.18 op(e2, e1) = e3) | (v6 = e3 & op(e2, e0) = e3)) & ((v18 = e2 & op(e2, % 85.98/12.18 e4) = e2) | (v17 = e2 & op(e2, e3) = e2) | (v16 = e2 & op(e2, e2) = % 85.98/12.18 e2) | (v13 = e2 & op(e2, e1) = e2) | (v6 = e2 & op(e2, e0) = e2)) & % 85.98/12.18 ((v18 = e1 & op(e2, e4) = e1) | (v17 = e1 & op(e2, e3) = e1) | (v16 = e1 & % 85.98/12.18 op(e2, e2) = e1) | (v13 = e1 & op(e2, e1) = e1) | (v6 = e1 & op(e2, e0) % 85.98/12.18 = e1)) & ((v18 = e0 & op(e2, e4) = e0) | (v17 = e0 & op(e2, e3) = e0) | % 85.98/12.18 (v16 = e0 & op(e2, e2) = e0) | (v13 = e0 & op(e2, e1) = e0) | (v6 = e0 & % 85.98/12.18 op(e2, e0) = e0)) & ((v15 = e4 & op(e4, e1) = e4) | (v14 = e4 & op(e3, % 85.98/12.18 e1) = e4) | (v13 = e4 & op(e2, e1) = e4) | (v9 = e4 & op(e1, e1) = e4) % 85.98/12.18 | (v1 = e4 & op(e0, e1) = e4)) & ((v15 = e3 & op(e4, e1) = e3) | (v14 = e3 % 85.98/12.18 & op(e3, e1) = e3) | (v13 = e3 & op(e2, e1) = e3) | (v9 = e3 & op(e1, % 85.98/12.18 e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v15 = e2 & op(e4, e1) = % 85.98/12.18 e2) | (v14 = e2 & op(e3, e1) = e2) | (v13 = e2 & op(e2, e1) = e2) | (v9 % 85.98/12.18 = e2 & op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v15 = e1 & % 85.98/12.18 op(e4, e1) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v13 = e1 & op(e2, e1) % 85.98/12.18 = e1) | (v9 = e1 & op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & % 85.98/12.18 ((v15 = e0 & op(e4, e1) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v13 = e0 & % 85.98/12.18 op(e2, e1) = e0) | (v9 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = % 85.98/12.18 e0)) & ((v12 = e4 & op(e1, e4) = e4) | (v11 = e4 & op(e1, e3) = e4) | % 85.98/12.18 (v10 = e4 & op(e1, e2) = e4) | (v9 = e4 & op(e1, e1) = e4) | (v5 = e4 & % 85.98/12.18 op(e1, e0) = e4)) & ((v12 = e3 & op(e1, e4) = e3) | (v11 = e3 & op(e1, % 85.98/12.18 e3) = e3) | (v10 = e3 & op(e1, e2) = e3) | (v9 = e3 & op(e1, e1) = e3) % 85.98/12.18 | (v5 = e3 & op(e1, e0) = e3)) & ((v12 = e2 & op(e1, e4) = e2) | (v11 = e2 % 85.98/12.18 & op(e1, e3) = e2) | (v10 = e2 & op(e1, e2) = e2) | (v9 = e2 & op(e1, % 85.98/12.18 e1) = e2) | (v5 = e2 & op(e1, e0) = e2)) & ((v12 = e1 & op(e1, e4) = % 85.98/12.18 e1) | (v11 = e1 & op(e1, e3) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v9 % 85.98/12.18 = e1 & op(e1, e1) = e1) | (v5 = e1 & op(e1, e0) = e1)) & ((v12 = e0 & % 85.98/12.18 op(e1, e4) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v10 = e0 & op(e1, e2) % 85.98/12.18 = e0) | (v9 = e0 & op(e1, e1) = e0) | (v5 = e0 & op(e1, e0) = e0)) & % 85.98/12.18 ((v8 = e4 & op(e4, e0) = e4) | (v7 = e4 & op(e3, e0) = e4) | (v6 = e4 & % 85.98/12.18 op(e2, e0) = e4) | (v5 = e4 & op(e1, e0) = e4) | (v0 = e4 & op(e0, e0) = % 85.98/12.18 e4)) & ((v8 = e3 & op(e4, e0) = e3) | (v7 = e3 & op(e3, e0) = e3) | (v6 % 85.98/12.18 = e3 & op(e2, e0) = e3) | (v5 = e3 & op(e1, e0) = e3) | (v0 = e3 & % 85.98/12.18 op(e0, e0) = e3)) & ((v8 = e2 & op(e4, e0) = e2) | (v7 = e2 & op(e3, e0) % 85.98/12.18 = e2) | (v6 = e2 & op(e2, e0) = e2) | (v5 = e2 & op(e1, e0) = e2) | (v0 % 85.98/12.18 = e2 & op(e0, e0) = e2)) & ((v8 = e1 & op(e4, e0) = e1) | (v7 = e1 & % 85.98/12.18 op(e3, e0) = e1) | (v6 = e1 & op(e2, e0) = e1) | (v5 = e1 & op(e1, e0) = % 85.98/12.18 e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v4 = e4 & op(e0, e4) = e4) | (v3 % 85.98/12.18 = e4 & op(e0, e3) = e4) | (v2 = e4 & op(e0, e2) = e4) | (v1 = e4 & % 85.98/12.18 op(e0, e1) = e4) | (v0 = e4 & op(e0, e0) = e4)) & ((v4 = e3 & op(e0, e4) % 85.98/12.18 = e3) | (v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 % 85.98/12.18 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v4 = e2 & % 85.98/12.18 op(e0, e4) = e2) | (v3 = e2 & op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = % 85.98/12.18 e2) | (v1 = e2 & op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v4 % 85.98/12.18 = e1 & op(e0, e4) = e1) | (v3 = e1 & op(e0, e3) = e1) | (v2 = e1 & % 85.98/12.18 op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = % 85.98/12.18 e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v8 = e0 & op(e4, e0) = e0) | % 85.98/12.18 (v7 = e0 & op(e3, e0) = e0) | (v6 = e0 & op(e2, e0) = e0) | (v5 = e0 & % 85.98/12.18 op(e1, e0) = e0)) & ((v4 = e0 & op(e0, e4) = e0) | (v3 = e0 & op(e0, % 85.98/12.18 e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 & op(e0, e1) = % 85.98/12.18 e0))))) % 85.98/12.18 % 85.98/12.18 (ax4) % 85.98/12.19 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 85.98/12.19 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 85.98/12.19 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 85.98/12.19 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 85.98/12.19 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 85.98/12.19 [v23: $i] : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & % 85.98/12.19 ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 = % 85.98/12.19 v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 = v18) & % 85.98/12.19 ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = v21) & ~ (v22 = % 85.98/12.19 v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = v7) & ~ (v22 = v2) & % 85.98/12.19 ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = v11) & ~ (v21 = v6) & ~ (v21 = % 85.98/12.19 v1) & ~ (v20 = v15) & ~ (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ % 85.98/12.19 (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = % 85.98/12.19 v14) & ~ (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & % 85.98/12.19 ~ (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 85.98/12.19 v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = v2) & % 85.98/12.19 ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = v1) & ~ (v15 = % 85.98/12.19 v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = v13) & ~ (v14 = v12) & % 85.98/12.19 ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = v9) & ~ (v14 = v4) & ~ (v13 = % 85.98/12.19 v12) & ~ (v13 = v11) & ~ (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) & % 85.98/12.19 ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = % 85.98/12.19 v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ % 85.98/12.19 (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ % 85.98/12.19 (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~ % 85.98/12.19 (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~ % 85.98/12.19 (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ % 85.98/12.19 (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & % 85.98/12.19 op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, e2) = v14 & op(e4, e1) = v9 & % 85.98/12.19 op(e4, e0) = v4 & op(e3, e4) = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 & % 85.98/12.19 op(e3, e1) = v8 & op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & % 85.98/12.19 op(e2, e2) = v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & % 85.98/12.19 op(e1, e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & % 85.98/12.19 op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & % 85.98/12.19 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) % 85.98/12.19 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 85.98/12.19 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 85.98/12.19 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 85.98/12.19 % 85.98/12.19 (ax5) % 85.98/12.19 ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ % 85.98/12.19 (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & $i(e4) % 85.98/12.19 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 85.98/12.19 % 85.98/12.19 (ax6) % 85.98/12.19 op(e4, e4) = e0 & op(e3, e4) = e1 & op(e2, e4) = e3 & op(e2, e2) = e4 & $i(e4) % 85.98/12.19 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 85.98/12.19 % 85.98/12.19 (co1) % 86.22/12.21 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 86.22/12.21 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 86.22/12.21 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 86.22/12.21 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 86.22/12.21 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 86.22/12.21 [v23: $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? % 86.22/12.21 [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? % 86.22/12.21 [v33: $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] : ? % 86.22/12.21 [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: $i] : ? % 86.22/12.21 [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? [v47: $i] : ? % 86.22/12.21 [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] : ? [v52: $i] : ? % 86.22/12.21 [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: $i] : ? [v57: $i] : ? % 86.22/12.21 [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? [v61: $i] : ? [v62: $i] : ? % 86.22/12.21 [v63: $i] : ? [v64: $i] : (((v64 = e3 & v48 = e4 & ~ (v61 = e3) & op(e4, e4) % 86.22/12.21 = e3 & op(e3, e4) = v61 & op(e3, e3) = e4 & $i(v61)) | (v64 = e3 & v48 = % 86.22/12.21 e4 & ~ (v49 = e4) & op(e4, e4) = e3 & op(e4, e3) = v49 & op(e3, e3) = % 86.22/12.21 e4 & $i(v49)) | (v64 = e2 & v32 = e4 & ~ (v58 = e2) & op(e4, e4) = e2 & % 86.22/12.21 op(e2, e4) = v58 & op(e2, e2) = e4 & $i(v58)) | (v64 = e2 & v32 = e4 & % 86.22/12.21 ~ (v36 = e4) & op(e4, e4) = e2 & op(e4, e2) = v36 & op(e2, e2) = e4 & % 86.22/12.21 $i(v36)) | (v64 = e1 & v16 = e4 & ~ (v55 = e1) & op(e4, e4) = e1 & % 86.22/12.21 op(e1, e4) = v55 & op(e1, e1) = e4 & $i(v55)) | (v64 = e1 & v16 = e4 & % 86.22/12.21 ~ (v23 = e4) & op(e4, e4) = e1 & op(e4, e1) = v23 & op(e1, e1) = e4 & % 86.22/12.21 $i(v23)) | (v64 = e0 & v0 = e4 & ~ (v10 = e4) & op(e4, e4) = e0 & % 86.22/12.21 op(e4, e0) = v10 & op(e0, e0) = e4 & $i(v10)) | (v48 = e2 & v32 = e3 & % 86.22/12.21 ~ (v45 = e2) & op(e3, e3) = e2 & op(e2, e3) = v45 & op(e2, e2) = e3 & % 86.22/12.21 $i(v45)) | (v48 = e2 & v32 = e3 & ~ (v33 = e3) & op(e3, e3) = e2 & % 86.22/12.21 op(e3, e2) = v33 & op(e2, e2) = e3 & $i(v33)) | (v48 = e1 & v16 = e3 & % 86.22/12.21 ~ (v42 = e1) & op(e3, e3) = e1 & op(e1, e3) = v42 & op(e1, e1) = e3 & % 86.22/12.21 $i(v42)) | (v48 = e1 & v16 = e3 & ~ (v20 = e3) & op(e3, e3) = e1 & % 86.22/12.21 op(e3, e1) = v20 & op(e1, e1) = e3 & $i(v20)) | (v48 = e0 & v0 = e3 & ~ % 86.22/12.21 (v7 = e3) & op(e3, e3) = e0 & op(e3, e0) = v7 & op(e0, e0) = e3 & % 86.22/12.21 $i(v7)) | (v32 = e1 & v16 = e2 & ~ (v29 = e1) & op(e2, e2) = e1 & % 86.22/12.21 op(e1, e2) = v29 & op(e1, e1) = e2 & $i(v29)) | (v32 = e1 & v16 = e2 & % 86.22/12.21 ~ (v17 = e2) & op(e2, e2) = e1 & op(e2, e1) = v17 & op(e1, e1) = e2 & % 86.22/12.21 $i(v17)) | (v32 = e0 & v0 = e2 & ~ (v4 = e2) & op(e2, e2) = e0 & op(e2, % 86.22/12.21 e0) = v4 & op(e0, e0) = e2 & $i(v4)) | (op(e0, e0) = v0 & $i(v0) & % 86.22/12.21 ((v64 = e0 & v0 = e4 & ~ (v52 = e0) & op(e4, e4) = e0 & op(e0, e4) = % 86.22/12.21 v52 & $i(v52)) | (v48 = e0 & v0 = e3 & ~ (v39 = e0) & op(e3, e3) = % 86.22/12.21 e0 & op(e0, e3) = v39 & $i(v39)) | (v32 = e0 & v0 = e2 & ~ (v26 = % 86.22/12.21 e0) & op(e2, e2) = e0 & op(e0, e2) = v26 & $i(v26)) | (v16 = e0 & % 86.22/12.21 v0 = e1 & ~ (v13 = e0) & op(e1, e1) = e0 & op(e0, e1) = v13 & % 86.22/12.21 $i(v13)) | (v16 = e0 & v0 = e1 & ~ (v1 = e1) & op(e1, e1) = e0 & % 86.22/12.21 op(e1, e0) = v1 & $i(v1))))) & ((v63 = e3 & ~ (v62 = e4) & op(e4, % 86.22/12.21 v61) = e3 & op(e3, v61) = v62 & op(e3, e4) = v61 & $i(v62) & $i(v61)) % 86.22/12.21 | (v60 = e2 & ~ (v59 = e4) & op(e4, v58) = e2 & op(e2, v58) = v59 & % 86.22/12.21 op(e2, e4) = v58 & $i(v59) & $i(v58)) | (v57 = e1 & ~ (v56 = e4) & % 86.22/12.21 op(e4, v55) = e1 & op(e1, v55) = v56 & op(e1, e4) = v55 & $i(v56) & % 86.22/12.21 $i(v55)) | (v54 = e0 & ~ (v53 = e4) & op(e4, v52) = e0 & op(e0, v52) = % 86.22/12.21 v53 & op(e0, e4) = v52 & $i(v53) & $i(v52))) & ((v51 = e4 & ~ (v50 = % 86.22/12.21 e3) & op(e4, v49) = v50 & op(e4, e3) = v49 & op(e3, v49) = e4 & % 86.22/12.21 $i(v50) & $i(v49)) | (v47 = e2 & ~ (v46 = e3) & op(e3, v45) = e2 & % 86.22/12.21 op(e2, v45) = v46 & op(e2, e3) = v45 & $i(v46) & $i(v45)) | (v44 = e1 & % 86.22/12.21 ~ (v43 = e3) & op(e3, v42) = e1 & op(e1, v42) = v43 & op(e1, e3) = v42 & % 86.22/12.21 $i(v43) & $i(v42)) | (v41 = e0 & ~ (v40 = e3) & op(e3, v39) = e0 & % 86.22/12.21 op(e0, v39) = v40 & op(e0, e3) = v39 & $i(v40) & $i(v39))) & ((v38 = e4 % 86.22/12.21 & ~ (v37 = e2) & op(e4, v36) = v37 & op(e4, e2) = v36 & op(e2, v36) = % 86.22/12.21 e4 & $i(v37) & $i(v36)) | (v35 = e3 & ~ (v34 = e2) & op(e3, v33) = v34 % 86.22/12.21 & op(e3, e2) = v33 & op(e2, v33) = e3 & $i(v34) & $i(v33)) | (v31 = e1 & % 86.22/12.21 ~ (v30 = e2) & op(e2, v29) = e1 & op(e1, v29) = v30 & op(e1, e2) = v29 % 86.22/12.21 & $i(v30) & $i(v29)) | (v28 = e0 & ~ (v27 = e2) & op(e2, v26) = e0 & % 86.22/12.21 op(e0, v26) = v27 & op(e0, e2) = v26 & $i(v27) & $i(v26))) & ((v25 = e4 % 86.22/12.21 & ~ (v24 = e1) & op(e4, v23) = v24 & op(e4, e1) = v23 & op(e1, v23) = % 86.22/12.21 e4 & $i(v24) & $i(v23)) | (v22 = e3 & ~ (v21 = e1) & op(e3, v20) = v21 % 86.22/12.21 & op(e3, e1) = v20 & op(e1, v20) = e3 & $i(v21) & $i(v20)) | (v19 = e2 & % 86.22/12.21 ~ (v18 = e1) & op(e2, v17) = v18 & op(e2, e1) = v17 & op(e1, v17) = e2 % 86.22/12.21 & $i(v18) & $i(v17)) | (v15 = e0 & ~ (v14 = e1) & op(e1, v13) = e0 & % 86.22/12.21 op(e0, v13) = v14 & op(e0, e1) = v13 & $i(v14) & $i(v13))) & ((v12 = e4 % 86.22/12.21 & ~ (v11 = e0) & op(e4, v10) = v11 & op(e4, e0) = v10 & op(e0, v10) = % 86.22/12.21 e4 & $i(v11) & $i(v10)) | (v9 = e3 & ~ (v8 = e0) & op(e3, v7) = v8 & % 86.22/12.21 op(e3, e0) = v7 & op(e0, v7) = e3 & $i(v8) & $i(v7)) | (v6 = e2 & ~ (v5 % 86.22/12.21 = e0) & op(e2, v4) = v5 & op(e2, e0) = v4 & op(e0, v4) = e2 & $i(v5) & % 86.22/12.21 $i(v4)) | (v3 = e1 & ~ (v2 = e0) & op(e1, v1) = v2 & op(e1, e0) = v1 & % 86.22/12.21 op(e0, v1) = e1 & $i(v2) & $i(v1)))) % 86.22/12.21 % 86.22/12.21 (function-axioms) % 86.22/12.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 86.22/12.21 v2) = v1) | ~ (op(v3, v2) = v0)) % 86.22/12.21 % 86.22/12.21 Those formulas are unsatisfiable: % 86.22/12.21 --------------------------------- % 86.22/12.21 % 86.22/12.21 Begin of proof % 86.22/12.22 | % 86.22/12.22 | ALPHA: (ax1) implies: % 86.22/12.22 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 86.22/12.22 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 86.22/12.22 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 86.22/12.22 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 86.22/12.22 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 86.22/12.22 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v22 & % 86.22/12.22 | op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 86.22/12.22 | v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, % 86.22/12.22 | e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 % 86.22/12.22 | & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = % 86.22/12.22 | v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) % 86.22/12.22 | = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) % 86.22/12.22 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) % 86.22/12.22 | & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 86.22/12.22 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 86.22/12.22 | $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | v24 = e2 | v24 = e1 % 86.22/12.22 | | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = e1 | v23 = % 86.22/12.22 | e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & (v21 % 86.22/12.22 | = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 % 86.22/12.22 | = e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 % 86.22/12.22 | = e2 | v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 % 86.22/12.22 | = e1 | v18 = e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 % 86.22/12.22 | = e0) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & % 86.22/12.22 | (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v14 = e4 | % 86.22/12.22 | v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e4 | v13 = e3 | % 86.22/12.22 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e4 | v12 = e3 | v12 = e2 | % 86.22/12.22 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e1 | % 86.22/12.22 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) % 86.22/12.22 | & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 = % 86.22/12.22 | e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 | % 86.22/12.22 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = % 86.22/12.22 | e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 % 86.22/12.22 | | v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 % 86.22/12.22 | = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 % 86.22/12.22 | | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & % 86.22/12.22 | (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 86.22/12.22 | % 86.22/12.22 | ALPHA: (ax2) implies: % 86.22/12.23 | (2) op(e0, unit) = e0 % 86.22/12.23 | (3) op(e1, unit) = e1 % 86.22/12.23 | (4) op(e2, unit) = e2 % 86.22/12.23 | (5) op(e3, unit) = e3 % 86.22/12.23 | (6) op(e4, unit) = e4 % 86.22/12.23 | (7) op(unit, e0) = e0 % 86.22/12.23 | (8) op(unit, e2) = e2 % 86.22/12.23 | (9) op(unit, e3) = e3 % 86.22/12.23 | (10) op(unit, e4) = e4 % 86.22/12.23 | (11) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 86.22/12.23 | % 86.22/12.23 | ALPHA: (ax3) implies: % 86.22/12.25 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 86.22/12.25 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 86.22/12.25 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 86.22/12.25 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 86.22/12.25 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 86.22/12.25 | : ? [v24: $i] : (((v24 = e4 & op(e4, e4) = e4) | (v23 = e4 & op(e4, % 86.22/12.25 | e3) = e4) | (v20 = e4 & op(e4, e2) = e4) | (v15 = e4 & op(e4, % 86.22/12.25 | e1) = e4) | (v8 = e4 & op(e4, e0) = e4)) & ((v24 = e4 & op(e4, % 86.22/12.25 | e4) = e4) | (v22 = e4 & op(e3, e4) = e4) | (v18 = e4 & op(e2, % 86.22/12.25 | e4) = e4) | (v12 = e4 & op(e1, e4) = e4) | (v4 = e4 & op(e0, % 86.22/12.25 | e4) = e4)) & ((v24 = e3 & op(e4, e4) = e3) | (v23 = e3 & % 86.22/12.25 | op(e4, e3) = e3) | (v20 = e3 & op(e4, e2) = e3) | (v15 = e3 & % 86.22/12.25 | op(e4, e1) = e3) | (v8 = e3 & op(e4, e0) = e3)) & ((v24 = e3 & % 86.22/12.25 | op(e4, e4) = e3) | (v22 = e3 & op(e3, e4) = e3) | (v18 = e3 & % 86.22/12.25 | op(e2, e4) = e3) | (v12 = e3 & op(e1, e4) = e3) | (v4 = e3 & % 86.22/12.25 | op(e0, e4) = e3)) & ((v24 = e2 & op(e4, e4) = e2) | (v23 = e2 & % 86.22/12.25 | op(e4, e3) = e2) | (v20 = e2 & op(e4, e2) = e2) | (v15 = e2 & % 86.22/12.25 | op(e4, e1) = e2) | (v8 = e2 & op(e4, e0) = e2)) & ((v24 = e2 & % 86.22/12.25 | op(e4, e4) = e2) | (v22 = e2 & op(e3, e4) = e2) | (v18 = e2 & % 86.22/12.25 | op(e2, e4) = e2) | (v12 = e2 & op(e1, e4) = e2) | (v4 = e2 & % 86.22/12.25 | op(e0, e4) = e2)) & ((v24 = e1 & op(e4, e4) = e1) | (v23 = e1 & % 86.22/12.25 | op(e4, e3) = e1) | (v20 = e1 & op(e4, e2) = e1) | (v15 = e1 & % 86.22/12.25 | op(e4, e1) = e1) | (v8 = e1 & op(e4, e0) = e1)) & ((v24 = e1 & % 86.22/12.25 | op(e4, e4) = e1) | (v22 = e1 & op(e3, e4) = e1) | (v18 = e1 & % 86.22/12.25 | op(e2, e4) = e1) | (v12 = e1 & op(e1, e4) = e1) | (v4 = e1 & % 86.22/12.25 | op(e0, e4) = e1)) & ((v24 = e0 & op(e4, e4) = e0) | (v23 = e0 & % 86.22/12.25 | op(e4, e3) = e0) | (v20 = e0 & op(e4, e2) = e0) | (v15 = e0 & % 86.22/12.25 | op(e4, e1) = e0) | (v8 = e0 & op(e4, e0) = e0)) & ((v24 = e0 & % 86.22/12.25 | op(e4, e4) = e0) | (v22 = e0 & op(e3, e4) = e0) | (v18 = e0 & % 86.22/12.25 | op(e2, e4) = e0) | (v12 = e0 & op(e1, e4) = e0) | (v4 = e0 & % 86.22/12.25 | op(e0, e4) = e0)) & ((v23 = e4 & op(e4, e3) = e4) | (v21 = e4 & % 86.22/12.25 | op(e3, e3) = e4) | (v17 = e4 & op(e2, e3) = e4) | (v11 = e4 & % 86.22/12.25 | op(e1, e3) = e4) | (v3 = e4 & op(e0, e3) = e4)) & ((v23 = e3 & % 86.22/12.25 | op(e4, e3) = e3) | (v21 = e3 & op(e3, e3) = e3) | (v17 = e3 & % 86.22/12.25 | op(e2, e3) = e3) | (v11 = e3 & op(e1, e3) = e3) | (v3 = e3 & % 86.22/12.25 | op(e0, e3) = e3)) & ((v23 = e2 & op(e4, e3) = e2) | (v21 = e2 & % 86.22/12.25 | op(e3, e3) = e2) | (v17 = e2 & op(e2, e3) = e2) | (v11 = e2 & % 86.22/12.25 | op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v23 = e1 & % 86.22/12.25 | op(e4, e3) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v17 = e1 & % 86.22/12.25 | op(e2, e3) = e1) | (v11 = e1 & op(e1, e3) = e1) | (v3 = e1 & % 86.22/12.25 | op(e0, e3) = e1)) & ((v23 = e0 & op(e4, e3) = e0) | (v21 = e0 & % 86.22/12.25 | op(e3, e3) = e0) | (v17 = e0 & op(e2, e3) = e0) | (v11 = e0 & % 86.22/12.25 | op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v22 = e4 & % 86.22/12.25 | op(e3, e4) = e4) | (v21 = e4 & op(e3, e3) = e4) | (v19 = e4 & % 86.22/12.25 | op(e3, e2) = e4) | (v14 = e4 & op(e3, e1) = e4) | (v7 = e4 & % 86.22/12.25 | op(e3, e0) = e4)) & ((v22 = e3 & op(e3, e4) = e3) | (v21 = e3 & % 86.22/12.25 | op(e3, e3) = e3) | (v19 = e3 & op(e3, e2) = e3) | (v14 = e3 & % 86.22/12.25 | op(e3, e1) = e3) | (v7 = e3 & op(e3, e0) = e3)) & ((v22 = e2 & % 86.22/12.25 | op(e3, e4) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v19 = e2 & % 86.22/12.25 | op(e3, e2) = e2) | (v14 = e2 & op(e3, e1) = e2) | (v7 = e2 & % 86.22/12.25 | op(e3, e0) = e2)) & ((v22 = e1 & op(e3, e4) = e1) | (v21 = e1 & % 86.22/12.25 | op(e3, e3) = e1) | (v19 = e1 & op(e3, e2) = e1) | (v14 = e1 & % 86.22/12.25 | op(e3, e1) = e1) | (v7 = e1 & op(e3, e0) = e1)) & ((v22 = e0 & % 86.22/12.25 | op(e3, e4) = e0) | (v21 = e0 & op(e3, e3) = e0) | (v19 = e0 & % 86.22/12.25 | op(e3, e2) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v7 = e0 & % 86.22/12.25 | op(e3, e0) = e0)) & ((v20 = e4 & op(e4, e2) = e4) | (v19 = e4 & % 86.22/12.25 | op(e3, e2) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v10 = e4 & % 86.22/12.25 | op(e1, e2) = e4) | (v2 = e4 & op(e0, e2) = e4)) & ((v20 = e3 & % 86.22/12.25 | op(e4, e2) = e3) | (v19 = e3 & op(e3, e2) = e3) | (v16 = e3 & % 86.22/12.25 | op(e2, e2) = e3) | (v10 = e3 & op(e1, e2) = e3) | (v2 = e3 & % 86.22/12.25 | op(e0, e2) = e3)) & ((v20 = e2 & op(e4, e2) = e2) | (v19 = e2 & % 86.22/12.25 | op(e3, e2) = e2) | (v16 = e2 & op(e2, e2) = e2) | (v10 = e2 & % 86.22/12.25 | op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v20 = e1 & % 86.22/12.25 | op(e4, e2) = e1) | (v19 = e1 & op(e3, e2) = e1) | (v16 = e1 & % 86.22/12.25 | op(e2, e2) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v2 = e1 & % 86.22/12.25 | op(e0, e2) = e1)) & ((v20 = e0 & op(e4, e2) = e0) | (v19 = e0 & % 86.22/12.25 | op(e3, e2) = e0) | (v16 = e0 & op(e2, e2) = e0) | (v10 = e0 & % 86.22/12.25 | op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v18 = e4 & % 86.22/12.25 | op(e2, e4) = e4) | (v17 = e4 & op(e2, e3) = e4) | (v16 = e4 & % 86.22/12.25 | op(e2, e2) = e4) | (v13 = e4 & op(e2, e1) = e4) | (v6 = e4 & % 86.22/12.25 | op(e2, e0) = e4)) & ((v18 = e3 & op(e2, e4) = e3) | (v17 = e3 & % 86.22/12.25 | op(e2, e3) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v13 = e3 & % 86.22/12.25 | op(e2, e1) = e3) | (v6 = e3 & op(e2, e0) = e3)) & ((v18 = e2 & % 86.22/12.25 | op(e2, e4) = e2) | (v17 = e2 & op(e2, e3) = e2) | (v16 = e2 & % 86.22/12.25 | op(e2, e2) = e2) | (v13 = e2 & op(e2, e1) = e2) | (v6 = e2 & % 86.22/12.25 | op(e2, e0) = e2)) & ((v18 = e1 & op(e2, e4) = e1) | (v17 = e1 & % 86.22/12.25 | op(e2, e3) = e1) | (v16 = e1 & op(e2, e2) = e1) | (v13 = e1 & % 86.22/12.25 | op(e2, e1) = e1) | (v6 = e1 & op(e2, e0) = e1)) & ((v18 = e0 & % 86.22/12.25 | op(e2, e4) = e0) | (v17 = e0 & op(e2, e3) = e0) | (v16 = e0 & % 86.22/12.25 | op(e2, e2) = e0) | (v13 = e0 & op(e2, e1) = e0) | (v6 = e0 & % 86.22/12.25 | op(e2, e0) = e0)) & ((v15 = e4 & op(e4, e1) = e4) | (v14 = e4 & % 86.22/12.25 | op(e3, e1) = e4) | (v13 = e4 & op(e2, e1) = e4) | (v9 = e4 & % 86.22/12.25 | op(e1, e1) = e4) | (v1 = e4 & op(e0, e1) = e4)) & ((v15 = e3 & % 86.22/12.25 | op(e4, e1) = e3) | (v14 = e3 & op(e3, e1) = e3) | (v13 = e3 & % 86.22/12.25 | op(e2, e1) = e3) | (v9 = e3 & op(e1, e1) = e3) | (v1 = e3 & % 86.22/12.25 | op(e0, e1) = e3)) & ((v15 = e2 & op(e4, e1) = e2) | (v14 = e2 & % 86.22/12.25 | op(e3, e1) = e2) | (v13 = e2 & op(e2, e1) = e2) | (v9 = e2 & % 86.22/12.25 | op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v15 = e1 & % 86.22/12.25 | op(e4, e1) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v13 = e1 & % 86.22/12.25 | op(e2, e1) = e1) | (v9 = e1 & op(e1, e1) = e1) | (v1 = e1 & % 86.22/12.25 | op(e0, e1) = e1)) & ((v15 = e0 & op(e4, e1) = e0) | (v14 = e0 & % 86.22/12.25 | op(e3, e1) = e0) | (v13 = e0 & op(e2, e1) = e0) | (v9 = e0 & % 86.22/12.25 | op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v12 = e4 & % 86.22/12.25 | op(e1, e4) = e4) | (v11 = e4 & op(e1, e3) = e4) | (v10 = e4 & % 86.22/12.25 | op(e1, e2) = e4) | (v9 = e4 & op(e1, e1) = e4) | (v5 = e4 & % 86.22/12.25 | op(e1, e0) = e4)) & ((v12 = e3 & op(e1, e4) = e3) | (v11 = e3 & % 86.22/12.25 | op(e1, e3) = e3) | (v10 = e3 & op(e1, e2) = e3) | (v9 = e3 & % 86.22/12.25 | op(e1, e1) = e3) | (v5 = e3 & op(e1, e0) = e3)) & ((v12 = e2 & % 86.22/12.25 | op(e1, e4) = e2) | (v11 = e2 & op(e1, e3) = e2) | (v10 = e2 & % 86.22/12.25 | op(e1, e2) = e2) | (v9 = e2 & op(e1, e1) = e2) | (v5 = e2 & % 86.22/12.25 | op(e1, e0) = e2)) & ((v12 = e1 & op(e1, e4) = e1) | (v11 = e1 & % 86.22/12.25 | op(e1, e3) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v9 = e1 & % 86.22/12.25 | op(e1, e1) = e1) | (v5 = e1 & op(e1, e0) = e1)) & ((v12 = e0 & % 86.22/12.25 | op(e1, e4) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v10 = e0 & % 86.22/12.25 | op(e1, e2) = e0) | (v9 = e0 & op(e1, e1) = e0) | (v5 = e0 & % 86.22/12.25 | op(e1, e0) = e0)) & ((v8 = e4 & op(e4, e0) = e4) | (v7 = e4 & % 86.22/12.25 | op(e3, e0) = e4) | (v6 = e4 & op(e2, e0) = e4) | (v5 = e4 & % 86.22/12.25 | op(e1, e0) = e4) | (v0 = e4 & op(e0, e0) = e4)) & ((v8 = e3 & % 86.22/12.25 | op(e4, e0) = e3) | (v7 = e3 & op(e3, e0) = e3) | (v6 = e3 & % 86.22/12.25 | op(e2, e0) = e3) | (v5 = e3 & op(e1, e0) = e3) | (v0 = e3 & % 86.22/12.25 | op(e0, e0) = e3)) & ((v8 = e2 & op(e4, e0) = e2) | (v7 = e2 & % 86.22/12.25 | op(e3, e0) = e2) | (v6 = e2 & op(e2, e0) = e2) | (v5 = e2 & % 86.22/12.25 | op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v8 = e1 & % 86.22/12.25 | op(e4, e0) = e1) | (v7 = e1 & op(e3, e0) = e1) | (v6 = e1 & % 86.22/12.25 | op(e2, e0) = e1) | (v5 = e1 & op(e1, e0) = e1) | (v0 = e1 & % 86.22/12.25 | op(e0, e0) = e1)) & ((v4 = e4 & op(e0, e4) = e4) | (v3 = e4 & % 86.22/12.25 | op(e0, e3) = e4) | (v2 = e4 & op(e0, e2) = e4) | (v1 = e4 & % 86.22/12.25 | op(e0, e1) = e4) | (v0 = e4 & op(e0, e0) = e4)) & ((v4 = e3 & % 86.22/12.25 | op(e0, e4) = e3) | (v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & % 86.22/12.25 | op(e0, e2) = e3) | (v1 = e3 & op(e0, e1) = e3) | (v0 = e3 & % 86.22/12.25 | op(e0, e0) = e3)) & ((v4 = e2 & op(e0, e4) = e2) | (v3 = e2 & % 86.22/12.25 | op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & % 86.22/12.25 | op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v4 = e1 & % 86.22/12.25 | op(e0, e4) = e1) | (v3 = e1 & op(e0, e3) = e1) | (v2 = e1 & % 86.22/12.25 | op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & % 86.22/12.25 | op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v8 = e0 & % 86.22/12.25 | op(e4, e0) = e0) | (v7 = e0 & op(e3, e0) = e0) | (v6 = e0 & % 86.22/12.25 | op(e2, e0) = e0) | (v5 = e0 & op(e1, e0) = e0)) & ((v4 = e0 % 86.22/12.25 | & op(e0, e4) = e0) | (v3 = e0 & op(e0, e3) = e0) | (v2 = e0 % 86.22/12.25 | & op(e0, e2) = e0) | (v1 = e0 & op(e0, e1) = e0))))) % 86.22/12.25 | % 86.22/12.25 | ALPHA: (ax4) implies: % 86.22/12.26 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 86.22/12.26 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 86.22/12.26 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 86.22/12.26 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 86.22/12.26 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 86.22/12.26 | : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & % 86.22/12.26 | ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ % 86.22/12.26 | (v24 = v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ % 86.22/12.26 | (v23 = v18) & ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ % 86.22/12.26 | (v22 = v21) & ~ (v22 = v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ % 86.22/12.26 | (v22 = v7) & ~ (v22 = v2) & ~ (v21 = v20) & ~ (v21 = v16) & ~ % 86.22/12.26 | (v21 = v11) & ~ (v21 = v6) & ~ (v21 = v1) & ~ (v20 = v15) & ~ % 86.22/12.26 | (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ (v19 = v18) & ~ % 86.22/12.26 | (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = v14) & ~ % 86.22/12.26 | (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & ~ % 86.22/12.26 | (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ % 86.22/12.26 | (v17 = v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ % 86.22/12.26 | (v17 = v2) & ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ % 86.22/12.26 | (v16 = v1) & ~ (v15 = v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ % 86.22/12.26 | (v14 = v13) & ~ (v14 = v12) & ~ (v14 = v11) & ~ (v14 = v10) & ~ % 86.22/12.26 | (v14 = v9) & ~ (v14 = v4) & ~ (v13 = v12) & ~ (v13 = v11) & ~ % 86.22/12.26 | (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) & ~ (v12 = v11) & ~ % 86.22/12.26 | (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = v10) & ~ % 86.22/12.26 | (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v9 % 86.22/12.26 | = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) % 86.22/12.26 | & ~ (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 % 86.22/12.26 | = v6) & ~ (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) % 86.22/12.26 | & ~ (v5 = v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 % 86.22/12.26 | = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) % 86.22/12.26 | & ~ (v2 = v0) & ~ (v1 = v0) & op(e4, e4) = v24 & op(e4, e3) = v19 % 86.22/12.26 | & op(e4, e2) = v14 & op(e4, e1) = v9 & op(e4, e0) = v4 & op(e3, e4) % 86.22/12.26 | = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 & op(e3, e1) = v8 & % 86.22/12.26 | op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & op(e2, e2) = % 86.22/12.26 | v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & op(e1, % 86.22/12.26 | e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & % 86.22/12.26 | op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) % 86.22/12.26 | = v5 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 86.22/12.26 | $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) % 86.22/12.26 | & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 86.22/12.26 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 86.22/12.26 | % 86.22/12.26 | ALPHA: (ax5) implies: % 86.22/12.26 | (14) ~ (e2 = e0) % 86.22/12.26 | (15) ~ (e2 = e1) % 86.22/12.26 | (16) ~ (e3 = e2) % 86.22/12.26 | (17) ~ (e4 = e0) % 86.22/12.26 | (18) ~ (e4 = e1) % 86.22/12.26 | (19) ~ (e4 = e2) % 86.22/12.26 | % 86.22/12.26 | ALPHA: (ax6) implies: % 86.22/12.26 | (20) op(e2, e2) = e4 % 86.22/12.26 | (21) op(e2, e4) = e3 % 86.22/12.26 | (22) op(e3, e4) = e1 % 86.22/12.26 | (23) op(e4, e4) = e0 % 86.22/12.26 | % 86.22/12.26 | ALPHA: (co1) implies: % 86.22/12.28 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 86.22/12.28 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 86.22/12.28 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 86.22/12.28 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 86.22/12.28 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 86.22/12.28 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 86.22/12.28 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? % 86.22/12.28 | [v33: $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] % 86.22/12.28 | : ? [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: % 86.22/12.28 | $i] : ? [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? % 86.22/12.28 | [v47: $i] : ? [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] % 86.22/12.28 | : ? [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: % 86.22/12.28 | $i] : ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? % 86.22/12.28 | [v61: $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : (((v64 = e3 & % 86.22/12.28 | v48 = e4 & ~ (v61 = e3) & op(e4, e4) = e3 & op(e3, e4) = v61 & % 86.22/12.28 | op(e3, e3) = e4 & $i(v61)) | (v64 = e3 & v48 = e4 & ~ (v49 = % 86.22/12.28 | e4) & op(e4, e4) = e3 & op(e4, e3) = v49 & op(e3, e3) = e4 & % 86.22/12.28 | $i(v49)) | (v64 = e2 & v32 = e4 & ~ (v58 = e2) & op(e4, e4) = % 86.22/12.28 | e2 & op(e2, e4) = v58 & op(e2, e2) = e4 & $i(v58)) | (v64 = e2 & % 86.22/12.28 | v32 = e4 & ~ (v36 = e4) & op(e4, e4) = e2 & op(e4, e2) = v36 & % 86.22/12.28 | op(e2, e2) = e4 & $i(v36)) | (v64 = e1 & v16 = e4 & ~ (v55 = % 86.22/12.28 | e1) & op(e4, e4) = e1 & op(e1, e4) = v55 & op(e1, e1) = e4 & % 86.22/12.28 | $i(v55)) | (v64 = e1 & v16 = e4 & ~ (v23 = e4) & op(e4, e4) = % 86.22/12.28 | e1 & op(e4, e1) = v23 & op(e1, e1) = e4 & $i(v23)) | (v64 = e0 & % 86.22/12.28 | v0 = e4 & ~ (v10 = e4) & op(e4, e4) = e0 & op(e4, e0) = v10 & % 86.22/12.28 | op(e0, e0) = e4 & $i(v10)) | (v48 = e2 & v32 = e3 & ~ (v45 = % 86.22/12.28 | e2) & op(e3, e3) = e2 & op(e2, e3) = v45 & op(e2, e2) = e3 & % 86.22/12.28 | $i(v45)) | (v48 = e2 & v32 = e3 & ~ (v33 = e3) & op(e3, e3) = % 86.22/12.28 | e2 & op(e3, e2) = v33 & op(e2, e2) = e3 & $i(v33)) | (v48 = e1 & % 86.22/12.28 | v16 = e3 & ~ (v42 = e1) & op(e3, e3) = e1 & op(e1, e3) = v42 & % 86.22/12.28 | op(e1, e1) = e3 & $i(v42)) | (v48 = e1 & v16 = e3 & ~ (v20 = % 86.22/12.28 | e3) & op(e3, e3) = e1 & op(e3, e1) = v20 & op(e1, e1) = e3 & % 86.22/12.28 | $i(v20)) | (v48 = e0 & v0 = e3 & ~ (v7 = e3) & op(e3, e3) = e0 % 86.22/12.28 | & op(e3, e0) = v7 & op(e0, e0) = e3 & $i(v7)) | (v32 = e1 & v16 % 86.22/12.28 | = e2 & ~ (v29 = e1) & op(e2, e2) = e1 & op(e1, e2) = v29 & % 86.22/12.28 | op(e1, e1) = e2 & $i(v29)) | (v32 = e1 & v16 = e2 & ~ (v17 = % 86.22/12.28 | e2) & op(e2, e2) = e1 & op(e2, e1) = v17 & op(e1, e1) = e2 & % 86.22/12.28 | $i(v17)) | (v32 = e0 & v0 = e2 & ~ (v4 = e2) & op(e2, e2) = e0 % 86.22/12.28 | & op(e2, e0) = v4 & op(e0, e0) = e2 & $i(v4)) | (op(e0, e0) = v0 % 86.22/12.28 | & $i(v0) & ((v64 = e0 & v0 = e4 & ~ (v52 = e0) & op(e4, e4) = % 86.22/12.28 | e0 & op(e0, e4) = v52 & $i(v52)) | (v48 = e0 & v0 = e3 & ~ % 86.22/12.28 | (v39 = e0) & op(e3, e3) = e0 & op(e0, e3) = v39 & $i(v39)) | % 86.22/12.28 | (v32 = e0 & v0 = e2 & ~ (v26 = e0) & op(e2, e2) = e0 & op(e0, % 86.22/12.28 | e2) = v26 & $i(v26)) | (v16 = e0 & v0 = e1 & ~ (v13 = e0) % 86.22/12.28 | & op(e1, e1) = e0 & op(e0, e1) = v13 & $i(v13)) | (v16 = e0 % 86.22/12.28 | & v0 = e1 & ~ (v1 = e1) & op(e1, e1) = e0 & op(e1, e0) = v1 % 86.22/12.28 | & $i(v1))))) & ((v63 = e3 & ~ (v62 = e4) & op(e4, v61) = e3 % 86.22/12.28 | & op(e3, v61) = v62 & op(e3, e4) = v61 & $i(v62) & $i(v61)) | % 86.22/12.28 | (v60 = e2 & ~ (v59 = e4) & op(e4, v58) = e2 & op(e2, v58) = v59 & % 86.22/12.28 | op(e2, e4) = v58 & $i(v59) & $i(v58)) | (v57 = e1 & ~ (v56 = % 86.22/12.28 | e4) & op(e4, v55) = e1 & op(e1, v55) = v56 & op(e1, e4) = v55 % 86.22/12.28 | & $i(v56) & $i(v55)) | (v54 = e0 & ~ (v53 = e4) & op(e4, v52) = % 86.22/12.28 | e0 & op(e0, v52) = v53 & op(e0, e4) = v52 & $i(v53) & $i(v52))) % 86.22/12.28 | & ((v51 = e4 & ~ (v50 = e3) & op(e4, v49) = v50 & op(e4, e3) = v49 % 86.22/12.28 | & op(e3, v49) = e4 & $i(v50) & $i(v49)) | (v47 = e2 & ~ (v46 = % 86.22/12.28 | e3) & op(e3, v45) = e2 & op(e2, v45) = v46 & op(e2, e3) = v45 % 86.22/12.28 | & $i(v46) & $i(v45)) | (v44 = e1 & ~ (v43 = e3) & op(e3, v42) = % 86.22/12.28 | e1 & op(e1, v42) = v43 & op(e1, e3) = v42 & $i(v43) & $i(v42)) | % 86.22/12.28 | (v41 = e0 & ~ (v40 = e3) & op(e3, v39) = e0 & op(e0, v39) = v40 & % 86.22/12.28 | op(e0, e3) = v39 & $i(v40) & $i(v39))) & ((v38 = e4 & ~ (v37 = % 86.22/12.28 | e2) & op(e4, v36) = v37 & op(e4, e2) = v36 & op(e2, v36) = e4 % 86.22/12.28 | & $i(v37) & $i(v36)) | (v35 = e3 & ~ (v34 = e2) & op(e3, v33) = % 86.22/12.28 | v34 & op(e3, e2) = v33 & op(e2, v33) = e3 & $i(v34) & $i(v33)) | % 86.22/12.28 | (v31 = e1 & ~ (v30 = e2) & op(e2, v29) = e1 & op(e1, v29) = v30 & % 86.22/12.28 | op(e1, e2) = v29 & $i(v30) & $i(v29)) | (v28 = e0 & ~ (v27 = % 86.22/12.28 | e2) & op(e2, v26) = e0 & op(e0, v26) = v27 & op(e0, e2) = v26 % 86.22/12.28 | & $i(v27) & $i(v26))) & ((v25 = e4 & ~ (v24 = e1) & op(e4, v23) % 86.22/12.28 | = v24 & op(e4, e1) = v23 & op(e1, v23) = e4 & $i(v24) & $i(v23)) % 86.22/12.28 | | (v22 = e3 & ~ (v21 = e1) & op(e3, v20) = v21 & op(e3, e1) = v20 % 86.22/12.28 | & op(e1, v20) = e3 & $i(v21) & $i(v20)) | (v19 = e2 & ~ (v18 = % 86.22/12.28 | e1) & op(e2, v17) = v18 & op(e2, e1) = v17 & op(e1, v17) = e2 % 86.22/12.28 | & $i(v18) & $i(v17)) | (v15 = e0 & ~ (v14 = e1) & op(e1, v13) = % 86.22/12.28 | e0 & op(e0, v13) = v14 & op(e0, e1) = v13 & $i(v14) & $i(v13))) % 86.22/12.28 | & ((v12 = e4 & ~ (v11 = e0) & op(e4, v10) = v11 & op(e4, e0) = v10 % 86.22/12.28 | & op(e0, v10) = e4 & $i(v11) & $i(v10)) | (v9 = e3 & ~ (v8 = % 86.22/12.28 | e0) & op(e3, v7) = v8 & op(e3, e0) = v7 & op(e0, v7) = e3 & % 86.22/12.28 | $i(v8) & $i(v7)) | (v6 = e2 & ~ (v5 = e0) & op(e2, v4) = v5 & % 86.22/12.28 | op(e2, e0) = v4 & op(e0, v4) = e2 & $i(v5) & $i(v4)) | (v3 = e1 % 86.22/12.28 | & ~ (v2 = e0) & op(e1, v1) = v2 & op(e1, e0) = v1 & op(e0, v1) % 86.22/12.28 | = e1 & $i(v2) & $i(v1)))) % 86.22/12.28 | % 86.22/12.28 | DELTA: instantiating (13) with fresh symbols all_4_0, all_4_1, all_4_2, % 86.22/12.28 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, % 86.22/12.28 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16, % 86.22/12.28 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23, % 86.22/12.28 | all_4_24 gives: % 86.22/12.28 | (25) ~ (all_4_0 = all_4_1) & ~ (all_4_0 = all_4_2) & ~ (all_4_0 = % 86.22/12.28 | all_4_3) & ~ (all_4_0 = all_4_4) & ~ (all_4_0 = all_4_5) & ~ % 86.22/12.28 | (all_4_0 = all_4_10) & ~ (all_4_0 = all_4_15) & ~ (all_4_0 = % 86.22/12.28 | all_4_20) & ~ (all_4_1 = all_4_2) & ~ (all_4_1 = all_4_3) & ~ % 86.22/12.28 | (all_4_1 = all_4_4) & ~ (all_4_1 = all_4_6) & ~ (all_4_1 = all_4_11) % 86.22/12.28 | & ~ (all_4_1 = all_4_16) & ~ (all_4_1 = all_4_21) & ~ (all_4_2 = % 86.22/12.28 | all_4_3) & ~ (all_4_2 = all_4_4) & ~ (all_4_2 = all_4_7) & ~ % 86.22/12.28 | (all_4_2 = all_4_12) & ~ (all_4_2 = all_4_17) & ~ (all_4_2 = % 86.22/12.28 | all_4_22) & ~ (all_4_3 = all_4_4) & ~ (all_4_3 = all_4_8) & ~ % 86.22/12.28 | (all_4_3 = all_4_13) & ~ (all_4_3 = all_4_18) & ~ (all_4_3 = % 86.22/12.28 | all_4_23) & ~ (all_4_4 = all_4_9) & ~ (all_4_4 = all_4_14) & ~ % 86.22/12.28 | (all_4_4 = all_4_19) & ~ (all_4_4 = all_4_24) & ~ (all_4_5 = % 86.22/12.28 | all_4_6) & ~ (all_4_5 = all_4_7) & ~ (all_4_5 = all_4_8) & ~ % 86.22/12.28 | (all_4_5 = all_4_9) & ~ (all_4_5 = all_4_10) & ~ (all_4_5 = % 86.22/12.28 | all_4_15) & ~ (all_4_5 = all_4_20) & ~ (all_4_6 = all_4_7) & ~ % 86.22/12.28 | (all_4_6 = all_4_8) & ~ (all_4_6 = all_4_9) & ~ (all_4_6 = all_4_11) % 86.22/12.28 | & ~ (all_4_6 = all_4_16) & ~ (all_4_6 = all_4_21) & ~ (all_4_7 = % 86.22/12.28 | all_4_8) & ~ (all_4_7 = all_4_9) & ~ (all_4_7 = all_4_12) & ~ % 86.22/12.28 | (all_4_7 = all_4_17) & ~ (all_4_7 = all_4_22) & ~ (all_4_8 = % 86.22/12.28 | all_4_9) & ~ (all_4_8 = all_4_13) & ~ (all_4_8 = all_4_18) & ~ % 86.22/12.28 | (all_4_8 = all_4_23) & ~ (all_4_9 = all_4_14) & ~ (all_4_9 = % 86.22/12.28 | all_4_19) & ~ (all_4_9 = all_4_24) & ~ (all_4_10 = all_4_11) & ~ % 86.22/12.28 | (all_4_10 = all_4_12) & ~ (all_4_10 = all_4_13) & ~ (all_4_10 = % 86.22/12.28 | all_4_14) & ~ (all_4_10 = all_4_15) & ~ (all_4_10 = all_4_20) & ~ % 86.22/12.28 | (all_4_11 = all_4_12) & ~ (all_4_11 = all_4_13) & ~ (all_4_11 = % 86.22/12.28 | all_4_14) & ~ (all_4_11 = all_4_16) & ~ (all_4_11 = all_4_21) & ~ % 86.22/12.28 | (all_4_12 = all_4_13) & ~ (all_4_12 = all_4_14) & ~ (all_4_12 = % 86.22/12.28 | all_4_17) & ~ (all_4_12 = all_4_22) & ~ (all_4_13 = all_4_14) & ~ % 86.22/12.28 | (all_4_13 = all_4_18) & ~ (all_4_13 = all_4_23) & ~ (all_4_14 = % 86.22/12.28 | all_4_19) & ~ (all_4_14 = all_4_24) & ~ (all_4_15 = all_4_16) & ~ % 86.22/12.28 | (all_4_15 = all_4_17) & ~ (all_4_15 = all_4_18) & ~ (all_4_15 = % 86.22/12.28 | all_4_19) & ~ (all_4_15 = all_4_20) & ~ (all_4_16 = all_4_17) & ~ % 86.22/12.28 | (all_4_16 = all_4_18) & ~ (all_4_16 = all_4_19) & ~ (all_4_16 = % 86.22/12.28 | all_4_21) & ~ (all_4_17 = all_4_18) & ~ (all_4_17 = all_4_19) & ~ % 86.22/12.28 | (all_4_17 = all_4_22) & ~ (all_4_18 = all_4_19) & ~ (all_4_18 = % 86.22/12.28 | all_4_23) & ~ (all_4_19 = all_4_24) & ~ (all_4_20 = all_4_21) & ~ % 86.22/12.28 | (all_4_20 = all_4_22) & ~ (all_4_20 = all_4_23) & ~ (all_4_20 = % 86.22/12.28 | all_4_24) & ~ (all_4_21 = all_4_22) & ~ (all_4_21 = all_4_23) & ~ % 86.22/12.28 | (all_4_21 = all_4_24) & ~ (all_4_22 = all_4_23) & ~ (all_4_22 = % 86.22/12.28 | all_4_24) & ~ (all_4_23 = all_4_24) & op(e4, e4) = all_4_0 & op(e4, % 86.22/12.28 | e3) = all_4_5 & op(e4, e2) = all_4_10 & op(e4, e1) = all_4_15 & % 86.22/12.28 | op(e4, e0) = all_4_20 & op(e3, e4) = all_4_1 & op(e3, e3) = all_4_6 & % 86.22/12.28 | op(e3, e2) = all_4_11 & op(e3, e1) = all_4_16 & op(e3, e0) = all_4_21 % 86.22/12.28 | & op(e2, e4) = all_4_2 & op(e2, e3) = all_4_7 & op(e2, e2) = all_4_12 % 86.22/12.28 | & op(e2, e1) = all_4_17 & op(e2, e0) = all_4_22 & op(e1, e4) = all_4_3 % 86.22/12.28 | & op(e1, e3) = all_4_8 & op(e1, e2) = all_4_13 & op(e1, e1) = all_4_18 % 86.22/12.28 | & op(e1, e0) = all_4_23 & op(e0, e4) = all_4_4 & op(e0, e3) = all_4_9 % 86.22/12.28 | & op(e0, e2) = all_4_14 & op(e0, e1) = all_4_19 & op(e0, e0) = % 86.22/12.28 | all_4_24 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & $i(all_4_3) & % 86.22/12.28 | $i(all_4_4) & $i(all_4_5) & $i(all_4_6) & $i(all_4_7) & $i(all_4_8) & % 86.22/12.28 | $i(all_4_9) & $i(all_4_10) & $i(all_4_11) & $i(all_4_12) & % 86.22/12.28 | $i(all_4_13) & $i(all_4_14) & $i(all_4_15) & $i(all_4_16) & % 86.22/12.28 | $i(all_4_17) & $i(all_4_18) & $i(all_4_19) & $i(all_4_20) & % 86.22/12.28 | $i(all_4_21) & $i(all_4_22) & $i(all_4_23) & $i(all_4_24) % 86.22/12.28 | % 86.22/12.28 | ALPHA: (25) implies: % 86.22/12.29 | (26) ~ (all_4_22 = all_4_23) % 86.22/12.29 | (27) ~ (all_4_20 = all_4_24) % 86.22/12.29 | (28) ~ (all_4_20 = all_4_23) % 86.22/12.29 | (29) ~ (all_4_20 = all_4_22) % 86.22/12.29 | (30) ~ (all_4_19 = all_4_24) % 86.22/12.29 | (31) ~ (all_4_18 = all_4_23) % 86.22/12.29 | (32) ~ (all_4_18 = all_4_19) % 86.22/12.29 | (33) ~ (all_4_17 = all_4_22) % 86.22/12.29 | (34) ~ (all_4_17 = all_4_19) % 86.22/12.29 | (35) ~ (all_4_17 = all_4_18) % 86.22/12.29 | (36) ~ (all_4_16 = all_4_21) % 86.22/12.29 | (37) ~ (all_4_16 = all_4_19) % 86.22/12.29 | (38) ~ (all_4_16 = all_4_18) % 86.22/12.29 | (39) ~ (all_4_16 = all_4_17) % 86.22/12.29 | (40) ~ (all_4_15 = all_4_20) % 86.22/12.29 | (41) ~ (all_4_15 = all_4_19) % 86.22/12.29 | (42) ~ (all_4_15 = all_4_18) % 86.22/12.29 | (43) ~ (all_4_15 = all_4_17) % 86.22/12.29 | (44) ~ (all_4_15 = all_4_16) % 86.22/12.29 | (45) ~ (all_4_14 = all_4_24) % 86.22/12.29 | (46) ~ (all_4_14 = all_4_19) % 86.22/12.29 | (47) ~ (all_4_13 = all_4_14) % 86.22/12.29 | (48) ~ (all_4_12 = all_4_22) % 86.22/12.29 | (49) ~ (all_4_12 = all_4_17) % 86.22/12.29 | (50) ~ (all_4_12 = all_4_14) % 86.22/12.29 | (51) ~ (all_4_11 = all_4_16) % 86.22/12.29 | (52) ~ (all_4_11 = all_4_14) % 86.22/12.29 | (53) ~ (all_4_11 = all_4_13) % 86.22/12.29 | (54) ~ (all_4_11 = all_4_12) % 86.22/12.29 | (55) ~ (all_4_10 = all_4_20) % 86.22/12.29 | (56) ~ (all_4_10 = all_4_15) % 86.22/12.29 | (57) ~ (all_4_10 = all_4_14) % 86.22/12.29 | (58) ~ (all_4_10 = all_4_13) % 86.22/12.29 | (59) ~ (all_4_10 = all_4_12) % 86.22/12.29 | (60) ~ (all_4_10 = all_4_11) % 86.22/12.29 | (61) ~ (all_4_9 = all_4_24) % 86.22/12.29 | (62) ~ (all_4_9 = all_4_19) % 86.22/12.29 | (63) ~ (all_4_9 = all_4_14) % 86.22/12.29 | (64) ~ (all_4_8 = all_4_9) % 86.22/12.29 | (65) ~ (all_4_7 = all_4_22) % 86.22/12.29 | (66) ~ (all_4_7 = all_4_17) % 86.22/12.29 | (67) ~ (all_4_7 = all_4_12) % 86.22/12.29 | (68) ~ (all_4_7 = all_4_9) % 86.22/12.29 | (69) ~ (all_4_6 = all_4_16) % 86.22/12.29 | (70) ~ (all_4_6 = all_4_11) % 86.22/12.29 | (71) ~ (all_4_6 = all_4_9) % 86.22/12.29 | (72) ~ (all_4_6 = all_4_7) % 86.22/12.29 | (73) ~ (all_4_5 = all_4_20) % 86.22/12.29 | (74) ~ (all_4_5 = all_4_15) % 86.22/12.29 | (75) ~ (all_4_5 = all_4_10) % 86.22/12.29 | (76) ~ (all_4_5 = all_4_9) % 86.22/12.29 | (77) ~ (all_4_5 = all_4_7) % 86.22/12.29 | (78) ~ (all_4_5 = all_4_6) % 86.22/12.29 | (79) ~ (all_4_4 = all_4_24) % 86.22/12.29 | (80) ~ (all_4_4 = all_4_19) % 86.22/12.29 | (81) ~ (all_4_4 = all_4_14) % 86.22/12.29 | (82) ~ (all_4_4 = all_4_9) % 86.22/12.29 | (83) ~ (all_4_3 = all_4_8) % 86.22/12.29 | (84) ~ (all_4_3 = all_4_4) % 86.22/12.29 | (85) ~ (all_4_2 = all_4_22) % 86.22/12.29 | (86) ~ (all_4_2 = all_4_17) % 86.22/12.29 | (87) ~ (all_4_2 = all_4_12) % 86.22/12.29 | (88) ~ (all_4_2 = all_4_7) % 86.22/12.29 | (89) ~ (all_4_2 = all_4_4) % 86.22/12.29 | (90) ~ (all_4_2 = all_4_3) % 86.22/12.29 | (91) ~ (all_4_1 = all_4_16) % 86.22/12.29 | (92) ~ (all_4_1 = all_4_11) % 86.22/12.29 | (93) ~ (all_4_1 = all_4_6) % 86.22/12.29 | (94) ~ (all_4_1 = all_4_4) % 86.22/12.29 | (95) ~ (all_4_1 = all_4_3) % 86.22/12.29 | (96) ~ (all_4_1 = all_4_2) % 86.22/12.29 | (97) ~ (all_4_0 = all_4_20) % 86.22/12.29 | (98) ~ (all_4_0 = all_4_10) % 86.22/12.29 | (99) ~ (all_4_0 = all_4_5) % 86.22/12.29 | (100) ~ (all_4_0 = all_4_4) % 86.22/12.29 | (101) ~ (all_4_0 = all_4_3) % 86.22/12.29 | (102) ~ (all_4_0 = all_4_2) % 86.22/12.29 | (103) ~ (all_4_0 = all_4_1) % 86.22/12.29 | (104) op(e0, e0) = all_4_24 % 86.22/12.29 | (105) op(e0, e1) = all_4_19 % 86.22/12.29 | (106) op(e0, e2) = all_4_14 % 86.22/12.29 | (107) op(e0, e3) = all_4_9 % 86.22/12.29 | (108) op(e0, e4) = all_4_4 % 86.22/12.29 | (109) op(e1, e0) = all_4_23 % 86.22/12.29 | (110) op(e1, e1) = all_4_18 % 86.22/12.29 | (111) op(e1, e2) = all_4_13 % 86.22/12.29 | (112) op(e1, e3) = all_4_8 % 86.22/12.29 | (113) op(e1, e4) = all_4_3 % 86.22/12.29 | (114) op(e2, e0) = all_4_22 % 86.22/12.29 | (115) op(e2, e1) = all_4_17 % 86.22/12.29 | (116) op(e2, e2) = all_4_12 % 86.22/12.29 | (117) op(e2, e3) = all_4_7 % 86.22/12.29 | (118) op(e2, e4) = all_4_2 % 86.22/12.29 | (119) op(e3, e0) = all_4_21 % 86.22/12.29 | (120) op(e3, e1) = all_4_16 % 86.22/12.29 | (121) op(e3, e2) = all_4_11 % 86.22/12.29 | (122) op(e3, e3) = all_4_6 % 86.22/12.29 | (123) op(e3, e4) = all_4_1 % 86.22/12.29 | (124) op(e4, e0) = all_4_20 % 86.22/12.29 | (125) op(e4, e1) = all_4_15 % 86.22/12.29 | (126) op(e4, e2) = all_4_10 % 86.22/12.29 | (127) op(e4, e3) = all_4_5 % 86.22/12.29 | (128) op(e4, e4) = all_4_0 % 86.22/12.29 | % 86.22/12.29 | DELTA: instantiating (1) with fresh symbols all_6_0, all_6_1, all_6_2, % 86.22/12.29 | all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9, % 86.22/12.29 | all_6_10, all_6_11, all_6_12, all_6_13, all_6_14, all_6_15, all_6_16, % 86.22/12.29 | all_6_17, all_6_18, all_6_19, all_6_20, all_6_21, all_6_22, all_6_23, % 86.22/12.29 | all_6_24 gives: % 86.22/12.30 | (129) op(e4, e4) = all_6_0 & op(e4, e3) = all_6_1 & op(e4, e2) = all_6_2 & % 86.22/12.30 | op(e4, e1) = all_6_3 & op(e4, e0) = all_6_4 & op(e3, e4) = all_6_5 & % 86.22/12.30 | op(e3, e3) = all_6_6 & op(e3, e2) = all_6_7 & op(e3, e1) = all_6_8 & % 86.22/12.30 | op(e3, e0) = all_6_9 & op(e2, e4) = all_6_10 & op(e2, e3) = all_6_11 % 86.22/12.30 | & op(e2, e2) = all_6_12 & op(e2, e1) = all_6_13 & op(e2, e0) = % 86.22/12.30 | all_6_14 & op(e1, e4) = all_6_15 & op(e1, e3) = all_6_16 & op(e1, e2) % 86.22/12.30 | = all_6_17 & op(e1, e1) = all_6_18 & op(e1, e0) = all_6_19 & op(e0, % 86.22/12.30 | e4) = all_6_20 & op(e0, e3) = all_6_21 & op(e0, e2) = all_6_22 & % 86.22/12.30 | op(e0, e1) = all_6_23 & op(e0, e0) = all_6_24 & $i(all_6_0) & % 86.22/12.30 | $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & $i(all_6_4) & $i(all_6_5) & % 86.22/12.30 | $i(all_6_6) & $i(all_6_7) & $i(all_6_8) & $i(all_6_9) & $i(all_6_10) % 86.22/12.30 | & $i(all_6_11) & $i(all_6_12) & $i(all_6_13) & $i(all_6_14) & % 86.22/12.30 | $i(all_6_15) & $i(all_6_16) & $i(all_6_17) & $i(all_6_18) & % 86.22/12.30 | $i(all_6_19) & $i(all_6_20) & $i(all_6_21) & $i(all_6_22) & % 86.22/12.30 | $i(all_6_23) & $i(all_6_24) & (all_6_0 = e4 | all_6_0 = e3 | all_6_0 % 86.22/12.30 | = e2 | all_6_0 = e1 | all_6_0 = e0) & (all_6_1 = e4 | all_6_1 = e3 % 86.22/12.30 | | all_6_1 = e2 | all_6_1 = e1 | all_6_1 = e0) & (all_6_2 = e4 | % 86.22/12.30 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0) & % 86.22/12.30 | (all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e2 | all_6_3 = e1 | all_6_3 % 86.22/12.30 | = e0) & (all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 % 86.22/12.30 | | all_6_4 = e0) & (all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e2 | % 86.22/12.30 | all_6_5 = e1 | all_6_5 = e0) & (all_6_6 = e4 | all_6_6 = e3 | % 86.22/12.30 | all_6_6 = e2 | all_6_6 = e1 | all_6_6 = e0) & (all_6_7 = e4 | % 86.22/12.30 | all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | all_6_7 = e0) & % 86.22/12.30 | (all_6_8 = e4 | all_6_8 = e3 | all_6_8 = e2 | all_6_8 = e1 | all_6_8 % 86.22/12.30 | = e0) & (all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e2 | all_6_9 = e1 % 86.22/12.30 | | all_6_9 = e0) & (all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e2 | % 86.22/12.30 | all_6_10 = e1 | all_6_10 = e0) & (all_6_11 = e4 | all_6_11 = e3 | % 86.22/12.30 | all_6_11 = e2 | all_6_11 = e1 | all_6_11 = e0) & (all_6_12 = e4 | % 86.22/12.30 | all_6_12 = e3 | all_6_12 = e2 | all_6_12 = e1 | all_6_12 = e0) & % 86.22/12.30 | (all_6_13 = e4 | all_6_13 = e3 | all_6_13 = e2 | all_6_13 = e1 | % 86.22/12.30 | all_6_13 = e0) & (all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e2 | % 86.22/12.30 | all_6_14 = e1 | all_6_14 = e0) & (all_6_15 = e4 | all_6_15 = e3 | % 86.22/12.30 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 = e0) & (all_6_16 = e4 | % 86.22/12.30 | all_6_16 = e3 | all_6_16 = e2 | all_6_16 = e1 | all_6_16 = e0) & % 86.22/12.30 | (all_6_17 = e4 | all_6_17 = e3 | all_6_17 = e2 | all_6_17 = e1 | % 86.22/12.30 | all_6_17 = e0) & (all_6_18 = e4 | all_6_18 = e3 | all_6_18 = e2 | % 86.22/12.30 | all_6_18 = e1 | all_6_18 = e0) & (all_6_19 = e4 | all_6_19 = e3 | % 86.22/12.30 | all_6_19 = e2 | all_6_19 = e1 | all_6_19 = e0) & (all_6_20 = e4 | % 86.22/12.30 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 = e0) & % 86.22/12.30 | (all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e2 | all_6_21 = e1 | % 86.22/12.30 | all_6_21 = e0) & (all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e2 | % 86.22/12.30 | all_6_22 = e1 | all_6_22 = e0) & (all_6_23 = e4 | all_6_23 = e3 | % 86.22/12.30 | all_6_23 = e2 | all_6_23 = e1 | all_6_23 = e0) & (all_6_24 = e4 | % 86.22/12.30 | all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | all_6_24 = e0) % 86.22/12.30 | % 86.22/12.30 | ALPHA: (129) implies: % 86.22/12.30 | (130) op(e0, e0) = all_6_24 % 86.22/12.30 | (131) op(e0, e1) = all_6_23 % 86.22/12.30 | (132) op(e0, e2) = all_6_22 % 86.22/12.30 | (133) op(e0, e3) = all_6_21 % 86.22/12.30 | (134) op(e0, e4) = all_6_20 % 86.22/12.30 | (135) op(e1, e0) = all_6_19 % 86.22/12.30 | (136) op(e1, e1) = all_6_18 % 86.22/12.30 | (137) op(e1, e3) = all_6_16 % 86.22/12.30 | (138) op(e1, e4) = all_6_15 % 86.22/12.30 | (139) op(e2, e0) = all_6_14 % 86.22/12.30 | (140) op(e2, e1) = all_6_13 % 86.22/12.30 | (141) op(e2, e2) = all_6_12 % 86.22/12.30 | (142) op(e2, e3) = all_6_11 % 86.22/12.30 | (143) op(e2, e4) = all_6_10 % 86.22/12.30 | (144) op(e3, e1) = all_6_8 % 86.22/12.30 | (145) op(e3, e2) = all_6_7 % 86.22/12.30 | (146) op(e3, e3) = all_6_6 % 86.22/12.30 | (147) op(e3, e4) = all_6_5 % 86.22/12.30 | (148) op(e4, e0) = all_6_4 % 86.22/12.30 | (149) op(e4, e1) = all_6_3 % 86.22/12.30 | (150) op(e4, e2) = all_6_2 % 86.22/12.30 | (151) op(e4, e3) = all_6_1 % 86.22/12.30 | (152) op(e4, e4) = all_6_0 % 86.22/12.30 | (153) all_6_24 = e4 | all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | % 86.22/12.30 | all_6_24 = e0 % 86.22/12.30 | (154) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e2 | all_6_22 = e1 | % 86.22/12.30 | all_6_22 = e0 % 86.22/12.30 | (155) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e2 | all_6_21 = e1 | % 86.22/12.30 | all_6_21 = e0 % 86.22/12.30 | (156) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 86.22/12.30 | all_6_20 = e0 % 86.22/12.30 | (157) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 86.22/12.30 | all_6_15 = e0 % 86.22/12.30 | (158) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | % 86.22/12.30 | all_6_14 = e0 % 86.22/12.30 | (159) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 86.22/12.30 | all_6_11 = e0 % 86.22/12.30 | (160) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | all_6_7 = % 86.22/12.30 | e0 % 86.22/12.30 | (161) all_6_6 = e4 | all_6_6 = e3 | all_6_6 = e2 | all_6_6 = e1 | all_6_6 = % 86.22/12.30 | e0 % 86.22/12.31 | (162) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 | all_6_4 = % 86.22/12.31 | e0 % 86.22/12.31 | (163) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = % 86.22/12.31 | e0 % 86.22/12.31 | % 86.22/12.31 | DELTA: instantiating (24) with fresh symbols all_8_0, all_8_1, all_8_2, % 86.22/12.31 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9, % 86.22/12.31 | all_8_10, all_8_11, all_8_12, all_8_13, all_8_14, all_8_15, all_8_16, % 86.22/12.31 | all_8_17, all_8_18, all_8_19, all_8_20, all_8_21, all_8_22, all_8_23, % 86.22/12.31 | all_8_24, all_8_25, all_8_26, all_8_27, all_8_28, all_8_29, all_8_30, % 86.22/12.31 | all_8_31, all_8_32, all_8_33, all_8_34, all_8_35, all_8_36, all_8_37, % 86.22/12.31 | all_8_38, all_8_39, all_8_40, all_8_41, all_8_42, all_8_43, all_8_44, % 86.22/12.31 | all_8_45, all_8_46, all_8_47, all_8_48, all_8_49, all_8_50, all_8_51, % 86.22/12.31 | all_8_52, all_8_53, all_8_54, all_8_55, all_8_56, all_8_57, all_8_58, % 86.22/12.31 | all_8_59, all_8_60, all_8_61, all_8_62, all_8_63, all_8_64 gives: % 86.22/12.31 | (164) ((all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = e3 % 86.22/12.31 | & op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3)) | % 86.22/12.31 | (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = % 86.22/12.31 | e3 & op(e4, e3) = all_8_15 & op(e3, e3) = e4 & $i(all_8_15)) | % 86.22/12.31 | (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 % 86.22/12.31 | & op(e2, e4) = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | % 86.22/12.31 | (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_28 = e4) & op(e4, e4) = % 86.22/12.31 | e2 & op(e4, e2) = all_8_28 & op(e2, e2) = e4 & $i(all_8_28)) | % 86.22/12.31 | (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = e1) & op(e4, e4) = e1 % 86.22/12.31 | & op(e1, e4) = all_8_9 & op(e1, e1) = e4 & $i(all_8_9)) | % 86.22/12.31 | (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) = % 86.22/12.31 | e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & $i(all_8_41)) | % 86.22/12.31 | (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) & op(e4, e4) = % 86.22/12.31 | e0 & op(e4, e0) = all_8_54 & op(e0, e0) = e4 & $i(all_8_54)) | % 86.22/12.31 | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = e2) & op(e3, e3) = % 86.22/12.31 | e2 & op(e2, e3) = all_8_19 & op(e2, e2) = e3 & $i(all_8_19)) | % 86.22/12.31 | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) & op(e3, e3) = % 86.22/12.31 | e2 & op(e3, e2) = all_8_31 & op(e2, e2) = e3 & $i(all_8_31)) | % 86.22/12.31 | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, e3) = % 86.22/12.31 | e1 & op(e1, e3) = all_8_22 & op(e1, e1) = e3 & $i(all_8_22)) | % 86.22/12.31 | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) & op(e3, e3) = % 86.22/12.31 | e1 & op(e3, e1) = all_8_44 & op(e1, e1) = e3 & $i(all_8_44)) | % 86.22/12.31 | (all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & op(e3, e3) = % 86.22/12.31 | e0 & op(e3, e0) = all_8_57 & op(e0, e0) = e3 & $i(all_8_57)) | % 86.22/12.31 | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) & op(e2, e2) = % 86.22/12.31 | e1 & op(e1, e2) = all_8_35 & op(e1, e1) = e2 & $i(all_8_35)) | % 86.22/12.31 | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, e2) = % 86.22/12.31 | e1 & op(e2, e1) = all_8_47 & op(e1, e1) = e2 & $i(all_8_47)) | % 86.22/12.31 | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) & op(e2, e2) = % 86.22/12.31 | e0 & op(e2, e0) = all_8_60 & op(e0, e0) = e2 & $i(all_8_60)) | % 86.22/12.31 | (op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = e0 & all_8_64 = % 86.22/12.31 | e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 & op(e0, e4) = % 86.22/12.31 | all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 & % 86.22/12.31 | ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 86.22/12.31 | $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 % 86.22/12.31 | = e0) & op(e2, e2) = e0 & op(e0, e2) = all_8_38 & % 86.22/12.31 | $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 % 86.22/12.31 | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_8_51 & % 86.22/12.31 | $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_63 % 86.22/12.31 | = e1) & op(e1, e1) = e0 & op(e1, e0) = all_8_63 & % 86.22/12.31 | $i(all_8_63))))) & ((all_8_1 = e3 & ~ (all_8_2 = e4) & % 86.22/12.31 | op(e4, all_8_3) = e3 & op(e3, all_8_3) = all_8_2 & op(e3, e4) = % 86.22/12.31 | all_8_3 & $i(all_8_2) & $i(all_8_3)) | (all_8_4 = e2 & ~ % 86.22/12.31 | (all_8_5 = e4) & op(e4, all_8_6) = e2 & op(e2, all_8_6) = all_8_5 % 86.22/12.31 | & op(e2, e4) = all_8_6 & $i(all_8_5) & $i(all_8_6)) | (all_8_7 = % 86.22/12.31 | e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) = e1 & op(e1, all_8_9) = % 86.22/12.31 | all_8_8 & op(e1, e4) = all_8_9 & $i(all_8_8) & $i(all_8_9)) | % 86.22/12.31 | (all_8_10 = e0 & ~ (all_8_11 = e4) & op(e4, all_8_12) = e0 & % 86.22/12.31 | op(e0, all_8_12) = all_8_11 & op(e0, e4) = all_8_12 & % 86.22/12.31 | $i(all_8_11) & $i(all_8_12))) & ((all_8_13 = e4 & ~ (all_8_14 = % 86.22/12.31 | e3) & op(e4, all_8_15) = all_8_14 & op(e4, e3) = all_8_15 & % 86.22/12.31 | op(e3, all_8_15) = e4 & $i(all_8_14) & $i(all_8_15)) | (all_8_17 % 86.22/12.31 | = e2 & ~ (all_8_18 = e3) & op(e3, all_8_19) = e2 & op(e2, % 86.22/12.31 | all_8_19) = all_8_18 & op(e2, e3) = all_8_19 & $i(all_8_18) & % 86.22/12.31 | $i(all_8_19)) | (all_8_20 = e1 & ~ (all_8_21 = e3) & op(e3, % 86.22/12.31 | all_8_22) = e1 & op(e1, all_8_22) = all_8_21 & op(e1, e3) = % 86.22/12.31 | all_8_22 & $i(all_8_21) & $i(all_8_22)) | (all_8_23 = e0 & ~ % 86.22/12.31 | (all_8_24 = e3) & op(e3, all_8_25) = e0 & op(e0, all_8_25) = % 86.22/12.31 | all_8_24 & op(e0, e3) = all_8_25 & $i(all_8_24) & $i(all_8_25))) % 86.22/12.31 | & ((all_8_26 = e4 & ~ (all_8_27 = e2) & op(e4, all_8_28) = all_8_27 % 86.22/12.31 | & op(e4, e2) = all_8_28 & op(e2, all_8_28) = e4 & $i(all_8_27) & % 86.22/12.31 | $i(all_8_28)) | (all_8_29 = e3 & ~ (all_8_30 = e2) & op(e3, % 86.22/12.31 | all_8_31) = all_8_30 & op(e3, e2) = all_8_31 & op(e2, all_8_31) % 86.22/12.31 | = e3 & $i(all_8_30) & $i(all_8_31)) | (all_8_33 = e1 & ~ % 86.22/12.31 | (all_8_34 = e2) & op(e2, all_8_35) = e1 & op(e1, all_8_35) = % 86.22/12.31 | all_8_34 & op(e1, e2) = all_8_35 & $i(all_8_34) & $i(all_8_35)) | % 86.22/12.31 | (all_8_36 = e0 & ~ (all_8_37 = e2) & op(e2, all_8_38) = e0 & % 86.22/12.31 | op(e0, all_8_38) = all_8_37 & op(e0, e2) = all_8_38 & % 86.22/12.31 | $i(all_8_37) & $i(all_8_38))) & ((all_8_39 = e4 & ~ (all_8_40 = % 86.22/12.31 | e1) & op(e4, all_8_41) = all_8_40 & op(e4, e1) = all_8_41 & % 86.22/12.31 | op(e1, all_8_41) = e4 & $i(all_8_40) & $i(all_8_41)) | (all_8_42 % 86.22/12.31 | = e3 & ~ (all_8_43 = e1) & op(e3, all_8_44) = all_8_43 & op(e3, % 86.22/12.31 | e1) = all_8_44 & op(e1, all_8_44) = e3 & $i(all_8_43) & % 86.22/12.31 | $i(all_8_44)) | (all_8_45 = e2 & ~ (all_8_46 = e1) & op(e2, % 86.22/12.31 | all_8_47) = all_8_46 & op(e2, e1) = all_8_47 & op(e1, all_8_47) % 86.22/12.31 | = e2 & $i(all_8_46) & $i(all_8_47)) | (all_8_49 = e0 & ~ % 86.22/12.31 | (all_8_50 = e1) & op(e1, all_8_51) = e0 & op(e0, all_8_51) = % 86.22/12.31 | all_8_50 & op(e0, e1) = all_8_51 & $i(all_8_50) & $i(all_8_51))) % 86.22/12.31 | & ((all_8_52 = e4 & ~ (all_8_53 = e0) & op(e4, all_8_54) = all_8_53 % 86.22/12.31 | & op(e4, e0) = all_8_54 & op(e0, all_8_54) = e4 & $i(all_8_53) & % 86.22/12.31 | $i(all_8_54)) | (all_8_55 = e3 & ~ (all_8_56 = e0) & op(e3, % 86.22/12.31 | all_8_57) = all_8_56 & op(e3, e0) = all_8_57 & op(e0, all_8_57) % 86.22/12.31 | = e3 & $i(all_8_56) & $i(all_8_57)) | (all_8_58 = e2 & ~ % 86.22/12.31 | (all_8_59 = e0) & op(e2, all_8_60) = all_8_59 & op(e2, e0) = % 86.22/12.31 | all_8_60 & op(e0, all_8_60) = e2 & $i(all_8_59) & $i(all_8_60)) | % 86.22/12.31 | (all_8_61 = e1 & ~ (all_8_62 = e0) & op(e1, all_8_63) = all_8_62 & % 86.22/12.31 | op(e1, e0) = all_8_63 & op(e0, all_8_63) = e1 & $i(all_8_62) & % 86.22/12.31 | $i(all_8_63))) % 86.22/12.31 | % 86.22/12.31 | ALPHA: (164) implies: % 86.22/12.32 | (165) (all_8_52 = e4 & ~ (all_8_53 = e0) & op(e4, all_8_54) = all_8_53 & % 86.22/12.32 | op(e4, e0) = all_8_54 & op(e0, all_8_54) = e4 & $i(all_8_53) & % 86.22/12.32 | $i(all_8_54)) | (all_8_55 = e3 & ~ (all_8_56 = e0) & op(e3, % 86.22/12.32 | all_8_57) = all_8_56 & op(e3, e0) = all_8_57 & op(e0, all_8_57) = % 86.22/12.32 | e3 & $i(all_8_56) & $i(all_8_57)) | (all_8_58 = e2 & ~ (all_8_59 = % 86.22/12.32 | e0) & op(e2, all_8_60) = all_8_59 & op(e2, e0) = all_8_60 & % 86.22/12.32 | op(e0, all_8_60) = e2 & $i(all_8_59) & $i(all_8_60)) | (all_8_61 = % 86.22/12.32 | e1 & ~ (all_8_62 = e0) & op(e1, all_8_63) = all_8_62 & op(e1, e0) % 86.22/12.32 | = all_8_63 & op(e0, all_8_63) = e1 & $i(all_8_62) & $i(all_8_63)) % 86.22/12.32 | (166) (all_8_26 = e4 & ~ (all_8_27 = e2) & op(e4, all_8_28) = all_8_27 & % 86.22/12.32 | op(e4, e2) = all_8_28 & op(e2, all_8_28) = e4 & $i(all_8_27) & % 86.22/12.32 | $i(all_8_28)) | (all_8_29 = e3 & ~ (all_8_30 = e2) & op(e3, % 86.22/12.32 | all_8_31) = all_8_30 & op(e3, e2) = all_8_31 & op(e2, all_8_31) = % 86.22/12.32 | e3 & $i(all_8_30) & $i(all_8_31)) | (all_8_33 = e1 & ~ (all_8_34 = % 86.22/12.32 | e2) & op(e2, all_8_35) = e1 & op(e1, all_8_35) = all_8_34 & % 86.22/12.32 | op(e1, e2) = all_8_35 & $i(all_8_34) & $i(all_8_35)) | (all_8_36 = % 86.22/12.32 | e0 & ~ (all_8_37 = e2) & op(e2, all_8_38) = e0 & op(e0, all_8_38) % 86.22/12.32 | = all_8_37 & op(e0, e2) = all_8_38 & $i(all_8_37) & $i(all_8_38)) % 86.22/12.32 | (167) (all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, all_8_3) = e3 & op(e3, % 86.22/12.32 | all_8_3) = all_8_2 & op(e3, e4) = all_8_3 & $i(all_8_2) & % 86.22/12.32 | $i(all_8_3)) | (all_8_4 = e2 & ~ (all_8_5 = e4) & op(e4, all_8_6) % 86.22/12.32 | = e2 & op(e2, all_8_6) = all_8_5 & op(e2, e4) = all_8_6 & % 86.22/12.32 | $i(all_8_5) & $i(all_8_6)) | (all_8_7 = e1 & ~ (all_8_8 = e4) & % 86.22/12.32 | op(e4, all_8_9) = e1 & op(e1, all_8_9) = all_8_8 & op(e1, e4) = % 86.22/12.32 | all_8_9 & $i(all_8_8) & $i(all_8_9)) | (all_8_10 = e0 & ~ % 86.22/12.32 | (all_8_11 = e4) & op(e4, all_8_12) = e0 & op(e0, all_8_12) = % 86.22/12.32 | all_8_11 & op(e0, e4) = all_8_12 & $i(all_8_11) & $i(all_8_12)) % 86.22/12.32 | (168) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = e3 & % 86.22/12.32 | op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = % 86.22/12.32 | e3 & all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = e3 & op(e4, % 86.22/12.32 | e3) = all_8_15 & op(e3, e3) = e4 & $i(all_8_15)) | (all_8_0 = e2 % 86.22/12.32 | & all_8_32 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 & op(e2, e4) % 86.22/12.32 | = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | (all_8_0 = e2 & % 86.22/12.32 | all_8_32 = e4 & ~ (all_8_28 = e4) & op(e4, e4) = e2 & op(e4, e2) = % 86.22/12.32 | all_8_28 & op(e2, e2) = e4 & $i(all_8_28)) | (all_8_0 = e1 & % 86.22/12.32 | all_8_48 = e4 & ~ (all_8_9 = e1) & op(e4, e4) = e1 & op(e1, e4) = % 86.22/12.32 | all_8_9 & op(e1, e1) = e4 & $i(all_8_9)) | (all_8_0 = e1 & all_8_48 % 86.22/12.32 | = e4 & ~ (all_8_41 = e4) & op(e4, e4) = e1 & op(e4, e1) = all_8_41 % 86.22/12.32 | & op(e1, e1) = e4 & $i(all_8_41)) | (all_8_0 = e0 & all_8_64 = e4 & % 86.22/12.32 | ~ (all_8_54 = e4) & op(e4, e4) = e0 & op(e4, e0) = all_8_54 & % 86.22/12.32 | op(e0, e0) = e4 & $i(all_8_54)) | (all_8_16 = e2 & all_8_32 = e3 & % 86.22/12.32 | ~ (all_8_19 = e2) & op(e3, e3) = e2 & op(e2, e3) = all_8_19 & % 86.22/12.32 | op(e2, e2) = e3 & $i(all_8_19)) | (all_8_16 = e2 & all_8_32 = e3 & % 86.22/12.32 | ~ (all_8_31 = e3) & op(e3, e3) = e2 & op(e3, e2) = all_8_31 & % 86.22/12.32 | op(e2, e2) = e3 & $i(all_8_31)) | (all_8_16 = e1 & all_8_48 = e3 & % 86.22/12.32 | ~ (all_8_22 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_8_22 & % 86.22/12.32 | op(e1, e1) = e3 & $i(all_8_22)) | (all_8_16 = e1 & all_8_48 = e3 & % 86.22/12.32 | ~ (all_8_44 = e3) & op(e3, e3) = e1 & op(e3, e1) = all_8_44 & % 86.22/12.32 | op(e1, e1) = e3 & $i(all_8_44)) | (all_8_16 = e0 & all_8_64 = e3 & % 86.22/12.32 | ~ (all_8_57 = e3) & op(e3, e3) = e0 & op(e3, e0) = all_8_57 & % 86.22/12.32 | op(e0, e0) = e3 & $i(all_8_57)) | (all_8_32 = e1 & all_8_48 = e2 & % 86.22/12.32 | ~ (all_8_35 = e1) & op(e2, e2) = e1 & op(e1, e2) = all_8_35 & % 86.22/12.32 | op(e1, e1) = e2 & $i(all_8_35)) | (all_8_32 = e1 & all_8_48 = e2 & % 86.22/12.32 | ~ (all_8_47 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_8_47 & % 86.22/12.32 | op(e1, e1) = e2 & $i(all_8_47)) | (all_8_32 = e0 & all_8_64 = e2 & % 86.22/12.32 | ~ (all_8_60 = e2) & op(e2, e2) = e0 & op(e2, e0) = all_8_60 & % 86.22/12.32 | op(e0, e0) = e2 & $i(all_8_60)) | (op(e0, e0) = all_8_64 & % 86.22/12.32 | $i(all_8_64) & ((all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) % 86.22/12.32 | & op(e4, e4) = e0 & op(e0, e4) = all_8_12 & $i(all_8_12)) | % 86.22/12.32 | (all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_25 = e0) & op(e3, e3) % 86.22/12.32 | = e0 & op(e0, e3) = all_8_25 & $i(all_8_25)) | (all_8_32 = e0 & % 86.22/12.32 | all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, e2) = e0 & op(e0, % 86.22/12.32 | e2) = all_8_38 & $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = % 86.22/12.32 | e1 & ~ (all_8_51 = e0) & op(e1, e1) = e0 & op(e0, e1) = % 86.22/12.32 | all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = e1 & ~ % 86.22/12.32 | (all_8_63 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_8_63 & % 86.22/12.32 | $i(all_8_63)))) % 86.22/12.32 | % 86.22/12.32 | DELTA: instantiating (12) with fresh symbols all_9_0, all_9_1, all_9_2, % 86.22/12.32 | all_9_3, all_9_4, all_9_5, all_9_6, all_9_7, all_9_8, all_9_9, % 86.22/12.32 | all_9_10, all_9_11, all_9_12, all_9_13, all_9_14, all_9_15, all_9_16, % 86.22/12.32 | all_9_17, all_9_18, all_9_19, all_9_20, all_9_21, all_9_22, all_9_23, % 86.22/12.32 | all_9_24 gives: % 86.22/12.34 | (169) ((all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) % 86.22/12.34 | | (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = % 86.22/12.34 | e4) | (all_9_16 = e4 & op(e4, e0) = e4)) & ((all_9_0 = e4 & % 86.22/12.34 | op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_6 = % 86.22/12.34 | e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 86.22/12.34 | (all_9_20 = e4 & op(e0, e4) = e4)) & ((all_9_0 = e3 & op(e4, e4) = % 86.22/12.34 | e3) | (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_4 = e3 & op(e4, % 86.22/12.34 | e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 & % 86.22/12.34 | op(e4, e0) = e3)) & ((all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 % 86.22/12.34 | = e3 & op(e3, e4) = e3) | (all_9_6 = e3 & op(e2, e4) = e3) | % 86.22/12.34 | (all_9_12 = e3 & op(e1, e4) = e3) | (all_9_20 = e3 & op(e0, e4) = % 86.22/12.34 | e3)) & ((all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, % 86.22/12.34 | e3) = e2) | (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 86.22/12.34 | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = e2)) & ((all_9_0 % 86.22/12.34 | = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 86.22/12.34 | (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = % 86.22/12.34 | e2) | (all_9_20 = e2 & op(e0, e4) = e2)) & ((all_9_0 = e1 & % 86.22/12.34 | op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | (all_9_4 = % 86.22/12.34 | e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 86.22/12.34 | (all_9_16 = e1 & op(e4, e0) = e1)) & ((all_9_0 = e1 & op(e4, e4) = % 86.22/12.34 | e1) | (all_9_2 = e1 & op(e3, e4) = e1) | (all_9_6 = e1 & op(e2, % 86.22/12.34 | e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_20 = e1 % 86.22/12.34 | & op(e0, e4) = e1)) & ((all_9_0 = e0 & op(e4, e4) = e0) | % 86.22/12.34 | (all_9_1 = e0 & op(e4, e3) = e0) | (all_9_4 = e0 & op(e4, e2) = e0) % 86.22/12.34 | | (all_9_9 = e0 & op(e4, e1) = e0) | (all_9_16 = e0 & op(e4, e0) = % 86.22/12.34 | e0)) & ((all_9_0 = e0 & op(e4, e4) = e0) | (all_9_2 = e0 & op(e3, % 86.22/12.34 | e4) = e0) | (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_12 = e0 & % 86.22/12.34 | op(e1, e4) = e0) | (all_9_20 = e0 & op(e0, e4) = e0)) & ((all_9_1 % 86.22/12.34 | = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 86.22/12.34 | (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 & op(e1, e3) = % 86.22/12.34 | e4) | (all_9_21 = e4 & op(e0, e3) = e4)) & ((all_9_1 = e3 & % 86.22/12.34 | op(e4, e3) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | (all_9_7 = % 86.22/12.34 | e3 & op(e2, e3) = e3) | (all_9_13 = e3 & op(e1, e3) = e3) | % 86.22/12.34 | (all_9_21 = e3 & op(e0, e3) = e3)) & ((all_9_1 = e2 & op(e4, e3) = % 86.22/12.34 | e2) | (all_9_3 = e2 & op(e3, e3) = e2) | (all_9_7 = e2 & op(e2, % 86.22/12.34 | e3) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | (all_9_21 = e2 % 86.22/12.34 | & op(e0, e3) = e2)) & ((all_9_1 = e1 & op(e4, e3) = e1) | % 86.22/12.34 | (all_9_3 = e1 & op(e3, e3) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) % 86.22/12.34 | | (all_9_13 = e1 & op(e1, e3) = e1) | (all_9_21 = e1 & op(e0, e3) = % 86.22/12.34 | e1)) & ((all_9_1 = e0 & op(e4, e3) = e0) | (all_9_3 = e0 & op(e3, % 86.22/12.34 | e3) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | (all_9_13 = e0 & % 86.22/12.34 | op(e1, e3) = e0) | (all_9_21 = e0 & op(e0, e3) = e0)) & ((all_9_2 % 86.22/12.34 | = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 86.22/12.34 | (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, e1) = % 86.22/12.34 | e4) | (all_9_17 = e4 & op(e3, e0) = e4)) & ((all_9_2 = e3 & % 86.22/12.34 | op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | (all_9_5 = % 86.22/12.34 | e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 86.22/12.34 | (all_9_17 = e3 & op(e3, e0) = e3)) & ((all_9_2 = e2 & op(e3, e4) = % 86.22/12.34 | e2) | (all_9_3 = e2 & op(e3, e3) = e2) | (all_9_5 = e2 & op(e3, % 86.22/12.34 | e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 % 86.22/12.34 | & op(e3, e0) = e2)) & ((all_9_2 = e1 & op(e3, e4) = e1) | % 86.22/12.34 | (all_9_3 = e1 & op(e3, e3) = e1) | (all_9_5 = e1 & op(e3, e2) = e1) % 86.22/12.34 | | (all_9_10 = e1 & op(e3, e1) = e1) | (all_9_17 = e1 & op(e3, e0) = % 86.22/12.34 | e1)) & ((all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & op(e3, % 86.22/12.34 | e3) = e0) | (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 & % 86.22/12.34 | op(e3, e1) = e0) | (all_9_17 = e0 & op(e3, e0) = e0)) & ((all_9_4 % 86.22/12.34 | = e4 & op(e4, e2) = e4) | (all_9_5 = e4 & op(e3, e2) = e4) | % 86.22/12.34 | (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_14 = e4 & op(e1, e2) = % 86.22/12.34 | e4) | (all_9_22 = e4 & op(e0, e2) = e4)) & ((all_9_4 = e3 & % 86.22/12.34 | op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_8 = % 86.22/12.34 | e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 86.22/12.34 | (all_9_22 = e3 & op(e0, e2) = e3)) & ((all_9_4 = e2 & op(e4, e2) = % 86.22/12.34 | e2) | (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_8 = e2 & op(e2, % 86.22/12.34 | e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 % 86.22/12.34 | & op(e0, e2) = e2)) & ((all_9_4 = e1 & op(e4, e2) = e1) | % 86.22/12.34 | (all_9_5 = e1 & op(e3, e2) = e1) | (all_9_8 = e1 & op(e2, e2) = e1) % 86.22/12.34 | | (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_22 = e1 & op(e0, e2) = % 86.22/12.34 | e1)) & ((all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & op(e3, % 86.22/12.34 | e2) = e0) | (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 & % 86.22/12.34 | op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) = e0)) & ((all_9_6 % 86.22/12.34 | = e4 & op(e2, e4) = e4) | (all_9_7 = e4 & op(e2, e3) = e4) | % 86.22/12.34 | (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_11 = e4 & op(e2, e1) = % 86.22/12.34 | e4) | (all_9_18 = e4 & op(e2, e0) = e4)) & ((all_9_6 = e3 & % 86.22/12.34 | op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_8 = % 86.22/12.34 | e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) = e3) | % 86.22/12.34 | (all_9_18 = e3 & op(e2, e0) = e3)) & ((all_9_6 = e2 & op(e2, e4) = % 86.22/12.34 | e2) | (all_9_7 = e2 & op(e2, e3) = e2) | (all_9_8 = e2 & op(e2, % 86.22/12.34 | e2) = e2) | (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 86.22/12.34 | & op(e2, e0) = e2)) & ((all_9_6 = e1 & op(e2, e4) = e1) | % 86.22/12.34 | (all_9_7 = e1 & op(e2, e3) = e1) | (all_9_8 = e1 & op(e2, e2) = e1) % 86.22/12.34 | | (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_18 = e1 & op(e2, e0) = % 86.22/12.34 | e1)) & ((all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, % 86.22/12.34 | e3) = e0) | (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & % 86.22/12.34 | op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) = e0)) & ((all_9_9 % 86.22/12.34 | = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 86.22/12.34 | (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = % 86.22/12.34 | e4) | (all_9_23 = e4 & op(e0, e1) = e4)) & ((all_9_9 = e3 & % 86.22/12.34 | op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_11 % 86.22/12.34 | = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = e3) | % 86.22/12.34 | (all_9_23 = e3 & op(e0, e1) = e3)) & ((all_9_9 = e2 & op(e4, e1) = % 86.22/12.34 | e2) | (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_11 = e2 & op(e2, % 86.22/12.34 | e1) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_23 = e2 % 86.22/12.34 | & op(e0, e1) = e2)) & ((all_9_9 = e1 & op(e4, e1) = e1) | % 86.22/12.34 | (all_9_10 = e1 & op(e3, e1) = e1) | (all_9_11 = e1 & op(e2, e1) = % 86.22/12.34 | e1) | (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_23 = e1 & op(e0, % 86.22/12.34 | e1) = e1)) & ((all_9_9 = e0 & op(e4, e1) = e0) | (all_9_10 = e0 % 86.22/12.34 | & op(e3, e1) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) | % 86.22/12.34 | (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_23 = e0 & op(e0, e1) = % 86.22/12.34 | e0)) & ((all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 & % 86.22/12.34 | op(e1, e3) = e4) | (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 % 86.22/12.34 | = e4 & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) = e4)) & % 86.22/12.34 | ((all_9_12 = e3 & op(e1, e4) = e3) | (all_9_13 = e3 & op(e1, e3) = % 86.22/12.34 | e3) | (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_15 = e3 & op(e1, % 86.22/12.34 | e1) = e3) | (all_9_19 = e3 & op(e1, e0) = e3)) & ((all_9_12 = % 86.22/12.34 | e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 86.22/12.34 | (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = % 86.22/12.34 | e2) | (all_9_19 = e2 & op(e1, e0) = e2)) & ((all_9_12 = e1 & % 86.22/12.34 | op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | (all_9_14 % 86.22/12.34 | = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 86.22/12.34 | (all_9_19 = e1 & op(e1, e0) = e1)) & ((all_9_12 = e0 & op(e1, e4) = % 86.22/12.34 | e0) | (all_9_13 = e0 & op(e1, e3) = e0) | (all_9_14 = e0 & op(e1, % 86.22/12.34 | e2) = e0) | (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_19 = e0 % 86.22/12.34 | & op(e1, e0) = e0)) & ((all_9_16 = e4 & op(e4, e0) = e4) | % 86.22/12.34 | (all_9_17 = e4 & op(e3, e0) = e4) | (all_9_18 = e4 & op(e2, e0) = % 86.22/12.34 | e4) | (all_9_19 = e4 & op(e1, e0) = e4) | (all_9_24 = e4 & op(e0, % 86.22/12.34 | e0) = e4)) & ((all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = % 86.22/12.34 | e3 & op(e3, e0) = e3) | (all_9_18 = e3 & op(e2, e0) = e3) | % 86.22/12.34 | (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) = % 86.22/12.34 | e3)) & ((all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & % 86.22/12.34 | op(e3, e0) = e2) | (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 % 86.22/12.34 | = e2 & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, e0) = e2)) & % 86.22/12.34 | ((all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = % 86.22/12.34 | e1) | (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, % 86.22/12.34 | e0) = e1) | (all_9_24 = e1 & op(e0, e0) = e1)) & ((all_9_20 = % 86.22/12.34 | e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) | % 86.22/12.34 | (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & op(e0, e1) = % 86.22/12.34 | e4) | (all_9_24 = e4 & op(e0, e0) = e4)) & ((all_9_20 = e3 & % 86.22/12.34 | op(e0, e4) = e3) | (all_9_21 = e3 & op(e0, e3) = e3) | (all_9_22 % 86.22/12.34 | = e3 & op(e0, e2) = e3) | (all_9_23 = e3 & op(e0, e1) = e3) | % 86.22/12.34 | (all_9_24 = e3 & op(e0, e0) = e3)) & ((all_9_20 = e2 & op(e0, e4) = % 86.22/12.34 | e2) | (all_9_21 = e2 & op(e0, e3) = e2) | (all_9_22 = e2 & op(e0, % 86.22/12.34 | e2) = e2) | (all_9_23 = e2 & op(e0, e1) = e2) | (all_9_24 = e2 % 86.22/12.34 | & op(e0, e0) = e2)) & ((all_9_20 = e1 & op(e0, e4) = e1) | % 86.22/12.34 | (all_9_21 = e1 & op(e0, e3) = e1) | (all_9_22 = e1 & op(e0, e2) = % 86.22/12.34 | e1) | (all_9_23 = e1 & op(e0, e1) = e1) | (all_9_24 = e1 & op(e0, % 86.22/12.34 | e0) = e1)) & ((all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = % 86.22/12.34 | e0 & op(e4, e0) = e0) | (all_9_17 = e0 & op(e3, e0) = e0) | % 86.22/12.34 | (all_9_18 = e0 & op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 86.22/12.34 | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 86.22/12.34 | & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) = e0) | % 86.22/12.34 | (all_9_23 = e0 & op(e0, e1) = e0)))) % 86.22/12.34 | % 86.22/12.34 | ALPHA: (169) implies: % 86.22/12.34 | (170) (all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = e0 & op(e4, e0) = % 86.22/12.34 | e0) | (all_9_17 = e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 86.22/12.34 | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & % 86.22/12.34 | ((all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = % 86.22/12.34 | e0) | (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 86.22/12.34 | op(e0, e1) = e0))) % 86.22/12.34 | (171) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 & op(e0, e3) = e1) % 86.22/12.34 | | (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 & op(e0, e1) = % 86.22/12.34 | e1) | (all_9_24 = e1 & op(e0, e0) = e1) % 86.22/12.34 | (172) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) % 86.22/12.34 | | (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & op(e0, e1) = % 86.22/12.34 | e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 86.22/12.34 | (173) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) % 86.22/12.34 | | (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = % 86.22/12.34 | e2) | (all_9_24 = e2 & op(e0, e0) = e2) % 86.22/12.34 | (174) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) % 86.22/12.34 | | (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = % 86.22/12.34 | e3) | (all_9_24 = e3 & op(e0, e0) = e3) % 86.22/12.34 | (175) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) % 86.22/12.34 | | (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = % 86.22/12.34 | e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 86.22/12.34 | (176) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 & op(e1, e3) = e0) % 86.22/12.34 | | (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 & op(e1, e1) = % 86.22/12.34 | e0) | (all_9_19 = e0 & op(e1, e0) = e0) % 86.22/12.34 | (177) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) % 86.22/12.34 | | (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = % 86.22/12.34 | e1) | (all_9_19 = e1 & op(e1, e0) = e1) % 86.22/12.34 | (178) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) % 86.22/12.34 | | (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = % 86.22/12.34 | e2) | (all_9_19 = e2 & op(e1, e0) = e2) % 86.22/12.34 | (179) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) % 86.22/12.34 | | (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = % 86.22/12.34 | e1) | (all_9_23 = e1 & op(e0, e1) = e1) % 86.22/12.34 | (180) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) % 86.22/12.34 | | (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = % 86.22/12.34 | e3) | (all_9_23 = e3 & op(e0, e1) = e3) % 86.22/12.34 | (181) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | % 86.22/12.34 | (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) % 86.22/12.34 | | (all_9_18 = e0 & op(e2, e0) = e0) % 86.22/12.34 | (182) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & op(e2, e3) = e2) | % 86.22/12.34 | (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 & op(e2, e1) = e2) % 86.22/12.34 | | (all_9_18 = e2 & op(e2, e0) = e2) % 86.22/12.34 | (183) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) = e3) | % 86.22/12.34 | (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) = e3) % 86.22/12.34 | | (all_9_18 = e3 & op(e2, e0) = e3) % 86.22/12.35 | (184) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_7 = e4 & op(e2, e3) = e4) | % 86.22/12.35 | (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_11 = e4 & op(e2, e1) = e4) % 86.22/12.35 | | (all_9_18 = e4 & op(e2, e0) = e4) % 86.22/12.35 | (185) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & op(e3, e2) = e0) | % 86.22/12.35 | (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 & op(e1, e2) = e0) % 86.22/12.35 | | (all_9_22 = e0 & op(e0, e2) = e0) % 86.22/12.35 | (186) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 86.22/12.35 | (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) % 86.22/12.35 | | (all_9_22 = e2 & op(e0, e2) = e2) % 86.22/12.35 | (187) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 86.22/12.35 | (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) % 86.22/12.35 | | (all_9_17 = e2 & op(e3, e0) = e2) % 86.22/12.35 | (188) (all_9_1 = e1 & op(e4, e3) = e1) | (all_9_3 = e1 & op(e3, e3) = e1) | % 86.22/12.35 | (all_9_7 = e1 & op(e2, e3) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) % 86.22/12.35 | | (all_9_21 = e1 & op(e0, e3) = e1) % 86.22/12.35 | (189) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 86.22/12.35 | (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 & op(e1, e3) = e3) % 86.22/12.35 | | (all_9_21 = e3 & op(e0, e3) = e3) % 86.22/12.35 | (190) (all_9_1 = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 86.22/12.35 | (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) % 86.22/12.35 | | (all_9_21 = e4 & op(e0, e3) = e4) % 86.22/12.35 | (191) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 86.22/12.35 | (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) % 86.22/12.35 | | (all_9_20 = e1 & op(e0, e4) = e1) % 86.22/12.35 | (192) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 86.22/12.35 | (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 86.22/12.35 | (all_9_16 = e1 & op(e4, e0) = e1) % 86.22/12.35 | (193) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 86.22/12.35 | (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) % 86.22/12.35 | | (all_9_20 = e2 & op(e0, e4) = e2) % 86.22/12.35 | (194) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 86.22/12.35 | (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 86.22/12.35 | (all_9_16 = e2 & op(e4, e0) = e2) % 86.22/12.35 | (195) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 86.22/12.35 | (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) % 86.22/12.35 | | (all_9_20 = e3 & op(e0, e4) = e3) % 86.22/12.35 | (196) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 86.22/12.35 | (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 86.22/12.35 | (all_9_16 = e3 & op(e4, e0) = e3) % 86.22/12.35 | (197) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 86.22/12.35 | (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 86.22/12.35 | | (all_9_20 = e4 & op(e0, e4) = e4) % 86.22/12.35 | (198) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 86.22/12.35 | (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 86.22/12.35 | (all_9_16 = e4 & op(e4, e0) = e4) % 86.22/12.35 | % 86.22/12.35 | GROUND_INST: instantiating (function-axioms) with all_4_24, all_6_24, e0, e0, % 86.22/12.35 | simplifying with (104), (130) gives: % 86.22/12.35 | (199) all_6_24 = all_4_24 % 86.22/12.35 | % 86.22/12.35 | GROUND_INST: instantiating (function-axioms) with all_4_19, all_6_23, e1, e0, % 86.22/12.35 | simplifying with (105), (131) gives: % 86.22/12.35 | (200) all_6_23 = all_4_19 % 86.22/12.35 | % 86.22/12.35 | GROUND_INST: instantiating (function-axioms) with all_4_14, all_6_22, e2, e0, % 86.22/12.35 | simplifying with (106), (132) gives: % 86.22/12.35 | (201) all_6_22 = all_4_14 % 86.22/12.35 | % 86.22/12.35 | GROUND_INST: instantiating (function-axioms) with all_4_9, all_6_21, e3, e0, % 86.22/12.35 | simplifying with (107), (133) gives: % 86.22/12.35 | (202) all_6_21 = all_4_9 % 86.22/12.35 | % 86.22/12.35 | GROUND_INST: instantiating (function-axioms) with all_4_4, all_6_20, e4, e0, % 86.22/12.35 | simplifying with (108), (134) gives: % 86.22/12.35 | (203) all_6_20 = all_4_4 % 86.22/12.35 | % 86.22/12.35 | GROUND_INST: instantiating (function-axioms) with all_4_4, e0, e4, e0, % 86.22/12.35 | simplifying with (108) gives: % 86.22/12.35 | (204) all_4_4 = e0 | ~ (op(e0, e4) = e0) % 86.22/12.35 | % 86.22/12.35 | GROUND_INST: instantiating (function-axioms) with all_4_9, e0, e3, e0, % 86.22/12.35 | simplifying with (107) gives: % 86.22/12.35 | (205) all_4_9 = e0 | ~ (op(e0, e3) = e0) % 86.22/12.35 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_6_22, e0, e2, e0, % 86.22/12.36 | simplifying with (132) gives: % 86.22/12.36 | (206) all_6_22 = e0 | ~ (op(e0, e2) = e0) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_14, e0, e2, e0, % 86.22/12.36 | simplifying with (106) gives: % 86.22/12.36 | (207) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_6_23, e0, e1, e0, % 86.22/12.36 | simplifying with (131) gives: % 86.22/12.36 | (208) all_6_23 = e0 | ~ (op(e0, e1) = e0) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_19, e0, e1, e0, % 86.22/12.36 | simplifying with (105) gives: % 86.22/12.36 | (209) all_4_19 = e0 | ~ (op(e0, e1) = e0) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_6_24, e0, e0, e0, % 86.22/12.36 | simplifying with (130) gives: % 86.22/12.36 | (210) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_23, all_6_19, e0, e1, % 86.22/12.36 | simplifying with (109), (135) gives: % 86.22/12.36 | (211) all_6_19 = all_4_23 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_18, all_6_18, e1, e1, % 86.22/12.36 | simplifying with (110), (136) gives: % 86.22/12.36 | (212) all_6_18 = all_4_18 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_8, all_6_16, e3, e1, % 86.22/12.36 | simplifying with (112), (137) gives: % 86.22/12.36 | (213) all_6_16 = all_4_8 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_3, all_6_15, e4, e1, % 86.22/12.36 | simplifying with (113), (138) gives: % 86.22/12.36 | (214) all_6_15 = all_4_3 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_3, e1, e4, e1, % 86.22/12.36 | simplifying with (113) gives: % 86.22/12.36 | (215) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_13, e1, e2, e1, % 86.22/12.36 | simplifying with (111) gives: % 86.22/12.36 | (216) all_4_13 = e1 | ~ (op(e1, e2) = e1) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_6_18, e1, e1, e1, % 86.22/12.36 | simplifying with (136) gives: % 86.22/12.36 | (217) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_6_19, e1, e0, e1, % 86.22/12.36 | simplifying with (135) gives: % 86.22/12.36 | (218) all_6_19 = e1 | ~ (op(e1, e0) = e1) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_23, e1, e0, e1, % 86.22/12.36 | simplifying with (109) gives: % 86.22/12.36 | (219) all_4_23 = e1 | ~ (op(e1, e0) = e1) % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_22, all_6_14, e0, e2, % 86.22/12.36 | simplifying with (114), (139) gives: % 86.22/12.36 | (220) all_6_14 = all_4_22 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_17, all_6_13, e1, e2, % 86.22/12.36 | simplifying with (115), (140) gives: % 86.22/12.36 | (221) all_6_13 = all_4_17 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_12, all_6_12, e2, e2, % 86.22/12.36 | simplifying with (116), (141) gives: % 86.22/12.36 | (222) all_6_12 = all_4_12 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with e4, all_6_12, e2, e2, % 86.22/12.36 | simplifying with (20), (141) gives: % 86.22/12.36 | (223) all_6_12 = e4 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_7, all_6_11, e3, e2, % 86.22/12.36 | simplifying with (117), (142) gives: % 86.22/12.36 | (224) all_6_11 = all_4_7 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_6_10, e4, e2, % 86.22/12.36 | simplifying with (118), (143) gives: % 86.22/12.36 | (225) all_6_10 = all_4_2 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with e3, all_6_10, e4, e2, % 86.22/12.36 | simplifying with (21), (143) gives: % 86.22/12.36 | (226) all_6_10 = e3 % 86.22/12.36 | % 86.22/12.36 | GROUND_INST: instantiating (function-axioms) with all_6_10, e2, e4, e2, % 86.22/12.36 | simplifying with (143) gives: % 86.87/12.36 | (227) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_7, e2, e3, e2, % 86.87/12.36 | simplifying with (117) gives: % 86.87/12.36 | (228) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with e4, e2, e2, e2, simplifying % 86.87/12.36 | with (20) gives: % 86.87/12.36 | (229) e4 = e2 | ~ (op(e2, e2) = e2) % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_6_13, e2, e1, e2, % 86.87/12.36 | simplifying with (140) gives: % 86.87/12.36 | (230) all_6_13 = e2 | ~ (op(e2, e1) = e2) % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_6_14, e2, e0, e2, % 86.87/12.36 | simplifying with (139) gives: % 86.87/12.36 | (231) all_6_14 = e2 | ~ (op(e2, e0) = e2) % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_22, e2, e0, e2, % 86.87/12.36 | simplifying with (114) gives: % 86.87/12.36 | (232) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_16, all_6_8, e1, e3, % 86.87/12.36 | simplifying with (120), (144) gives: % 86.87/12.36 | (233) all_6_8 = all_4_16 % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_11, all_6_7, e2, e3, % 86.87/12.36 | simplifying with (121), (145) gives: % 86.87/12.36 | (234) all_6_7 = all_4_11 % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_6, all_6_6, e3, e3, % 86.87/12.36 | simplifying with (122), (146) gives: % 86.87/12.36 | (235) all_6_6 = all_4_6 % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_6_5, e4, e3, % 86.87/12.36 | simplifying with (123), (147) gives: % 86.87/12.36 | (236) all_6_5 = all_4_1 % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with e1, all_6_5, e4, e3, % 86.87/12.36 | simplifying with (22), (147) gives: % 86.87/12.36 | (237) all_6_5 = e1 % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with e1, e3, e4, e3, simplifying % 86.87/12.36 | with (22) gives: % 86.87/12.36 | (238) e3 = e1 | ~ (op(e3, e4) = e3) % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_6, e3, e3, e3, % 86.87/12.36 | simplifying with (122) gives: % 86.87/12.36 | (239) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 86.87/12.36 | % 86.87/12.36 | GROUND_INST: instantiating (function-axioms) with all_4_16, e3, e1, e3, % 86.87/12.36 | simplifying with (120) gives: % 86.87/12.36 | (240) all_4_16 = e3 | ~ (op(e3, e1) = e3) % 86.87/12.36 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_21, e3, e0, e3, % 86.87/12.37 | simplifying with (119) gives: % 86.87/12.37 | (241) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_20, all_6_4, e0, e4, % 86.87/12.37 | simplifying with (124), (148) gives: % 86.87/12.37 | (242) all_6_4 = all_4_20 % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_15, all_6_3, e1, e4, % 86.87/12.37 | simplifying with (125), (149) gives: % 86.87/12.37 | (243) all_6_3 = all_4_15 % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_10, all_6_2, e2, e4, % 86.87/12.37 | simplifying with (126), (150) gives: % 86.87/12.37 | (244) all_6_2 = all_4_10 % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_5, all_6_1, e3, e4, % 86.87/12.37 | simplifying with (127), (151) gives: % 86.87/12.37 | (245) all_6_1 = all_4_5 % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_6_0, e4, e4, % 86.87/12.37 | simplifying with (128), (152) gives: % 86.87/12.37 | (246) all_6_0 = all_4_0 % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with e0, all_6_0, e4, e4, % 86.87/12.37 | simplifying with (23), (152) gives: % 86.87/12.37 | (247) all_6_0 = e0 % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_0, e4, e4, e4, % 86.87/12.37 | simplifying with (128) gives: % 86.87/12.37 | (248) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_1, e4, e3, e4, % 86.87/12.37 | simplifying with (151) gives: % 86.87/12.37 | (249) all_6_1 = e4 | ~ (op(e4, e3) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_2, e4, e2, e4, % 86.87/12.37 | simplifying with (150) gives: % 86.87/12.37 | (250) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_3, e4, e1, e4, % 86.87/12.37 | simplifying with (149) gives: % 86.87/12.37 | (251) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_15, e4, e1, e4, % 86.87/12.37 | simplifying with (125) gives: % 86.87/12.37 | (252) all_4_15 = e4 | ~ (op(e4, e1) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_20, e4, e0, e4, % 86.87/12.37 | simplifying with (124) gives: % 86.87/12.37 | (253) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_4, e0, e0, e4, % 86.87/12.37 | simplifying with (148) gives: % 86.87/12.37 | (254) all_6_4 = e0 | ~ (op(e4, e0) = e0) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_14, e0, e0, e2, % 86.87/12.37 | simplifying with (139) gives: % 86.87/12.37 | (255) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_22, e0, e0, e2, % 86.87/12.37 | simplifying with (114) gives: % 86.87/12.37 | (256) all_4_22 = e0 | ~ (op(e2, e0) = e0) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_23, e0, e0, e1, % 86.87/12.37 | simplifying with (109) gives: % 86.87/12.37 | (257) all_4_23 = e0 | ~ (op(e1, e0) = e0) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_3, e1, e1, e4, % 86.87/12.37 | simplifying with (149) gives: % 86.87/12.37 | (258) all_6_3 = e1 | ~ (op(e4, e1) = e1) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_8, e1, e1, e3, % 86.87/12.37 | simplifying with (144) gives: % 86.87/12.37 | (259) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_2, e2, e2, e4, % 86.87/12.37 | simplifying with (150) gives: % 86.87/12.37 | (260) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_10, e2, e2, e4, % 86.87/12.37 | simplifying with (126) gives: % 86.87/12.37 | (261) all_4_10 = e2 | ~ (op(e4, e2) = e2) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_7, e2, e2, e3, % 86.87/12.37 | simplifying with (145) gives: % 86.87/12.37 | (262) all_6_7 = e2 | ~ (op(e3, e2) = e2) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_11, e2, e2, e3, % 86.87/12.37 | simplifying with (121) gives: % 86.87/12.37 | (263) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_13, e2, e2, e1, % 86.87/12.37 | simplifying with (111) gives: % 86.87/12.37 | (264) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_22, e2, e2, e0, % 86.87/12.37 | simplifying with (132) gives: % 86.87/12.37 | (265) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_1, e3, e3, e4, % 86.87/12.37 | simplifying with (151) gives: % 86.87/12.37 | (266) all_6_1 = e3 | ~ (op(e4, e3) = e3) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_5, e3, e3, e4, % 86.87/12.37 | simplifying with (127) gives: % 86.87/12.37 | (267) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_11, e3, e3, e2, % 86.87/12.37 | simplifying with (142) gives: % 86.87/12.37 | (268) all_6_11 = e3 | ~ (op(e2, e3) = e3) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_8, e3, e3, e1, % 86.87/12.37 | simplifying with (112) gives: % 86.87/12.37 | (269) all_4_8 = e3 | ~ (op(e1, e3) = e3) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_21, e3, e3, e0, % 86.87/12.37 | simplifying with (133) gives: % 86.87/12.37 | (270) all_6_21 = e3 | ~ (op(e0, e3) = e3) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_5, e4, e4, e3, % 86.87/12.37 | simplifying with (147) gives: % 86.87/12.37 | (271) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_2, e4, e4, e2, % 86.87/12.37 | simplifying with (118) gives: % 86.87/12.37 | (272) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with e3, e4, e4, e2, simplifying % 86.87/12.37 | with (21) gives: % 86.87/12.37 | (273) e4 = e3 | ~ (op(e2, e4) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_15, e4, e4, e1, % 86.87/12.37 | simplifying with (138) gives: % 86.87/12.37 | (274) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_3, e4, e4, e1, % 86.87/12.37 | simplifying with (113) gives: % 86.87/12.37 | (275) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_6_20, e4, e4, e0, % 86.87/12.37 | simplifying with (134) gives: % 86.87/12.37 | (276) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 86.87/12.37 | % 86.87/12.37 | GROUND_INST: instantiating (function-axioms) with all_4_4, e4, e4, e0, % 86.87/12.37 | simplifying with (108) gives: % 86.87/12.37 | (277) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 86.87/12.37 | % 86.87/12.37 | COMBINE_EQS: (246), (247) imply: % 86.87/12.37 | (278) all_4_0 = e0 % 86.87/12.37 | % 86.87/12.37 | SIMP: (278) implies: % 86.87/12.37 | (279) all_4_0 = e0 % 86.87/12.37 | % 86.87/12.37 | COMBINE_EQS: (236), (237) imply: % 86.87/12.37 | (280) all_4_1 = e1 % 86.87/12.37 | % 86.87/12.37 | SIMP: (280) implies: % 86.87/12.37 | (281) all_4_1 = e1 % 86.87/12.37 | % 86.87/12.37 | COMBINE_EQS: (225), (226) imply: % 86.87/12.37 | (282) all_4_2 = e3 % 86.87/12.37 | % 86.87/12.37 | SIMP: (282) implies: % 86.87/12.37 | (283) all_4_2 = e3 % 86.87/12.37 | % 86.87/12.37 | COMBINE_EQS: (222), (223) imply: % 86.87/12.37 | (284) all_4_12 = e4 % 86.87/12.37 | % 86.87/12.37 | SIMP: (284) implies: % 86.87/12.37 | (285) all_4_12 = e4 % 86.87/12.37 | % 86.87/12.37 | REDUCE: (103), (279), (281) imply: % 86.87/12.37 | (286) ~ (e1 = e0) % 86.87/12.37 | % 86.87/12.37 | SIMP: (286) implies: % 86.87/12.38 | (287) ~ (e1 = e0) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (102), (279), (283) imply: % 86.87/12.38 | (288) ~ (e3 = e0) % 86.87/12.38 | % 86.87/12.38 | SIMP: (288) implies: % 86.87/12.38 | (289) ~ (e3 = e0) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (101), (279) imply: % 86.87/12.38 | (290) ~ (all_4_3 = e0) % 86.87/12.38 | % 86.87/12.38 | SIMP: (290) implies: % 86.87/12.38 | (291) ~ (all_4_3 = e0) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (100), (279) imply: % 86.87/12.38 | (292) ~ (all_4_4 = e0) % 86.87/12.38 | % 86.87/12.38 | SIMP: (292) implies: % 86.87/12.38 | (293) ~ (all_4_4 = e0) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (99), (279) imply: % 86.87/12.38 | (294) ~ (all_4_5 = e0) % 86.87/12.38 | % 86.87/12.38 | SIMP: (294) implies: % 86.87/12.38 | (295) ~ (all_4_5 = e0) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (98), (279) imply: % 86.87/12.38 | (296) ~ (all_4_10 = e0) % 86.87/12.38 | % 86.87/12.38 | SIMP: (296) implies: % 86.87/12.38 | (297) ~ (all_4_10 = e0) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (97), (279) imply: % 86.87/12.38 | (298) ~ (all_4_20 = e0) % 86.87/12.38 | % 86.87/12.38 | SIMP: (298) implies: % 86.87/12.38 | (299) ~ (all_4_20 = e0) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (96), (281), (283) imply: % 86.87/12.38 | (300) ~ (e3 = e1) % 86.87/12.38 | % 86.87/12.38 | SIMP: (300) implies: % 86.87/12.38 | (301) ~ (e3 = e1) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (95), (281) imply: % 86.87/12.38 | (302) ~ (all_4_3 = e1) % 86.87/12.38 | % 86.87/12.38 | SIMP: (302) implies: % 86.87/12.38 | (303) ~ (all_4_3 = e1) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (94), (281) imply: % 86.87/12.38 | (304) ~ (all_4_4 = e1) % 86.87/12.38 | % 86.87/12.38 | SIMP: (304) implies: % 86.87/12.38 | (305) ~ (all_4_4 = e1) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (93), (281) imply: % 86.87/12.38 | (306) ~ (all_4_6 = e1) % 86.87/12.38 | % 86.87/12.38 | SIMP: (306) implies: % 86.87/12.38 | (307) ~ (all_4_6 = e1) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (92), (281) imply: % 86.87/12.38 | (308) ~ (all_4_11 = e1) % 86.87/12.38 | % 86.87/12.38 | SIMP: (308) implies: % 86.87/12.38 | (309) ~ (all_4_11 = e1) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (91), (281) imply: % 86.87/12.38 | (310) ~ (all_4_16 = e1) % 86.87/12.38 | % 86.87/12.38 | SIMP: (310) implies: % 86.87/12.38 | (311) ~ (all_4_16 = e1) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (90), (283) imply: % 86.87/12.38 | (312) ~ (all_4_3 = e3) % 86.87/12.38 | % 86.87/12.38 | SIMP: (312) implies: % 86.87/12.38 | (313) ~ (all_4_3 = e3) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (89), (283) imply: % 86.87/12.38 | (314) ~ (all_4_4 = e3) % 86.87/12.38 | % 86.87/12.38 | SIMP: (314) implies: % 86.87/12.38 | (315) ~ (all_4_4 = e3) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (88), (283) imply: % 86.87/12.38 | (316) ~ (all_4_7 = e3) % 86.87/12.38 | % 86.87/12.38 | SIMP: (316) implies: % 86.87/12.38 | (317) ~ (all_4_7 = e3) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (87), (283), (285) imply: % 86.87/12.38 | (318) ~ (e4 = e3) % 86.87/12.38 | % 86.87/12.38 | SIMP: (318) implies: % 86.87/12.38 | (319) ~ (e4 = e3) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (86), (283) imply: % 86.87/12.38 | (320) ~ (all_4_17 = e3) % 86.87/12.38 | % 86.87/12.38 | SIMP: (320) implies: % 86.87/12.38 | (321) ~ (all_4_17 = e3) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (85), (283) imply: % 86.87/12.38 | (322) ~ (all_4_22 = e3) % 86.87/12.38 | % 86.87/12.38 | SIMP: (322) implies: % 86.87/12.38 | (323) ~ (all_4_22 = e3) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (67), (285) imply: % 86.87/12.38 | (324) ~ (all_4_7 = e4) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (59), (285) imply: % 86.87/12.38 | (325) ~ (all_4_10 = e4) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (54), (285) imply: % 86.87/12.38 | (326) ~ (all_4_11 = e4) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (50), (285) imply: % 86.87/12.38 | (327) ~ (all_4_14 = e4) % 86.87/12.38 | % 86.87/12.38 | SIMP: (327) implies: % 86.87/12.38 | (328) ~ (all_4_14 = e4) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (49), (285) imply: % 86.87/12.38 | (329) ~ (all_4_17 = e4) % 86.87/12.38 | % 86.87/12.38 | SIMP: (329) implies: % 86.87/12.38 | (330) ~ (all_4_17 = e4) % 86.87/12.38 | % 86.87/12.38 | REDUCE: (48), (285) imply: % 86.87/12.38 | (331) ~ (all_4_22 = e4) % 86.87/12.38 | % 86.87/12.38 | SIMP: (331) implies: % 86.87/12.38 | (332) ~ (all_4_22 = e4) % 86.87/12.38 | % 86.87/12.38 | BETA: splitting (191) gives: % 86.87/12.38 | % 86.87/12.38 | Case 1: % 86.87/12.38 | | % 86.87/12.38 | | (333) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) % 86.87/12.38 | | % 86.87/12.38 | | BETA: splitting (333) gives: % 86.87/12.38 | | % 86.87/12.38 | | Case 1: % 86.87/12.38 | | | % 86.87/12.38 | | | (334) all_9_0 = e1 & op(e4, e4) = e1 % 86.87/12.38 | | | % 86.87/12.38 | | | ALPHA: (334) implies: % 86.87/12.38 | | | (335) op(e4, e4) = e1 % 86.87/12.38 | | | % 86.87/12.39 | | | REF_CLOSE: (23), (287), (335), (function-axioms) are inconsistent by % 86.87/12.39 | | | sub-proof #132. % 86.87/12.39 | | | % 86.87/12.39 | | Case 2: % 86.87/12.39 | | | % 86.87/12.39 | | | (336) all_9_2 = e1 & op(e3, e4) = e1 % 86.87/12.39 | | | % 86.87/12.39 | | | ALPHA: (336) implies: % 86.87/12.39 | | | (337) all_9_2 = e1 % 86.87/12.39 | | | % 86.87/12.39 | | | BETA: splitting (183) gives: % 86.87/12.39 | | | % 86.87/12.39 | | | Case 1: % 86.87/12.39 | | | | % 86.87/12.39 | | | | (338) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) = % 86.87/12.39 | | | | e3) % 86.87/12.39 | | | | % 86.87/12.39 | | | | BETA: splitting (338) gives: % 86.87/12.39 | | | | % 86.87/12.39 | | | | Case 1: % 86.87/12.39 | | | | | % 86.87/12.39 | | | | | (339) all_9_6 = e3 & op(e2, e4) = e3 % 86.87/12.39 | | | | | % 86.87/12.39 | | | | | ALPHA: (339) implies: % 86.87/12.39 | | | | | (340) all_9_6 = e3 % 86.87/12.39 | | | | | % 86.87/12.40 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), % 86.87/12.40 | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (26), % 86.87/12.40 | | | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 86.87/12.40 | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 86.87/12.40 | | | | | (47), (51), (52), (53), (55), (56), (57), (58), (60), (61), % 86.87/12.40 | | | | | (62), (63), (64), (65), (66), (68), (69), (70), (71), (72), % 86.87/12.40 | | | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), % 86.87/12.40 | | | | | (83), (84), (104), (105), (106), (107), (108), (109), % 86.87/12.40 | | | | | (110), (112), (113), (114), (115), (117), (121), (122), % 86.87/12.40 | | | | | (124), (125), (126), (127), (153), (154), (155), (156), % 86.87/12.40 | | | | | (157), (158), (159), (160), (161), (162), (163), (165), % 86.87/12.40 | | | | | (166), (167), (168), (170), (171), (172), (173), (174), % 86.87/12.40 | | | | | (175), (176), (177), (178), (179), (180), (181), (182), % 86.87/12.40 | | | | | (185), (186), (187), (188), (189), (190), (191), (192), % 86.87/12.40 | | | | | (193), (194), (195), (196), (197), (198), (199), (200), % 86.87/12.40 | | | | | (201), (202), (203), (204), (205), (206), (207), (208), % 86.87/12.40 | | | | | (209), (210), (211), (212), (214), (215), (216), (217), % 86.87/12.40 | | | | | (218), (219), (220), (221), (224), (226), (227), (228), % 86.87/12.40 | | | | | (229), (230), (231), (232), (233), (234), (235), (237), % 86.87/12.40 | | | | | (238), (239), (240), (241), (242), (243), (244), (245), % 86.87/12.40 | | | | | (248), (249), (250), (251), (252), (253), (254), (255), % 86.87/12.40 | | | | | (256), (257), (258), (259), (260), (261), (262), (263), % 86.87/12.40 | | | | | (264), (265), (266), (267), (268), (269), (270), (271), % 86.87/12.40 | | | | | (272), (273), (274), (275), (276), (277), (279), (283), % 86.87/12.40 | | | | | (287), (289), (291), (293), (295), (297), (299), (301), % 86.87/12.40 | | | | | (303), (305), (307), (309), (311), (313), (315), (317), % 86.87/12.40 | | | | | (319), (323), (324), (325), (326), (328), (332), (337), % 86.87/12.40 | | | | | (340), (function-axioms) are inconsistent by sub-proof #3. % 86.87/12.40 | | | | | % 86.87/12.40 | | | | Case 2: % 86.87/12.40 | | | | | % 86.87/12.40 | | | | | (341) all_9_7 = e3 & op(e2, e3) = e3 % 86.87/12.40 | | | | | % 86.87/12.40 | | | | | REF_CLOSE: (224), (268), (317), (341) are inconsistent by sub-proof % 86.87/12.40 | | | | | #106. % 86.87/12.40 | | | | | % 86.87/12.40 | | | | End of split % 86.87/12.40 | | | | % 86.87/12.40 | | | Case 2: % 86.87/12.40 | | | | % 86.87/12.40 | | | | (342) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) % 86.87/12.40 | | | | = e3) | (all_9_18 = e3 & op(e2, e0) = e3) % 86.87/12.40 | | | | % 86.87/12.40 | | | | REF_CLOSE: (114), (115), (117), (184), (272), (283), (319), (321), % 86.87/12.40 | | | | (323), (324), (330), (332), (342), (function-axioms) are % 86.87/12.40 | | | | inconsistent by sub-proof #2. % 86.87/12.40 | | | | % 86.87/12.40 | | | End of split % 86.87/12.40 | | | % 86.87/12.40 | | End of split % 86.87/12.40 | | % 86.87/12.40 | Case 2: % 86.87/12.40 | | % 86.87/12.40 | | (343) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = % 86.87/12.40 | | e1) | (all_9_20 = e1 & op(e0, e4) = e1) % 86.87/12.40 | | % 86.87/12.40 | | BETA: splitting (343) gives: % 86.87/12.40 | | % 86.87/12.40 | | Case 1: % 86.87/12.40 | | | % 86.87/12.40 | | | (344) all_9_6 = e1 & op(e2, e4) = e1 % 86.87/12.40 | | | % 86.87/12.40 | | | ALPHA: (344) implies: % 86.87/12.40 | | | (345) all_9_6 = e1 % 86.87/12.40 | | | % 86.87/12.40 | | | BETA: splitting (183) gives: % 86.87/12.40 | | | % 86.87/12.40 | | | Case 1: % 86.87/12.40 | | | | % 86.87/12.40 | | | | (346) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) = % 86.87/12.40 | | | | e3) % 86.87/12.40 | | | | % 86.87/12.40 | | | | BETA: splitting (346) gives: % 86.87/12.40 | | | | % 86.87/12.40 | | | | Case 1: % 86.87/12.40 | | | | | % 86.87/12.40 | | | | | (347) all_9_6 = e3 & op(e2, e4) = e3 % 86.87/12.40 | | | | | % 86.87/12.40 | | | | | REF_CLOSE: (301), (345), (347) are inconsistent by sub-proof #102. % 86.87/12.40 | | | | | % 86.87/12.40 | | | | Case 2: % 86.87/12.40 | | | | | % 86.87/12.40 | | | | | (348) all_9_7 = e3 & op(e2, e3) = e3 % 86.87/12.40 | | | | | % 86.87/12.40 | | | | | REF_CLOSE: (224), (268), (317), (348) are inconsistent by sub-proof % 86.87/12.40 | | | | | #106. % 86.87/12.40 | | | | | % 86.87/12.40 | | | | End of split % 86.87/12.40 | | | | % 86.87/12.40 | | | Case 2: % 86.87/12.40 | | | | % 86.87/12.40 | | | | (349) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) % 86.87/12.40 | | | | = e3) | (all_9_18 = e3 & op(e2, e0) = e3) % 86.87/12.40 | | | | % 86.87/12.40 | | | | REF_CLOSE: (114), (115), (117), (184), (272), (283), (319), (321), % 86.87/12.40 | | | | (323), (324), (330), (332), (349), (function-axioms) are % 86.87/12.40 | | | | inconsistent by sub-proof #2. % 86.87/12.40 | | | | % 86.87/12.40 | | | End of split % 86.87/12.40 | | | % 86.87/12.40 | | Case 2: % 86.87/12.40 | | | % 86.87/12.40 | | | (350) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_20 = e1 & op(e0, e4) = % 86.87/12.40 | | | e1) % 86.87/12.40 | | | % 86.87/12.40 | | | BETA: splitting (350) gives: % 86.87/12.40 | | | % 86.87/12.40 | | | Case 1: % 86.87/12.40 | | | | % 86.87/12.40 | | | | (351) all_9_12 = e1 & op(e1, e4) = e1 % 86.87/12.40 | | | | % 86.87/12.40 | | | | ALPHA: (351) implies: % 86.87/12.40 | | | | (352) op(e1, e4) = e1 % 86.87/12.40 | | | | % 86.87/12.40 | | | | REF_CLOSE: (215), (303), (352) are inconsistent by sub-proof #87. % 86.87/12.40 | | | | % 86.87/12.40 | | | Case 2: % 86.87/12.40 | | | | % 86.87/12.40 | | | | (353) all_9_20 = e1 & op(e0, e4) = e1 % 86.87/12.40 | | | | % 86.87/12.40 | | | | ALPHA: (353) implies: % 86.87/12.40 | | | | (354) all_9_20 = e1 % 86.87/12.40 | | | | % 86.87/12.40 | | | | BETA: splitting (183) gives: % 86.87/12.40 | | | | % 86.87/12.40 | | | | Case 1: % 86.87/12.40 | | | | | % 86.87/12.40 | | | | | (355) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) % 86.87/12.40 | | | | | = e3) % 86.87/12.40 | | | | | % 86.87/12.40 | | | | | BETA: splitting (355) gives: % 86.87/12.40 | | | | | % 86.87/12.40 | | | | | Case 1: % 86.87/12.40 | | | | | | % 86.87/12.40 | | | | | | (356) all_9_6 = e3 & op(e2, e4) = e3 % 86.87/12.40 | | | | | | % 86.87/12.40 | | | | | | ALPHA: (356) implies: % 86.87/12.40 | | | | | | (357) all_9_6 = e3 % 86.87/12.40 | | | | | | % 86.87/12.40 | | | | | | BETA: splitting (193) gives: % 86.87/12.40 | | | | | | % 86.87/12.40 | | | | | | Case 1: % 86.87/12.40 | | | | | | | % 86.87/12.40 | | | | | | | (358) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, % 86.87/12.40 | | | | | | | e4) = e2) % 86.87/12.40 | | | | | | | % 86.87/12.40 | | | | | | | BETA: splitting (358) gives: % 86.87/12.40 | | | | | | | % 86.87/12.40 | | | | | | | Case 1: % 86.87/12.40 | | | | | | | | % 86.87/12.40 | | | | | | | | (359) all_9_0 = e2 & op(e4, e4) = e2 % 86.87/12.40 | | | | | | | | % 86.87/12.40 | | | | | | | | ALPHA: (359) implies: % 86.87/12.40 | | | | | | | | (360) op(e4, e4) = e2 % 86.87/12.40 | | | | | | | | % 86.87/12.40 | | | | | | | | REF_CLOSE: (14), (23), (360), (function-axioms) are inconsistent % 86.87/12.40 | | | | | | | | by sub-proof #128. % 86.87/12.40 | | | | | | | | % 86.87/12.40 | | | | | | | Case 2: % 86.87/12.40 | | | | | | | | % 86.87/12.40 | | | | | | | | (361) all_9_2 = e2 & op(e3, e4) = e2 % 86.87/12.40 | | | | | | | | % 86.87/12.40 | | | | | | | | ALPHA: (361) implies: % 86.87/12.40 | | | | | | | | (362) all_9_2 = e2 % 86.87/12.40 | | | | | | | | (363) op(e3, e4) = e2 % 86.87/12.40 | | | | | | | | % 86.87/12.40 | | | | | | | | BETA: splitting (197) gives: % 86.87/12.40 | | | | | | | | % 86.87/12.40 | | | | | | | | Case 1: % 86.87/12.40 | | | | | | | | | % 86.87/12.40 | | | | | | | | | (364) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 86.87/12.40 | | | | | | | | | op(e3, e4) = e4) % 86.87/12.40 | | | | | | | | | % 86.87/12.40 | | | | | | | | | BETA: splitting (364) gives: % 86.87/12.40 | | | | | | | | | % 86.87/12.40 | | | | | | | | | Case 1: % 86.87/12.40 | | | | | | | | | | % 86.87/12.40 | | | | | | | | | | (365) all_9_0 = e4 & op(e4, e4) = e4 % 86.87/12.40 | | | | | | | | | | % 86.87/12.40 | | | | | | | | | | ALPHA: (365) implies: % 86.87/12.40 | | | | | | | | | | (366) op(e4, e4) = e4 % 86.87/12.40 | | | | | | | | | | % 86.87/12.40 | | | | | | | | | | REF_CLOSE: (17), (248), (279), (366) are inconsistent by % 86.87/12.40 | | | | | | | | | | sub-proof #131. % 86.87/12.40 | | | | | | | | | | % 86.87/12.40 | | | | | | | | | Case 2: % 86.87/12.40 | | | | | | | | | | % 86.87/12.40 | | | | | | | | | | (367) all_9_2 = e4 & op(e3, e4) = e4 % 86.87/12.40 | | | | | | | | | | % 86.87/12.40 | | | | | | | | | | ALPHA: (367) implies: % 86.87/12.40 | | | | | | | | | | (368) all_9_2 = e4 % 86.87/12.40 | | | | | | | | | | (369) op(e3, e4) = e4 % 86.87/12.40 | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 86.87/12.41 | | | | | | | | | | (11), (14), (15), (16), (17), (18), (19), (20), % 86.87/12.41 | | | | | | | | | | (21), (22), (23), (26), (27), (28), (29), (30), % 86.87/12.41 | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 86.87/12.41 | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 86.87/12.41 | | | | | | | | | | (47), (51), (52), (53), (55), (56), (57), (58), % 86.87/12.41 | | | | | | | | | | (60), (61), (62), (63), (64), (65), (66), (68), % 86.87/12.41 | | | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76), % 86.87/12.41 | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (84), % 86.87/12.41 | | | | | | | | | | (104), (105), (106), (107), (108), (109), (110), % 86.87/12.41 | | | | | | | | | | (112), (113), (114), (115), (117), (121), (122), % 86.87/12.41 | | | | | | | | | | (124), (125), (126), (127), (153), (154), (155), % 86.87/12.41 | | | | | | | | | | (156), (157), (158), (159), (160), (161), (162), % 86.87/12.41 | | | | | | | | | | (163), (165), (166), (167), (168), (170), (171), % 86.87/12.41 | | | | | | | | | | (172), (173), (174), (175), (176), (177), (178), % 86.87/12.41 | | | | | | | | | | (179), (180), (181), (182), (185), (186), (187), % 86.87/12.41 | | | | | | | | | | (188), (189), (190), (191), (192), (193), (194), % 86.87/12.41 | | | | | | | | | | (195), (196), (197), (198), (199), (200), (201), % 86.87/12.41 | | | | | | | | | | (202), (203), (204), (205), (206), (207), (208), % 86.87/12.41 | | | | | | | | | | (209), (210), (211), (212), (214), (215), (216), % 86.87/12.41 | | | | | | | | | | (217), (218), (219), (220), (221), (224), (226), % 86.87/12.41 | | | | | | | | | | (227), (228), (229), (230), (231), (232), (233), % 86.87/12.41 | | | | | | | | | | (234), (235), (237), (238), (239), (240), (241), % 86.87/12.41 | | | | | | | | | | (242), (243), (244), (245), (248), (249), (250), % 86.87/12.41 | | | | | | | | | | (251), (252), (253), (254), (255), (256), (257), % 86.87/12.41 | | | | | | | | | | (258), (259), (260), (261), (262), (263), (264), % 86.87/12.41 | | | | | | | | | | (265), (266), (267), (268), (269), (270), (271), % 86.87/12.41 | | | | | | | | | | (272), (273), (274), (275), (276), (277), (279), % 86.87/12.41 | | | | | | | | | | (283), (287), (289), (291), (293), (295), (297), % 86.87/12.41 | | | | | | | | | | (299), (301), (303), (305), (307), (309), (311), % 86.87/12.41 | | | | | | | | | | (313), (315), (317), (319), (323), (324), (325), % 86.87/12.41 | | | | | | | | | | (326), (328), (332), (357), (368), (369), % 86.87/12.41 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 86.87/12.41 | | | | | | | | | | #1. % 86.87/12.41 | | | | | | | | | | % 86.87/12.41 | | | | | | | | | End of split % 86.87/12.41 | | | | | | | | | % 86.87/12.41 | | | | | | | | Case 2: % 86.87/12.41 | | | | | | | | | % 86.87/12.41 | | | | | | | | | (370) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 86.87/12.41 | | | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 86.87/12.41 | | | | | | | | | e4) % 86.87/12.41 | | | | | | | | | % 86.87/12.41 | | | | | | | | | BETA: splitting (370) gives: % 86.87/12.41 | | | | | | | | | % 86.87/12.41 | | | | | | | | | Case 1: % 86.87/12.41 | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | (371) all_9_6 = e4 & op(e2, e4) = e4 % 86.87/12.41 | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | ALPHA: (371) implies: % 86.87/12.41 | | | | | | | | | | (372) op(e2, e4) = e4 % 86.87/12.41 | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | REF_CLOSE: (272), (283), (319), (372) are inconsistent by % 86.87/12.41 | | | | | | | | | | sub-proof #129. % 86.87/12.41 | | | | | | | | | | % 86.87/12.41 | | | | | | | | | Case 2: % 86.87/12.41 | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | (373) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 86.87/12.41 | | | | | | | | | | & op(e0, e4) = e4) % 86.87/12.41 | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | BETA: splitting (373) gives: % 86.87/12.41 | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | Case 1: % 86.87/12.41 | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | (374) all_9_12 = e4 & op(e1, e4) = e4 % 86.87/12.41 | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | ALPHA: (374) implies: % 86.87/12.41 | | | | | | | | | | | (375) op(e1, e4) = e4 % 86.87/12.41 | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | BETA: splitting (274) gives: % 86.87/12.41 | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | Case 1: % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | (376) ~ (op(e1, e4) = e4) % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | PRED_UNIFY: (375), (376) imply: % 86.87/12.41 | | | | | | | | | | | | (377) $false % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | CLOSE: (377) is inconsistent. % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | Case 2: % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | (378) all_6_15 = e4 % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | COMBINE_EQS: (214), (378) imply: % 86.87/12.41 | | | | | | | | | | | | (379) all_4_3 = e4 % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | SIMP: (379) implies: % 86.87/12.41 | | | | | | | | | | | | (380) all_4_3 = e4 % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | REDUCE: (84), (380) imply: % 86.87/12.41 | | | | | | | | | | | | (381) ~ (all_4_4 = e4) % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | SIMP: (381) implies: % 86.87/12.41 | | | | | | | | | | | | (382) ~ (all_4_4 = e4) % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | BETA: splitting (156) gives: % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | Case 1: % 86.87/12.41 | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | (383) all_6_20 = e4 % 86.87/12.41 | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | REF_CLOSE: (203), (382), (383) are inconsistent by sub-proof % 86.87/12.41 | | | | | | | | | | | | | #123. % 86.87/12.41 | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | Case 2: % 86.87/12.41 | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | (384) ~ (all_6_20 = e4) % 86.87/12.41 | | | | | | | | | | | | | (385) all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 86.87/12.41 | | | | | | | | | | | | | all_6_20 = e0 % 86.87/12.41 | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | BETA: splitting (385) gives: % 86.87/12.41 | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | Case 1: % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | (386) all_6_20 = e2 % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | COMBINE_EQS: (203), (386) imply: % 86.87/12.41 | | | | | | | | | | | | | | (387) all_4_4 = e2 % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | SIMP: (387) implies: % 86.87/12.41 | | | | | | | | | | | | | | (388) all_4_4 = e2 % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | REDUCE: (382), (388) imply: % 86.87/12.41 | | | | | | | | | | | | | | (389) ~ (e4 = e2) % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | REDUCE: (315), (388) imply: % 86.87/12.41 | | | | | | | | | | | | | | (390) ~ (e3 = e2) % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e4, % 86.87/12.41 | | | | | | | | | | | | | | e3, simplifying with (22), (363) gives: % 86.87/12.41 | | | | | | | | | | | | | | (391) e2 = e1 % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | COMBINE_EQS: (362), (391) imply: % 86.87/12.41 | | | | | | | | | | | | | | (392) all_9_2 = e1 % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 86.87/12.41 | | | | | | | | | | | | | | (11), (14), (15), (16), (17), (18), (19), (20), % 86.87/12.41 | | | | | | | | | | | | | | (21), (22), (23), (26), (27), (28), (29), (30), % 86.87/12.41 | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 86.87/12.41 | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 86.87/12.41 | | | | | | | | | | | | | | (47), (51), (52), (53), (55), (56), (57), (58), % 86.87/12.41 | | | | | | | | | | | | | | (60), (61), (62), (63), (64), (65), (66), (68), % 86.87/12.41 | | | | | | | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76), % 86.87/12.41 | | | | | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (84), % 86.87/12.41 | | | | | | | | | | | | | | (104), (105), (106), (107), (108), (109), (110), % 86.87/12.41 | | | | | | | | | | | | | | (112), (113), (114), (115), (117), (121), (122), % 86.87/12.41 | | | | | | | | | | | | | | (124), (125), (126), (127), (153), (154), (155), % 86.87/12.41 | | | | | | | | | | | | | | (156), (157), (158), (159), (160), (161), (162), % 86.87/12.41 | | | | | | | | | | | | | | (163), (165), (166), (167), (168), (170), (171), % 86.87/12.41 | | | | | | | | | | | | | | (172), (173), (174), (175), (176), (177), (178), % 86.87/12.41 | | | | | | | | | | | | | | (179), (180), (181), (182), (185), (186), (187), % 86.87/12.41 | | | | | | | | | | | | | | (188), (189), (190), (191), (192), (193), (194), % 86.87/12.41 | | | | | | | | | | | | | | (195), (196), (197), (198), (199), (200), (201), % 86.87/12.41 | | | | | | | | | | | | | | (202), (203), (204), (205), (206), (207), (208), % 86.87/12.41 | | | | | | | | | | | | | | (209), (210), (211), (212), (214), (215), (216), % 86.87/12.41 | | | | | | | | | | | | | | (217), (218), (219), (220), (221), (224), (226), % 86.87/12.41 | | | | | | | | | | | | | | (227), (228), (229), (230), (231), (232), (233), % 86.87/12.41 | | | | | | | | | | | | | | (234), (235), (237), (238), (239), (240), (241), % 86.87/12.41 | | | | | | | | | | | | | | (242), (243), (244), (245), (248), (249), (250), % 86.87/12.41 | | | | | | | | | | | | | | (251), (252), (253), (254), (255), (256), (257), % 86.87/12.41 | | | | | | | | | | | | | | (258), (259), (260), (261), (262), (263), (264), % 86.87/12.41 | | | | | | | | | | | | | | (265), (266), (267), (268), (269), (270), (271), % 86.87/12.41 | | | | | | | | | | | | | | (272), (273), (274), (275), (276), (277), (279), % 86.87/12.41 | | | | | | | | | | | | | | (283), (287), (289), (291), (293), (295), (297), % 86.87/12.41 | | | | | | | | | | | | | | (299), (301), (303), (305), (307), (309), (311), % 86.87/12.41 | | | | | | | | | | | | | | (313), (315), (317), (319), (323), (324), (325), % 86.87/12.41 | | | | | | | | | | | | | | (326), (328), (332), (357), (392), % 86.87/12.41 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 86.87/12.41 | | | | | | | | | | | | | | #3. % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | Case 2: % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | (393) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | | REF_CLOSE: (203), (293), (305), (315), (393) are inconsistent % 86.87/12.41 | | | | | | | | | | | | | | by sub-proof #88. % 86.87/12.41 | | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | | End of split % 86.87/12.41 | | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | | End of split % 86.87/12.41 | | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | End of split % 86.87/12.41 | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | Case 2: % 86.87/12.41 | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | (394) all_9_20 = e4 & op(e0, e4) = e4 % 86.87/12.41 | | | | | | | | | | | % 86.87/12.41 | | | | | | | | | | | REF_CLOSE: (18), (354), (394) are inconsistent by sub-proof % 86.87/12.42 | | | | | | | | | | | #85. % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | End of split % 86.87/12.42 | | | | | | | | | | % 86.87/12.42 | | | | | | | | | End of split % 86.87/12.42 | | | | | | | | | % 86.87/12.42 | | | | | | | | End of split % 86.87/12.42 | | | | | | | | % 86.87/12.42 | | | | | | | End of split % 86.87/12.42 | | | | | | | % 86.87/12.42 | | | | | | Case 2: % 86.87/12.42 | | | | | | | % 86.87/12.42 | | | | | | | (395) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & % 86.87/12.42 | | | | | | | op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 86.87/12.42 | | | | | | | % 86.87/12.42 | | | | | | | BETA: splitting (395) gives: % 86.87/12.42 | | | | | | | % 86.87/12.42 | | | | | | | Case 1: % 86.87/12.42 | | | | | | | | % 86.87/12.42 | | | | | | | | (396) all_9_6 = e2 & op(e2, e4) = e2 % 86.87/12.42 | | | | | | | | % 86.87/12.42 | | | | | | | | REF_CLOSE: (16), (226), (227), (396) are inconsistent by % 86.87/12.42 | | | | | | | | sub-proof #125. % 86.87/12.42 | | | | | | | | % 86.87/12.42 | | | | | | | Case 2: % 86.87/12.42 | | | | | | | | % 86.87/12.42 | | | | | | | | (397) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & % 86.87/12.42 | | | | | | | | op(e0, e4) = e2) % 86.87/12.42 | | | | | | | | % 86.87/12.42 | | | | | | | | BETA: splitting (397) gives: % 86.87/12.42 | | | | | | | | % 86.87/12.42 | | | | | | | | Case 1: % 86.87/12.42 | | | | | | | | | % 86.87/12.42 | | | | | | | | | (398) all_9_12 = e2 & op(e1, e4) = e2 % 86.87/12.42 | | | | | | | | | % 86.87/12.42 | | | | | | | | | ALPHA: (398) implies: % 86.87/12.42 | | | | | | | | | (399) all_9_12 = e2 % 86.87/12.42 | | | | | | | | | % 86.87/12.42 | | | | | | | | | BETA: splitting (197) gives: % 86.87/12.42 | | | | | | | | | % 86.87/12.42 | | | | | | | | | Case 1: % 86.87/12.42 | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | (400) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 86.87/12.42 | | | | | | | | | | op(e3, e4) = e4) % 86.87/12.42 | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | BETA: splitting (400) gives: % 86.87/12.42 | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | Case 1: % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | (401) all_9_0 = e4 & op(e4, e4) = e4 % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | ALPHA: (401) implies: % 86.87/12.42 | | | | | | | | | | | (402) op(e4, e4) = e4 % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | REF_CLOSE: (17), (248), (279), (402) are inconsistent by % 86.87/12.42 | | | | | | | | | | | sub-proof #131. % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | Case 2: % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | (403) all_9_2 = e4 & op(e3, e4) = e4 % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | ALPHA: (403) implies: % 86.87/12.42 | | | | | | | | | | | (404) all_9_2 = e4 % 86.87/12.42 | | | | | | | | | | | (405) op(e3, e4) = e4 % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 86.87/12.42 | | | | | | | | | | | (11), (14), (15), (16), (17), (18), (19), (20), % 86.87/12.42 | | | | | | | | | | | (21), (22), (23), (26), (27), (28), (29), (30), % 86.87/12.42 | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 86.87/12.42 | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 86.87/12.42 | | | | | | | | | | | (47), (51), (52), (53), (55), (56), (57), (58), % 86.87/12.42 | | | | | | | | | | | (60), (61), (62), (63), (64), (65), (66), (68), % 86.87/12.42 | | | | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76), % 86.87/12.42 | | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (84), % 86.87/12.42 | | | | | | | | | | | (104), (105), (106), (107), (108), (109), (110), % 86.87/12.42 | | | | | | | | | | | (112), (113), (114), (115), (117), (121), (122), % 86.87/12.42 | | | | | | | | | | | (124), (125), (126), (127), (153), (154), (155), % 86.87/12.42 | | | | | | | | | | | (156), (157), (158), (159), (160), (161), (162), % 86.87/12.42 | | | | | | | | | | | (163), (165), (166), (167), (168), (170), (171), % 86.87/12.42 | | | | | | | | | | | (172), (173), (174), (175), (176), (177), (178), % 86.87/12.42 | | | | | | | | | | | (179), (180), (181), (182), (185), (186), (187), % 86.87/12.42 | | | | | | | | | | | (188), (189), (190), (191), (192), (193), (194), % 86.87/12.42 | | | | | | | | | | | (195), (196), (197), (198), (199), (200), (201), % 86.87/12.42 | | | | | | | | | | | (202), (203), (204), (205), (206), (207), (208), % 86.87/12.42 | | | | | | | | | | | (209), (210), (211), (212), (214), (215), (216), % 86.87/12.42 | | | | | | | | | | | (217), (218), (219), (220), (221), (224), (226), % 86.87/12.42 | | | | | | | | | | | (227), (228), (229), (230), (231), (232), (233), % 86.87/12.42 | | | | | | | | | | | (234), (235), (237), (238), (239), (240), (241), % 86.87/12.42 | | | | | | | | | | | (242), (243), (244), (245), (248), (249), (250), % 86.87/12.42 | | | | | | | | | | | (251), (252), (253), (254), (255), (256), (257), % 86.87/12.42 | | | | | | | | | | | (258), (259), (260), (261), (262), (263), (264), % 86.87/12.42 | | | | | | | | | | | (265), (266), (267), (268), (269), (270), (271), % 86.87/12.42 | | | | | | | | | | | (272), (273), (274), (275), (276), (277), (279), % 86.87/12.42 | | | | | | | | | | | (283), (287), (289), (291), (293), (295), (297), % 86.87/12.42 | | | | | | | | | | | (299), (301), (303), (305), (307), (309), (311), % 86.87/12.42 | | | | | | | | | | | (313), (315), (317), (319), (323), (324), (325), % 86.87/12.42 | | | | | | | | | | | (326), (328), (332), (357), (404), (405), % 86.87/12.42 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 86.87/12.42 | | | | | | | | | | | #1. % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | End of split % 86.87/12.42 | | | | | | | | | | % 86.87/12.42 | | | | | | | | | Case 2: % 86.87/12.42 | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | (406) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 86.87/12.42 | | | | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 86.87/12.42 | | | | | | | | | | e4) % 86.87/12.42 | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | BETA: splitting (406) gives: % 86.87/12.42 | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | Case 1: % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | (407) all_9_6 = e4 & op(e2, e4) = e4 % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | ALPHA: (407) implies: % 86.87/12.42 | | | | | | | | | | | (408) op(e2, e4) = e4 % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | REF_CLOSE: (272), (283), (319), (408) are inconsistent by % 86.87/12.42 | | | | | | | | | | | sub-proof #129. % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | Case 2: % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | (409) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 86.87/12.42 | | | | | | | | | | | & op(e0, e4) = e4) % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | | REF_CLOSE: (18), (19), (354), (399), (409) are inconsistent % 86.87/12.42 | | | | | | | | | | | by sub-proof #84. % 86.87/12.42 | | | | | | | | | | | % 86.87/12.42 | | | | | | | | | | End of split % 86.87/12.42 | | | | | | | | | | % 86.87/12.42 | | | | | | | | | End of split % 86.87/12.42 | | | | | | | | | % 86.87/12.42 | | | | | | | | Case 2: % 86.87/12.42 | | | | | | | | | % 86.87/12.42 | | | | | | | | | (410) all_9_20 = e2 & op(e0, e4) = e2 % 86.87/12.42 | | | | | | | | | % 86.87/12.42 | | | | | | | | | REF_CLOSE: (15), (354), (410) are inconsistent by sub-proof % 86.87/12.42 | | | | | | | | | #83. % 86.87/12.42 | | | | | | | | | % 86.87/12.42 | | | | | | | | End of split % 86.87/12.42 | | | | | | | | % 86.87/12.42 | | | | | | | End of split % 86.87/12.42 | | | | | | | % 86.87/12.42 | | | | | | End of split % 86.87/12.42 | | | | | | % 86.87/12.42 | | | | | Case 2: % 86.87/12.42 | | | | | | % 86.87/12.42 | | | | | | (411) all_9_7 = e3 & op(e2, e3) = e3 % 86.87/12.42 | | | | | | % 86.87/12.42 | | | | | | REF_CLOSE: (224), (268), (317), (411) are inconsistent by sub-proof % 86.87/12.42 | | | | | | #106. % 86.87/12.42 | | | | | | % 86.87/12.42 | | | | | End of split % 86.87/12.42 | | | | | % 86.87/12.42 | | | | Case 2: % 86.87/12.42 | | | | | % 86.87/12.42 | | | | | (412) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, % 86.87/12.42 | | | | | e1) = e3) | (all_9_18 = e3 & op(e2, e0) = e3) % 86.87/12.42 | | | | | % 86.87/12.42 | | | | | REF_CLOSE: (114), (115), (117), (184), (272), (283), (319), (321), % 86.87/12.42 | | | | | (323), (324), (330), (332), (412), (function-axioms) are % 86.87/12.42 | | | | | inconsistent by sub-proof #2. % 86.87/12.42 | | | | | % 86.87/12.42 | | | | End of split % 86.87/12.42 | | | | % 86.87/12.42 | | | End of split % 86.87/12.42 | | | % 86.87/12.42 | | End of split % 86.87/12.42 | | % 86.87/12.42 | End of split % 86.87/12.42 | % 86.87/12.42 End of proof % 86.87/12.42 % 86.87/12.42 Sub-proof #1 shows that the following formulas are inconsistent: % 86.87/12.42 ---------------------------------------------------------------- % 86.87/12.42 (1) ~ (all_4_22 = all_4_23) % 86.87/12.42 (2) ~ (all_4_6 = all_4_7) % 86.87/12.42 (3) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 86.87/12.42 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 86.87/12.42 (all_9_20 = e3 & op(e0, e4) = e3) % 86.87/12.42 (4) ~ (all_4_20 = all_4_24) % 86.87/12.42 (5) ~ (all_4_9 = all_4_24) % 86.87/12.42 (6) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | all_6_14 % 86.87/12.42 = e0 % 86.87/12.42 (7) op(e0, e2) = all_4_14 % 86.87/12.42 (8) all_6_11 = all_4_7 % 86.87/12.42 (9) ~ (all_4_5 = all_4_10) % 86.87/12.42 (10) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 86.87/12.42 (11) all_6_1 = all_4_5 % 86.87/12.42 (12) op(e4, e3) = all_4_5 % 86.87/12.42 (13) ~ (all_4_10 = e0) % 86.87/12.42 (14) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 86.87/12.43 (15) op(e0, unit) = e0 % 86.87/12.43 (16) ~ (all_4_7 = all_4_9) % 86.87/12.43 (17) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | all_6_7 = e0 % 86.87/12.43 (18) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 86.87/12.43 (19) all_6_6 = e4 | all_6_6 = e3 | all_6_6 = e2 | all_6_6 = e1 | all_6_6 = e0 % 86.87/12.43 (20) op(unit, e2) = e2 % 86.87/12.43 (21) all_4_23 = e1 | ~ (op(e1, e0) = e1) % 86.87/12.43 (22) ~ (all_4_10 = all_4_15) % 86.87/12.43 (23) all_6_7 = all_4_11 % 86.87/12.43 (24) op(e3, e4) = e4 % 86.87/12.43 (25) all_6_23 = all_4_19 % 86.87/12.43 (26) ~ (e3 = e2) % 86.87/12.43 (27) ~ (all_4_7 = e4) % 86.87/12.43 (28) op(e2, e4) = e3 % 86.87/12.43 (29) op(e2, unit) = e2 % 86.87/12.43 (30) ~ (e3 = e0) % 86.87/12.43 (31) ~ (all_4_15 = all_4_20) % 86.87/12.43 (32) ~ (e4 = e3) % 86.87/12.43 (33) ~ (all_4_3 = e0) % 86.87/12.43 (34) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 86.87/12.43 (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 & op(e1, e3) = e3) | % 86.87/12.43 (all_9_21 = e3 & op(e0, e3) = e3) % 86.87/12.43 (35) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 86.87/12.43 (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 86.87/12.43 (all_9_17 = e2 & op(e3, e0) = e2) % 86.87/12.43 (36) all_6_5 = e1 % 86.87/12.43 (37) ~ (all_4_11 = all_4_13) % 86.87/12.43 (38) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 86.87/12.43 (39) ~ (all_4_10 = all_4_14) % 86.87/12.43 (40) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 86.87/12.43 (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 86.87/12.43 (all_9_16 = e4 & op(e4, e0) = e4) % 86.87/12.43 (41) all_6_13 = all_4_17 % 86.87/12.43 (42) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 86.87/12.43 (43) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 86.87/12.43 (44) ~ (all_4_3 = e3) % 86.87/12.43 (45) ~ (e4 = e1) % 86.87/12.43 (46) ~ (e4 = e2) % 86.87/12.43 (47) op(e1, e0) = all_4_23 % 86.87/12.43 (48) ~ (all_4_6 = e1) % 86.87/12.43 (49) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) | % 86.87/12.43 (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & op(e0, e1) = e4) | % 86.87/12.43 (all_9_24 = e4 & op(e0, e0) = e4) % 86.87/12.43 (50) e3 = e1 | ~ (op(e3, e4) = e3) % 86.87/12.43 (51) ~ (all_4_20 = e0) % 86.87/12.43 (52) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 86.87/12.43 (53) ~ (all_4_15 = all_4_16) % 86.87/12.43 (54) ~ (all_4_11 = all_4_16) % 86.87/12.43 (55) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 86.87/12.43 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 86.87/12.43 (all_9_24 = e2 & op(e0, e0) = e2) % 86.87/12.43 (56) ~ (all_4_19 = all_4_24) % 86.87/12.43 (57) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 86.87/12.43 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 86.87/12.43 (all_9_16 = e1 & op(e4, e0) = e1) % 86.87/12.43 (58) all_6_22 = all_4_14 % 86.87/12.43 (59) all_4_0 = e0 % 86.87/12.43 (60) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 86.87/12.43 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 86.87/12.43 (all_9_24 = e3 & op(e0, e0) = e3) % 86.87/12.43 (61) ~ (all_4_20 = all_4_22) % 86.87/12.43 (62) ~ (all_4_3 = e1) % 86.87/12.43 (63) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & op(e3, e2) = e0) | % 86.87/12.43 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 & op(e1, e2) = e0) | % 86.87/12.43 (all_9_22 = e0 & op(e0, e2) = e0) % 86.87/12.43 (64) all_4_10 = e2 | ~ (op(e4, e2) = e2) % 86.87/12.43 (65) op(e2, e0) = all_4_22 % 86.87/12.43 (66) all_6_19 = all_4_23 % 86.87/12.43 (67) all_6_8 = all_4_16 % 86.87/12.43 (68) op(e3, e3) = all_4_6 % 86.87/12.43 (69) ~ (all_4_5 = e0) % 86.87/12.43 (70) ~ (all_4_4 = e3) % 86.87/12.43 (71) ~ (all_4_3 = all_4_4) % 86.87/12.43 (72) ~ (all_4_3 = all_4_8) % 86.87/12.43 (73) op(e3, e2) = all_4_11 % 86.87/12.43 (74) ~ (all_4_5 = all_4_6) % 86.87/12.43 (75) all_6_3 = all_4_15 % 86.87/12.43 (76) ~ (all_4_6 = all_4_11) % 86.87/12.43 (77) op(unit, e0) = e0 % 86.87/12.43 (78) ~ (all_4_6 = all_4_9) % 86.87/12.43 (79) all_9_6 = e3 % 86.87/12.43 (80) ~ (all_4_4 = all_4_9) % 86.87/12.43 (81) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0 % 86.87/12.43 (82) ~ (all_4_7 = all_4_22) % 86.87/12.43 (83) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 86.87/12.43 (84) all_4_9 = e0 | ~ (op(e0, e3) = e0) % 86.87/12.43 (85) ~ (e4 = e0) % 86.87/12.43 (86) ~ (all_4_18 = all_4_19) % 86.87/12.43 (87) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 86.87/12.43 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 86.87/12.43 (all_9_16 = e3 & op(e4, e0) = e3) % 86.87/12.43 (88) e4 = e2 | ~ (op(e2, e2) = e2) % 86.87/12.43 (89) ~ (all_4_7 = all_4_17) % 86.87/12.43 (90) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 86.87/12.43 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 86.87/12.43 (all_9_20 = e4 & op(e0, e4) = e4) % 86.87/12.43 (91) ~ (all_4_9 = all_4_14) % 86.87/12.43 (92) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 86.87/12.43 (93) all_6_6 = all_4_6 % 86.87/12.43 (94) all_6_1 = e3 | ~ (op(e4, e3) = e3) % 86.87/12.43 (95) ~ (all_4_11 = e4) % 86.87/12.43 (96) ~ (all_4_14 = all_4_19) % 86.87/12.43 (97) ~ (all_4_4 = all_4_14) % 86.87/12.43 (98) all_6_4 = e0 | ~ (op(e4, e0) = e0) % 86.87/12.43 (99) ~ (all_4_16 = all_4_19) % 86.87/12.43 (100) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 86.87/12.43 (101) ~ (all_4_22 = e4) % 86.87/12.43 (102) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 86.87/12.43 (103) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 86.87/12.43 (104) all_6_11 = e3 | ~ (op(e2, e3) = e3) % 86.87/12.43 (105) ~ (all_4_18 = all_4_23) % 86.87/12.43 (106) ~ (all_4_14 = all_4_24) % 86.87/12.43 (107) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 86.87/12.43 (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = e3) | % 86.87/12.43 (all_9_23 = e3 & op(e0, e1) = e3) % 86.87/12.43 (108) all_6_24 = all_4_24 % 86.87/12.43 (109) op(e1, unit) = e1 % 86.87/12.43 (110) ~ (all_4_7 = e3) % 86.87/12.43 (111) ~ (all_4_10 = all_4_11) % 86.87/12.43 (112) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 & op(e1, e3) = e0) | % 86.87/12.43 (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 & op(e1, e1) = e0) | % 86.87/12.43 (all_9_19 = e0 & op(e1, e0) = e0) % 86.87/12.43 (113) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 86.87/12.43 (114) op(e3, unit) = e3 % 86.87/12.43 (115) all_6_10 = e3 % 86.87/12.43 (116) ~ (all_4_6 = all_4_16) % 86.87/12.43 (117) all_6_24 = e4 | all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | % 86.87/12.43 all_6_24 = e0 % 86.87/12.44 (118) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 & op(e0, e3) = e1) | % 86.87/12.44 (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 & op(e0, e1) = e1) | % 86.87/12.44 (all_9_24 = e1 & op(e0, e0) = e1) % 86.87/12.44 (119) op(e2, e2) = e4 % 86.87/12.44 (120) ~ (all_4_10 = e4) % 86.87/12.44 (121) ~ (e2 = e0) % 86.87/12.44 (122) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 86.87/12.44 (123) all_6_20 = all_4_4 % 86.87/12.44 (124) all_6_13 = e2 | ~ (op(e2, e1) = e2) % 86.87/12.44 (125) ~ (all_4_5 = all_4_20) % 86.87/12.44 (126) all_9_2 = e4 % 86.87/12.44 (127) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 86.87/12.44 all_6_15 = e0 % 86.87/12.44 (128) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & op(e2, e3) = e2) | % 86.87/12.44 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 & op(e2, e1) = e2) | % 86.87/12.44 (all_9_18 = e2 & op(e2, e0) = e2) % 86.87/12.44 (129) ~ (all_4_17 = all_4_22) % 86.87/12.44 (130) ~ (all_4_11 = e1) % 86.87/12.44 (131) ~ (all_4_15 = all_4_17) % 86.87/12.44 (132) ~ (e2 = e1) % 86.87/12.44 (133) op(unit, e3) = e3 % 86.87/12.44 (134) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 86.87/12.44 (135) all_6_23 = e0 | ~ (op(e0, e1) = e0) % 86.87/12.44 (136) ~ (all_4_10 = all_4_20) % 86.87/12.44 (137) all_4_8 = e3 | ~ (op(e1, e3) = e3) % 86.87/12.44 (138) e4 = e3 | ~ (op(e2, e4) = e4) % 86.87/12.44 (139) op(e0, e3) = all_4_9 % 86.87/12.44 (140) all_6_22 = e0 | ~ (op(e0, e2) = e0) % 86.87/12.44 (141) all_6_14 = e2 | ~ (op(e2, e0) = e2) % 86.87/12.44 (142) ~ (all_4_4 = e1) % 86.87/12.44 (143) ~ (all_4_4 = all_4_19) % 86.87/12.44 (144) all_6_2 = all_4_10 % 86.87/12.44 (145) ~ (all_4_8 = all_4_9) % 86.87/12.44 (146) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 86.87/12.44 (147) op(e4, e4) = e0 % 86.87/12.44 (148) op(e1, e1) = all_4_18 % 86.87/12.44 (149) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 86.87/12.44 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 86.87/12.44 (all_9_19 = e2 & op(e1, e0) = e2) % 86.87/12.44 (150) op(e4, e1) = all_4_15 % 86.87/12.44 (151) ~ (e3 = e1) % 86.87/12.44 (152) ~ (all_4_20 = all_4_23) % 86.87/12.44 (153) all_4_23 = e0 | ~ (op(e1, e0) = e0) % 86.87/12.44 (154) ~ (all_4_5 = all_4_15) % 86.87/12.44 (155) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 86.87/12.44 all_6_20 = e0 % 86.87/12.44 (156) op(e0, e0) = all_4_24 % 86.87/12.44 (157) ~ (all_4_15 = all_4_18) % 86.87/12.44 (158) ~ (all_4_13 = all_4_14) % 86.87/12.44 (159) op(e3, e4) = e1 % 86.87/12.44 (160) op(e1, e3) = all_4_8 % 86.87/12.44 (161) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 86.87/12.44 (162) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 86.87/12.44 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 86.87/12.44 (all_9_22 = e2 & op(e0, e2) = e2) % 86.87/12.44 (163) all_6_14 = all_4_22 % 86.87/12.44 (164) ~ (all_4_10 = all_4_13) % 86.87/12.44 (165) all_4_22 = e0 | ~ (op(e2, e0) = e0) % 86.87/12.44 (166) ~ (all_4_4 = all_4_24) % 86.87/12.44 (167) all_4_19 = e0 | ~ (op(e0, e1) = e0) % 86.87/12.44 (168) ~ (all_4_4 = e0) % 86.87/12.44 (169) ~ (all_4_14 = e4) % 86.87/12.44 (170) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 86.87/12.44 (171) op(e0, e1) = all_4_19 % 86.87/12.44 (172) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 86.87/12.44 (173) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e2 | all_6_21 = e1 | % 86.87/12.44 all_6_21 = e0 % 86.87/12.44 (174) op(e1, e4) = all_4_3 % 86.87/12.44 (175) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 86.87/12.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 86.87/12.44 (176) all_6_18 = all_4_18 % 86.87/12.44 (177) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 86.87/12.44 (178) (all_8_52 = e4 & ~ (all_8_53 = e0) & op(e4, all_8_54) = all_8_53 & % 86.87/12.44 op(e4, e0) = all_8_54 & op(e0, all_8_54) = e4 & $i(all_8_53) & % 86.87/12.44 $i(all_8_54)) | (all_8_55 = e3 & ~ (all_8_56 = e0) & op(e3, % 86.87/12.44 all_8_57) = all_8_56 & op(e3, e0) = all_8_57 & op(e0, all_8_57) = % 86.87/12.44 e3 & $i(all_8_56) & $i(all_8_57)) | (all_8_58 = e2 & ~ (all_8_59 = % 86.87/12.44 e0) & op(e2, all_8_60) = all_8_59 & op(e2, e0) = all_8_60 & op(e0, % 86.87/12.44 all_8_60) = e2 & $i(all_8_59) & $i(all_8_60)) | (all_8_61 = e1 & ~ % 86.87/12.44 (all_8_62 = e0) & op(e1, all_8_63) = all_8_62 & op(e1, e0) = all_8_63 % 86.87/12.44 & op(e0, all_8_63) = e1 & $i(all_8_62) & $i(all_8_63)) % 86.87/12.44 (179) all_6_3 = e1 | ~ (op(e4, e1) = e1) % 86.87/12.44 (180) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 86.87/12.44 (181) op(e0, e4) = all_4_4 % 86.87/12.44 (182) all_4_16 = e3 | ~ (op(e3, e1) = e3) % 86.87/12.44 (183) ~ (all_4_15 = all_4_19) % 86.87/12.44 (184) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | % 86.87/12.44 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) | % 86.87/12.44 (all_9_18 = e0 & op(e2, e0) = e0) % 86.87/12.44 (185) (all_8_26 = e4 & ~ (all_8_27 = e2) & op(e4, all_8_28) = all_8_27 & % 86.87/12.44 op(e4, e2) = all_8_28 & op(e2, all_8_28) = e4 & $i(all_8_27) & % 86.87/12.44 $i(all_8_28)) | (all_8_29 = e3 & ~ (all_8_30 = e2) & op(e3, % 86.87/12.44 all_8_31) = all_8_30 & op(e3, e2) = all_8_31 & op(e2, all_8_31) = % 86.87/12.44 e3 & $i(all_8_30) & $i(all_8_31)) | (all_8_33 = e1 & ~ (all_8_34 = % 86.87/12.44 e2) & op(e2, all_8_35) = e1 & op(e1, all_8_35) = all_8_34 & op(e1, % 86.87/12.44 e2) = all_8_35 & $i(all_8_34) & $i(all_8_35)) | (all_8_36 = e0 & ~ % 86.87/12.44 (all_8_37 = e2) & op(e2, all_8_38) = e0 & op(e0, all_8_38) = all_8_37 % 86.87/12.44 & op(e0, e2) = all_8_38 & $i(all_8_37) & $i(all_8_38)) % 86.87/12.44 (186) ~ (all_4_22 = e3) % 86.87/12.44 (187) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 86.87/12.44 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 86.87/12.44 (all_9_23 = e1 & op(e0, e1) = e1) % 86.87/12.44 (188) all_4_15 = e4 | ~ (op(e4, e1) = e4) % 86.87/12.44 (189) all_6_15 = all_4_3 % 86.87/12.44 (190) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 86.87/12.44 (191) ~ (all_4_5 = all_4_7) % 86.87/12.44 (192) ~ (all_4_5 = all_4_9) % 86.87/12.45 (193) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = e3 & % 86.87/12.45 op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = e3 % 86.87/12.45 & all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = e3 & op(e4, e3) = % 86.87/12.45 all_8_15 & op(e3, e3) = e4 & $i(all_8_15)) | (all_8_0 = e2 & all_8_32 % 86.87/12.45 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 & op(e2, e4) = all_8_6 & % 86.87/12.45 op(e2, e2) = e4 & $i(all_8_6)) | (all_8_0 = e2 & all_8_32 = e4 & ~ % 86.87/12.45 (all_8_28 = e4) & op(e4, e4) = e2 & op(e4, e2) = all_8_28 & op(e2, % 86.87/12.45 e2) = e4 & $i(all_8_28)) | (all_8_0 = e1 & all_8_48 = e4 & ~ % 86.87/12.45 (all_8_9 = e1) & op(e4, e4) = e1 & op(e1, e4) = all_8_9 & op(e1, e1) % 86.87/12.45 = e4 & $i(all_8_9)) | (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_41 = % 86.87/12.45 e4) & op(e4, e4) = e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & % 86.87/12.45 $i(all_8_41)) | (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) & % 86.87/12.45 op(e4, e4) = e0 & op(e4, e0) = all_8_54 & op(e0, e0) = e4 & % 86.87/12.45 $i(all_8_54)) | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = e2) & % 86.87/12.45 op(e3, e3) = e2 & op(e2, e3) = all_8_19 & op(e2, e2) = e3 & % 86.87/12.45 $i(all_8_19)) | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) & % 86.87/12.45 op(e3, e3) = e2 & op(e3, e2) = all_8_31 & op(e2, e2) = e3 & % 86.87/12.45 $i(all_8_31)) | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & % 86.87/12.45 op(e3, e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) = e3 & % 86.87/12.45 $i(all_8_22)) | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) & % 86.87/12.45 op(e3, e3) = e1 & op(e3, e1) = all_8_44 & op(e1, e1) = e3 & % 86.87/12.45 $i(all_8_44)) | (all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & % 86.87/12.45 op(e3, e3) = e0 & op(e3, e0) = all_8_57 & op(e0, e0) = e3 & % 86.87/12.45 $i(all_8_57)) | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) & % 86.87/12.45 op(e2, e2) = e1 & op(e1, e2) = all_8_35 & op(e1, e1) = e2 & % 86.87/12.45 $i(all_8_35)) | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & % 86.87/12.45 op(e2, e2) = e1 & op(e2, e1) = all_8_47 & op(e1, e1) = e2 & % 86.87/12.45 $i(all_8_47)) | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) & % 86.87/12.45 op(e2, e2) = e0 & op(e2, e0) = all_8_60 & op(e0, e0) = e2 & % 86.87/12.45 $i(all_8_60)) | (op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = % 86.87/12.45 e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 & % 86.87/12.45 op(e0, e4) = all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & all_8_64 % 86.87/12.45 = e3 & ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, e3) = % 86.87/12.45 all_8_25 & $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = e2 & ~ % 86.87/12.45 (all_8_38 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_8_38 & % 86.87/12.45 $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 = % 86.87/12.45 e0) & op(e1, e1) = e0 & op(e0, e1) = all_8_51 & $i(all_8_51)) | % 86.87/12.45 (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, e1) = % 86.87/12.45 e0 & op(e1, e0) = all_8_63 & $i(all_8_63)))) % 86.87/12.45 (194) ~ (all_4_16 = all_4_17) % 86.87/12.45 (195) (all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, all_8_3) = e3 & op(e3, % 86.87/12.45 all_8_3) = all_8_2 & op(e3, e4) = all_8_3 & $i(all_8_2) & % 86.87/12.45 $i(all_8_3)) | (all_8_4 = e2 & ~ (all_8_5 = e4) & op(e4, all_8_6) = % 86.87/12.45 e2 & op(e2, all_8_6) = all_8_5 & op(e2, e4) = all_8_6 & $i(all_8_5) & % 86.87/12.45 $i(all_8_6)) | (all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) = % 86.87/12.45 e1 & op(e1, all_8_9) = all_8_8 & op(e1, e4) = all_8_9 & $i(all_8_8) & % 86.87/12.45 $i(all_8_9)) | (all_8_10 = e0 & ~ (all_8_11 = e4) & op(e4, all_8_12) % 86.87/12.45 = e0 & op(e0, all_8_12) = all_8_11 & op(e0, e4) = all_8_12 & % 86.87/12.45 $i(all_8_11) & $i(all_8_12)) % 86.87/12.45 (196) ~ (all_4_16 = e1) % 86.87/12.45 (197) all_6_7 = e2 | ~ (op(e3, e2) = e2) % 86.87/12.45 (198) all_4_2 = e3 % 86.87/12.45 (199) op(e2, e3) = all_4_7 % 86.87/12.45 (200) op(e4, e2) = all_4_10 % 86.87/12.45 (201) all_6_19 = e1 | ~ (op(e1, e0) = e1) % 86.87/12.45 (202) ~ (all_4_11 = all_4_14) % 86.87/12.45 (203) (all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = e0 & op(e4, e0) = e0) % 86.87/12.45 | (all_9_17 = e0 & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) = % 86.87/12.45 e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & ((all_9_20 = e0 & % 86.87/12.45 op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 % 86.87/12.45 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 & op(e0, e1) = e0))) % 86.87/12.45 (204) all_6_21 = all_4_9 % 86.87/12.45 (205) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 86.87/12.45 all_6_11 = e0 % 86.87/12.45 (206) op(e4, unit) = e4 % 86.87/12.45 (207) (all_9_1 = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 86.87/12.45 (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) | % 86.87/12.45 (all_9_21 = e4 & op(e0, e3) = e4) % 86.87/12.45 (208) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 86.87/12.45 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 86.87/12.45 (all_9_20 = e1 & op(e0, e4) = e1) % 86.87/12.45 (209) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 86.87/12.45 (210) (all_9_1 = e1 & op(e4, e3) = e1) | (all_9_3 = e1 & op(e3, e3) = e1) | % 86.87/12.45 (all_9_7 = e1 & op(e2, e3) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | % 86.87/12.45 (all_9_21 = e1 & op(e0, e3) = e1) % 86.87/12.45 (211) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 86.87/12.45 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 86.87/12.45 (all_9_24 = e4 & op(e0, e0) = e4) % 86.87/12.45 (212) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 86.87/12.45 (213) op(e2, e1) = all_4_17 % 86.87/12.45 (214) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 86.87/12.45 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 86.87/12.45 (all_9_16 = e2 & op(e4, e0) = e2) % 86.87/12.45 (215) all_4_4 = e0 | ~ (op(e0, e4) = e0) % 86.87/12.45 (216) op(e4, e0) = all_4_20 % 86.87/12.45 (217) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 86.87/12.45 (218) op(unit, e4) = e4 % 86.87/12.45 (219) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e2 | all_6_22 = e1 | % 86.87/12.45 all_6_22 = e0 % 86.87/12.45 (220) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 86.87/12.45 (221) all_4_13 = e1 | ~ (op(e1, e2) = e1) % 86.87/12.45 (222) ~ (all_4_9 = all_4_19) % 86.87/12.45 (223) ~ (all_4_17 = all_4_18) % 86.87/12.45 (224) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 | all_6_4 = % 86.87/12.45 e0 % 86.87/12.45 (225) ~ (all_4_17 = all_4_19) % 86.87/12.45 (226) ~ (all_4_16 = all_4_21) % 86.87/12.45 (227) all_6_21 = e3 | ~ (op(e0, e3) = e3) % 86.87/12.45 (228) all_6_4 = all_4_20 % 86.87/12.45 (229) all_6_1 = e4 | ~ (op(e4, e3) = e4) % 86.87/12.45 (230) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | % 86.87/12.45 (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 86.87/12.45 (all_9_19 = e1 & op(e1, e0) = e1) % 86.87/12.45 (231) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 86.87/12.45 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 86.87/12.45 (all_9_20 = e2 & op(e0, e4) = e2) % 86.87/12.45 (232) ~ (all_4_16 = all_4_18) % 86.87/12.45 (233) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 86.87/12.45 (234) ~ (e1 = e0) % 86.87/12.45 % 86.87/12.45 Begin of proof % 86.87/12.45 | % 86.87/12.45 | BETA: splitting (209) gives: % 86.87/12.45 | % 86.87/12.45 | Case 1: % 86.87/12.45 | | % 86.87/12.45 | | (235) ~ (op(e3, e4) = e4) % 86.87/12.45 | | % 86.87/12.45 | | PRED_UNIFY: (24), (235) imply: % 86.87/12.45 | | (236) $false % 86.87/12.45 | | % 86.87/12.45 | | CLOSE: (236) is inconsistent. % 86.87/12.45 | | % 86.87/12.45 | Case 2: % 86.87/12.45 | | % 86.87/12.45 | | (237) all_6_5 = e4 % 86.87/12.45 | | % 86.87/12.45 | | COMBINE_EQS: (36), (237) imply: % 86.87/12.45 | | (238) e4 = e1 % 86.87/12.45 | | % 86.87/12.45 | | COMBINE_EQS: (126), (238) imply: % 86.87/12.45 | | (239) all_9_2 = e1 % 86.87/12.45 | | % 86.87/12.46 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 86.87/12.46 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 86.87/12.46 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 86.87/12.46 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 86.87/12.46 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), % 86.87/12.46 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 86.87/12.46 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 86.87/12.46 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), % 86.87/12.46 | | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), % 86.87/12.46 | | (101), (102), (103), (104), (105), (106), (107), (108), (109), % 86.87/12.46 | | (110), (111), (112), (113), (114), (115), (116), (117), (118), % 86.87/12.46 | | (119), (120), (121), (122), (123), (124), (125), (127), (128), % 86.87/12.46 | | (129), (130), (131), (132), (133), (134), (135), (136), (137), % 86.87/12.46 | | (138), (139), (140), (141), (142), (143), (144), (145), (146), % 86.87/12.46 | | (147), (148), (149), (150), (151), (152), (153), (154), (155), % 86.87/12.46 | | (156), (157), (158), (159), (160), (161), (162), (163), (164), % 86.87/12.46 | | (165), (166), (167), (168), (169), (170), (171), (172), (173), % 86.87/12.46 | | (174), (175), (176), (177), (178), (179), (180), (181), (182), % 86.87/12.46 | | (183), (184), (185), (186), (187), (188), (189), (190), (191), % 86.87/12.46 | | (192), (193), (194), (195), (196), (197), (198), (199), (200), % 86.87/12.46 | | (201), (202), (203), (204), (205), (206), (207), (208), (209), % 86.87/12.46 | | (210), (211), (212), (213), (214), (215), (216), (217), (218), % 86.87/12.46 | | (219), (220), (221), (222), (223), (224), (225), (226), (227), % 86.87/12.46 | | (228), (229), (230), (231), (232), (233), (234), (239) are % 86.87/12.46 | | inconsistent by sub-proof #3. % 86.87/12.46 | | % 86.87/12.46 | End of split % 86.87/12.46 | % 86.87/12.46 End of proof % 86.87/12.46 % 86.87/12.46 Sub-proof #2 shows that the following formulas are inconsistent: % 86.87/12.46 ---------------------------------------------------------------- % 86.87/12.46 (1) ~ (all_4_7 = e4) % 86.87/12.46 (2) ~ (e4 = e3) % 86.87/12.46 (3) ~ (all_4_17 = e4) % 86.87/12.46 (4) op(e2, e0) = all_4_22 % 86.87/12.46 (5) ~ (all_4_22 = e4) % 86.87/12.46 (6) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) = e3) | % 86.87/12.46 (all_9_18 = e3 & op(e2, e0) = e3) % 86.87/12.46 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 86.87/12.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 86.87/12.46 (8) ~ (all_4_22 = e3) % 86.87/12.46 (9) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_7 = e4 & op(e2, e3) = e4) | % 86.87/12.46 (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_11 = e4 & op(e2, e1) = e4) | % 86.87/12.46 (all_9_18 = e4 & op(e2, e0) = e4) % 86.87/12.46 (10) all_4_2 = e3 % 86.87/12.46 (11) op(e2, e3) = all_4_7 % 86.87/12.46 (12) op(e2, e1) = all_4_17 % 86.87/12.46 (13) ~ (all_4_17 = e3) % 86.87/12.46 (14) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 86.87/12.46 % 86.87/12.46 Begin of proof % 86.87/12.46 | % 86.87/12.46 | BETA: splitting (6) gives: % 86.87/12.46 | % 86.87/12.46 | Case 1: % 86.87/12.46 | | % 86.87/12.46 | | (15) all_9_8 = e3 & op(e2, e2) = e3 % 86.87/12.46 | | % 86.87/12.46 | | ALPHA: (15) implies: % 86.87/12.46 | | (16) all_9_8 = e3 % 86.87/12.46 | | % 86.87/12.46 | | BETA: splitting (9) gives: % 86.87/12.46 | | % 86.87/12.46 | | Case 1: % 86.87/12.46 | | | % 86.87/12.46 | | | (17) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_7 = e4 & op(e2, e3) = % 86.87/12.46 | | | e4) % 86.87/12.46 | | | % 86.87/12.46 | | | BETA: splitting (17) gives: % 86.87/12.46 | | | % 86.87/12.46 | | | Case 1: % 86.87/12.46 | | | | % 86.87/12.46 | | | | (18) all_9_6 = e4 & op(e2, e4) = e4 % 86.87/12.46 | | | | % 86.87/12.46 | | | | ALPHA: (18) implies: % 86.87/12.46 | | | | (19) op(e2, e4) = e4 % 86.87/12.46 | | | | % 86.87/12.46 | | | | REF_CLOSE: (2), (10), (14), (19) are inconsistent by sub-proof #129. % 86.87/12.46 | | | | % 86.87/12.46 | | | Case 2: % 86.87/12.46 | | | | % 86.87/12.46 | | | | (20) all_9_7 = e4 & op(e2, e3) = e4 % 86.87/12.46 | | | | % 86.87/12.46 | | | | REF_CLOSE: (1), (7), (11), (20) are inconsistent by sub-proof #59. % 86.87/12.46 | | | | % 86.87/12.46 | | | End of split % 86.87/12.46 | | | % 86.87/12.46 | | Case 2: % 86.87/12.46 | | | % 86.87/12.46 | | | (21) (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_11 = e4 & op(e2, e1) = % 86.87/12.46 | | | e4) | (all_9_18 = e4 & op(e2, e0) = e4) % 86.87/12.46 | | | % 86.87/12.46 | | | BETA: splitting (21) gives: % 86.87/12.46 | | | % 86.87/12.46 | | | Case 1: % 86.87/12.46 | | | | % 86.87/12.46 | | | | (22) all_9_8 = e4 & op(e2, e2) = e4 % 86.87/12.46 | | | | % 86.87/12.46 | | | | ALPHA: (22) implies: % 86.87/12.46 | | | | (23) all_9_8 = e4 % 86.87/12.46 | | | | % 86.87/12.46 | | | | COMBINE_EQS: (16), (23) imply: % 86.87/12.46 | | | | (24) e4 = e3 % 86.87/12.46 | | | | % 86.87/12.46 | | | | SIMP: (24) implies: % 86.87/12.46 | | | | (25) e4 = e3 % 86.87/12.46 | | | | % 86.87/12.46 | | | | REDUCE: (2), (25) imply: % 86.87/12.46 | | | | (26) $false % 86.87/12.46 | | | | % 86.87/12.46 | | | | CLOSE: (26) is inconsistent. % 86.87/12.46 | | | | % 86.87/12.46 | | | Case 2: % 86.87/12.46 | | | | % 86.87/12.46 | | | | (27) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_18 = e4 & op(e2, e0) % 86.87/12.46 | | | | = e4) % 86.87/12.46 | | | | % 86.87/12.46 | | | | BETA: splitting (27) gives: % 86.87/12.46 | | | | % 86.87/12.46 | | | | Case 1: % 86.87/12.46 | | | | | % 86.87/12.46 | | | | | (28) all_9_11 = e4 & op(e2, e1) = e4 % 86.87/12.46 | | | | | % 86.87/12.46 | | | | | ALPHA: (28) implies: % 86.87/12.46 | | | | | (29) op(e2, e1) = e4 % 86.87/12.46 | | | | | % 86.87/12.46 | | | | | GROUND_INST: instantiating (7) with all_4_17, e4, e1, e2, simplifying % 86.87/12.46 | | | | | with (12), (29) gives: % 86.87/12.46 | | | | | (30) all_4_17 = e4 % 86.87/12.46 | | | | | % 86.87/12.46 | | | | | REDUCE: (3), (30) imply: % 86.87/12.46 | | | | | (31) $false % 86.87/12.46 | | | | | % 86.87/12.46 | | | | | CLOSE: (31) is inconsistent. % 86.87/12.46 | | | | | % 86.87/12.46 | | | | Case 2: % 86.87/12.46 | | | | | % 86.87/12.46 | | | | | (32) all_9_18 = e4 & op(e2, e0) = e4 % 86.87/12.46 | | | | | % 86.87/12.46 | | | | | REF_CLOSE: (4), (5), (7), (32) are inconsistent by sub-proof #50. % 86.87/12.46 | | | | | % 86.87/12.46 | | | | End of split % 86.87/12.46 | | | | % 86.87/12.46 | | | End of split % 86.87/12.46 | | | % 86.87/12.46 | | End of split % 86.87/12.46 | | % 86.87/12.46 | Case 2: % 86.87/12.46 | | % 86.87/12.46 | | (33) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_18 = e3 & op(e2, e0) = % 86.87/12.46 | | e3) % 86.87/12.46 | | % 86.87/12.46 | | BETA: splitting (33) gives: % 86.87/12.46 | | % 86.87/12.46 | | Case 1: % 86.87/12.46 | | | % 86.87/12.46 | | | (34) all_9_11 = e3 & op(e2, e1) = e3 % 86.87/12.46 | | | % 86.87/12.46 | | | REF_CLOSE: (7), (12), (13), (34) are inconsistent by sub-proof #39. % 86.87/12.46 | | | % 86.87/12.46 | | Case 2: % 86.87/12.46 | | | % 86.87/12.46 | | | (35) all_9_18 = e3 & op(e2, e0) = e3 % 86.87/12.46 | | | % 86.87/12.46 | | | ALPHA: (35) implies: % 86.87/12.46 | | | (36) op(e2, e0) = e3 % 86.87/12.46 | | | % 86.87/12.46 | | | REF_CLOSE: (4), (7), (8), (36) are inconsistent by sub-proof #45. % 86.87/12.46 | | | % 86.87/12.46 | | End of split % 86.87/12.46 | | % 86.87/12.46 | End of split % 86.87/12.46 | % 86.87/12.46 End of proof % 86.87/12.46 % 86.87/12.46 Sub-proof #3 shows that the following formulas are inconsistent: % 86.87/12.46 ---------------------------------------------------------------- % 86.87/12.46 (1) ~ (all_4_22 = all_4_23) % 86.87/12.46 (2) ~ (all_4_6 = all_4_7) % 86.87/12.46 (3) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 86.87/12.46 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 86.87/12.46 (all_9_20 = e3 & op(e0, e4) = e3) % 86.87/12.46 (4) ~ (all_4_20 = all_4_24) % 86.87/12.46 (5) ~ (all_4_9 = all_4_24) % 86.87/12.46 (6) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | all_6_14 % 86.87/12.46 = e0 % 86.87/12.46 (7) op(e0, e2) = all_4_14 % 86.87/12.46 (8) all_6_11 = all_4_7 % 86.87/12.46 (9) ~ (all_4_5 = all_4_10) % 87.36/12.46 (10) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 87.36/12.46 (11) all_6_1 = all_4_5 % 87.36/12.46 (12) op(e4, e3) = all_4_5 % 87.36/12.46 (13) ~ (all_4_10 = e0) % 87.36/12.46 (14) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 87.36/12.46 (15) op(e0, unit) = e0 % 87.36/12.46 (16) ~ (all_4_7 = all_4_9) % 87.36/12.46 (17) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | all_6_7 = e0 % 87.36/12.46 (18) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 87.36/12.46 (19) all_6_6 = e4 | all_6_6 = e3 | all_6_6 = e2 | all_6_6 = e1 | all_6_6 = e0 % 87.36/12.46 (20) op(unit, e2) = e2 % 87.36/12.46 (21) all_4_23 = e1 | ~ (op(e1, e0) = e1) % 87.36/12.46 (22) ~ (all_4_10 = all_4_15) % 87.36/12.46 (23) all_6_7 = all_4_11 % 87.36/12.46 (24) all_6_23 = all_4_19 % 87.36/12.46 (25) ~ (e3 = e2) % 87.36/12.46 (26) ~ (all_4_7 = e4) % 87.36/12.46 (27) op(e2, e4) = e3 % 87.36/12.46 (28) op(e2, unit) = e2 % 87.36/12.46 (29) ~ (e3 = e0) % 87.36/12.46 (30) ~ (all_4_15 = all_4_20) % 87.36/12.46 (31) ~ (e4 = e3) % 87.36/12.46 (32) ~ (all_4_3 = e0) % 87.36/12.46 (33) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 87.36/12.46 (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 & op(e1, e3) = e3) | % 87.36/12.46 (all_9_21 = e3 & op(e0, e3) = e3) % 87.36/12.46 (34) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 87.36/12.46 (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 87.36/12.46 (all_9_17 = e2 & op(e3, e0) = e2) % 87.36/12.46 (35) all_6_5 = e1 % 87.36/12.46 (36) ~ (all_4_11 = all_4_13) % 87.36/12.46 (37) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 87.36/12.46 (38) ~ (all_4_10 = all_4_14) % 87.36/12.47 (39) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 87.36/12.47 (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 87.36/12.47 (all_9_16 = e4 & op(e4, e0) = e4) % 87.36/12.47 (40) all_6_13 = all_4_17 % 87.36/12.47 (41) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 87.36/12.47 (42) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 87.36/12.47 (43) ~ (all_4_3 = e3) % 87.36/12.47 (44) ~ (e4 = e1) % 87.36/12.47 (45) ~ (e4 = e2) % 87.36/12.47 (46) op(e1, e0) = all_4_23 % 87.36/12.47 (47) ~ (all_4_6 = e1) % 87.36/12.47 (48) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) | % 87.36/12.47 (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & op(e0, e1) = e4) | % 87.36/12.47 (all_9_24 = e4 & op(e0, e0) = e4) % 87.36/12.47 (49) e3 = e1 | ~ (op(e3, e4) = e3) % 87.36/12.47 (50) ~ (all_4_20 = e0) % 87.36/12.47 (51) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 87.36/12.47 (52) ~ (all_4_15 = all_4_16) % 87.36/12.47 (53) ~ (all_4_11 = all_4_16) % 87.36/12.47 (54) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 87.36/12.47 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 87.36/12.47 (all_9_24 = e2 & op(e0, e0) = e2) % 87.36/12.47 (55) ~ (all_4_19 = all_4_24) % 87.36/12.47 (56) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 87.36/12.47 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 87.36/12.47 (all_9_16 = e1 & op(e4, e0) = e1) % 87.36/12.47 (57) all_6_22 = all_4_14 % 87.36/12.47 (58) all_4_0 = e0 % 87.36/12.47 (59) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 87.36/12.47 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 87.36/12.47 (all_9_24 = e3 & op(e0, e0) = e3) % 87.36/12.47 (60) ~ (all_4_20 = all_4_22) % 87.36/12.47 (61) ~ (all_4_3 = e1) % 87.36/12.47 (62) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & op(e3, e2) = e0) | % 87.36/12.47 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 & op(e1, e2) = e0) | % 87.36/12.47 (all_9_22 = e0 & op(e0, e2) = e0) % 87.36/12.47 (63) all_4_10 = e2 | ~ (op(e4, e2) = e2) % 87.36/12.47 (64) op(e2, e0) = all_4_22 % 87.36/12.47 (65) all_6_19 = all_4_23 % 87.36/12.47 (66) all_6_8 = all_4_16 % 87.36/12.47 (67) op(e3, e3) = all_4_6 % 87.36/12.47 (68) ~ (all_4_5 = e0) % 87.36/12.47 (69) ~ (all_4_4 = e3) % 87.36/12.47 (70) ~ (all_4_3 = all_4_4) % 87.36/12.47 (71) ~ (all_4_3 = all_4_8) % 87.36/12.47 (72) op(e3, e2) = all_4_11 % 87.36/12.47 (73) ~ (all_4_5 = all_4_6) % 87.36/12.47 (74) all_6_3 = all_4_15 % 87.36/12.47 (75) ~ (all_4_6 = all_4_11) % 87.36/12.47 (76) op(unit, e0) = e0 % 87.36/12.47 (77) ~ (all_4_6 = all_4_9) % 87.36/12.47 (78) all_9_6 = e3 % 87.36/12.47 (79) ~ (all_4_4 = all_4_9) % 87.36/12.47 (80) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0 % 87.36/12.47 (81) ~ (all_4_7 = all_4_22) % 87.36/12.47 (82) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 87.36/12.47 (83) all_4_9 = e0 | ~ (op(e0, e3) = e0) % 87.36/12.47 (84) ~ (e4 = e0) % 87.36/12.47 (85) ~ (all_4_18 = all_4_19) % 87.36/12.47 (86) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 87.36/12.47 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 87.36/12.47 (all_9_16 = e3 & op(e4, e0) = e3) % 87.36/12.47 (87) e4 = e2 | ~ (op(e2, e2) = e2) % 87.36/12.47 (88) ~ (all_4_7 = all_4_17) % 87.36/12.47 (89) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 87.36/12.47 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 87.36/12.47 (all_9_20 = e4 & op(e0, e4) = e4) % 87.36/12.47 (90) ~ (all_4_9 = all_4_14) % 87.36/12.47 (91) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 87.36/12.47 (92) all_6_6 = all_4_6 % 87.36/12.47 (93) all_6_1 = e3 | ~ (op(e4, e3) = e3) % 87.36/12.47 (94) ~ (all_4_11 = e4) % 87.36/12.47 (95) ~ (all_4_14 = all_4_19) % 87.36/12.47 (96) ~ (all_4_4 = all_4_14) % 87.36/12.47 (97) all_6_4 = e0 | ~ (op(e4, e0) = e0) % 87.36/12.47 (98) ~ (all_4_16 = all_4_19) % 87.36/12.47 (99) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 87.36/12.47 (100) ~ (all_4_22 = e4) % 87.36/12.47 (101) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 87.36/12.47 (102) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 87.36/12.47 (103) all_6_11 = e3 | ~ (op(e2, e3) = e3) % 87.36/12.47 (104) ~ (all_4_18 = all_4_23) % 87.36/12.47 (105) ~ (all_4_14 = all_4_24) % 87.36/12.47 (106) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 87.36/12.47 (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = e3) | % 87.36/12.47 (all_9_23 = e3 & op(e0, e1) = e3) % 87.36/12.47 (107) all_6_24 = all_4_24 % 87.36/12.47 (108) op(e1, unit) = e1 % 87.36/12.47 (109) ~ (all_4_7 = e3) % 87.36/12.47 (110) ~ (all_4_10 = all_4_11) % 87.36/12.47 (111) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 & op(e1, e3) = e0) | % 87.36/12.47 (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 & op(e1, e1) = e0) | % 87.36/12.47 (all_9_19 = e0 & op(e1, e0) = e0) % 87.36/12.47 (112) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 87.36/12.47 (113) op(e3, unit) = e3 % 87.36/12.47 (114) all_6_10 = e3 % 87.36/12.47 (115) ~ (all_4_6 = all_4_16) % 87.36/12.47 (116) all_6_24 = e4 | all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | % 87.36/12.47 all_6_24 = e0 % 87.36/12.47 (117) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 & op(e0, e3) = e1) | % 87.36/12.47 (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 & op(e0, e1) = e1) | % 87.36/12.47 (all_9_24 = e1 & op(e0, e0) = e1) % 87.36/12.47 (118) op(e2, e2) = e4 % 87.36/12.47 (119) ~ (all_4_10 = e4) % 87.36/12.47 (120) all_9_2 = e1 % 87.36/12.47 (121) ~ (e2 = e0) % 87.36/12.47 (122) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 87.36/12.47 (123) all_6_20 = all_4_4 % 87.36/12.47 (124) all_6_13 = e2 | ~ (op(e2, e1) = e2) % 87.36/12.47 (125) ~ (all_4_5 = all_4_20) % 87.36/12.47 (126) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 87.36/12.47 all_6_15 = e0 % 87.36/12.47 (127) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & op(e2, e3) = e2) | % 87.36/12.47 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 & op(e2, e1) = e2) | % 87.36/12.47 (all_9_18 = e2 & op(e2, e0) = e2) % 87.36/12.47 (128) ~ (all_4_17 = all_4_22) % 87.36/12.47 (129) ~ (all_4_11 = e1) % 87.36/12.47 (130) ~ (all_4_15 = all_4_17) % 87.36/12.47 (131) ~ (e2 = e1) % 87.36/12.47 (132) op(unit, e3) = e3 % 87.36/12.47 (133) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 87.36/12.47 (134) all_6_23 = e0 | ~ (op(e0, e1) = e0) % 87.36/12.47 (135) ~ (all_4_10 = all_4_20) % 87.36/12.47 (136) all_4_8 = e3 | ~ (op(e1, e3) = e3) % 87.36/12.48 (137) e4 = e3 | ~ (op(e2, e4) = e4) % 87.36/12.48 (138) op(e0, e3) = all_4_9 % 87.36/12.48 (139) all_6_22 = e0 | ~ (op(e0, e2) = e0) % 87.36/12.48 (140) all_6_14 = e2 | ~ (op(e2, e0) = e2) % 87.36/12.48 (141) ~ (all_4_4 = e1) % 87.36/12.48 (142) ~ (all_4_4 = all_4_19) % 87.36/12.48 (143) all_6_2 = all_4_10 % 87.36/12.48 (144) ~ (all_4_8 = all_4_9) % 87.36/12.48 (145) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 87.36/12.48 (146) op(e4, e4) = e0 % 87.36/12.48 (147) op(e1, e1) = all_4_18 % 87.36/12.48 (148) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 87.36/12.48 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 87.36/12.48 (all_9_19 = e2 & op(e1, e0) = e2) % 87.36/12.48 (149) op(e4, e1) = all_4_15 % 87.36/12.48 (150) ~ (e3 = e1) % 87.36/12.48 (151) ~ (all_4_20 = all_4_23) % 87.36/12.48 (152) all_4_23 = e0 | ~ (op(e1, e0) = e0) % 87.36/12.48 (153) ~ (all_4_5 = all_4_15) % 87.36/12.48 (154) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 87.36/12.48 all_6_20 = e0 % 87.36/12.48 (155) op(e0, e0) = all_4_24 % 87.36/12.48 (156) ~ (all_4_15 = all_4_18) % 87.36/12.48 (157) ~ (all_4_13 = all_4_14) % 87.36/12.48 (158) op(e3, e4) = e1 % 87.36/12.48 (159) op(e1, e3) = all_4_8 % 87.36/12.48 (160) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 87.36/12.48 (161) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 87.36/12.48 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 87.36/12.48 (all_9_22 = e2 & op(e0, e2) = e2) % 87.36/12.48 (162) all_6_14 = all_4_22 % 87.36/12.48 (163) ~ (all_4_10 = all_4_13) % 87.36/12.48 (164) all_4_22 = e0 | ~ (op(e2, e0) = e0) % 87.36/12.48 (165) ~ (all_4_4 = all_4_24) % 87.36/12.48 (166) all_4_19 = e0 | ~ (op(e0, e1) = e0) % 87.36/12.48 (167) ~ (all_4_4 = e0) % 87.36/12.48 (168) ~ (all_4_14 = e4) % 87.36/12.48 (169) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 87.36/12.48 (170) op(e0, e1) = all_4_19 % 87.36/12.48 (171) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 87.36/12.48 (172) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e2 | all_6_21 = e1 | % 87.36/12.48 all_6_21 = e0 % 87.36/12.48 (173) op(e1, e4) = all_4_3 % 87.36/12.48 (174) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 87.36/12.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 87.36/12.48 (175) all_6_18 = all_4_18 % 87.36/12.48 (176) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 87.36/12.48 (177) (all_8_52 = e4 & ~ (all_8_53 = e0) & op(e4, all_8_54) = all_8_53 & % 87.36/12.48 op(e4, e0) = all_8_54 & op(e0, all_8_54) = e4 & $i(all_8_53) & % 87.36/12.48 $i(all_8_54)) | (all_8_55 = e3 & ~ (all_8_56 = e0) & op(e3, % 87.36/12.48 all_8_57) = all_8_56 & op(e3, e0) = all_8_57 & op(e0, all_8_57) = % 87.36/12.48 e3 & $i(all_8_56) & $i(all_8_57)) | (all_8_58 = e2 & ~ (all_8_59 = % 87.36/12.48 e0) & op(e2, all_8_60) = all_8_59 & op(e2, e0) = all_8_60 & op(e0, % 87.36/12.48 all_8_60) = e2 & $i(all_8_59) & $i(all_8_60)) | (all_8_61 = e1 & ~ % 87.36/12.48 (all_8_62 = e0) & op(e1, all_8_63) = all_8_62 & op(e1, e0) = all_8_63 % 87.36/12.48 & op(e0, all_8_63) = e1 & $i(all_8_62) & $i(all_8_63)) % 87.36/12.48 (178) all_6_3 = e1 | ~ (op(e4, e1) = e1) % 87.36/12.48 (179) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 87.36/12.48 (180) op(e0, e4) = all_4_4 % 87.36/12.48 (181) all_4_16 = e3 | ~ (op(e3, e1) = e3) % 87.36/12.48 (182) ~ (all_4_15 = all_4_19) % 87.36/12.48 (183) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | % 87.36/12.48 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) | % 87.36/12.48 (all_9_18 = e0 & op(e2, e0) = e0) % 87.36/12.48 (184) (all_8_26 = e4 & ~ (all_8_27 = e2) & op(e4, all_8_28) = all_8_27 & % 87.36/12.48 op(e4, e2) = all_8_28 & op(e2, all_8_28) = e4 & $i(all_8_27) & % 87.36/12.48 $i(all_8_28)) | (all_8_29 = e3 & ~ (all_8_30 = e2) & op(e3, % 87.36/12.48 all_8_31) = all_8_30 & op(e3, e2) = all_8_31 & op(e2, all_8_31) = % 87.36/12.48 e3 & $i(all_8_30) & $i(all_8_31)) | (all_8_33 = e1 & ~ (all_8_34 = % 87.36/12.48 e2) & op(e2, all_8_35) = e1 & op(e1, all_8_35) = all_8_34 & op(e1, % 87.36/12.48 e2) = all_8_35 & $i(all_8_34) & $i(all_8_35)) | (all_8_36 = e0 & ~ % 87.36/12.48 (all_8_37 = e2) & op(e2, all_8_38) = e0 & op(e0, all_8_38) = all_8_37 % 87.36/12.48 & op(e0, e2) = all_8_38 & $i(all_8_37) & $i(all_8_38)) % 87.36/12.48 (185) ~ (all_4_22 = e3) % 87.36/12.48 (186) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 87.36/12.48 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 87.36/12.48 (all_9_23 = e1 & op(e0, e1) = e1) % 87.36/12.48 (187) all_4_15 = e4 | ~ (op(e4, e1) = e4) % 87.36/12.48 (188) all_6_15 = all_4_3 % 87.36/12.48 (189) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 87.36/12.48 (190) ~ (all_4_5 = all_4_7) % 87.36/12.48 (191) ~ (all_4_5 = all_4_9) % 87.36/12.49 (192) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = e3 & % 87.36/12.49 op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = e3 % 87.36/12.49 & all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = e3 & op(e4, e3) = % 87.36/12.49 all_8_15 & op(e3, e3) = e4 & $i(all_8_15)) | (all_8_0 = e2 & all_8_32 % 87.36/12.49 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 & op(e2, e4) = all_8_6 & % 87.36/12.49 op(e2, e2) = e4 & $i(all_8_6)) | (all_8_0 = e2 & all_8_32 = e4 & ~ % 87.36/12.49 (all_8_28 = e4) & op(e4, e4) = e2 & op(e4, e2) = all_8_28 & op(e2, % 87.36/12.49 e2) = e4 & $i(all_8_28)) | (all_8_0 = e1 & all_8_48 = e4 & ~ % 87.36/12.49 (all_8_9 = e1) & op(e4, e4) = e1 & op(e1, e4) = all_8_9 & op(e1, e1) % 87.36/12.49 = e4 & $i(all_8_9)) | (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_41 = % 87.36/12.49 e4) & op(e4, e4) = e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & % 87.36/12.49 $i(all_8_41)) | (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) & % 87.36/12.49 op(e4, e4) = e0 & op(e4, e0) = all_8_54 & op(e0, e0) = e4 & % 87.36/12.49 $i(all_8_54)) | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = e2) & % 87.36/12.49 op(e3, e3) = e2 & op(e2, e3) = all_8_19 & op(e2, e2) = e3 & % 87.36/12.49 $i(all_8_19)) | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) & % 87.36/12.49 op(e3, e3) = e2 & op(e3, e2) = all_8_31 & op(e2, e2) = e3 & % 87.36/12.49 $i(all_8_31)) | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & % 87.36/12.49 op(e3, e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) = e3 & % 87.36/12.49 $i(all_8_22)) | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) & % 87.36/12.49 op(e3, e3) = e1 & op(e3, e1) = all_8_44 & op(e1, e1) = e3 & % 87.36/12.49 $i(all_8_44)) | (all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & % 87.36/12.49 op(e3, e3) = e0 & op(e3, e0) = all_8_57 & op(e0, e0) = e3 & % 87.36/12.49 $i(all_8_57)) | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) & % 87.36/12.49 op(e2, e2) = e1 & op(e1, e2) = all_8_35 & op(e1, e1) = e2 & % 87.36/12.49 $i(all_8_35)) | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & % 87.36/12.49 op(e2, e2) = e1 & op(e2, e1) = all_8_47 & op(e1, e1) = e2 & % 87.36/12.49 $i(all_8_47)) | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) & % 87.36/12.49 op(e2, e2) = e0 & op(e2, e0) = all_8_60 & op(e0, e0) = e2 & % 87.36/12.49 $i(all_8_60)) | (op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = % 87.36/12.49 e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 & % 87.36/12.49 op(e0, e4) = all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & all_8_64 % 87.36/12.49 = e3 & ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, e3) = % 87.36/12.49 all_8_25 & $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = e2 & ~ % 87.36/12.49 (all_8_38 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_8_38 & % 87.36/12.49 $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 = % 87.36/12.49 e0) & op(e1, e1) = e0 & op(e0, e1) = all_8_51 & $i(all_8_51)) | % 87.36/12.49 (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, e1) = % 87.36/12.49 e0 & op(e1, e0) = all_8_63 & $i(all_8_63)))) % 87.36/12.49 (193) ~ (all_4_16 = all_4_17) % 87.36/12.49 (194) (all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, all_8_3) = e3 & op(e3, % 87.36/12.49 all_8_3) = all_8_2 & op(e3, e4) = all_8_3 & $i(all_8_2) & % 87.36/12.49 $i(all_8_3)) | (all_8_4 = e2 & ~ (all_8_5 = e4) & op(e4, all_8_6) = % 87.36/12.49 e2 & op(e2, all_8_6) = all_8_5 & op(e2, e4) = all_8_6 & $i(all_8_5) & % 87.36/12.49 $i(all_8_6)) | (all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) = % 87.36/12.49 e1 & op(e1, all_8_9) = all_8_8 & op(e1, e4) = all_8_9 & $i(all_8_8) & % 87.36/12.49 $i(all_8_9)) | (all_8_10 = e0 & ~ (all_8_11 = e4) & op(e4, all_8_12) % 87.36/12.49 = e0 & op(e0, all_8_12) = all_8_11 & op(e0, e4) = all_8_12 & % 87.36/12.49 $i(all_8_11) & $i(all_8_12)) % 87.36/12.49 (195) ~ (all_4_16 = e1) % 87.36/12.49 (196) all_6_7 = e2 | ~ (op(e3, e2) = e2) % 87.36/12.49 (197) all_4_2 = e3 % 87.36/12.49 (198) op(e2, e3) = all_4_7 % 87.36/12.49 (199) op(e4, e2) = all_4_10 % 87.36/12.49 (200) all_6_19 = e1 | ~ (op(e1, e0) = e1) % 87.36/12.49 (201) ~ (all_4_11 = all_4_14) % 87.36/12.49 (202) (all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = e0 & op(e4, e0) = e0) % 87.36/12.49 | (all_9_17 = e0 & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) = % 87.36/12.49 e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & ((all_9_20 = e0 & % 87.36/12.49 op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 % 87.36/12.49 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 & op(e0, e1) = e0))) % 87.36/12.49 (203) all_6_21 = all_4_9 % 87.36/12.49 (204) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 87.36/12.49 all_6_11 = e0 % 87.36/12.49 (205) op(e4, unit) = e4 % 87.36/12.49 (206) (all_9_1 = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 87.36/12.49 (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) | % 87.36/12.49 (all_9_21 = e4 & op(e0, e3) = e4) % 87.36/12.49 (207) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 87.36/12.49 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 87.36/12.49 (all_9_20 = e1 & op(e0, e4) = e1) % 87.36/12.49 (208) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 87.36/12.49 (209) (all_9_1 = e1 & op(e4, e3) = e1) | (all_9_3 = e1 & op(e3, e3) = e1) | % 87.36/12.49 (all_9_7 = e1 & op(e2, e3) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | % 87.36/12.49 (all_9_21 = e1 & op(e0, e3) = e1) % 87.36/12.49 (210) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 87.36/12.49 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 87.36/12.49 (all_9_24 = e4 & op(e0, e0) = e4) % 87.36/12.49 (211) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 87.36/12.49 (212) op(e2, e1) = all_4_17 % 87.36/12.49 (213) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 87.36/12.49 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 87.36/12.49 (all_9_16 = e2 & op(e4, e0) = e2) % 87.36/12.49 (214) all_4_4 = e0 | ~ (op(e0, e4) = e0) % 87.36/12.49 (215) op(e4, e0) = all_4_20 % 87.36/12.49 (216) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 87.36/12.49 (217) op(unit, e4) = e4 % 87.36/12.49 (218) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e2 | all_6_22 = e1 | % 87.36/12.49 all_6_22 = e0 % 87.36/12.49 (219) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 87.36/12.49 (220) all_4_13 = e1 | ~ (op(e1, e2) = e1) % 87.36/12.49 (221) ~ (all_4_9 = all_4_19) % 87.36/12.49 (222) ~ (all_4_17 = all_4_18) % 87.36/12.49 (223) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 | all_6_4 = % 87.36/12.49 e0 % 87.36/12.49 (224) ~ (all_4_17 = all_4_19) % 87.36/12.49 (225) ~ (all_4_16 = all_4_21) % 87.36/12.49 (226) all_6_21 = e3 | ~ (op(e0, e3) = e3) % 87.36/12.49 (227) all_6_4 = all_4_20 % 87.36/12.49 (228) all_6_1 = e4 | ~ (op(e4, e3) = e4) % 87.36/12.49 (229) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | % 87.36/12.49 (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 87.36/12.49 (all_9_19 = e1 & op(e1, e0) = e1) % 87.36/12.49 (230) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 87.36/12.49 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 87.36/12.49 (all_9_20 = e2 & op(e0, e4) = e2) % 87.36/12.49 (231) ~ (all_4_16 = all_4_18) % 87.36/12.49 (232) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 87.36/12.49 (233) ~ (e1 = e0) % 87.36/12.49 % 87.36/12.49 Begin of proof % 87.36/12.49 | % 87.36/12.49 | BETA: splitting (171) gives: % 87.36/12.49 | % 87.36/12.49 | Case 1: % 87.36/12.49 | | % 87.36/12.49 | | (234) ~ (op(e0, e4) = e4) % 87.36/12.49 | | % 87.36/12.49 | | PRED_UNIFY: (217), (234) imply: % 87.36/12.49 | | (235) ~ (unit = e0) % 87.36/12.49 | | % 87.36/12.49 | | BETA: splitting (89) gives: % 87.36/12.49 | | % 87.36/12.49 | | Case 1: % 87.36/12.49 | | | % 87.36/12.49 | | | (236) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = % 87.36/12.49 | | | e4) % 87.36/12.49 | | | % 87.36/12.49 | | | REF_CLOSE: (44), (58), (84), (91), (120), (236) are inconsistent by % 87.36/12.49 | | | sub-proof #130. % 87.36/12.49 | | | % 87.36/12.49 | | Case 2: % 87.36/12.49 | | | % 87.36/12.49 | | | (237) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = % 87.36/12.49 | | | e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 87.36/12.49 | | | % 87.36/12.49 | | | BETA: splitting (237) gives: % 87.36/12.49 | | | % 87.36/12.49 | | | Case 1: % 87.36/12.49 | | | | % 87.36/12.49 | | | | (238) all_9_6 = e4 & op(e2, e4) = e4 % 87.36/12.49 | | | | % 87.36/12.49 | | | | ALPHA: (238) implies: % 87.36/12.49 | | | | (239) op(e2, e4) = e4 % 87.36/12.49 | | | | % 87.36/12.49 | | | | REF_CLOSE: (31), (197), (232), (239) are inconsistent by sub-proof #129. % 87.36/12.49 | | | | % 87.36/12.49 | | | Case 2: % 87.36/12.49 | | | | % 87.36/12.49 | | | | (240) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) % 87.36/12.49 | | | | = e4) % 87.36/12.49 | | | | % 87.36/12.49 | | | | BETA: splitting (240) gives: % 87.36/12.49 | | | | % 87.36/12.49 | | | | Case 1: % 87.36/12.49 | | | | | % 87.36/12.49 | | | | | (241) all_9_12 = e4 & op(e1, e4) = e4 % 87.36/12.49 | | | | | % 87.36/12.49 | | | | | ALPHA: (241) implies: % 87.36/12.49 | | | | | (242) all_9_12 = e4 % 87.36/12.49 | | | | | (243) op(e1, e4) = e4 % 87.36/12.49 | | | | | % 87.36/12.49 | | | | | BETA: splitting (41) gives: % 87.36/12.49 | | | | | % 87.36/12.49 | | | | | Case 1: % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | | (244) ~ (op(e1, e4) = e4) % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | | PRED_UNIFY: (243), (244) imply: % 87.36/12.49 | | | | | | (245) $false % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | | CLOSE: (245) is inconsistent. % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | Case 2: % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | | (246) all_6_15 = e4 % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | | COMBINE_EQS: (188), (246) imply: % 87.36/12.49 | | | | | | (247) all_4_3 = e4 % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | | SIMP: (247) implies: % 87.36/12.49 | | | | | | (248) all_4_3 = e4 % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | | REDUCE: (70), (248) imply: % 87.36/12.49 | | | | | | (249) ~ (all_4_4 = e4) % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | | SIMP: (249) implies: % 87.36/12.49 | | | | | | (250) ~ (all_4_4 = e4) % 87.36/12.49 | | | | | | % 87.36/12.49 | | | | | | REDUCE: (71), (248) imply: % 87.36/12.49 | | | | | | (251) ~ (all_4_8 = e4) % 87.36/12.50 | | | | | | % 87.36/12.50 | | | | | | SIMP: (251) implies: % 87.36/12.50 | | | | | | (252) ~ (all_4_8 = e4) % 87.36/12.50 | | | | | | % 87.36/12.50 | | | | | | BETA: splitting (230) gives: % 87.36/12.50 | | | | | | % 87.36/12.50 | | | | | | Case 1: % 87.36/12.50 | | | | | | | % 87.36/12.50 | | | | | | | (253) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, % 87.36/12.50 | | | | | | | e4) = e2) % 87.36/12.50 | | | | | | | % 87.36/12.50 | | | | | | | REF_CLOSE: (120), (121), (131), (146), (174), (253) are % 87.36/12.50 | | | | | | | inconsistent by sub-proof #126. % 87.36/12.50 | | | | | | | % 87.36/12.50 | | | | | | Case 2: % 87.36/12.50 | | | | | | | % 87.36/12.50 | | | | | | | (254) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & % 87.36/12.50 | | | | | | | op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 87.36/12.50 | | | | | | | % 87.36/12.50 | | | | | | | BETA: splitting (254) gives: % 87.36/12.50 | | | | | | | % 87.36/12.50 | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | % 87.36/12.50 | | | | | | | | (255) all_9_6 = e2 & op(e2, e4) = e2 % 87.36/12.50 | | | | | | | | % 87.36/12.50 | | | | | | | | REF_CLOSE: (25), (99), (114), (255) are inconsistent by % 87.36/12.50 | | | | | | | | sub-proof #125. % 87.36/12.50 | | | | | | | | % 87.36/12.50 | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | % 87.36/12.50 | | | | | | | | (256) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & % 87.36/12.50 | | | | | | | | op(e0, e4) = e2) % 87.36/12.50 | | | | | | | | % 87.36/12.50 | | | | | | | | BETA: splitting (256) gives: % 87.36/12.50 | | | | | | | | % 87.36/12.50 | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | % 87.36/12.50 | | | | | | | | | (257) all_9_12 = e2 & op(e1, e4) = e2 % 87.36/12.50 | | | | | | | | | % 87.36/12.50 | | | | | | | | | ALPHA: (257) implies: % 87.36/12.50 | | | | | | | | | (258) all_9_12 = e2 % 87.36/12.50 | | | | | | | | | % 87.36/12.50 | | | | | | | | | REF_CLOSE: (45), (242), (258) are inconsistent by sub-proof % 87.36/12.50 | | | | | | | | | #124. % 87.36/12.50 | | | | | | | | | % 87.36/12.50 | | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | | % 87.36/12.50 | | | | | | | | | (259) all_9_20 = e2 & op(e0, e4) = e2 % 87.36/12.50 | | | | | | | | | % 87.36/12.50 | | | | | | | | | ALPHA: (259) implies: % 87.36/12.50 | | | | | | | | | (260) all_9_20 = e2 % 87.36/12.50 | | | | | | | | | % 87.36/12.50 | | | | | | | | | BETA: splitting (154) gives: % 87.36/12.50 | | | | | | | | | % 87.36/12.50 | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | (261) all_6_20 = e4 % 87.36/12.50 | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | REF_CLOSE: (123), (250), (261) are inconsistent by sub-proof % 87.36/12.50 | | | | | | | | | | #123. % 87.36/12.50 | | | | | | | | | | % 87.36/12.50 | | | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | (262) ~ (all_6_20 = e4) % 87.36/12.50 | | | | | | | | | | (263) all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 87.36/12.50 | | | | | | | | | | all_6_20 = e0 % 87.36/12.50 | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | BETA: splitting (263) gives: % 87.36/12.50 | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | (264) all_6_20 = e2 % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | COMBINE_EQS: (123), (264) imply: % 87.36/12.50 | | | | | | | | | | | (265) all_4_4 = e2 % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | SIMP: (265) implies: % 87.36/12.50 | | | | | | | | | | | (266) all_4_4 = e2 % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | REDUCE: (79), (266) imply: % 87.36/12.50 | | | | | | | | | | | (267) ~ (all_4_9 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | SIMP: (267) implies: % 87.36/12.50 | | | | | | | | | | | (268) ~ (all_4_9 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | REDUCE: (96), (266) imply: % 87.36/12.50 | | | | | | | | | | | (269) ~ (all_4_14 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | SIMP: (269) implies: % 87.36/12.50 | | | | | | | | | | | (270) ~ (all_4_14 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | REDUCE: (142), (266) imply: % 87.36/12.50 | | | | | | | | | | | (271) ~ (all_4_19 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | SIMP: (271) implies: % 87.36/12.50 | | | | | | | | | | | (272) ~ (all_4_19 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | REDUCE: (165), (266) imply: % 87.36/12.50 | | | | | | | | | | | (273) ~ (all_4_24 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | SIMP: (273) implies: % 87.36/12.50 | | | | | | | | | | | (274) ~ (all_4_24 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | REDUCE: (250), (266) imply: % 87.36/12.50 | | | | | | | | | | | (275) ~ (e4 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | REDUCE: (69), (266) imply: % 87.36/12.50 | | | | | | | | | | | (276) ~ (e3 = e2) % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | REDUCE: (180), (266) imply: % 87.36/12.50 | | | | | | | | | | | (277) op(e0, e4) = e2 % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | BETA: splitting (226) gives: % 87.36/12.50 | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | (278) ~ (op(e0, e3) = e3) % 87.36/12.50 | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | PRED_UNIFY: (138), (278) imply: % 87.36/12.50 | | | | | | | | | | | | (279) ~ (all_4_9 = e3) % 87.36/12.50 | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | BETA: splitting (93) gives: % 87.36/12.50 | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | (280) ~ (op(e4, e3) = e3) % 87.36/12.50 | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | PRED_UNIFY: (132), (280) imply: % 87.36/12.50 | | | | | | | | | | | | | (281) ~ (unit = e4) % 87.36/12.50 | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | PRED_UNIFY: (12), (280) imply: % 87.36/12.50 | | | | | | | | | | | | | (282) ~ (all_4_5 = e3) % 87.36/12.50 | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | BETA: splitting (232) gives: % 87.36/12.50 | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | (283) ~ (op(e2, e4) = e4) % 87.36/12.50 | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | PRED_UNIFY: (217), (283) imply: % 87.36/12.50 | | | | | | | | | | | | | | (284) ~ (unit = e2) % 87.36/12.50 | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | BETA: splitting (228) gives: % 87.36/12.50 | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | (285) ~ (op(e4, e3) = e4) % 87.36/12.50 | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | PRED_UNIFY: (205), (285) imply: % 87.36/12.50 | | | | | | | | | | | | | | | (286) ~ (unit = e3) % 87.36/12.50 | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 87.36/12.50 | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | (287) unit = e4 % 87.36/12.50 | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | REDUCE: (281), (287) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | (288) $false % 87.36/12.50 | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | CLOSE: (288) is inconsistent. % 87.36/12.50 | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | (289) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 87.36/12.50 | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 87.36/12.50 | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | (290) unit = e2 % 87.36/12.50 | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | REDUCE: (284), (290) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | (291) $false % 87.36/12.50 | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 87.36/12.50 | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | (292) unit = e3 | unit = e1 | unit = e0 % 87.36/12.50 | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 87.36/12.50 | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | (293) unit = e3 % 87.36/12.50 | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | REDUCE: (286), (293) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | (294) $false % 87.36/12.50 | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent. % 87.36/12.50 | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | (295) unit = e1 | unit = e0 % 87.36/12.50 | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 87.36/12.50 | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | (296) unit = e1 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | REDUCE: (20), (296) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | (297) op(e1, e2) = e2 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | REDUCE: (76), (296) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | (298) op(e1, e0) = e0 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | REDUCE: (205), (296) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | (299) op(e4, e1) = e4 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | REDUCE: (113), (296) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | (300) op(e3, e1) = e3 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | REDUCE: (28), (296) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | (301) op(e2, e1) = e2 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | REDUCE: (108), (296) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | (302) op(e1, e1) = e1 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | REDUCE: (15), (296) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | (303) op(e0, e1) = e0 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | (304) ~ (op(e1, e0) = e0) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (298), (304) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | (305) $false % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | (306) all_4_23 = e0 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (306) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | (307) all_6_19 = e0 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (104), (306) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | (308) ~ (all_4_18 = e0) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1), (306) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | (309) ~ (all_4_22 = e0) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | (310) ~ (op(e1, e2) = e2) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (297), (310) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | (311) $false % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | CLOSE: (311) is inconsistent. % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | (312) all_4_13 = e2 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (312) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | (313) ~ (all_4_10 = e2) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (312) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | (314) ~ (all_4_11 = e2) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (315) ~ (op(e3, e1) = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (300), (315) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (316) $false % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (316) is inconsistent. % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (317) all_4_16 = e3 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (317) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (318) ~ (all_4_6 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (317) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (319) ~ (all_4_11 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (317) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (320) ~ (all_4_15 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (317) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (321) ~ (all_4_17 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | SIMP: (321) implies: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (322) ~ (all_4_17 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (231), (317) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (323) ~ (all_4_18 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | SIMP: (323) implies: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (324) ~ (all_4_18 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (317) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (325) ~ (all_4_19 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | SIMP: (325) implies: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (326) ~ (all_4_19 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (225), (317) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (327) ~ (all_4_21 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | SIMP: (327) implies: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | (328) ~ (all_4_21 = e3) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (op(e1, e1) = e1) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (302), (329) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | (330) $false % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent. % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | (331) all_6_18 = e1 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (331) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | (332) all_4_18 = e1 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (332) implies: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | (333) all_4_18 = e1 % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (333) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | (334) ~ (all_4_15 = e1) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (333) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | (335) ~ (all_4_17 = e1) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (333) imply: % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | (336) ~ (all_4_19 = e1) % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.50 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | (337) ~ (all_4_19 = e1) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (324), (333) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | (338) ~ (e3 = e1) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (339) ~ (op(e4, e1) = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (299), (339) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (340) $false % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (341) all_6_3 = e4 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (341) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (342) all_4_15 = e4 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (153), (342) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (343) ~ (all_4_5 = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (342) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (344) ~ (all_4_17 = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (344) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (345) ~ (all_4_17 = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (342) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_4_19 = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (346) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (347) ~ (all_4_19 = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (342) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (348) ~ (all_4_20 = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_4_20 = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | (350) ~ (op(e2, e1) = e2) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (301), (350) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | (351) $false % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (351) is inconsistent. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_6_13 = e2 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (352) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_4_17 = e2 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (353) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_4_7 = e2) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (353) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | (355) ~ (all_4_22 = e2) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (355) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | (356) ~ (all_4_22 = e2) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (357) ~ (op(e0, e1) = e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (303), (357) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (358) $false % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (358) is inconsistent. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_6_23 = e0 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24), (359) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_4_19 = e0 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (360) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_4_19 = e0 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (221), (361) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (362) ~ (all_4_9 = e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (361) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (363) ~ (all_4_14 = e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (361) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (364) ~ (all_4_24 = e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (364) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (365) ~ (all_4_24 = e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (361) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) ~ (e4 = e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (326), (361) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (367) ~ (e3 = e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (272), (361) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (368) ~ (e2 = e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (337), (361) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (369) ~ (e1 = e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_9_9 = e3 & op(e4, e1) = e3 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_9_9 = e3 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (37), (39), (44), (45), (58), (84), % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (91), (101), (119), (120), (143), (197), % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (232), (242), (260), (343), (349), (372) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #115. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_9_10 = e3 & op(e3, e1) = e3 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_9_10 = e3 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e2) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (99), (114), (176), (354), (375) are % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) | (all_9_18 = e2 & op(e2, e0) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (376) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_9_8 = e2 & op(e2, e2) = e2 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (87), (377) are inconsistent by sub-proof % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #113. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e2) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_9_11 = e2 & op(e2, e1) = e2 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (379) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_9_11 = e2 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) (all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_3) = e3 & op(e3, all_8_3) = all_8_2 & % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_3 & $i(all_8_2) & % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_3)) | (all_8_4 = e2 & ~ (all_8_5 = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, all_8_6) = e2 & op(e2, all_8_6) = % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_5 & op(e2, e4) = all_8_6 & $i(all_8_5) & % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_6)) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (381) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, all_8_3) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, all_8_3) = all_8_2 & op(e3, e4) = % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_3 & $i(all_8_2) & $i(all_8_3) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) op(e3, e4) = all_8_3 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) op(e4, all_8_3) = e3 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (31), (35), (44), (45), (49), (58), (84), % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (91), (113), (120), (150), (158), (174), % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (205), (208), (217), (232), (235), (242), % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260), (284), (383), (384) are inconsistent by % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #110. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_8_4 = e2 & ~ (all_8_5 = e4) & op(e4, all_8_6) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, all_8_6) = all_8_5 & op(e2, e4) = % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_6 & $i(all_8_5) & $i(all_8_6) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (385) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) op(e2, e4) = all_8_6 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) op(e4, all_8_6) = e2 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (58), (84), (91), (228), (343), (388) are % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #121. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) = % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (389) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_9_4 = e4 & op(e4, e2) = e4 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (119), (143), (390) are inconsistent by % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (391) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_9_9 = e4 & op(e4, e1) = e4 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (392) implies: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_9_9 = e4 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_6_7 = e4 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (394) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_4_11 = e4 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (395) imply: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) $false % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (396) is inconsistent. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) ~ (all_6_7 = e4) % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_7 = e0 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) all_6_14 = e4 % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (162), (399) are inconsistent by sub-proof % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #109. % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.36/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) ~ (all_6_14 = e4) % 87.61/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | % 87.61/12.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e3) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (402) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_9_1 = e3 & op(e4, e3) = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (403) are inconsistent by sub-proof #108. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_9_3 = e3 & op(e3, e3) = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (404) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) op(e3, e3) = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (318), (405) are inconsistent by sub-proof % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #107. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e3) | (all_9_21 = e3 & op(e0, e3) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_9_7 = e3 & op(e2, e3) = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (103), (109), (407) are inconsistent by % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #106. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) (all_9_13 = e3 & op(e1, e3) = e3) | (all_9_21 = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e3) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (408) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_9_13 = e3 & op(e1, e3) = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (409) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_9_13 = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e0) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (411) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_9_4 = e0 & op(e4, e2) = e0 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (412) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_9_4 = e0 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e3) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (146), (174), (280), (414) are inconsistent % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #104. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_9_4 = e3 & op(e4, e2) = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (416) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_9_4 = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (417) imply: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) e3 = e0 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (418) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) e3 = e0 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (419) imply: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) $false % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (420) is inconsistent. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e3) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_9_9 = e3 & op(e4, e1) = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_9_9 = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (37), (39), (44), (45), (58), (84), % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (91), (101), (119), (120), (143), (197), % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (232), (242), (260), (343), (349), (423) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #115. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_9_16 = e3 & op(e4, e0) = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (424) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_9_16 = e3 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e2) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (426) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_9_0 = e2 & op(e4, e4) = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) op(e4, e4) = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (146), (174), (428) are inconsistent by % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #128. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_9_1 = e2 & op(e4, e3) = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (429) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_9_1 = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e1) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (431) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_9_0 = e1 & op(e4, e4) = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (432) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) op(e4, e4) = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (174), (233), (433) are inconsistent by % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #132. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_9_1 = e1 & op(e4, e3) = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (131), (430), (434) are inconsistent by sub-proof % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #103. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e1) | (all_9_16 = e1 & op(e4, e0) = % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_9_4 = e1 & op(e4, e2) = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_9_4 = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (437) imply: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) e1 = e0 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (438) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) e1 = e0 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (120), (121), % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (123), (126), (131), (137), (141), (146), % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150), (154), (167), (174), (180), (188), (207), % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (233), (439) are inconsistent by sub-proof % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #82. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_16 = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e1) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (440) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_9_9 = e1 & op(e4, e1) = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (178), (334), (441) are inconsistent by % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #81. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_9_16 = e1 & op(e4, e0) = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (442) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) all_9_16 = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (443) imply: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) e3 = e1 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (444) imply: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) $false % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (445) is inconsistent. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (446) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_9_4 = e2 & op(e4, e2) = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (143), (313), (447) are inconsistent by % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #80. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e2) % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (448) gives: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) all_9_9 = e2 & op(e4, e1) = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (393), (449) are inconsistent by sub-proof % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #79. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_9_16 = e2 & op(e4, e0) = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (450) implies: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_9_16 = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (451) imply: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) e3 = e2 % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (452) imply: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) $false % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (453) is inconsistent. % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_9_5 = e0 & op(e3, e2) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (454) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_9_5 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (401) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_6_14 = e2 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (356), (456) are inconsistent by sub-proof % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #78. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) ~ (all_6_14 = e2) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e0) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (459) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_9_6 = e0 & op(e2, e4) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) all_9_6 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (461) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) e3 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (462) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) $false % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (463) is inconsistent. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_9_7 = e0 & op(e2, e3) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (464) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) all_9_7 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_6_14 = e3 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (185), (466) are inconsistent by sub-proof % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #77. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) ~ (all_6_14 = e3) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_6_14 = e1 | all_6_14 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (398) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_6_7 = e2 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (469) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_4_11 = e2 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (470) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) $false % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (471) is inconsistent. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) ~ (all_6_7 = e2) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (473) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_6_7 = e3 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (474) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_4_11 = e3 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (319), (475) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) $false % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (476) is inconsistent. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) ~ (all_6_7 = e3) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_6_7 = e1 | all_6_7 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_6_7 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (479) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_4_11 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (480) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) $false % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (481) is inconsistent. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_6_7 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (482) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_4_11 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (483) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) ~ (all_4_14 = e0) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (483) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) op(e3, e2) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e0) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (486) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_9_12 = e0 & op(e1, e4) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (487) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_9_12 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (242), (488) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) e4 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (489) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) $false % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (490) is inconsistent. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_9_13 = e0 & op(e1, e3) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (491) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_9_13 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (410), (492) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) e3 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (493) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) $false % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (494) is inconsistent. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e0) | (all_9_19 = e0 & op(e1, e0) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (495) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_9_14 = e0 & op(e1, e2) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_9_14 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (57), (58), (61), (69), % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (70), (84), (87), (89), (91), (99), (112), (114), % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (120), (121), (122), (123), (126), (131), (133), % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (141), (143), (146), (148), (150), (154), % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (167), (174), (180), (188), (200), (207), % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (229), (230), (233), (242), (270), (307), % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313), (410), (483), (497) are inconsistent by % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #65. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_19 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e0) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (498) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_9_15 = e0 & op(e1, e1) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (499) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) op(e1, e1) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (147), (174), (308), (500) are inconsistent by % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #64. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_9_19 = e0 & op(e1, e0) = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (501) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_9_19 = e0 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (468) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_6_14 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (503) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_4_22 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (504) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_4_22 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (505) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) ~ (all_4_7 = e1) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (505) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) ~ (all_4_20 = e1) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (505) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) ~ (e4 = e1) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (505) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) ~ (e2 = e1) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (505) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) op(e2, e0) = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e1) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (61), (150), (410), (511) are inconsistent % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #76. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e1) | (all_9_19 = e1 & op(e1, e0) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (512) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_9_14 = e1 & op(e1, e2) = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (513) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) op(e1, e2) = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) ~ (op(e1, e2) = e1) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (514), (515) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) $false % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (516) is inconsistent. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_4_13 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (517) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) e2 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (518) imply: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) $false % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (519) is inconsistent. % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_19 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (520) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) all_9_15 = e1 & op(e1, e1) = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (521) implies: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_9_15 = e1 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e2) % 87.61/12.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (45), (242), (410), (523) are inconsistent % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #75. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2) | (all_9_19 = e2 & op(e1, e0) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (524) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_9_14 = e2 & op(e1, e2) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (525) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_9_14 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_6_11 = e4 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (26), (527) are inconsistent by sub-proof % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #63. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) ~ (all_6_11 = e4) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_11 = e0 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_6_11 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (354), (530) are inconsistent by sub-proof % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #62. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (531) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_6_11 = e3 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (109), (532) are inconsistent by sub-proof % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #61. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) ~ (all_6_11 = e3) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_6_11 = e1 | all_6_11 = e0 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (534) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_6_11 = e1 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (506), (535) are inconsistent by sub-proof % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #60. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_6_11 = e0 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (536) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_4_7 = e0 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (537) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_4_7 = e0 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (538) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) ~ (all_4_6 = e0) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (538) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) ~ (all_4_9 = e0) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e3, all_8_6, e4, e2, % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (27), (386) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) all_8_6 = e3 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (283), (386) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) ~ (all_8_6 = e4) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_5, e2, e3, e4, % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (12) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) all_4_5 = e2 | ~ (op(e4, e3) = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_20, e2, e0, e4, % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (215) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) all_4_20 = e2 | ~ (op(e4, e0) = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (542) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) ~ (e4 = e3) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (541) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) op(e4, e3) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (543) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) ~ (op(e4, e3) = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (546), (547) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) $false % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (548) is inconsistent. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) all_4_5 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (549) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) ~ (all_4_6 = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (550) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) ~ (all_4_6 = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (549) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) ~ (all_4_10 = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (549) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) ~ (all_4_20 = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (553) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) ~ (all_4_20 = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (555) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_9_2 = e2 & op(e3, e4) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (131), (556) are inconsistent by sub-proof % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #127. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) all_9_3 = e2 & op(e3, e3) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (557) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_9_3 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (559) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_9_0 = e2 & op(e4, e4) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) op(e4, e4) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (146), (174), (561) are inconsistent by % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #128. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_9_1 = e2 & op(e4, e3) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (562) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_9_1 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) (all_9_1 = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (564) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_9_1 = e4 & op(e4, e3) = e4 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (228), (343), (565) are inconsistent by % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #122. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_9_3 = e4 & op(e3, e3) = e4 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (566) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_9_3 = e4 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (558), (567) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) e4 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (568) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) e4 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (569) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) $false % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (570) is inconsistent. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) | (all_9_21 = e4 & op(e0, e3) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (26), (27), (29), (31), (32), (41), % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (42), (43), (44), (45), (47), (51), (58), (61), % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (67), (69), (70), (84), (89), (91), (99), (114), % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (120), (121), (122), (123), (126), (131), (137), % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141), (146), (150), (154), (159), (167), (174), % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180), (188), (198), (207), (209), (230), (233), % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (410), (465), (563), (571) are inconsistent % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #56. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (572) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_9_4 = e2 & op(e4, e2) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (143), (313), (573) are inconsistent by % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #80. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (574) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_9_9 = e2 & op(e4, e1) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (393), (575) are inconsistent by sub-proof % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #79. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_9_16 = e2 & op(e4, e0) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (554), (576) are inconsistent by sub-proof % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #55. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e2) | (all_9_17 = e2 & op(e3, e0) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (577) gives: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) all_9_5 = e2 & op(e3, e2) = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (578) implies: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_9_5 = e2 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (455), (579) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) e2 = e0 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (526), (580) imply: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_9_14 = e0 % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (45), (57), (87), (112), (121), (131), % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (133), (143), (148), (161), (211), (242), (270), % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313), (410), (483), (522), (581) are inconsistent % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #67. % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (582) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) all_9_10 = e2 & op(e3, e1) = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (583) implies: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_9_10 = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (584) imply: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) e3 = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (585) imply: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) $false % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (586) is inconsistent. % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_9_17 = e2 & op(e3, e0) = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) op(e3, e0) = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e2) % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (589) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_9_0 = e2 & op(e4, e4) = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (590) implies: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) op(e4, e4) = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (146), (174), (591) are inconsistent by % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #128. % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) all_9_1 = e2 & op(e4, e3) = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (592) implies: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) all_9_1 = e2 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) (all_9_1 = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4) % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (594) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) all_9_1 = e4 & op(e4, e3) = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (228), (343), (595) are inconsistent by % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #122. % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) all_9_3 = e4 & op(e3, e3) = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) op(e3, e3) = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e4) % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (598) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) all_9_20 = e4 & op(e0, e4) = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (234), (599) are inconsistent by sub-proof #54. % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_9_21 = e4 & op(e0, e3) = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (47), (51), (58), (61), (67), % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (70), (84), (89), (91), (99), (114), (120), % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (122), (123), (126), (131), (137), (141), % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (150), (154), (167), (174), (180), (188), % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (230), (233), (410), (465), (593), % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) are inconsistent by sub-proof #57. % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e4) | (all_9_24 = e4 & op(e0, e0) % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (601) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) all_9_22 = e4 & op(e0, e2) = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (174), (602) are inconsistent by % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #53. % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) (all_9_23 = e4 & op(e0, e1) = e4) | (all_9_24 = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e4) % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (603) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_9_23 = e4 & op(e0, e1) = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (604) implies: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) op(e0, e1) = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_19, e4, e1, e0, % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (170), (605) gives: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) all_4_19 = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (606) imply: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) $false % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (607) is inconsistent. % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_9_24 = e4 & op(e0, e0) = e4 % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.61/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (608) implies: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_9_24 = e4 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (610) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) all_9_16 = e3 & op(e4, e0) = e3 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (611) implies: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_9_16 = e3 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_6_6 = e4 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (613) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) all_4_6 = e4 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (614) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) ~ (all_4_9 = e4) % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (615) implies: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) ~ (all_4_9 = e4) % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_6_21 = e4 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (617) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) all_4_9 = e4 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (618) implies: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_4_9 = e4 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (616), (619) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) $false % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (620) is inconsistent. % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) all_6_21 = e3 | all_6_21 = e2 | all_6_21 = e1 | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_21 = e0 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (621) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_6_21 = e2 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (622) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_4_9 = e2 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (623) implies: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) all_4_9 = e2 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (624) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) $false % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (625) is inconsistent. % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (626) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_6_21 = e3 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (627) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_4_9 = e3 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (628) implies: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_4_9 = e3 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (629) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) $false % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (630) is inconsistent. % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_6_21 = e1 | all_6_21 = e0 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) all_6_21 = e1 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (632) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) all_4_9 = e1 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (633) implies: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_4_9 = e1 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (634) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) ~ (all_4_14 = e1) % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (635) implies: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) ~ (all_4_14 = e1) % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (634) imply: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) op(e0, e3) = e1 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) (all_8_52 = e4 & ~ (all_8_53 = e0) & op(e4, % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) = all_8_53 & op(e4, e0) = all_8_54 & % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_54) = e4 & $i(all_8_53) & % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) | (all_8_55 = e3 & ~ (all_8_56 = % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, all_8_57) = all_8_56 & op(e3, e0) % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_57 & op(e0, all_8_57) = e3 & % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_56) & $i(all_8_57)) % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (638) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_8_52 = e4 & ~ (all_8_53 = e0) & op(e4, % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) = all_8_53 & op(e4, e0) = all_8_54 & % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_54) = e4 & $i(all_8_53) & % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54) % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (639) implies: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) op(e0, all_8_54) = e4 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) op(e4, e0) = all_8_54 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_6_4 = e4 % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (642) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_4_20 = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (643) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (644) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) ~ (all_6_4 = e4) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_4 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (646) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) all_6_4 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (647) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_4_20 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (648) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (649) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) ~ (all_6_4 = e2) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (651) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) all_6_4 = e3 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (652) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_4_20 = e3 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (653) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) ~ (all_4_10 = e3) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (653) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) op(e4, e0) = e3 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) all_6_2 = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (656) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) all_4_10 = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (657) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (658) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) ~ (all_6_2 = e4) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (660) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) all_6_2 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (661) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) all_4_10 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (313), (662) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (663) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) ~ (all_6_2 = e2) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (665) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_6_2 = e3 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (666) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_4_10 = e3 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (654), (667) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (668) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_6_2 = e1 | all_6_2 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (669) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) all_6_2 = e1 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (670) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_4_10 = e1 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e1, e4, e3, e0, % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (637) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) e4 = e1 | ~ (op(e0, e3) = e4) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e3, all_8_54, e0, e4, % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (641), (655) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) all_8_54 = e3 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (640), (673) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) op(e0, e3) = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (672) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) ~ (op(e0, e3) = e4) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (674), (675) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (676) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) e4 = e1 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (609), (677) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) all_9_24 = e1 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e4) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (679) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_9_16 = e4 & op(e4, e0) = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (349), (680) are inconsistent by sub-proof % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #116. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) all_9_17 = e4 & op(e3, e0) = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (681) implies: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) all_9_17 = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (683) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) all_9_16 = e2 & op(e4, e0) = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (684) implies: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) all_9_16 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (612), (685) are inconsistent by sub-proof % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #52. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_9_17 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (682), (686) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) e4 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (687) implies: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) e4 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (688) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (689) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, e0) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (690) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_9_18 = e2 & op(e2, e0) = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (691) implies: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) op(e2, e0) = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (162), (356), (692) are inconsistent by % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #51. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) (all_9_19 = e2 & op(e1, e0) = e2) | (all_9_24 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (693) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) all_9_19 = e2 & op(e1, e0) = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (694) implies: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) all_9_19 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (502), (695) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) e2 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (526), (696) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) all_9_14 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (45), (57), (87), (112), (121), (131), % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (133), (143), (148), (161), (211), (242), (270), % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313), (410), (483), (522), (695), (697) are % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #68. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) all_9_24 = e2 & op(e0, e0) = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (698) implies: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) all_9_24 = e2 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (678), (699) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) e2 = e1 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (700) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (701) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e4) | (all_9_24 = e4 & op(e0, e0) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (702) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_9_18 = e4 & op(e2, e0) = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (100), (174), (703) are inconsistent by % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #50. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) (all_9_19 = e4 & op(e1, e0) = e4) | (all_9_24 = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e4) % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (704) gives: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) all_9_19 = e4 & op(e1, e0) = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (705) implies: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) all_9_19 = e4 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (502), (706) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) e4 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (707) implies: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) e4 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (708) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (709) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (609), (678) are inconsistent by sub-proof % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #49. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) all_6_2 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (710) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) all_4_10 = e0 % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (711) imply: % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) $false % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (712) is inconsistent. % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) all_6_4 = e1 | all_6_4 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (713) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) all_6_4 = e1 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (714) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) all_4_20 = e1 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (507), (715) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (716) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_6_4 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (717) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) all_4_20 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (718) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (719) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) all_8_55 = e3 & ~ (all_8_56 = e0) & op(e3, % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57) = all_8_56 & op(e3, e0) = all_8_57 & % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_57) = e3 & $i(all_8_56) & % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (720) implies: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) ~ (all_8_56 = e0) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) op(e3, e0) = all_8_57 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) op(e3, all_8_57) = all_8_56 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_6_4 = e4 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (724) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) all_4_20 = e4 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (725) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (726) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e2, all_8_57, e0, e3, % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (588), (722) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) all_8_57 = e2 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e0, all_8_56, e2, e3, % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (485) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) all_8_56 = e0 | ~ (op(e3, e2) = all_8_56) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (723), (727) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) op(e3, e2) = all_8_56 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (728) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) ~ (op(e3, e2) = all_8_56) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (729), (730) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (731) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_8_56 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (721), (732) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (733) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) (all_8_58 = e2 & ~ (all_8_59 = e0) & op(e2, % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60) = all_8_59 & op(e2, e0) = all_8_60 & % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_60) = e2 & $i(all_8_59) & % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60)) | (all_8_61 = e1 & ~ (all_8_62 = % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, all_8_63) = all_8_62 & op(e1, e0) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_63 & op(e0, all_8_63) = e1 & % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_62) & $i(all_8_63)) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (734) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) all_8_58 = e2 & ~ (all_8_59 = e0) & op(e2, % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60) = all_8_59 & op(e2, e0) = all_8_60 & % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_60) = e2 & $i(all_8_59) & % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (735) implies: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) op(e0, all_8_60) = e2 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) op(e2, e0) = all_8_60 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) ~ (op(e2, e0) = e2) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) all_6_22 = e4 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (168), (739) are inconsistent by sub-proof % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #48. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) ~ (all_6_22 = e4) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) all_6_22 = e3 | all_6_22 = e2 | all_6_22 = e1 | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_22 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_6_22 = e2 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (270), (742) are inconsistent by sub-proof % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #70. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) ~ (all_6_22 = e2) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) all_6_22 = e3 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (745) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) all_4_14 = e3 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (746) implies: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) all_4_14 = e3 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (747) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) ~ (all_4_10 = e3) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) all_6_2 = e4 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (749) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) all_4_10 = e4 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (750) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (751) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) ~ (all_6_2 = e4) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_6_2 = e2 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (754) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) all_4_10 = e2 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (313), (755) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (756) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) ~ (all_6_2 = e2) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) all_6_2 = e3 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (759) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) all_4_10 = e3 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (748), (760) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (761) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) ~ (all_6_2 = e3) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_6_2 = e1 | all_6_2 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_6_2 = e1 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (764) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_4_10 = e1 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e0, e2, e1, e0, % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (303) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) e2 = e0 | ~ (op(e0, e1) = e2) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e1, all_8_60, e0, e2, % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (510), (737) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) all_8_60 = e1 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (737), (738) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) ~ (all_8_60 = e2) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (736), (767) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) op(e0, e1) = e2 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) ~ (op(e0, e1) = e2) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (769), (770) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (771) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) e2 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (593), (772) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) all_9_1 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (589) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) all_9_0 = e2 & op(e4, e4) = e2 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (774) implies: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) op(e4, e4) = e2 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (146), (174), (775) are inconsistent by % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #128. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (593), (773) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) e2 = e0 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (772) imply: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) $false % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (777) is inconsistent. % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) all_9_4 = e2 & op(e4, e2) = e2 % 87.79/12.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (143), (313), (779) are inconsistent by % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #80. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e2) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (780) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_9_9 = e2 & op(e4, e1) = e2 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (393), (781) are inconsistent by sub-proof % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #79. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) all_9_16 = e2 & op(e4, e0) = e2 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (782) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) all_9_16 = e2 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e3) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (146), (174), (280), (784) are inconsistent % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #104. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) all_9_4 = e3 & op(e4, e2) = e3 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (786) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) all_9_4 = e3 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e1) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) all_9_0 = e1 & op(e4, e4) = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (789) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) op(e4, e4) = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (174), (233), (790) are inconsistent by % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #132. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) all_9_1 = e1 & op(e4, e3) = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (791) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_9_1 = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (773), (792) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) e1 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (793) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) e1 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (120), (121), % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (123), (126), (131), (137), (141), (146), % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150), (154), (167), (174), (180), (188), (207), % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (233), (794) are inconsistent by sub-proof % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #82. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e1) | (all_9_16 = e1 & op(e4, e0) = % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (795) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_9_4 = e1 & op(e4, e2) = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (796) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) all_9_4 = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (787), (797) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) e3 = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (798) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) $false % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (799) is inconsistent. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_16 = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e1) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (800) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) all_9_9 = e1 & op(e4, e1) = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (178), (334), (801) are inconsistent by % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #81. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) all_9_16 = e1 & op(e4, e0) = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (802) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) all_9_16 = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (783), (803) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) e2 = e1 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (804) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) $false % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (805) is inconsistent. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e3) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (806) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) all_9_9 = e3 & op(e4, e1) = e3 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) all_9_9 = e3 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (37), (39), (44), (45), (58), (84), % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (91), (101), (119), (120), (143), (197), % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (232), (242), (260), (343), (349), (808) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #115. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (612), (783) are inconsistent by sub-proof % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #52. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) all_6_2 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (809) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) all_4_10 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (810) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) $false % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (811) is inconsistent. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) all_6_22 = e1 | all_6_22 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (363), (636), (812) are inconsistent by % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #46. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) op(e2, e0) = e2 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (162), (356), (813) are inconsistent by % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #51. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) all_8_61 = e1 & ~ (all_8_62 = e0) & op(e1, % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_63) = all_8_62 & op(e1, e0) = all_8_63 & % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_63) = e1 & $i(all_8_62) & % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (814) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) ~ (all_8_62 = e0) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) op(e1, e0) = all_8_63 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) op(e1, all_8_63) = all_8_62 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) all_6_22 = e4 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (168), (818) are inconsistent by sub-proof % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #48. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_6_22 = e3 | all_6_22 = e2 | all_6_22 = e1 | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_22 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (819) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) all_6_22 = e2 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (270), (820) are inconsistent by sub-proof % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #70. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (821) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e0, all_8_63, e0, e1, % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (298), (816) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) all_8_63 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e0, all_8_62, e0, e1, % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (298) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) all_8_62 = e0 | ~ (op(e1, e0) = all_8_62) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (817), (822) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) op(e1, e0) = all_8_62 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (823) gives: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) ~ (op(e1, e0) = all_8_62) % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (824), (825) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) $false % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (826) is inconsistent. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) all_8_62 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (815), (827) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) $false % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (828) is inconsistent. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_6_22 = e1 | all_6_22 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (363), (636), (829) are inconsistent by % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #46. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) all_6_21 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (830) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) all_4_9 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (831) implies: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) all_4_9 = e0 % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (832) imply: % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) $false % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (833) is inconsistent. % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) ~ (all_6_6 = e4) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (834) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) ~ (all_4_6 = e4) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_6, e4, e3, e3, % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (597) gives: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) all_4_6 = e4 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (835), (836) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) $false % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (837) is inconsistent. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) all_9_17 = e3 & op(e3, e0) = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (838) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) op(e3, e0) = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) ~ (op(e3, e0) = e3) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (839), (840) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) $false % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (841) is inconsistent. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) all_4_21 = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (328), (842) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) $false % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (843) is inconsistent. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (844) gives: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) all_9_18 = e3 & op(e2, e0) = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (845) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) op(e2, e0) = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (174), (185), (846) are inconsistent by % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #45. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (847) gives: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) all_9_19 = e3 & op(e1, e0) = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (848) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) all_9_19 = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (502), (849) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) e3 = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (850) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) $false % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (851) is inconsistent. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) all_9_24 = e3 & op(e0, e0) = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (852) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) all_9_24 = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (609), (853) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) e4 = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (854) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) e4 = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (855) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) all_9_9 = e3 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (37), (39), (44), (45), (58), (84), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (91), (101), (119), (120), (143), (197), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (232), (242), (260), (343), (349), (856) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #115. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) | (all_9_21 = e4 & op(e0, e3) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (26), (27), (29), (31), (32), (41), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (42), (43), (44), (45), (47), (51), (58), (61), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (67), (69), (70), (84), (89), (91), (99), (114), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (120), (121), (122), (123), (126), (131), (137), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141), (146), (150), (154), (159), (167), (174), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180), (188), (198), (207), (209), (230), (233), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (410), (465), (593), (857) are inconsistent % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #56. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (858) gives: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) all_9_4 = e2 & op(e4, e2) = e2 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (143), (313), (859) are inconsistent by % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #80. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e2) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (860) gives: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) all_9_9 = e2 & op(e4, e1) = e2 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (861) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) all_9_9 = e2 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (862) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) e4 = e2 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (863) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) e4 = e2 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (864) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) $false % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (865) is inconsistent. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) all_9_16 = e2 & op(e4, e0) = e2 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (554), (866) are inconsistent by sub-proof % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #55. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_19 = e2 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e2) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (131), (502), (522), (867) are inconsistent % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #72. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) all_9_19 = e1 & op(e1, e0) = e1 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (868) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) op(e1, e0) = e1 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (120), (121), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (123), (126), (131), (137), (141), (146), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150), (154), (167), (174), (180), (188), (200), % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (230), (233), (307), (869) are inconsistent % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #66. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) all_6_14 = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (309), (870) are inconsistent by sub-proof % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #44. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (871) gives: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) all_9_8 = e0 & op(e2, e2) = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (872) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) op(e2, e2) = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (118), (174), (873) are inconsistent by % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #43. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e0) % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (874) gives: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_9_11 = e0 & op(e2, e1) = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (875) implies: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) all_9_11 = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (876) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) e2 = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (877) imply: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) $false % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (878) is inconsistent. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) all_9_18 = e0 & op(e2, e0) = e0 % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (162), (309), (879) are inconsistent by % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #42. % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (880) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) all_9_8 = e0 & op(e2, e2) = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (881) implies: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) op(e2, e2) = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (118), (174), (882) are inconsistent by % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #43. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_22 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (883) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_9_14 = e0 & op(e1, e2) = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (884) implies: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) all_9_14 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (398) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) all_6_7 = e2 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (886) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) all_4_11 = e2 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (887) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) $false % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (888) is inconsistent. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) ~ (all_6_7 = e2) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (890) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) all_6_7 = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (891) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) all_4_11 = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (319), (892) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) $false % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (893) is inconsistent. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) ~ (all_6_7 = e3) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) all_6_7 = e1 | all_6_7 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (895) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) all_6_7 = e1 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (896) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) all_4_11 = e1 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (897) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) $false % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (898) is inconsistent. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) all_6_7 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (899) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) all_4_11 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (57), (58), (61), (69), % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (70), (84), (87), (89), (91), (99), (112), (114), % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (120), (121), (122), (123), (126), (131), (133), % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (141), (143), (146), (148), (150), (154), % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (167), (174), (180), (188), (200), (207), % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (229), (230), (233), (242), (270), (307), % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313), (410), (885), (900) are inconsistent by % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #65. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) all_9_22 = e0 & op(e0, e2) = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (219), (363), (901) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #41. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) all_9_21 = e3 & op(e0, e3) = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (902) implies: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) op(e0, e3) = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (278), (903) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) $false % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (904) is inconsistent. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) all_9_16 = e4 & op(e4, e0) = e4 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (349), (905) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #116. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) (all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_9) = e1 & op(e1, all_8_9) = all_8_8 & % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_9 & $i(all_8_8) & % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_9)) | (all_8_10 = e0 & ~ (all_8_11 = % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_12) = e0 & op(e0, all_8_12) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_11 & op(e0, e4) = all_8_12 & % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_11) & $i(all_8_12)) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (906) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, all_8_9) = all_8_8 & op(e1, e4) = % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_9 & $i(all_8_8) & $i(all_8_9) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (907) implies: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) op(e1, e4) = all_8_9 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) op(e4, all_8_9) = e1 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) all_6_14 = e4 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (162), (910) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #109. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (911) all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (911) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) all_6_14 = e2 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (356), (912) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #78. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (913) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) all_6_14 = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (185), (914) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #77. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) all_6_14 = e1 | all_6_14 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (915) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_6_14 = e1 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (916) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) all_4_22 = e1 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (917) implies: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) all_4_22 = e1 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (918) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) ~ (all_4_7 = e1) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) all_6_11 = e4 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (26), (920) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #63. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_11 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (921) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) all_6_11 = e2 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (354), (922) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #62. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (923) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) all_6_11 = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (109), (924) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #61. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) all_6_11 = e1 | all_6_11 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (925) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) all_6_11 = e1 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (919), (926) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #60. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) all_6_11 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (927) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) all_4_7 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (928) implies: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) all_4_7 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e4, all_8_9, e4, e1, % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (243), (908) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) all_8_9 = e4 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (909), (930) imply: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) op(e4, e4) = e1 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (174), (233), (931) are inconsistent by % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #132. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_6_14 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (309), (932) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #44. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) all_8_10 = e0 & ~ (all_8_11 = e4) & op(e4, % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_12) = e0 & op(e0, all_8_12) = all_8_11 & % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_12 & $i(all_8_11) & % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_12) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (933) implies: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) op(e0, e4) = all_8_12 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) op(e4, all_8_12) = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) all_6_11 = e4 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (26), (936) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #63. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_11 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (937) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) all_6_11 = e2 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (354), (938) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #62. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (939) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) all_6_11 = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (109), (940) are inconsistent by sub-proof % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #61. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e2, all_8_12, e4, e0, % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (277), (934) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) all_8_12 = e2 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (174), (199), (935), (941) are inconsistent % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #40. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) all_9_18 = e2 & op(e2, e0) = e2 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (942) implies: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) op(e2, e0) = e2 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (162), (356), (943) are inconsistent by % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #51. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, e1) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (944) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_9_11 = e3 & op(e2, e1) = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (212), (322), (945) are inconsistent by % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #39. % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_23 = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e3) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (946) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) all_9_15 = e3 & op(e1, e1) = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (947) implies: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) all_9_15 = e3 % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e2) % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (99), (114), (176), (354), (949) are % 87.79/12.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) | (all_9_18 = e2 & op(e2, e0) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (950) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) all_9_8 = e2 & op(e2, e2) = e2 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (87), (951) are inconsistent by sub-proof % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #113. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e2) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (952) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_9_11 = e2 & op(e2, e1) = e2 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (953) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_9_11 = e2 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e4) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (58), (84), (91), (228), (343), (955) are % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #121. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) = % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (956) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) all_9_4 = e4 & op(e4, e2) = e4 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (119), (143), (957) are inconsistent by % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e4) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (958) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) all_9_9 = e4 & op(e4, e1) = e4 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (959) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) all_9_9 = e4 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) all_9_24 = e0 & op(e0, e0) = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (169), (365), (961) are inconsistent by % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #38. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (962) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (963) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (121), (260), (362), (964) are inconsistent % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #36. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e0) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (965) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) all_9_22 = e0 & op(e0, e2) = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (219), (363), (966) are inconsistent by sub-proof % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #41. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) all_9_23 = e0 & op(e0, e1) = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (967) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_9_23 = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e1) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (969) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_9_9 = e1 & op(e4, e1) = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (970) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) all_9_9 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (960), (971) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) e4 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (972) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) $false % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (973) is inconsistent. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) all_9_10 = e1 & op(e3, e1) = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (974) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) op(e3, e1) = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) ~ (op(e3, e1) = e1) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (975), (976) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) $false % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (977) is inconsistent. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) all_6_8 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (978) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) all_4_16 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (195), (979) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) $false % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (980) is inconsistent. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e1) | (all_9_23 = e1 & op(e0, e1) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (981) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) all_9_11 = e1 & op(e2, e1) = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (982) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) all_9_11 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (954), (983) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (984) e2 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (984) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (985) $false % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (985) is inconsistent. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_23 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e1) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (986) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) all_9_15 = e1 & op(e1, e1) = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (987) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) all_9_15 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (948), (988) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) e3 = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (989) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) $false % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (990) is inconsistent. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) all_9_23 = e1 & op(e0, e1) = e1 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (120), (121), % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (123), (126), (131), (137), (141), (146), % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150), (154), (167), (174), (180), (188), (207), % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (233), (968), (991) are inconsistent by % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) all_9_16 = e4 & op(e4, e0) = e4 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (349), (992) are inconsistent by sub-proof % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #116. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) all_9_18 = e2 & op(e2, e0) = e2 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (993) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) op(e2, e0) = e2 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (162), (356), (994) are inconsistent by % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #51. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) all_9_23 = e3 & op(e0, e1) = e3 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (995) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) all_9_23 = e3 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) all_9_24 = e0 & op(e0, e0) = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (169), (365), (997) are inconsistent by % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #38. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (998) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (999) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (121), (260), (362), (1000) are inconsistent % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #36. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e0) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1001) gives: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) all_9_22 = e0 & op(e0, e2) = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (219), (363), (1002) are inconsistent by sub-proof % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #41. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) all_9_23 = e0 & op(e0, e1) = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1003) implies: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) all_9_23 = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (996), (1004) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) e3 = e0 % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (1005) imply: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) $false % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1006) is inconsistent. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | (1007) ~ (unit = e1) % 87.79/12.61 | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (31), (35), (44), (51), (61), (108), (137), % 87.79/12.61 | | | | | | | | | | | | | | | | | | | (197), (208), (217), (232), (235), (1007) are % 87.79/12.61 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #33. % 87.79/12.61 | | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | End of split % 87.79/12.61 | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | Case 2: % 87.79/12.61 | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | (1008) all_6_1 = e4 % 87.79/12.61 | | | | | | | | | | | | | | | % 87.79/12.61 | | | | | | | | | | | | | | | COMBINE_EQS: (11), (1008) imply: % 87.79/12.61 | | | | | | | | | | | | | | | (1009) all_4_5 = e4 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | REDUCE: (9), (1009) imply: % 87.79/12.62 | | | | | | | | | | | | | | | (1010) ~ (all_4_10 = e4) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | REDUCE: (153), (1009) imply: % 87.79/12.62 | | | | | | | | | | | | | | | (1011) ~ (all_4_15 = e4) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | SIMP: (1011) implies: % 87.79/12.62 | | | | | | | | | | | | | | | (1012) ~ (all_4_15 = e4) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | REDUCE: (125), (1009) imply: % 87.79/12.62 | | | | | | | | | | | | | | | (1013) ~ (all_4_20 = e4) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | SIMP: (1013) implies: % 87.79/12.62 | | | | | | | | | | | | | | | (1014) ~ (all_4_20 = e4) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (27), (31), (35), (37), (39), (44), % 87.79/12.62 | | | | | | | | | | | | | | | (45), (49), (58), (84), (89), (91), (101), (113), % 87.79/12.62 | | | | | | | | | | | | | | | (119), (120), (143), (146), (150), (158), (174), % 87.79/12.62 | | | | | | | | | | | | | | | (187), (194), (197), (199), (205), (208), (217), % 87.79/12.62 | | | | | | | | | | | | | | | (232), (233), (235), (242), (243), (260), (277), % 87.79/12.62 | | | | | | | | | | | | | | | (284), (1012), (1014) are inconsistent by % 87.79/12.62 | | | | | | | | | | | | | | | sub-proof #29. % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | (1015) op(e2, e4) = e4 % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | REF_CLOSE: (31), (197), (232), (1015) are inconsistent by % 87.79/12.62 | | | | | | | | | | | | | | sub-proof #129. % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | (1016) all_6_1 = e3 % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | COMBINE_EQS: (11), (1016) imply: % 87.79/12.62 | | | | | | | | | | | | | (1017) all_4_5 = e3 % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | REDUCE: (153), (1017) imply: % 87.79/12.62 | | | | | | | | | | | | | (1018) ~ (all_4_15 = e3) % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | SIMP: (1018) implies: % 87.79/12.62 | | | | | | | | | | | | | (1019) ~ (all_4_15 = e3) % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | REDUCE: (12), (1017) imply: % 87.79/12.62 | | | | | | | | | | | | | (1020) op(e4, e3) = e3 % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | BETA: splitting (194) gives: % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | (1021) (all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, % 87.79/12.62 | | | | | | | | | | | | | | all_8_3) = e3 & op(e3, all_8_3) = all_8_2 & % 87.79/12.62 | | | | | | | | | | | | | | op(e3, e4) = all_8_3 & $i(all_8_2) & % 87.79/12.62 | | | | | | | | | | | | | | $i(all_8_3)) | (all_8_4 = e2 & ~ (all_8_5 = e4) % 87.79/12.62 | | | | | | | | | | | | | | & op(e4, all_8_6) = e2 & op(e2, all_8_6) = % 87.79/12.62 | | | | | | | | | | | | | | all_8_5 & op(e2, e4) = all_8_6 & $i(all_8_5) & % 87.79/12.62 | | | | | | | | | | | | | | $i(all_8_6)) % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | BETA: splitting (1021) gives: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | (1022) all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, all_8_3) % 87.79/12.62 | | | | | | | | | | | | | | | = e3 & op(e3, all_8_3) = all_8_2 & op(e3, e4) = % 87.79/12.62 | | | | | | | | | | | | | | | all_8_3 & $i(all_8_2) & $i(all_8_3) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | ALPHA: (1022) implies: % 87.79/12.62 | | | | | | | | | | | | | | | (1023) op(e3, e4) = all_8_3 % 87.79/12.62 | | | | | | | | | | | | | | | (1024) op(e4, all_8_3) = e3 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e1, all_8_3, e4, e3, % 87.79/12.62 | | | | | | | | | | | | | | | simplifying with (158), (1023) gives: % 87.79/12.62 | | | | | | | | | | | | | | | (1025) all_8_3 = e1 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_15, e3, e1, e4, % 87.79/12.62 | | | | | | | | | | | | | | | simplifying with (149) gives: % 87.79/12.62 | | | | | | | | | | | | | | | (1026) all_4_15 = e3 | ~ (op(e4, e1) = e3) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | REDUCE: (1024), (1025) imply: % 87.79/12.62 | | | | | | | | | | | | | | | (1027) op(e4, e1) = e3 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | BETA: splitting (1026) gives: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | (1028) ~ (op(e4, e1) = e3) % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | PRED_UNIFY: (1027), (1028) imply: % 87.79/12.62 | | | | | | | | | | | | | | | | (1029) $false % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | CLOSE: (1029) is inconsistent. % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | (1030) all_4_15 = e3 % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | REDUCE: (1019), (1030) imply: % 87.79/12.62 | | | | | | | | | | | | | | | | (1031) $false % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | CLOSE: (1031) is inconsistent. % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | (1032) all_8_4 = e2 & ~ (all_8_5 = e4) & op(e4, all_8_6) % 87.79/12.62 | | | | | | | | | | | | | | | = e2 & op(e2, all_8_6) = all_8_5 & op(e2, e4) = % 87.79/12.62 | | | | | | | | | | | | | | | all_8_6 & $i(all_8_5) & $i(all_8_6) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | ALPHA: (1032) implies: % 87.79/12.62 | | | | | | | | | | | | | | | (1033) op(e2, e4) = all_8_6 % 87.79/12.62 | | | | | | | | | | | | | | | (1034) op(e4, all_8_6) = e2 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e3, all_8_6, e4, e2, % 87.79/12.62 | | | | | | | | | | | | | | | simplifying with (27), (1033) gives: % 87.79/12.62 | | | | | | | | | | | | | | | (1035) all_8_6 = e3 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e3, e2, e3, e4, % 87.79/12.62 | | | | | | | | | | | | | | | simplifying with (1020) gives: % 87.79/12.62 | | | | | | | | | | | | | | | (1036) e3 = e2 | ~ (op(e4, e3) = e2) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | REDUCE: (1034), (1035) imply: % 87.79/12.62 | | | | | | | | | | | | | | | (1037) op(e4, e3) = e2 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | BETA: splitting (1036) gives: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | (1038) ~ (op(e4, e3) = e2) % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | PRED_UNIFY: (1037), (1038) imply: % 87.79/12.62 | | | | | | | | | | | | | | | | (1039) $false % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | CLOSE: (1039) is inconsistent. % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | (1040) e3 = e2 % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | REDUCE: (25), (1040) imply: % 87.79/12.62 | | | | | | | | | | | | | | | | (1041) $false % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | CLOSE: (1041) is inconsistent. % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | (1042) (all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, % 87.79/12.62 | | | | | | | | | | | | | | all_8_9) = e1 & op(e1, all_8_9) = all_8_8 & % 87.79/12.62 | | | | | | | | | | | | | | op(e1, e4) = all_8_9 & $i(all_8_8) & % 87.79/12.62 | | | | | | | | | | | | | | $i(all_8_9)) | (all_8_10 = e0 & ~ (all_8_11 = % 87.79/12.62 | | | | | | | | | | | | | | e4) & op(e4, all_8_12) = e0 & op(e0, all_8_12) % 87.79/12.62 | | | | | | | | | | | | | | = all_8_11 & op(e0, e4) = all_8_12 & % 87.79/12.62 | | | | | | | | | | | | | | $i(all_8_11) & $i(all_8_12)) % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | REF_CLOSE: (13), (146), (174), (199), (233), (243), (277), % 87.79/12.62 | | | | | | | | | | | | | | (1042) are inconsistent by sub-proof #30. % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | (1043) all_6_21 = e3 % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | COMBINE_EQS: (203), (1043) imply: % 87.79/12.62 | | | | | | | | | | | | (1044) all_4_9 = e3 % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | SIMP: (1044) implies: % 87.79/12.62 | | | | | | | | | | | | (1045) all_4_9 = e3 % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | REDUCE: (191), (1045) imply: % 87.79/12.62 | | | | | | | | | | | | (1046) ~ (all_4_5 = e3) % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | REDUCE: (77), (1045) imply: % 87.79/12.62 | | | | | | | | | | | | (1047) ~ (all_4_6 = e3) % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | REDUCE: (144), (1045) imply: % 87.79/12.62 | | | | | | | | | | | | (1048) ~ (all_4_8 = e3) % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | REDUCE: (90), (1045) imply: % 87.79/12.62 | | | | | | | | | | | | (1049) ~ (all_4_14 = e3) % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | SIMP: (1049) implies: % 87.79/12.62 | | | | | | | | | | | | (1050) ~ (all_4_14 = e3) % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | REDUCE: (221), (1045) imply: % 87.79/12.62 | | | | | | | | | | | | (1051) ~ (all_4_19 = e3) % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | SIMP: (1051) implies: % 87.79/12.62 | | | | | | | | | | | | (1052) ~ (all_4_19 = e3) % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | REDUCE: (5), (1045) imply: % 87.79/12.62 | | | | | | | | | | | | (1053) ~ (all_4_24 = e3) % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | SIMP: (1053) implies: % 87.79/12.62 | | | | | | | | | | | | (1054) ~ (all_4_24 = e3) % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | BETA: splitting (33) gives: % 87.79/12.62 | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | (1055) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & % 87.79/12.62 | | | | | | | | | | | | | op(e3, e3) = e3) % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | BETA: splitting (1055) gives: % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | (1056) all_9_1 = e3 & op(e4, e3) = e3 % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | ALPHA: (1056) implies: % 87.79/12.62 | | | | | | | | | | | | | | (1057) op(e4, e3) = e3 % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | BETA: splitting (216) gives: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | (1058) ~ (op(e4, e3) = e3) % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | PRED_UNIFY: (1057), (1058) imply: % 87.79/12.62 | | | | | | | | | | | | | | | (1059) $false % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | CLOSE: (1059) is inconsistent. % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | (1060) all_4_5 = e3 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | REDUCE: (1046), (1060) imply: % 87.79/12.62 | | | | | | | | | | | | | | | (1061) $false % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | CLOSE: (1061) is inconsistent. % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | (1062) all_9_3 = e3 & op(e3, e3) = e3 % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | ALPHA: (1062) implies: % 87.79/12.62 | | | | | | | | | | | | | | (1063) op(e3, e3) = e3 % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | REF_CLOSE: (160), (1047), (1063) are inconsistent by % 87.79/12.62 | | | | | | | | | | | | | | sub-proof #107. % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | (1064) (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 % 87.79/12.62 | | | | | | | | | | | | | & op(e1, e3) = e3) | (all_9_21 = e3 & op(e0, e3) % 87.79/12.62 | | | | | | | | | | | | | = e3) % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | BETA: splitting (1064) gives: % 87.79/12.62 | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | (1065) all_9_7 = e3 & op(e2, e3) = e3 % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | REF_CLOSE: (8), (103), (109), (1065) are inconsistent by % 87.79/12.62 | | | | | | | | | | | | | | sub-proof #106. % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | (1066) (all_9_13 = e3 & op(e1, e3) = e3) | (all_9_21 = e3 % 87.79/12.62 | | | | | | | | | | | | | | & op(e0, e3) = e3) % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | BETA: splitting (1066) gives: % 87.79/12.62 | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | (1067) all_9_13 = e3 & op(e1, e3) = e3 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | ALPHA: (1067) implies: % 87.79/12.62 | | | | | | | | | | | | | | | (1068) op(e1, e3) = e3 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | BETA: splitting (136) gives: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | (1069) ~ (op(e1, e3) = e3) % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | PRED_UNIFY: (1068), (1069) imply: % 87.79/12.62 | | | | | | | | | | | | | | | | (1070) $false % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | CLOSE: (1070) is inconsistent. % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | (1071) all_4_8 = e3 % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | REDUCE: (1048), (1071) imply: % 87.79/12.62 | | | | | | | | | | | | | | | | (1072) $false % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | CLOSE: (1072) is inconsistent. % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | End of split % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | (1073) all_9_21 = e3 & op(e0, e3) = e3 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | ALPHA: (1073) implies: % 87.79/12.62 | | | | | | | | | | | | | | | (1074) all_9_21 = e3 % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 87.79/12.62 | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | (1075) ~ (op(e2, e4) = e4) % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | PRED_UNIFY: (217), (1075) imply: % 87.79/12.62 | | | | | | | | | | | | | | | | (1076) ~ (unit = e2) % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 87.79/12.62 | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | (1077) ~ (op(e4, e3) = e4) % 87.79/12.62 | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | PRED_UNIFY: (205), (1077) imply: % 87.79/12.62 | | | | | | | | | | | | | | | | | (1078) ~ (unit = e3) % 87.79/12.62 | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 87.79/12.62 | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | | (1079) (all_9_1 = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & % 87.79/12.62 | | | | | | | | | | | | | | | | | | op(e3, e3) = e4) % 87.79/12.62 | | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | | BETA: splitting (1079) gives: % 87.79/12.62 | | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.62 | | | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | | | (1080) all_9_1 = e4 & op(e4, e3) = e4 % 87.79/12.62 | | | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1077), (1080) are inconsistent by sub-proof #28. % 87.79/12.62 | | | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.62 | | | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | | | (1081) all_9_3 = e4 & op(e3, e3) = e4 % 87.79/12.62 | | | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | | | ALPHA: (1081) implies: % 87.79/12.62 | | | | | | | | | | | | | | | | | | | (1082) op(e3, e3) = e4 % 87.79/12.62 | | | | | | | | | | | | | | | | | | | % 87.79/12.62 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_6, e4, e3, e3, % 87.79/12.62 | | | | | | | | | | | | | | | | | | | simplifying with (67), (1082) gives: % 87.79/12.62 | | | | | | | | | | | | | | | | | | | (1083) all_4_6 = e4 % 87.79/12.62 | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | REDUCE: (73), (1083) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | (1084) ~ (all_4_5 = e4) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | REDUCE: (75), (1083) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | (1085) ~ (all_4_11 = e4) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | (1086) ~ (op(e0, e0) = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | (1087) ~ (op(e3, e2) = e2) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (72), (1087) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | (1088) ~ (all_4_11 = e2) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1089) ~ (op(e0, e1) = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (15), (1089) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1090) ~ (unit = e1) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (31), (51), (61), (108), (137), (197), % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (217), (232), (235), (1078), (1090) are % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #34. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1091) all_4_19 = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (1091) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1092) ~ (all_4_14 = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (224), (1091) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1093) ~ (all_4_17 = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (1091) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1094) ~ (all_4_18 = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (1091) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1095) ~ (all_4_24 = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1095) implies: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1096) ~ (all_4_24 = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1052), (1091) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1097) ~ (e3 = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (272), (1091) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | (1098) ~ (e2 = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | (1099) all_6_22 = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (168), (1099) are inconsistent by sub-proof % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | #48. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | (1100) ~ (all_6_22 = e4) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | (1101) all_6_22 = e3 | all_6_22 = e2 | all_6_22 = e1 | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | all_6_22 = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1101) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | (1102) all_6_22 = e2 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (270), (1102) are inconsistent by sub-proof % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | #70. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | (1103) ~ (all_6_22 = e2) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1104) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | (1105) all_6_22 = e3 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (1105) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_4_14 = e3 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1106) implies: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_4_14 = e3 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1050), (1107) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | (1108) $false % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1108) is inconsistent. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | (1109) ~ (all_6_22 = e3) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_6_22 = e1 | all_6_22 = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1110) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_6_22 = e1 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (1111) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_4_14 = e1 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1112) implies: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_4_14 = e1 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (1113) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) ~ (all_4_10 = e1) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (1113) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) ~ (all_4_24 = e1) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1115) implies: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) ~ (all_4_24 = e1) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (1113) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) ~ (e4 = e1) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1050), (1113) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) ~ (e3 = e1) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (1113) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) ~ (e2 = e1) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_6_24 = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (1120) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) all_4_24 = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (1121) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) ~ (all_4_20 = e4) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (1121) imply: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) op(e0, e0) = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e4) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1124) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) all_9_0 = e4 & op(e4, e4) = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1125) implies: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) op(e4, e4) = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (84), (91), (1126) are inconsistent by % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #131. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) all_9_1 = e4 & op(e4, e3) = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1077), (1127) are inconsistent by sub-proof #28. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) = % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1128) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) all_9_4 = e4 & op(e4, e2) = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (119), (143), (1129) are inconsistent by % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e4) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1130) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_9_9 = e4 & op(e4, e1) = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1131) implies: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) op(e4, e1) = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) all_9_24 = e0 & op(e0, e0) = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (174), (1123), (1133) are inconsistent by % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #27. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1134) implies: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1135) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1136) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) all_9_20 = e0 & op(e0, e4) = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (260), (1137) are inconsistent by sub-proof % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #37. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) all_9_21 = e0 & op(e0, e3) = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (1074), (1138) are inconsistent by sub-proof % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #26. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1139) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) all_9_22 = e0 & op(e0, e2) = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1140) implies: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) op(e0, e2) = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (120), (121), % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (123), (126), (131), (137), (139), (141), % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (150), (154), (167), (174), (180), (188), % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (230), (233), (1111), (1141) are % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) all_9_23 = e0 & op(e0, e1) = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1142) implies: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) all_9_23 = e0 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e4) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (44), (45), (58), (84), (89), (91), (120), % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (232), (234), (242), (260), (1074), (1144) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e4) | (all_9_24 = e4 & op(e0, e0) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1145) gives: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) all_9_22 = e4 & op(e0, e2) = e4 % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 87.79/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (174), (1146) are inconsistent by % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #53. % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) (all_9_23 = e4 & op(e0, e1) = e4) | (all_9_24 = e4 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e4) % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1147) gives: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) all_9_23 = e4 & op(e0, e1) = e4 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1148) implies: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) all_9_23 = e4 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1143), (1149) imply: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) e4 = e0 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1150) implies: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) e4 = e0 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (1151) imply: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) $false % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1152) is inconsistent. % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) all_9_24 = e4 & op(e0, e0) = e4 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1153) implies: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) all_9_24 = e4 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e1) % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1155) gives: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) all_9_20 = e1 & op(e0, e4) = e1 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1156) implies: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1157) all_9_20 = e1 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1157) imply: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1158) e2 = e1 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (1158) imply: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1159) $false % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1159) is inconsistent. % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1160) all_9_21 = e1 & op(e0, e3) = e1 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1160) implies: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1161) all_9_21 = e1 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1074), (1161) imply: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1162) e3 = e1 % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (1162) imply: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1163) $false % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1163) is inconsistent. % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1164) (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e1) | (all_9_24 = e1 & op(e0, e0) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1164) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165) all_9_22 = e1 & op(e0, e2) = e1 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1165) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166) all_9_22 = e1 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1167) op(e0, e2) = e1 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168) (all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_3) = e3 & op(e3, all_8_3) = all_8_2 & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_3 & $i(all_8_2) & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_3)) | (all_8_4 = e2 & ~ (all_8_5 = e4) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, all_8_6) = e2 & op(e2, all_8_6) = % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_5 & op(e2, e4) = all_8_6 & $i(all_8_5) & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_6)) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1168) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169) all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, all_8_3) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, all_8_3) = all_8_2 & op(e3, e4) = % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_3 & $i(all_8_2) & $i(all_8_3) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1169) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170) op(e3, e4) = all_8_3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171) op(e4, all_8_3) = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) ~ (op(e3, e4) = e4) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (45), (58), (84), (89), (91), (120), (158), % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (197), (232), (242), (260), (1132), (1170), % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171), (1172) are inconsistent by sub-proof #112. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1173) all_6_5 = e4 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (1173) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174) e4 = e1 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1174) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1175) e4 = e1 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (1175) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1176) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) all_8_4 = e2 & ~ (all_8_5 = e4) & op(e4, all_8_6) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, all_8_6) = all_8_5 & op(e2, e4) = % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_6 & $i(all_8_5) & $i(all_8_6) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1177) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) op(e2, e4) = all_8_6 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) op(e4, all_8_6) = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (1120) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1180) all_4_24 = e4 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e3, all_8_6, e4, e2, % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (27), (1178) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1181) all_8_6 = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_5, e2, e3, e4, % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (12) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1182) all_4_5 = e2 | ~ (op(e4, e3) = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1179), (1181) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1183) op(e4, e3) = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1182) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1184) ~ (op(e4, e3) = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1183), (1184) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1185) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1185) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186) all_4_5 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1186) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1187) ~ (all_4_10 = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1187) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1188) ~ (all_4_10 = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (1186) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1189) ~ (all_4_20 = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1189) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1190) ~ (all_4_20 = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1191) all_6_2 = e4 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (1191) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1192) all_4_10 = e4 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1192) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1193) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1193) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1194) all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1194) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1195) all_6_2 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (1195) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1196) all_4_10 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1188), (1196) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1197) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1197) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1198) ~ (all_6_2 = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1199) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1199) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1200) all_6_2 = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (1200) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1201) all_4_10 = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (1201) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1202) ~ (all_4_11 = e3) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1202) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1203) ~ (all_4_11 = e3) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1201) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1204) ~ (all_4_20 = e3) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1204) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1205) ~ (all_4_20 = e3) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (1201) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1206) op(e4, e2) = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1207) all_6_7 = e4 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (1207) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1208) all_4_11 = e4 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (1208) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1209) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1209) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1210) all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_7 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1210) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1211) all_6_7 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (1211) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1212) all_4_11 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1088), (1212) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1213) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1213) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1214) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1214) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) all_6_7 = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (1215) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1216) all_4_11 = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1203), (1216) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1217) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1217) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1218) all_6_7 = e1 | all_6_7 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1218) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1219) all_6_7 = e1 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (1219) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1220) all_4_11 = e1 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (1220) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1221) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1221) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1222) all_6_7 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (1222) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1223) all_4_11 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (1223) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1224) op(e3, e2) = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1225) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1226) all_9_4 = e2 & op(e4, e2) = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (143), (1188), (1226) are inconsistent by % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #80. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1227) all_9_5 = e2 & op(e3, e2) = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1087), (1227) are inconsistent by sub-proof #23. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1228) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) | (all_9_22 = e2 & op(e0, e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1228) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229) all_9_8 = e2 & op(e2, e2) = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (87), (1229) are inconsistent by sub-proof % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #113. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1230) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1230) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1231) all_9_14 = e2 & op(e1, e2) = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1231) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1232) op(e1, e2) = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1233) (all_8_26 = e4 & ~ (all_8_27 = e2) & op(e4, % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_28) = all_8_27 & op(e4, e2) = all_8_28 & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, all_8_28) = e4 & $i(all_8_27) & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_28)) | (all_8_29 = e3 & ~ (all_8_30 = % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, all_8_31) = all_8_30 & op(e3, e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_31 & op(e2, all_8_31) = e3 & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_30) & $i(all_8_31)) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1233) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1234) all_8_26 = e4 & ~ (all_8_27 = e2) & op(e4, % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_28) = all_8_27 & op(e4, e2) = all_8_28 & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, all_8_28) = e4 & $i(all_8_27) & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_28) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1234) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1235) ~ (all_8_27 = e2) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1236) op(e4, e2) = all_8_28 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1237) op(e4, all_8_28) = all_8_27 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e3, all_8_28, e2, e4, % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1206), (1236) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1238) all_8_28 = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e2, all_8_27, e3, e4, % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1183) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1239) all_8_27 = e2 | ~ (op(e4, e3) = all_8_27) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1237), (1238) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1240) op(e4, e3) = all_8_27 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1239) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1241) ~ (op(e4, e3) = all_8_27) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1240), (1241) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1242) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1242) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1243) all_8_27 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1235), (1243) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1244) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1244) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1245) all_8_29 = e3 & ~ (all_8_30 = e2) & op(e3, % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_31) = all_8_30 & op(e3, e2) = all_8_31 & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, all_8_31) = e3 & $i(all_8_30) & % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_31) % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1245) implies: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246) op(e2, all_8_31) = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1247) op(e3, e2) = all_8_31 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1248) all_6_4 = e4 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1248) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1249) all_4_20 = e4 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1122), (1249) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1250) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1250) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1251) all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_4 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1251) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252) all_6_4 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1252) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1253) all_4_20 = e2 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1190), (1253) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1254) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1254) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1255) all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1255) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1256) all_6_4 = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1256) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257) all_4_20 = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1205), (1257) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1258) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1258) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1259) all_6_4 = e1 | all_6_4 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1259) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e0, all_8_31, e2, e3, % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1224), (1247) gives: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1260) all_8_31 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1246), (1260) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1261) op(e2, e0) = e3 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (174), (185), (1261) are inconsistent by % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #45. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1262) all_6_4 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1262) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1263) all_4_20 = e0 % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (1263) imply: % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1264) $false % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1264) is inconsistent. % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265) (all_8_33 = e1 & ~ (all_8_34 = e2) & op(e2, % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_35) = e1 & op(e1, all_8_35) = all_8_34 & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_35 & $i(all_8_34) & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_35)) | (all_8_36 = e0 & ~ (all_8_37 = % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, all_8_38) = e0 & op(e0, all_8_38) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_37 & op(e0, e2) = all_8_38 & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_37) & $i(all_8_38)) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1265) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1266) all_8_33 = e1 & ~ (all_8_34 = e2) & op(e2, % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_35) = e1 & op(e1, all_8_35) = all_8_34 & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_35 & $i(all_8_34) & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_35) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1266) implies: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267) op(e1, e2) = all_8_35 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1268) op(e2, all_8_35) = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1269) all_6_4 = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1269) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270) all_4_20 = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1122), (1270) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1271) $false % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1271) is inconsistent. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1272) ~ (all_6_4 = e4) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1273) all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_4 = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1273) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1274) all_6_4 = e2 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1274) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1275) all_4_20 = e2 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1190), (1275) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1276) $false % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1276) is inconsistent. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277) all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1277) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1278) all_6_4 = e3 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1278) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1279) all_4_20 = e3 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1205), (1279) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1280) $false % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1280) is inconsistent. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1281) all_6_4 = e1 | all_6_4 = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1281) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1282) all_6_4 = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1282) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1283) all_4_20 = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e2, all_8_35, e2, e1, % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1232), (1267) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1284) all_8_35 = e2 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1268), (1284) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1285) op(e2, e2) = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (118), (174), (1285) are inconsistent by % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #22. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286) all_6_4 = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1286) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1287) all_4_20 = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (1287) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1288) $false % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1288) is inconsistent. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289) all_8_36 = e0 & ~ (all_8_37 = e2) & op(e2, % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_38) = e0 & op(e0, all_8_38) = all_8_37 & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_8_38 & $i(all_8_37) & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_38) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1289) implies: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1290) op(e0, e2) = all_8_38 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1291) op(e2, all_8_38) = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e1, all_8_38, e2, e0, % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1167), (1290) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1292) all_8_38 = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_17, e0, e1, e2, % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (212) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1293) all_4_17 = e0 | ~ (op(e2, e1) = e0) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1291), (1292) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1294) op(e2, e1) = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1293) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1295) ~ (op(e2, e1) = e0) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1294), (1295) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1296) $false % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1296) is inconsistent. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1297) all_4_17 = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1093), (1297) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1298) $false % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1298) is inconsistent. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1299) all_9_22 = e2 & op(e0, e2) = e2 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (211), (270), (1299) are inconsistent by % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #69. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1300) all_6_2 = e1 | all_6_2 = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1300) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1301) all_6_2 = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (1301) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1302) all_4_10 = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1114), (1302) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1303) $false % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1303) is inconsistent. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1304) all_6_2 = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (1304) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1305) all_4_10 = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (1305) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1306) $false % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1306) is inconsistent. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1307) ~ (all_6_24 = e4) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (25), (27), (29), (31), (32), (41), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (42), (43), (44), (45), (47), (48), (51), (58), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (67), (69), (70), (84), (89), (91), (99), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (114), (118), (120), (121), (122), (123), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (126), (131), (137), (141), (146), (147), (150), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (154), (155), (167), (168), (174), (180), (188), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (197), (202), (207), (230), (232), (233), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (242), (260), (1054), (1074), (1082), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094), (1166), (1307) are inconsistent by % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #10. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1308) (all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_9) = e1 & op(e1, all_8_9) = all_8_8 & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_9 & $i(all_8_8) & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_9)) | (all_8_10 = e0 & ~ (all_8_11 = % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_12) = e0 & op(e0, all_8_12) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_11 & op(e0, e4) = all_8_12 & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_11) & $i(all_8_12)) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1308) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1309) all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, all_8_9) = all_8_8 & op(e1, e4) = % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_9 & $i(all_8_8) & $i(all_8_9) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (174), (233), (243), (1309) are % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #31. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1310) all_8_10 = e0 & ~ (all_8_11 = e4) & op(e4, % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_12) = e0 & op(e0, all_8_12) = all_8_11 & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_12 & $i(all_8_11) & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_12) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1310) implies: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1311) op(e0, e4) = all_8_12 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1312) op(e4, all_8_12) = e0 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (1120) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1313) all_4_24 = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1314) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e4) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (44), (45), (58), (84), (89), (91), (120), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (232), (234), (242), (260), (1074), (1314) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1145) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1315) all_9_22 = e4 & op(e0, e2) = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (174), (1315) are inconsistent by % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #53. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1147) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1316) all_9_23 = e4 & op(e0, e1) = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1316) implies: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1317) all_9_23 = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (120), (121), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (123), (126), (131), (137), (141), (146), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150), (154), (167), (174), (180), (188), (202), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (230), (233), (260), (1074), (1123), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166), (1317) are inconsistent by sub-proof #12. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e2, all_8_12, e4, e0, % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (277), (1311) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1318) all_8_12 = e2 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (174), (199), (1312), (1318) are % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #40. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1319) ~ (all_6_24 = e4) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (25), (27), (29), (31), (32), (41), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (42), (43), (44), (45), (47), (48), (51), (58), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (67), (69), (70), (84), (89), (91), (99), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (114), (118), (120), (121), (122), (123), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (126), (131), (137), (141), (146), (147), (150), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (154), (155), (167), (168), (174), (180), (188), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (197), (202), (207), (230), (232), (233), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (242), (260), (1054), (1074), (1082), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094), (1166), (1319) are inconsistent by % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #10. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1320) (all_9_23 = e1 & op(e0, e1) = e1) | (all_9_24 = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1320) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1321) all_9_23 = e1 & op(e0, e1) = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (120), (121), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (123), (126), (131), (137), (141), (146), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150), (154), (167), (174), (180), (188), (207), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (233), (1143), (1321) are inconsistent by % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1322) all_9_24 = e1 & op(e0, e0) = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1322) implies: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1323) all_9_24 = e1 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (1154), (1323) are inconsistent by sub-proof % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #49. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1324) all_9_16 = e4 & op(e4, e0) = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (1122), (1324) are inconsistent by sub-proof % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #116. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1325) ~ (all_6_24 = e4) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (1325) imply: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) ~ (all_4_24 = e4) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e4) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (44), (45), (58), (84), (89), (91), (120), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (232), (234), (242), (260), (1074), (1327) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e4) | (all_9_24 = e4 & op(e0, e0) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1328) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) all_9_22 = e4 & op(e0, e2) = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (174), (1329) are inconsistent by % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #53. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1330) (all_9_23 = e4 & op(e0, e1) = e4) | (all_9_24 = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e4) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1330) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1331) all_9_23 = e4 & op(e0, e1) = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1331) implies: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1332) all_9_23 = e4 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1333) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e2) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (20), (58), (63), (84), (91), (163), % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (235), (1076), (1078), (1087), (1333) are % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #8. % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1334) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) | (all_9_22 = e2 & op(e0, e2) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1334) gives: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1335) all_9_8 = e2 & op(e2, e2) = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (87), (1335) are inconsistent by sub-proof % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #113. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1336) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1336) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1337) all_9_14 = e2 & op(e1, e2) = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1337) implies: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1338) all_9_14 = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1339) all_9_24 = e0 & op(e0, e0) = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1339) implies: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1340) op(e0, e0) = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1086), (1340) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1341) $false % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1341) is inconsistent. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1342) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1342) implies: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1343) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1343) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1344) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1344) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1345) all_9_20 = e0 & op(e0, e4) = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1345) implies: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1346) all_9_20 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1346) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1347) e2 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1338), (1347) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1348) all_9_14 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1349) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e2) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (20), (58), (63), (84), (91), (163), % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (235), (1076), (1078), (1087), (1349) are % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #8. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1334) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1350) all_9_8 = e2 & op(e2, e2) = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (87), (1350) are inconsistent by sub-proof % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #113. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1336) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (1337), (1348) are inconsistent by % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #74. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1351) all_9_22 = e2 & op(e0, e2) = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (211), (270), (1351) are inconsistent by % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #69. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1352) all_9_21 = e0 & op(e0, e3) = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (1074), (1352) are inconsistent by sub-proof % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #26. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1353) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e0) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1353) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1354) all_9_22 = e0 & op(e0, e2) = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1354) implies: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1355) op(e0, e2) = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (120), (121), % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (123), (126), (131), (137), (139), (141), % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (150), (154), (167), (174), (180), (188), % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (230), (233), (1111), (1355) are % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1356) all_9_23 = e0 & op(e0, e1) = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (1332), (1356) are inconsistent by sub-proof % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #13. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1357) all_9_22 = e2 & op(e0, e2) = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (211), (270), (1357) are inconsistent by % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #69. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1358) all_9_24 = e4 & op(e0, e0) = e4 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1358) implies: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1359) op(e0, e0) = e4 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (174), (1326), (1359) are inconsistent by % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #18. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (1360) all_6_22 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (1092), (1360) are inconsistent by sub-proof % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | #47. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | (1361) all_6_7 = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (1361) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | (1362) all_4_11 = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1362) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | (1363) ~ (all_4_13 = e2) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (20), (58), (84), (91), (217), (235), % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | (1076), (1078), (1363) are inconsistent by % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | sub-proof #9. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | (1364) all_6_24 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (1364) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | (1365) all_4_24 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (1054), (1365) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | (1366) ~ (e3 = e0) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (1365) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | (1367) ~ (e2 = e0) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (1365) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | (1368) op(e0, e0) = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | (1369) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e3 & op(e3, e4) = all_8_3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = e3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | = e3 & op(e4, e3) = all_8_15 & op(e3, e3) = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_15)) | (all_8_0 = e2 & all_8_32 = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | ~ (all_8_6 = e2) & op(e4, e4) = e2 & op(e2, e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_28 = e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e2 & op(e4, e2) = all_8_28 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e4 & $i(all_8_28)) | (all_8_0 = e1 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | & all_8_48 = e4 & ~ (all_8_9 = e1) & op(e4, e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e4) = all_8_9 & op(e1, e1) = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_9)) | (all_8_0 = e1 & all_8_48 = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | ~ (all_8_41 = e4) & op(e4, e4) = e1 & op(e4, e1) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | = all_8_41 & op(e1, e1) = e4 & $i(all_8_41)) | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e4, e0) = all_8_54 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4 & $i(all_8_54)) | (all_8_16 = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | & all_8_32 = e3 & ~ (all_8_19 = e2) & op(e3, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e3) = e2 & op(e2, e3) = all_8_19 & op(e2, e2) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | = e3 & $i(all_8_19)) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1369) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | (1370) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e3 & op(e3, e4) = all_8_3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = e3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e4, e3) = all_8_15 & op(e3, e3) = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_15)) | (all_8_0 = e2 & all_8_32 = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_6 = e2) & op(e4, e4) = e2 & op(e2, e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_28 = e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e2 & op(e4, e2) = all_8_28 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e4 & $i(all_8_28)) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (121), (146), (174), (1370) are inconsistent % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #20. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | (1371) (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = e1) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e1 & op(e1, e4) = all_8_9 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e4 & $i(all_8_9)) | (all_8_0 = e1 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_41)) | (all_8_0 = e0 & all_8_64 = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_54 = e4) & op(e4, e4) = e0 & op(e4, e0) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | = all_8_54 & op(e0, e0) = e4 & $i(all_8_54)) | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e3) = e2 & op(e2, e3) = all_8_19 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_8_19)) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1371) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | (1372) (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = e1) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e1 & op(e1, e4) = all_8_9 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e4 & $i(all_8_9)) | (all_8_0 = e1 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_41)) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (174), (233), (1372) are inconsistent by % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #19. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | (1373) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e4, e0) = all_8_54 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4 & $i(all_8_54)) | (all_8_16 = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | & all_8_32 = e3 & ~ (all_8_19 = e2) & op(e3, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | e3) = e2 & op(e2, e3) = all_8_19 & op(e2, e2) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | = e3 & $i(all_8_19)) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1373) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | (1374) all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e4, e0) = all_8_54 & op(e0, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e4 & $i(all_8_54) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1374) implies: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | (1375) op(e0, e0) = e4 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e0, e4, e0, e0, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1368), (1375) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | (1376) e4 = e0 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (1376) imply: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | (1377) $false % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1377) is inconsistent. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | (1378) all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = e2) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2 & op(e2, e3) = all_8_19 & op(e2, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_8_19) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1378) implies: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | (1379) op(e2, e2) = e3 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | (1380) op(e3, e3) = e2 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (118), (174), (1082), (1379), (1380) are % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #17. % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | (1381) (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_8_31 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_8_31)) | (all_8_16 = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | = e3 & $i(all_8_22)) | (all_8_16 = e1 & all_8_48 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | = e3 & ~ (all_8_44 = e3) & op(e3, e3) = e1 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_8_44 & op(e1, e1) = e3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_44)) | (all_8_16 = e0 & all_8_64 = e3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | ~ (all_8_57 = e3) & op(e3, e3) = e0 & op(e3, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e0) = all_8_57 & op(e0, e0) = e3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_57)) | (all_8_32 = e1 & all_8_48 = e2 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | ~ (all_8_35 = e1) & op(e2, e2) = e1 & op(e1, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e2) = all_8_35 & op(e1, e1) = e2 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_35)) | (all_8_32 = e1 & all_8_48 = e2 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | ~ (all_8_47 = e2) & op(e2, e2) = e1 & op(e2, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e1) = all_8_47 & op(e1, e1) = e2 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_47)) | (all_8_32 = e0 & all_8_64 = e2 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | ~ (all_8_60 = e2) & op(e2, e2) = e0 & op(e2, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e0) = all_8_60 & op(e0, e0) = e2 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_60)) | (op(e0, e0) = all_8_64 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_64) & ((all_8_0 = e0 & all_8_64 = e4 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | ~ (all_8_12 = e0) & op(e4, e4) = e0 & op(e0, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e4) = all_8_12 & $i(all_8_12)) | (all_8_16 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | = e0 & all_8_64 = e3 & ~ (all_8_25 = e0) & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_38 = e0) & op(e2, e2) = e0 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_8_38 & $i(all_8_38)) | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | e1) = e0 & op(e1, e0) = all_8_63 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | $i(all_8_63)))) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1381) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | (1382) (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_8_31 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_8_31)) | (all_8_16 = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | = e3 & $i(all_8_22)) | (all_8_16 = e1 & all_8_48 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | = e3 & ~ (all_8_44 = e3) & op(e3, e3) = e1 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_8_44 & op(e1, e1) = e3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_44)) | (all_8_16 = e0 & all_8_64 = e3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_57 = e3) & op(e3, e3) = e0 & op(e3, % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | e0) = all_8_57 & op(e0, e0) = e3 & % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57)) % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1382) gives: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | (1383) (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_8_31 % 88.16/12.66 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_8_31)) | (all_8_16 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | = e3 & $i(all_8_22)) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1383) gives: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1384) all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2 & op(e3, e2) = all_8_31 & op(e2, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_8_31) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1384) implies: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1385) op(e2, e2) = e3 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1386) op(e3, e3) = e2 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (118), (174), (1082), (1385), (1386) are % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #17. % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1387) all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1 & op(e1, e3) = all_8_22 & op(e1, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_8_22) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1387) implies: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1388) op(e3, e3) = e1 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (67), (174), (1388) are inconsistent by % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #58. % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | (1389) (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_8_44 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_8_44)) | (all_8_16 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & op(e3, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & op(e3, e0) = all_8_57 & op(e0, e0) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | = e3 & $i(all_8_57)) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (67), (155), (174), (1054), (1389) are % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #15. % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | (1390) (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_8_35 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_8_35)) | (all_8_32 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | e2) = e1 & op(e2, e1) = all_8_47 & op(e1, e1) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | = e2 & $i(all_8_47)) | (all_8_32 = e0 & all_8_64 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_8_60 = e2) & op(e2, e2) = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_8_60 & op(e0, e0) = e2 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60)) | (op(e0, e0) = all_8_64 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_64) & ((all_8_0 = e0 & all_8_64 = e4 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_12 = e0) & op(e4, e4) = e0 & op(e0, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_12 & $i(all_8_12)) | (all_8_16 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_8_64 = e3 & ~ (all_8_25 = e0) & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_38 = e0) & op(e2, e2) = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_8_38 & $i(all_8_38)) | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | e1) = e0 & op(e1, e0) = all_8_63 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63)))) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1390) gives: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | (1391) (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_8_35 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_8_35)) | (all_8_32 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e2) = e1 & op(e2, e1) = all_8_47 & op(e1, e1) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | = e2 & $i(all_8_47)) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (118), (174), (1391) are inconsistent by % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #14. % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | (1392) (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_8_60 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_8_60)) | (op(e0, e0) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | = all_8_64 & $i(all_8_64) & ((all_8_0 = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e4) = e0 & op(e0, e4) = all_8_12 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e3 & ~ (all_8_25 = e0) & op(e3, e3) = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_8_25 & $i(all_8_25)) | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = e0 & op(e0, e2) = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | all_8_38 & $i(all_8_38)) | (all_8_48 = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e1) = e0 & op(e0, e1) = all_8_51 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_8_63 = e1) & op(e1, e1) = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_8_63 & $i(all_8_63)))) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1392) gives: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1393) all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0 & op(e2, e0) = all_8_60 & op(e0, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_8_60) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1393) implies: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1394) op(e2, e2) = e0 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (118), (174), (1394) are inconsistent by % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #43. % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1395) op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e4) = e0 & op(e0, e4) = all_8_12 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_25 = e0) & op(e3, e3) = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_8_25 & $i(all_8_25)) | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | all_8_38 & $i(all_8_38)) | (all_8_48 = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0 & op(e0, e1) = all_8_51 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = e1 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_63 = e1) & op(e1, e1) = e0 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_8_63 & $i(all_8_63))) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1395) implies: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1396) op(e0, e0) = all_8_64 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1397) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e0, e4) = all_8_12 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_25 & $i(all_8_25)) | (all_8_32 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_8_38 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_51 = e0) & op(e1, e1) = e0 & op(e0, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_51 & $i(all_8_51)) | (all_8_48 = % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0 & op(e1, e0) = all_8_63 & % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63)) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e0, all_8_64, e0, e0, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1368), (1396) gives: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (1398) all_8_64 = e0 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (118), (120), % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (121), (122), (123), (126), (131), (137), (141), % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (146), (150), (154), (167), (174), (180), (188), % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | (207), (230), (233), (1397), (1398) are % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7. % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | (1399) (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) | (all_9_21 = e4 & op(e0, e3) % 88.16/12.67 | | | | | | | | | | | | | | | | | | = e4) % 88.16/12.67 | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | BETA: splitting (1399) gives: % 88.16/12.67 | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | (1400) all_9_7 = e4 & op(e2, e3) = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | ALPHA: (1400) implies: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | (1401) op(e2, e3) = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_7, e4, e3, e2, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | simplifying with (198), (1401) gives: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | (1402) all_4_7 = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | REDUCE: (26), (1402) imply: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | (1403) $false % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | CLOSE: (1403) is inconsistent. % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | (1404) (all_9_13 = e4 & op(e1, e3) = e4) | (all_9_21 = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e4) % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | BETA: splitting (1404) gives: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | (1405) all_9_13 = e4 & op(e1, e3) = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | ALPHA: (1405) implies: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | (1406) op(e1, e3) = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_8, e4, e3, e1, % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | simplifying with (159), (1406) gives: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | (1407) all_4_8 = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | REDUCE: (252), (1407) imply: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | (1408) $false % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | CLOSE: (1408) is inconsistent. % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | (1409) all_9_21 = e4 & op(e0, e3) = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | ALPHA: (1409) implies: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | (1410) all_9_21 = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1074), (1410) imply: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | (1411) e4 = e3 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (242), (1411) imply: % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | (1412) all_9_12 = e3 % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (44), (45), (58), (84), (89), (91), (120), % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | (197), (232), (260), (1412) are inconsistent by % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | sub-proof #117. % 88.16/12.67 | | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | (1413) all_6_1 = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (1413) imply: % 88.16/12.67 | | | | | | | | | | | | | | | | | (1414) all_4_5 = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | REDUCE: (9), (1414) imply: % 88.16/12.67 | | | | | | | | | | | | | | | | | (1415) ~ (all_4_10 = e4) % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | REDUCE: (153), (1414) imply: % 88.16/12.67 | | | | | | | | | | | | | | | | | (1416) ~ (all_4_15 = e4) % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | SIMP: (1416) implies: % 88.16/12.67 | | | | | | | | | | | | | | | | | (1417) ~ (all_4_15 = e4) % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | REDUCE: (125), (1414) imply: % 88.16/12.67 | | | | | | | | | | | | | | | | | (1418) ~ (all_4_20 = e4) % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | SIMP: (1418) implies: % 88.16/12.67 | | | | | | | | | | | | | | | | | (1419) ~ (all_4_20 = e4) % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (27), (31), (35), (37), (39), (44), % 88.16/12.67 | | | | | | | | | | | | | | | | | (45), (49), (58), (84), (89), (91), (101), (113), % 88.16/12.67 | | | | | | | | | | | | | | | | | (119), (120), (143), (146), (150), (158), (174), % 88.16/12.67 | | | | | | | | | | | | | | | | | (187), (194), (197), (199), (205), (208), (217), % 88.16/12.67 | | | | | | | | | | | | | | | | | (232), (233), (235), (242), (243), (260), (277), % 88.16/12.67 | | | | | | | | | | | | | | | | | (1076), (1417), (1419) are inconsistent by % 88.16/12.67 | | | | | | | | | | | | | | | | | sub-proof #29. % 88.16/12.67 | | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | (1420) op(e2, e4) = e4 % 88.16/12.67 | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | | REF_CLOSE: (31), (197), (232), (1420) are inconsistent by % 88.16/12.67 | | | | | | | | | | | | | | | | sub-proof #129. % 88.16/12.67 | | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | (1421) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 88.16/12.67 | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | REF_CLOSE: (69), (123), (141), (167), (1421) are inconsistent % 88.16/12.67 | | | | | | | | | | | by sub-proof #88. % 88.16/12.67 | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | | % 88.16/12.67 | | | | | | | | | End of split % 88.16/12.67 | | | | | | | | | % 88.16/12.67 | | | | | | | | End of split % 88.16/12.67 | | | | | | | | % 88.16/12.67 | | | | | | | End of split % 88.16/12.67 | | | | | | | % 88.16/12.67 | | | | | | End of split % 88.16/12.67 | | | | | | % 88.16/12.67 | | | | | End of split % 88.16/12.67 | | | | | % 88.16/12.67 | | | | Case 2: % 88.16/12.67 | | | | | % 88.16/12.67 | | | | | (1422) all_9_20 = e4 & op(e0, e4) = e4 % 88.16/12.67 | | | | | % 88.16/12.67 | | | | | REF_CLOSE: (234), (1422) are inconsistent by sub-proof #54. % 88.16/12.67 | | | | | % 88.16/12.67 | | | | End of split % 88.16/12.67 | | | | % 88.16/12.67 | | | End of split % 88.16/12.67 | | | % 88.16/12.67 | | End of split % 88.16/12.67 | | % 88.16/12.67 | Case 2: % 88.16/12.67 | | % 88.16/12.67 | | (1423) all_6_20 = e4 % 88.16/12.67 | | % 88.16/12.67 | | COMBINE_EQS: (123), (1423) imply: % 88.16/12.67 | | (1424) all_4_4 = e4 % 88.16/12.67 | | % 88.16/12.67 | | REDUCE: (70), (1424) imply: % 88.16/12.67 | | (1425) ~ (all_4_3 = e4) % 88.16/12.67 | | % 88.16/12.67 | | REDUCE: (79), (1424) imply: % 88.16/12.67 | | (1426) ~ (all_4_9 = e4) % 88.16/12.67 | | % 88.16/12.67 | | SIMP: (1426) implies: % 88.16/12.67 | | (1427) ~ (all_4_9 = e4) % 88.16/12.67 | | % 88.16/12.67 | | REDUCE: (165), (1424) imply: % 88.16/12.67 | | (1428) ~ (all_4_24 = e4) % 88.16/12.67 | | % 88.16/12.67 | | SIMP: (1428) implies: % 88.16/12.67 | | (1429) ~ (all_4_24 = e4) % 88.16/12.67 | | % 88.16/12.67 | | BETA: splitting (230) gives: % 88.16/12.67 | | % 88.16/12.67 | | Case 1: % 88.16/12.67 | | | % 88.16/12.67 | | | (1430) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = % 88.16/12.67 | | | e2) % 88.16/12.67 | | | % 88.16/12.67 | | | REF_CLOSE: (120), (121), (131), (146), (174), (1430) are inconsistent by % 88.16/12.67 | | | sub-proof #126. % 88.16/12.67 | | | % 88.16/12.67 | | Case 2: % 88.16/12.67 | | | % 88.16/12.67 | | | (1431) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = % 88.16/12.67 | | | e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 88.16/12.67 | | | % 88.16/12.67 | | | BETA: splitting (1431) gives: % 88.16/12.67 | | | % 88.16/12.67 | | | Case 1: % 88.16/12.67 | | | | % 88.16/12.67 | | | | (1432) all_9_6 = e2 & op(e2, e4) = e2 % 88.16/12.67 | | | | % 88.16/12.67 | | | | REF_CLOSE: (25), (99), (114), (1432) are inconsistent by sub-proof #125. % 88.16/12.67 | | | | % 88.16/12.67 | | | Case 2: % 88.16/12.67 | | | | % 88.16/12.67 | | | | (1433) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, % 88.16/12.67 | | | | e4) = e2) % 88.16/12.67 | | | | % 88.16/12.67 | | | | BETA: splitting (1433) gives: % 88.16/12.67 | | | | % 88.16/12.67 | | | | Case 1: % 88.16/12.67 | | | | | % 88.16/12.67 | | | | | (1434) all_9_12 = e2 & op(e1, e4) = e2 % 88.16/12.67 | | | | | % 88.16/12.67 | | | | | ALPHA: (1434) implies: % 88.16/12.67 | | | | | (1435) all_9_12 = e2 % 88.16/12.67 | | | | | % 88.16/12.67 | | | | | BETA: splitting (126) gives: % 88.16/12.67 | | | | | % 88.16/12.67 | | | | | Case 1: % 88.16/12.67 | | | | | | % 88.16/12.67 | | | | | | (1436) all_6_15 = e4 % 88.16/12.67 | | | | | | % 88.16/12.67 | | | | | | REF_CLOSE: (188), (1425), (1436) are inconsistent by sub-proof #100. % 88.16/12.67 | | | | | | % 88.16/12.67 | | | | | Case 2: % 88.16/12.67 | | | | | | % 88.16/12.67 | | | | | | (1437) ~ (all_6_15 = e4) % 88.16/12.67 | | | | | | (1438) all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 = % 88.16/12.67 | | | | | | e0 % 88.16/12.67 | | | | | | % 88.16/12.67 | | | | | | BETA: splitting (89) gives: % 88.16/12.67 | | | | | | % 88.16/12.67 | | | | | | Case 1: % 88.16/12.67 | | | | | | | % 88.16/12.67 | | | | | | | (1439) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 88.16/12.67 | | | | | | | op(e3, e4) = e4) % 88.16/12.67 | | | | | | | % 88.16/12.67 | | | | | | | REF_CLOSE: (44), (58), (84), (91), (120), (1439) are inconsistent % 88.16/12.67 | | | | | | | by sub-proof #130. % 88.16/12.67 | | | | | | | % 88.16/12.67 | | | | | | Case 2: % 88.16/12.67 | | | | | | | % 88.16/12.67 | | | | | | | (1440) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 88.16/12.67 | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 88.16/12.67 | | | | | | | % 88.16/12.67 | | | | | | | BETA: splitting (1440) gives: % 88.16/12.67 | | | | | | | % 88.16/12.67 | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | % 88.16/12.67 | | | | | | | | (1441) all_9_6 = e4 & op(e2, e4) = e4 % 88.16/12.67 | | | | | | | | % 88.16/12.67 | | | | | | | | ALPHA: (1441) implies: % 88.16/12.67 | | | | | | | | (1442) op(e2, e4) = e4 % 88.16/12.67 | | | | | | | | % 88.16/12.67 | | | | | | | | REF_CLOSE: (31), (197), (232), (1442) are inconsistent by % 88.16/12.67 | | | | | | | | sub-proof #129. % 88.16/12.67 | | | | | | | | % 88.16/12.67 | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | % 88.16/12.67 | | | | | | | | (1443) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & % 88.16/12.67 | | | | | | | | op(e0, e4) = e4) % 88.16/12.67 | | | | | | | | % 88.16/12.67 | | | | | | | | BETA: splitting (1443) gives: % 88.16/12.67 | | | | | | | | % 88.16/12.67 | | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | | % 88.16/12.67 | | | | | | | | | (1444) all_9_12 = e4 & op(e1, e4) = e4 % 88.16/12.67 | | | | | | | | | % 88.16/12.67 | | | | | | | | | REF_CLOSE: (45), (1435), (1444) are inconsistent by sub-proof % 88.16/12.67 | | | | | | | | | #92. % 88.16/12.67 | | | | | | | | | % 88.16/12.67 | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | % 88.16/12.67 | | | | | | | | | (1445) all_9_20 = e4 & op(e0, e4) = e4 % 88.16/12.67 | | | | | | | | | % 88.16/12.67 | | | | | | | | | ALPHA: (1445) implies: % 88.16/12.67 | | | | | | | | | (1446) all_9_20 = e4 % 88.16/12.67 | | | | | | | | | % 88.16/12.67 | | | | | | | | | BETA: splitting (1438) gives: % 88.16/12.67 | | | | | | | | | % 88.16/12.67 | | | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | (1447) all_6_15 = e2 % 88.16/12.67 | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | COMBINE_EQS: (188), (1447) imply: % 88.16/12.67 | | | | | | | | | | (1448) all_4_3 = e2 % 88.16/12.67 | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | SIMP: (1448) implies: % 88.16/12.67 | | | | | | | | | | (1449) all_4_3 = e2 % 88.16/12.67 | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | REDUCE: (1425), (1449) imply: % 88.16/12.67 | | | | | | | | | | (1450) ~ (e4 = e2) % 88.16/12.67 | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | REDUCE: (43), (1449) imply: % 88.16/12.67 | | | | | | | | | | (1451) ~ (e3 = e2) % 88.16/12.67 | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | BETA: splitting (41) gives: % 88.16/12.67 | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | (1452) ~ (op(e1, e4) = e4) % 88.16/12.67 | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | PRED_UNIFY: (217), (1452) imply: % 88.16/12.67 | | | | | | | | | | | (1453) ~ (unit = e1) % 88.16/12.67 | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | BETA: splitting (226) gives: % 88.16/12.67 | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | Case 1: % 88.16/12.67 | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | (1454) ~ (op(e0, e3) = e3) % 88.16/12.67 | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | PRED_UNIFY: (132), (1454) imply: % 88.16/12.67 | | | | | | | | | | | | (1455) ~ (unit = e0) % 88.16/12.67 | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | | REF_CLOSE: (14), (31), (35), (44), (51), (61), (108), (137), % 88.16/12.67 | | | | | | | | | | | | (197), (208), (217), (232), (1453), (1455) are % 88.16/12.67 | | | | | | | | | | | | inconsistent by sub-proof #33. % 88.16/12.67 | | | | | | | | | | | | % 88.16/12.67 | | | | | | | | | | | Case 2: % 88.16/12.67 | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | (1456) all_6_21 = e3 % 88.16/12.68 | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | COMBINE_EQS: (203), (1456) imply: % 88.16/12.68 | | | | | | | | | | | | (1457) all_4_9 = e3 % 88.16/12.68 | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | SIMP: (1457) implies: % 88.16/12.68 | | | | | | | | | | | | (1458) all_4_9 = e3 % 88.16/12.68 | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | REDUCE: (77), (1458) imply: % 88.16/12.68 | | | | | | | | | | | | (1459) ~ (all_4_6 = e3) % 88.16/12.68 | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | REDUCE: (5), (1458) imply: % 88.16/12.68 | | | | | | | | | | | | (1460) ~ (all_4_24 = e3) % 88.16/12.68 | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | SIMP: (1460) implies: % 88.16/12.68 | | | | | | | | | | | | (1461) ~ (all_4_24 = e3) % 88.16/12.68 | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | REDUCE: (1427), (1458) imply: % 88.16/12.68 | | | | | | | | | | | | (1462) ~ (e4 = e3) % 88.16/12.68 | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | BETA: splitting (192) gives: % 88.16/12.68 | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | Case 1: % 88.16/12.68 | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | (1463) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) % 88.16/12.68 | | | | | | | | | | | | | & op(e4, e4) = e3 & op(e3, e4) = all_8_3 & % 88.16/12.68 | | | | | | | | | | | | | op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = e3 & % 88.16/12.68 | | | | | | | | | | | | | all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) % 88.16/12.68 | | | | | | | | | | | | | = e3 & op(e4, e3) = all_8_15 & op(e3, e3) = e4 & % 88.16/12.68 | | | | | | | | | | | | | $i(all_8_15)) | (all_8_0 = e2 & all_8_32 = e4 & % 88.16/12.68 | | | | | | | | | | | | | ~ (all_8_6 = e2) & op(e4, e4) = e2 & op(e2, e4) % 88.16/12.68 | | | | | | | | | | | | | = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | % 88.16/12.68 | | | | | | | | | | | | | (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_28 = e4) % 88.16/12.68 | | | | | | | | | | | | | & op(e4, e4) = e2 & op(e4, e2) = all_8_28 & % 88.16/12.68 | | | | | | | | | | | | | op(e2, e2) = e4 & $i(all_8_28)) | (all_8_0 = e1 % 88.16/12.68 | | | | | | | | | | | | | & all_8_48 = e4 & ~ (all_8_9 = e1) & op(e4, e4) % 88.16/12.68 | | | | | | | | | | | | | = e1 & op(e1, e4) = all_8_9 & op(e1, e1) = e4 & % 88.16/12.68 | | | | | | | | | | | | | $i(all_8_9)) | (all_8_0 = e1 & all_8_48 = e4 & % 88.16/12.68 | | | | | | | | | | | | | ~ (all_8_41 = e4) & op(e4, e4) = e1 & op(e4, e1) % 88.16/12.68 | | | | | | | | | | | | | = all_8_41 & op(e1, e1) = e4 & $i(all_8_41)) | % 88.16/12.68 | | | | | | | | | | | | | (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) % 88.16/12.68 | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e4, e0) = all_8_54 & % 88.16/12.68 | | | | | | | | | | | | | op(e0, e0) = e4 & $i(all_8_54)) | (all_8_16 = e2 % 88.16/12.68 | | | | | | | | | | | | | & all_8_32 = e3 & ~ (all_8_19 = e2) & op(e3, % 88.16/12.68 | | | | | | | | | | | | | e3) = e2 & op(e2, e3) = all_8_19 & op(e2, e2) % 88.16/12.68 | | | | | | | | | | | | | = e3 & $i(all_8_19)) % 88.16/12.68 | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | BETA: splitting (1463) gives: % 88.16/12.68 | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | Case 1: % 88.16/12.68 | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | (1464) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) % 88.16/12.68 | | | | | | | | | | | | | | & op(e4, e4) = e3 & op(e3, e4) = all_8_3 & % 88.16/12.68 | | | | | | | | | | | | | | op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = e3 & % 88.16/12.68 | | | | | | | | | | | | | | all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) % 88.16/12.68 | | | | | | | | | | | | | | = e3 & op(e4, e3) = all_8_15 & op(e3, e3) = e4 & % 88.16/12.68 | | | | | | | | | | | | | | $i(all_8_15)) | (all_8_0 = e2 & all_8_32 = e4 & % 88.16/12.68 | | | | | | | | | | | | | | ~ (all_8_6 = e2) & op(e4, e4) = e2 & op(e2, e4) % 88.16/12.68 | | | | | | | | | | | | | | = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | % 88.16/12.68 | | | | | | | | | | | | | | (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_28 = e4) % 88.16/12.68 | | | | | | | | | | | | | | & op(e4, e4) = e2 & op(e4, e2) = all_8_28 & % 88.16/12.68 | | | | | | | | | | | | | | op(e2, e2) = e4 & $i(all_8_28)) % 88.16/12.68 | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | BETA: splitting (1464) gives: % 88.16/12.68 | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | Case 1: % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | (1465) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) % 88.16/12.68 | | | | | | | | | | | | | | | & op(e4, e4) = e3 & op(e3, e4) = all_8_3 & % 88.16/12.68 | | | | | | | | | | | | | | | op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = e3 & % 88.16/12.68 | | | | | | | | | | | | | | | all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) % 88.16/12.68 | | | | | | | | | | | | | | | = e3 & op(e4, e3) = all_8_15 & op(e3, e3) = e4 & % 88.16/12.68 | | | | | | | | | | | | | | | $i(all_8_15)) % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | BETA: splitting (1465) gives: % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | Case 1: % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | (1466) all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & % 88.16/12.68 | | | | | | | | | | | | | | | | op(e4, e4) = e3 & op(e3, e4) = all_8_3 & op(e3, % 88.16/12.68 | | | | | | | | | | | | | | | | e3) = e4 & $i(all_8_3) % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | ALPHA: (1466) implies: % 88.16/12.68 | | | | | | | | | | | | | | | | (1467) op(e4, e4) = e3 % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | REF_CLOSE: (29), (146), (174), (1467) are inconsistent by % 88.16/12.68 | | | | | | | | | | | | | | | | sub-proof #105. % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | Case 2: % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | (1468) all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_15 = e4) % 88.16/12.68 | | | | | | | | | | | | | | | | & op(e4, e4) = e3 & op(e4, e3) = all_8_15 & op(e3, % 88.16/12.68 | | | | | | | | | | | | | | | | e3) = e4 & $i(all_8_15) % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | ALPHA: (1468) implies: % 88.16/12.68 | | | | | | | | | | | | | | | | (1469) op(e4, e4) = e3 % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e0, e3, e4, e4, % 88.16/12.68 | | | | | | | | | | | | | | | | simplifying with (146), (1469) gives: % 88.16/12.68 | | | | | | | | | | | | | | | | (1470) e3 = e0 % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | REDUCE: (29), (1470) imply: % 88.16/12.68 | | | | | | | | | | | | | | | | (1471) $false % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | CLOSE: (1471) is inconsistent. % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | End of split % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | Case 2: % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | (1472) (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_6 = e2) % 88.16/12.68 | | | | | | | | | | | | | | | & op(e4, e4) = e2 & op(e2, e4) = all_8_6 & % 88.16/12.68 | | | | | | | | | | | | | | | op(e2, e2) = e4 & $i(all_8_6)) | (all_8_0 = e2 & % 88.16/12.68 | | | | | | | | | | | | | | | all_8_32 = e4 & ~ (all_8_28 = e4) & op(e4, e4) % 88.16/12.68 | | | | | | | | | | | | | | | = e2 & op(e4, e2) = all_8_28 & op(e2, e2) = e4 & % 88.16/12.68 | | | | | | | | | | | | | | | $i(all_8_28)) % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | REF_CLOSE: (121), (146), (174), (1472) are inconsistent by % 88.16/12.68 | | | | | | | | | | | | | | | sub-proof #21. % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | End of split % 88.16/12.68 | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | Case 2: % 88.16/12.68 | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | (1473) (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = e1) % 88.16/12.68 | | | | | | | | | | | | | | & op(e4, e4) = e1 & op(e1, e4) = all_8_9 & % 88.16/12.68 | | | | | | | | | | | | | | op(e1, e1) = e4 & $i(all_8_9)) | (all_8_0 = e1 & % 88.16/12.68 | | | | | | | | | | | | | | all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) % 88.16/12.68 | | | | | | | | | | | | | | = e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & % 88.16/12.68 | | | | | | | | | | | | | | $i(all_8_41)) | (all_8_0 = e0 & all_8_64 = e4 & % 88.16/12.68 | | | | | | | | | | | | | | ~ (all_8_54 = e4) & op(e4, e4) = e0 & op(e4, e0) % 88.16/12.68 | | | | | | | | | | | | | | = all_8_54 & op(e0, e0) = e4 & $i(all_8_54)) | % 88.16/12.68 | | | | | | | | | | | | | | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = % 88.16/12.68 | | | | | | | | | | | | | | e2) & op(e3, e3) = e2 & op(e2, e3) = all_8_19 % 88.16/12.68 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_8_19)) % 88.16/12.68 | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | BETA: splitting (1473) gives: % 88.16/12.68 | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | Case 1: % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | (1474) (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = e1) % 88.16/12.68 | | | | | | | | | | | | | | | & op(e4, e4) = e1 & op(e1, e4) = all_8_9 & % 88.16/12.68 | | | | | | | | | | | | | | | op(e1, e1) = e4 & $i(all_8_9)) | (all_8_0 = e1 & % 88.16/12.68 | | | | | | | | | | | | | | | all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) % 88.16/12.68 | | | | | | | | | | | | | | | = e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & % 88.16/12.68 | | | | | | | | | | | | | | | $i(all_8_41)) % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | REF_CLOSE: (146), (174), (233), (1474) are inconsistent by % 88.16/12.68 | | | | | | | | | | | | | | | sub-proof #19. % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | Case 2: % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | (1475) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) % 88.16/12.68 | | | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e4, e0) = all_8_54 & % 88.16/12.68 | | | | | | | | | | | | | | | op(e0, e0) = e4 & $i(all_8_54)) | (all_8_16 = e2 % 88.16/12.68 | | | | | | | | | | | | | | | & all_8_32 = e3 & ~ (all_8_19 = e2) & op(e3, % 88.16/12.68 | | | | | | | | | | | | | | | e3) = e2 & op(e2, e3) = all_8_19 & op(e2, e2) % 88.16/12.68 | | | | | | | | | | | | | | | = e3 & $i(all_8_19)) % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | BETA: splitting (1475) gives: % 88.16/12.68 | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | Case 1: % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | (1476) all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) % 88.16/12.68 | | | | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e4, e0) = all_8_54 & op(e0, % 88.16/12.68 | | | | | | | | | | | | | | | | e0) = e4 & $i(all_8_54) % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | ALPHA: (1476) implies: % 88.16/12.68 | | | | | | | | | | | | | | | | (1477) op(e0, e0) = e4 % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_24, e4, e0, e0, % 88.16/12.68 | | | | | | | | | | | | | | | | simplifying with (155), (1477) gives: % 88.16/12.68 | | | | | | | | | | | | | | | | (1478) all_4_24 = e4 % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | REDUCE: (1429), (1478) imply: % 88.16/12.68 | | | | | | | | | | | | | | | | (1479) $false % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | CLOSE: (1479) is inconsistent. % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | Case 2: % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | (1480) all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = e2) % 88.16/12.68 | | | | | | | | | | | | | | | | & op(e3, e3) = e2 & op(e2, e3) = all_8_19 & op(e2, % 88.16/12.68 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_8_19) % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | ALPHA: (1480) implies: % 88.16/12.68 | | | | | | | | | | | | | | | | (1481) op(e2, e2) = e3 % 88.16/12.68 | | | | | | | | | | | | | | | | % 88.16/12.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e4, e3, e2, e2, % 88.16/12.68 | | | | | | | | | | | | | | | | simplifying with (118), (1481) gives: % 88.37/12.68 | | | | | | | | | | | | | | | | (1482) e4 = e3 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | REF_CLOSE: (31), (44), (45), (58), (84), (89), (91), (120), % 88.37/12.68 | | | | | | | | | | | | | | | | (197), (232), (1435), (1446), (1482) are % 88.37/12.68 | | | | | | | | | | | | | | | | inconsistent by sub-proof #6. % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | End of split % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | End of split % 88.37/12.68 | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | End of split % 88.37/12.68 | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | Case 2: % 88.37/12.68 | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | (1483) (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = % 88.37/12.68 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_8_31 % 88.37/12.68 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_8_31)) | (all_8_16 = % 88.37/12.68 | | | | | | | | | | | | | e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, % 88.37/12.68 | | | | | | | | | | | | | e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) % 88.37/12.68 | | | | | | | | | | | | | = e3 & $i(all_8_22)) | (all_8_16 = e1 & all_8_48 % 88.37/12.68 | | | | | | | | | | | | | = e3 & ~ (all_8_44 = e3) & op(e3, e3) = e1 & % 88.37/12.68 | | | | | | | | | | | | | op(e3, e1) = all_8_44 & op(e1, e1) = e3 & % 88.37/12.68 | | | | | | | | | | | | | $i(all_8_44)) | (all_8_16 = e0 & all_8_64 = e3 & % 88.37/12.68 | | | | | | | | | | | | | ~ (all_8_57 = e3) & op(e3, e3) = e0 & op(e3, % 88.37/12.68 | | | | | | | | | | | | | e0) = all_8_57 & op(e0, e0) = e3 & % 88.37/12.68 | | | | | | | | | | | | | $i(all_8_57)) | (all_8_32 = e1 & all_8_48 = e2 & % 88.37/12.68 | | | | | | | | | | | | | ~ (all_8_35 = e1) & op(e2, e2) = e1 & op(e1, % 88.37/12.68 | | | | | | | | | | | | | e2) = all_8_35 & op(e1, e1) = e2 & % 88.37/12.68 | | | | | | | | | | | | | $i(all_8_35)) | (all_8_32 = e1 & all_8_48 = e2 & % 88.37/12.68 | | | | | | | | | | | | | ~ (all_8_47 = e2) & op(e2, e2) = e1 & op(e2, % 88.37/12.68 | | | | | | | | | | | | | e1) = all_8_47 & op(e1, e1) = e2 & % 88.37/12.68 | | | | | | | | | | | | | $i(all_8_47)) | (all_8_32 = e0 & all_8_64 = e2 & % 88.37/12.68 | | | | | | | | | | | | | ~ (all_8_60 = e2) & op(e2, e2) = e0 & op(e2, % 88.37/12.68 | | | | | | | | | | | | | e0) = all_8_60 & op(e0, e0) = e2 & % 88.37/12.68 | | | | | | | | | | | | | $i(all_8_60)) | (op(e0, e0) = all_8_64 & % 88.37/12.68 | | | | | | | | | | | | | $i(all_8_64) & ((all_8_0 = e0 & all_8_64 = e4 & % 88.37/12.68 | | | | | | | | | | | | | ~ (all_8_12 = e0) & op(e4, e4) = e0 & op(e0, % 88.37/12.68 | | | | | | | | | | | | | e4) = all_8_12 & $i(all_8_12)) | (all_8_16 % 88.37/12.68 | | | | | | | | | | | | | = e0 & all_8_64 = e3 & ~ (all_8_25 = e0) & % 88.37/12.68 | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 88.37/12.68 | | | | | | | | | | | | | $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = % 88.37/12.68 | | | | | | | | | | | | | e2 & ~ (all_8_38 = e0) & op(e2, e2) = e0 & % 88.37/12.68 | | | | | | | | | | | | | op(e0, e2) = all_8_38 & $i(all_8_38)) | % 88.37/12.68 | | | | | | | | | | | | | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 % 88.37/12.68 | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) = % 88.37/12.68 | | | | | | | | | | | | | all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & % 88.37/12.68 | | | | | | | | | | | | | all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, % 88.37/12.68 | | | | | | | | | | | | | e1) = e0 & op(e1, e0) = all_8_63 & % 88.37/12.68 | | | | | | | | | | | | | $i(all_8_63)))) % 88.37/12.68 | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | BETA: splitting (1483) gives: % 88.37/12.68 | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | Case 1: % 88.37/12.68 | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | (1484) (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = % 88.37/12.68 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_8_31 % 88.37/12.68 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_8_31)) | (all_8_16 = % 88.37/12.68 | | | | | | | | | | | | | | e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, % 88.37/12.68 | | | | | | | | | | | | | | e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) % 88.37/12.68 | | | | | | | | | | | | | | = e3 & $i(all_8_22)) | (all_8_16 = e1 & all_8_48 % 88.37/12.68 | | | | | | | | | | | | | | = e3 & ~ (all_8_44 = e3) & op(e3, e3) = e1 & % 88.37/12.68 | | | | | | | | | | | | | | op(e3, e1) = all_8_44 & op(e1, e1) = e3 & % 88.37/12.68 | | | | | | | | | | | | | | $i(all_8_44)) | (all_8_16 = e0 & all_8_64 = e3 & % 88.37/12.68 | | | | | | | | | | | | | | ~ (all_8_57 = e3) & op(e3, e3) = e0 & op(e3, % 88.37/12.68 | | | | | | | | | | | | | | e0) = all_8_57 & op(e0, e0) = e3 & % 88.37/12.68 | | | | | | | | | | | | | | $i(all_8_57)) % 88.37/12.68 | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | BETA: splitting (1484) gives: % 88.37/12.68 | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | Case 1: % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | (1485) (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = % 88.37/12.68 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_8_31 % 88.37/12.68 | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_8_31)) | (all_8_16 = % 88.37/12.68 | | | | | | | | | | | | | | | e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, % 88.37/12.68 | | | | | | | | | | | | | | | e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) % 88.37/12.68 | | | | | | | | | | | | | | | = e3 & $i(all_8_22)) % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | BETA: splitting (1485) gives: % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | Case 1: % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | (1486) all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) % 88.37/12.68 | | | | | | | | | | | | | | | | & op(e3, e3) = e2 & op(e3, e2) = all_8_31 & op(e2, % 88.37/12.68 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_8_31) % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | ALPHA: (1486) implies: % 88.37/12.68 | | | | | | | | | | | | | | | | (1487) op(e2, e2) = e3 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e4, e3, e2, e2, % 88.37/12.68 | | | | | | | | | | | | | | | | simplifying with (118), (1487) gives: % 88.37/12.68 | | | | | | | | | | | | | | | | (1488) e4 = e3 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | REF_CLOSE: (31), (44), (45), (58), (84), (89), (91), (120), % 88.37/12.68 | | | | | | | | | | | | | | | | (197), (232), (1435), (1446), (1488) are % 88.37/12.68 | | | | | | | | | | | | | | | | inconsistent by sub-proof #6. % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | Case 2: % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | (1489) all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) % 88.37/12.68 | | | | | | | | | | | | | | | | & op(e3, e3) = e1 & op(e1, e3) = all_8_22 & op(e1, % 88.37/12.68 | | | | | | | | | | | | | | | | e1) = e3 & $i(all_8_22) % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | ALPHA: (1489) implies: % 88.37/12.68 | | | | | | | | | | | | | | | | (1490) op(e3, e3) = e1 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | REF_CLOSE: (47), (67), (174), (1490) are inconsistent by % 88.37/12.68 | | | | | | | | | | | | | | | | sub-proof #58. % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | End of split % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | Case 2: % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | (1491) (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = % 88.37/12.68 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_8_44 % 88.37/12.68 | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_8_44)) | (all_8_16 = % 88.37/12.68 | | | | | | | | | | | | | | | e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & op(e3, % 88.37/12.68 | | | | | | | | | | | | | | | e3) = e0 & op(e3, e0) = all_8_57 & op(e0, e0) % 88.37/12.68 | | | | | | | | | | | | | | | = e3 & $i(all_8_57)) % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | BETA: splitting (1491) gives: % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | Case 1: % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | (1492) all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) % 88.37/12.68 | | | | | | | | | | | | | | | | & op(e3, e3) = e1 & op(e3, e1) = all_8_44 & op(e1, % 88.37/12.68 | | | | | | | | | | | | | | | | e1) = e3 & $i(all_8_44) % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | ALPHA: (1492) implies: % 88.37/12.68 | | | | | | | | | | | | | | | | (1493) op(e3, e3) = e1 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_6, e1, e3, e3, % 88.37/12.68 | | | | | | | | | | | | | | | | simplifying with (67), (1493) gives: % 88.37/12.68 | | | | | | | | | | | | | | | | (1494) all_4_6 = e1 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | REDUCE: (47), (1494) imply: % 88.37/12.68 | | | | | | | | | | | | | | | | (1495) $false % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | CLOSE: (1495) is inconsistent. % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | Case 2: % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | (1496) all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_57 = e3) % 88.37/12.68 | | | | | | | | | | | | | | | | & op(e3, e3) = e0 & op(e3, e0) = all_8_57 & op(e0, % 88.37/12.68 | | | | | | | | | | | | | | | | e0) = e3 & $i(all_8_57) % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | ALPHA: (1496) implies: % 88.37/12.68 | | | | | | | | | | | | | | | | (1497) op(e0, e0) = e3 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | REF_CLOSE: (155), (174), (1461), (1497) are inconsistent by % 88.37/12.68 | | | | | | | | | | | | | | | | sub-proof #16. % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | End of split % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | End of split % 88.37/12.68 | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | Case 2: % 88.37/12.68 | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | (1498) (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = % 88.37/12.68 | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_8_35 % 88.37/12.68 | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_8_35)) | (all_8_32 = % 88.37/12.68 | | | | | | | | | | | | | | e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, % 88.37/12.68 | | | | | | | | | | | | | | e2) = e1 & op(e2, e1) = all_8_47 & op(e1, e1) % 88.37/12.68 | | | | | | | | | | | | | | = e2 & $i(all_8_47)) | (all_8_32 = e0 & all_8_64 % 88.37/12.68 | | | | | | | | | | | | | | = e2 & ~ (all_8_60 = e2) & op(e2, e2) = e0 & % 88.37/12.68 | | | | | | | | | | | | | | op(e2, e0) = all_8_60 & op(e0, e0) = e2 & % 88.37/12.68 | | | | | | | | | | | | | | $i(all_8_60)) | (op(e0, e0) = all_8_64 & % 88.37/12.68 | | | | | | | | | | | | | | $i(all_8_64) & ((all_8_0 = e0 & all_8_64 = e4 & % 88.37/12.68 | | | | | | | | | | | | | | ~ (all_8_12 = e0) & op(e4, e4) = e0 & op(e0, % 88.37/12.68 | | | | | | | | | | | | | | e4) = all_8_12 & $i(all_8_12)) | (all_8_16 % 88.37/12.68 | | | | | | | | | | | | | | = e0 & all_8_64 = e3 & ~ (all_8_25 = e0) & % 88.37/12.68 | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 88.37/12.68 | | | | | | | | | | | | | | $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = % 88.37/12.68 | | | | | | | | | | | | | | e2 & ~ (all_8_38 = e0) & op(e2, e2) = e0 & % 88.37/12.68 | | | | | | | | | | | | | | op(e0, e2) = all_8_38 & $i(all_8_38)) | % 88.37/12.68 | | | | | | | | | | | | | | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 % 88.37/12.68 | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) = % 88.37/12.68 | | | | | | | | | | | | | | all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & % 88.37/12.68 | | | | | | | | | | | | | | all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, % 88.37/12.68 | | | | | | | | | | | | | | e1) = e0 & op(e1, e0) = all_8_63 & % 88.37/12.68 | | | | | | | | | | | | | | $i(all_8_63)))) % 88.37/12.68 | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | BETA: splitting (1498) gives: % 88.37/12.68 | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | Case 1: % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | (1499) (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = % 88.37/12.68 | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_8_35 % 88.37/12.68 | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_8_35)) | (all_8_32 = % 88.37/12.68 | | | | | | | | | | | | | | | e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, % 88.37/12.68 | | | | | | | | | | | | | | | e2) = e1 & op(e2, e1) = all_8_47 & op(e1, e1) % 88.37/12.68 | | | | | | | | | | | | | | | = e2 & $i(all_8_47)) % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | BETA: splitting (1499) gives: % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | Case 1: % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | (1500) all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) % 88.37/12.68 | | | | | | | | | | | | | | | | & op(e2, e2) = e1 & op(e1, e2) = all_8_35 & op(e1, % 88.37/12.68 | | | | | | | | | | | | | | | | e1) = e2 & $i(all_8_35) % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | ALPHA: (1500) implies: % 88.37/12.68 | | | | | | | | | | | | | | | | (1501) op(e2, e2) = e1 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e4, e1, e2, e2, % 88.37/12.68 | | | | | | | | | | | | | | | | simplifying with (118), (1501) gives: % 88.37/12.68 | | | | | | | | | | | | | | | | (1502) e4 = e1 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | REDUCE: (44), (1502) imply: % 88.37/12.68 | | | | | | | | | | | | | | | | (1503) $false % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | CLOSE: (1503) is inconsistent. % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | Case 2: % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | (1504) all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_47 = e2) % 88.37/12.68 | | | | | | | | | | | | | | | | & op(e2, e2) = e1 & op(e2, e1) = all_8_47 & op(e1, % 88.37/12.68 | | | | | | | | | | | | | | | | e1) = e2 & $i(all_8_47) % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | ALPHA: (1504) implies: % 88.37/12.68 | | | | | | | | | | | | | | | | (1505) op(e2, e2) = e1 % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | | REF_CLOSE: (44), (118), (174), (1505) are inconsistent by % 88.37/12.68 | | | | | | | | | | | | | | | | sub-proof #22. % 88.37/12.68 | | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | End of split % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | Case 2: % 88.37/12.68 | | | | | | | | | | | | | | | % 88.37/12.68 | | | | | | | | | | | | | | | (1506) (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = % 88.37/12.68 | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_8_60 % 88.37/12.68 | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_8_60)) | (op(e0, e0) % 88.37/12.68 | | | | | | | | | | | | | | | = all_8_64 & $i(all_8_64) & ((all_8_0 = e0 & % 88.37/12.68 | | | | | | | | | | | | | | | all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, % 88.37/12.68 | | | | | | | | | | | | | | | e4) = e0 & op(e0, e4) = all_8_12 & % 88.37/12.68 | | | | | | | | | | | | | | | $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = % 88.37/12.68 | | | | | | | | | | | | | | | e3 & ~ (all_8_25 = e0) & op(e3, e3) = e0 & % 88.37/12.68 | | | | | | | | | | | | | | | op(e0, e3) = all_8_25 & $i(all_8_25)) | % 88.37/12.69 | | | | | | | | | | | | | | | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 % 88.37/12.69 | | | | | | | | | | | | | | | = e0) & op(e2, e2) = e0 & op(e0, e2) = % 88.37/12.69 | | | | | | | | | | | | | | | all_8_38 & $i(all_8_38)) | (all_8_48 = e0 & % 88.37/12.69 | | | | | | | | | | | | | | | all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, % 88.37/12.69 | | | | | | | | | | | | | | | e1) = e0 & op(e0, e1) = all_8_51 & % 88.37/12.69 | | | | | | | | | | | | | | | $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = % 88.37/12.69 | | | | | | | | | | | | | | | e1 & ~ (all_8_63 = e1) & op(e1, e1) = e0 & % 88.37/12.69 | | | | | | | | | | | | | | | op(e1, e0) = all_8_63 & $i(all_8_63)))) % 88.37/12.69 | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | BETA: splitting (1506) gives: % 88.37/12.69 | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | (1507) all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) % 88.37/12.69 | | | | | | | | | | | | | | | | & op(e2, e2) = e0 & op(e2, e0) = all_8_60 & op(e0, % 88.37/12.69 | | | | | | | | | | | | | | | | e0) = e2 & $i(all_8_60) % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | ALPHA: (1507) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | (1508) op(e2, e2) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | REF_CLOSE: (84), (118), (174), (1508) are inconsistent by % 88.37/12.69 | | | | | | | | | | | | | | | | sub-proof #43. % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | (1509) op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = % 88.37/12.69 | | | | | | | | | | | | | | | | e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & % 88.37/12.69 | | | | | | | | | | | | | | | | op(e4, e4) = e0 & op(e0, e4) = all_8_12 & % 88.37/12.69 | | | | | | | | | | | | | | | | $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | & ~ (all_8_25 = e0) & op(e3, e3) = e0 & % 88.37/12.69 | | | | | | | | | | | | | | | | op(e0, e3) = all_8_25 & $i(all_8_25)) | % 88.37/12.69 | | | | | | | | | | | | | | | | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = % 88.37/12.69 | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = % 88.37/12.69 | | | | | | | | | | | | | | | | all_8_38 & $i(all_8_38)) | (all_8_48 = e0 & % 88.37/12.69 | | | | | | | | | | | | | | | | all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, % 88.37/12.69 | | | | | | | | | | | | | | | | e1) = e0 & op(e0, e1) = all_8_51 & % 88.37/12.69 | | | | | | | | | | | | | | | | $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = e1 % 88.37/12.69 | | | | | | | | | | | | | | | | & ~ (all_8_63 = e1) & op(e1, e1) = e0 & % 88.37/12.69 | | | | | | | | | | | | | | | | op(e1, e0) = all_8_63 & $i(all_8_63))) % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | ALPHA: (1509) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | (1510) op(e0, e0) = all_8_64 % 88.37/12.69 | | | | | | | | | | | | | | | | (1511) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e0, e4) = all_8_12 & % 88.37/12.69 | | | | | | | | | | | | | | | | $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 & % 88.37/12.69 | | | | | | | | | | | | | | | | ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, % 88.37/12.69 | | | | | | | | | | | | | | | | e3) = all_8_25 & $i(all_8_25)) | (all_8_32 = % 88.37/12.69 | | | | | | | | | | | | | | | | e0 & all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, % 88.37/12.69 | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_8_38 & % 88.37/12.69 | | | | | | | | | | | | | | | | $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 & % 88.37/12.69 | | | | | | | | | | | | | | | | ~ (all_8_51 = e0) & op(e1, e1) = e0 & op(e0, % 88.37/12.69 | | | | | | | | | | | | | | | | e1) = all_8_51 & $i(all_8_51)) | (all_8_48 = % 88.37/12.69 | | | | | | | | | | | | | | | | e0 & all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, % 88.37/12.69 | | | | | | | | | | | | | | | | e1) = e0 & op(e1, e0) = all_8_63 & % 88.37/12.69 | | | | | | | | | | | | | | | | $i(all_8_63)) % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_24, all_8_64, e0, % 88.37/12.69 | | | | | | | | | | | | | | | | e0, simplifying with (155), (1510) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | (1512) all_8_64 = all_4_24 % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with e0, all_8_64, e0, e0, % 88.37/12.69 | | | | | | | | | | | | | | | | simplifying with (1510) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | (1513) all_8_64 = e0 | ~ (op(e0, e0) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | (1514) ~ (op(e2, e4) = e4) % 88.37/12.69 | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | PRED_UNIFY: (217), (1514) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | (1515) ~ (unit = e2) % 88.37/12.69 | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | (1516) ~ (op(e0, e4) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (15), (1516) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | (1517) ~ (unit = e4) % 88.37/12.69 | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | (1518) ~ (op(e1, e0) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (46), (1518) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | (1519) ~ (all_4_23 = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | (1520) ~ (op(e2, e0) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (64), (1520) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | (1521) ~ (all_4_22 = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1522) ~ (op(e4, e0) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1523) ~ (op(e4, e0) = e4) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (205), (1523) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1524) ~ (unit = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (113), (160), (1453), (1459), (1515), % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1517), (1524) are inconsistent by sub-proof #4. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1525) all_4_20 = e4 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (1525) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1526) ~ (all_4_5 = e4) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (1525) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1527) ~ (all_4_15 = e4) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | (1528) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e4) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (58), (84), (91), (228), (1526), (1528) are % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #121. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | (1529) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) = % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | e4) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1529) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | (1530) all_9_4 = e4 & op(e4, e2) = e4 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (119), (143), (1530) are inconsistent by % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | (1531) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e4) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1531) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | (1532) all_9_9 = e4 & op(e4, e1) = e4 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (187), (1527), (1532) are inconsistent by % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #32. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | (1533) all_9_16 = e4 & op(e4, e0) = e4 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1533) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | (1534) all_9_16 = e4 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) all_9_24 = e0 & op(e0, e0) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1535) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) op(e0, e0) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1513) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) ~ (op(e0, e0) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1536), (1537) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1538) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1539) all_8_64 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1512), (1539) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1540) all_4_24 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1429), (1540) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1541) ~ (e4 = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1461), (1540) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542) ~ (e3 = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (27), (29), (31), (32), (41), (42), % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (58), (61), (69), (70), % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (91), (99), (114), (118), (120), % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (122), (123), (126), (131), (137), (141), % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (150), (154), (167), (174), (180), (188), % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (230), (233), (1511), (1539) are % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1543) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1543) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1544) (all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_19 = e0 & op(e1, e0) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1544) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1545) (all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1545) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1546) all_9_16 = e0 & op(e4, e0) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1546) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547) op(e4, e0) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1522), (1547) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1548) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1548) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1549) all_9_17 = e0 & op(e3, e0) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1549) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550) all_9_17 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1551) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1551) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_9_16 = e3 & op(e4, e0) = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1552) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_9_16 = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1534), (1553) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) e4 = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1554) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) e4 = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (44), (45), (58), (84), (89), (91), (120), % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (232), (1435), (1446), (1555) are % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #6. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_9_17 = e3 & op(e3, e0) = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1556) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) all_9_17 = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1550), (1557) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) e3 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (1558) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1559) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1560) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) all_9_18 = e3 & op(e2, e0) = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1561) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) op(e2, e0) = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (174), (185), (1562) are inconsistent by % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #45. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1563) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) all_9_19 = e3 & op(e1, e0) = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1564) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) op(e1, e0) = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (174) with all_4_23, e3, e0, e1, % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (46), (1565) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) all_4_23 = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) ~ (op(e1, e0) = e1) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (108), (1567) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) ~ (unit = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (113), (160), (1453), (1459), (1515), % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517), (1568) are inconsistent by sub-proof #4. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) all_4_23 = e1 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1566), (1569) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) e3 = e1 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1570) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1571) e3 = e1 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (1571) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1572) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1572) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1573) all_9_24 = e3 & op(e0, e0) = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1573) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1574) op(e0, e0) = e3 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (174), (1461), (1574) are inconsistent by % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #16. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1575) (all_9_18 = e0 & op(e2, e0) = e0) | (all_9_19 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1575) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576) all_9_18 = e0 & op(e2, e0) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (162), (1521), (1576) are inconsistent by % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #42. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1577) all_9_19 = e0 & op(e1, e0) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1577) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1578) op(e1, e0) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1518), (1578) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1579) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1579) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1580) all_4_23 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1519), (1580) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1581) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1581) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1582) op(e4, e0) = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1583) ~ (op(e4, e0) = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1582), (1583) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1584) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1584) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1585) all_6_4 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (1585) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1586) all_4_20 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1586) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1587) all_4_20 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (1587) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1588) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1588) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | (1589) all_4_22 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1590) ~ (op(e2, e0) = e2) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (28), (1590) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1591) ~ (unit = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1592) unit = e4 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1517), (1592) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1593) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1593) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1594) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (160), (1453), (1459), (1515), (1591), % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | (1594) are inconsistent by sub-proof #5. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1595) all_4_22 = e2 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1589), (1595) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1596) e2 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1596) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1597) $false % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1597) is inconsistent. % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.69 | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | (1598) all_4_23 = e0 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | REDUCE: (104), (1598) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | (1599) ~ (all_4_18 = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (1511) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | (1600) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e0, e4) = all_8_12 & % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 & % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | e3) = all_8_25 & $i(all_8_25)) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1600) gives: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | Case 1: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1601) all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | & op(e4, e4) = e0 & op(e0, e4) = all_8_12 & % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | $i(all_8_12) % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1601) implies: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1602) all_8_64 = e4 % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1512), (1602) imply: % 88.37/12.69 | | | | | | | | | | | | | | | | | | | | | (1603) all_4_24 = e4 % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1429), (1603) imply: % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | (1604) $false % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1604) is inconsistent. % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | (1605) all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_25 = e0) % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | $i(all_8_25) % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1605) implies: % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | (1606) all_8_64 = e3 % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1512), (1606) imply: % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | (1607) all_4_24 = e3 % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1461), (1607) imply: % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | (1608) $false % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1608) is inconsistent. % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | (1609) (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_8_38 % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | & $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | & ~ (all_8_51 = e0) & op(e1, e1) = e0 & op(e0, % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | e1) = all_8_51 & $i(all_8_51)) | (all_8_48 = % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | e0 & all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | e1) = e0 & op(e1, e0) = all_8_63 & % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | $i(all_8_63)) % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (118), (147), (174), (1599), (1609) are % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #11. % 88.37/12.70 | | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | Case 2: % 88.37/12.70 | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | (1610) all_4_4 = e0 % 88.37/12.70 | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (1610) imply: % 88.37/12.70 | | | | | | | | | | | | | | | | | | (1611) e4 = e0 % 88.37/12.70 | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | SIMP: (1611) implies: % 88.37/12.70 | | | | | | | | | | | | | | | | | | (1612) e4 = e0 % 88.37/12.70 | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | REDUCE: (84), (1612) imply: % 88.37/12.70 | | | | | | | | | | | | | | | | | | (1613) $false % 88.37/12.70 | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | | CLOSE: (1613) is inconsistent. % 88.37/12.70 | | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | Case 2: % 88.37/12.70 | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | (1614) op(e2, e4) = e4 % 88.37/12.70 | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (197), (232), (1614) are inconsistent by % 88.37/12.70 | | | | | | | | | | | | | | | | | sub-proof #129. % 88.37/12.70 | | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | Case 2: % 88.37/12.70 | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | (1615) all_6_15 = e4 % 88.37/12.70 | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | COMBINE_EQS: (1447), (1615) imply: % 88.37/12.70 | | | | | | | | | | | (1616) e4 = e2 % 88.37/12.70 | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | REDUCE: (45), (1616) imply: % 88.37/12.70 | | | | | | | | | | | (1617) $false % 88.37/12.70 | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | | CLOSE: (1617) is inconsistent. % 88.37/12.70 | | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | | % 88.37/12.70 | | | | | | | | | Case 2: % 88.37/12.70 | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | (1618) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 88.37/12.70 | | | | | | | | | | % 88.37/12.70 | | | | | | | | | | REF_CLOSE: (32), (43), (61), (188), (1618) are inconsistent % 88.37/12.70 | | | | | | | | | | by sub-proof #93. % 88.37/12.70 | | | | | | | | | | % 88.37/12.70 | | | | | | | | | End of split % 88.37/12.70 | | | | | | | | | % 88.37/12.70 | | | | | | | | End of split % 88.37/12.70 | | | | | | | | % 88.37/12.70 | | | | | | | End of split % 88.37/12.70 | | | | | | | % 88.37/12.70 | | | | | | End of split % 88.37/12.70 | | | | | | % 88.37/12.70 | | | | | End of split % 88.37/12.70 | | | | | % 88.37/12.70 | | | | Case 2: % 88.37/12.70 | | | | | % 88.37/12.70 | | | | | (1619) all_9_20 = e2 & op(e0, e4) = e2 % 88.37/12.70 | | | | | % 88.37/12.70 | | | | | ALPHA: (1619) implies: % 88.37/12.70 | | | | | (1620) all_9_20 = e2 % 88.37/12.70 | | | | | % 88.37/12.70 | | | | | BETA: splitting (89) gives: % 88.37/12.70 | | | | | % 88.37/12.70 | | | | | Case 1: % 88.37/12.70 | | | | | | % 88.37/12.70 | | | | | | (1621) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, % 88.37/12.70 | | | | | | e4) = e4) % 88.37/12.70 | | | | | | % 88.37/12.70 | | | | | | REF_CLOSE: (44), (58), (84), (91), (120), (1621) are inconsistent by % 88.37/12.70 | | | | | | sub-proof #130. % 88.37/12.70 | | | | | | % 88.37/12.70 | | | | | Case 2: % 88.37/12.70 | | | | | | % 88.37/12.70 | | | | | | (1622) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, % 88.37/12.70 | | | | | | e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 88.37/12.70 | | | | | | % 88.37/12.70 | | | | | | BETA: splitting (1622) gives: % 88.37/12.70 | | | | | | % 88.37/12.70 | | | | | | Case 1: % 88.37/12.70 | | | | | | | % 88.37/12.70 | | | | | | | (1623) all_9_6 = e4 & op(e2, e4) = e4 % 88.37/12.70 | | | | | | | % 88.37/12.70 | | | | | | | ALPHA: (1623) implies: % 88.37/12.70 | | | | | | | (1624) op(e2, e4) = e4 % 88.37/12.70 | | | | | | | % 88.37/12.70 | | | | | | | REF_CLOSE: (31), (197), (232), (1624) are inconsistent by % 88.37/12.70 | | | | | | | sub-proof #129. % 88.37/12.70 | | | | | | | % 88.37/12.70 | | | | | | Case 2: % 88.37/12.70 | | | | | | | % 88.37/12.70 | | | | | | | (1625) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & % 88.37/12.70 | | | | | | | op(e0, e4) = e4) % 88.37/12.70 | | | | | | | % 88.37/12.70 | | | | | | | BETA: splitting (1625) gives: % 88.37/12.70 | | | | | | | % 88.37/12.70 | | | | | | | Case 1: % 88.37/12.70 | | | | | | | | % 88.37/12.70 | | | | | | | | (1626) all_9_12 = e4 & op(e1, e4) = e4 % 88.37/12.70 | | | | | | | | % 88.37/12.70 | | | | | | | | ALPHA: (1626) implies: % 88.37/12.70 | | | | | | | | (1627) op(e1, e4) = e4 % 88.37/12.70 | | | | | | | | % 88.37/12.70 | | | | | | | | BETA: splitting (41) gives: % 88.37/12.70 | | | | | | | | % 88.37/12.70 | | | | | | | | Case 1: % 88.37/12.70 | | | | | | | | | % 88.37/12.70 | | | | | | | | | (1628) ~ (op(e1, e4) = e4) % 88.37/12.70 | | | | | | | | | % 88.37/12.70 | | | | | | | | | PRED_UNIFY: (1627), (1628) imply: % 88.37/12.70 | | | | | | | | | (1629) $false % 88.37/12.70 | | | | | | | | | % 88.37/12.70 | | | | | | | | | CLOSE: (1629) is inconsistent. % 88.37/12.70 | | | | | | | | | % 88.37/12.70 | | | | | | | | Case 2: % 88.37/12.70 | | | | | | | | | % 88.37/12.70 | | | | | | | | | (1630) all_6_15 = e4 % 88.37/12.70 | | | | | | | | | % 88.37/12.70 | | | | | | | | | REF_CLOSE: (188), (1425), (1630) are inconsistent by sub-proof % 88.37/12.70 | | | | | | | | | #100. % 88.37/12.70 | | | | | | | | | % 88.37/12.70 | | | | | | | | End of split % 88.37/12.70 | | | | | | | | % 88.37/12.70 | | | | | | | Case 2: % 88.37/12.70 | | | | | | | | % 88.37/12.70 | | | | | | | | (1631) all_9_20 = e4 & op(e0, e4) = e4 % 88.37/12.70 | | | | | | | | % 88.37/12.70 | | | | | | | | REF_CLOSE: (45), (1620), (1631) are inconsistent by sub-proof % 88.37/12.70 | | | | | | | | #118. % 88.37/12.70 | | | | | | | | % 88.37/12.70 | | | | | | | End of split % 88.37/12.70 | | | | | | | % 88.37/12.70 | | | | | | End of split % 88.37/12.70 | | | | | | % 88.37/12.70 | | | | | End of split % 88.37/12.70 | | | | | % 88.37/12.70 | | | | End of split % 88.37/12.70 | | | | % 88.37/12.70 | | | End of split % 88.37/12.70 | | | % 88.37/12.70 | | End of split % 88.37/12.70 | | % 88.37/12.70 | End of split % 88.37/12.70 | % 88.37/12.70 End of proof % 88.37/12.70 % 88.37/12.70 Sub-proof #4 shows that the following formulas are inconsistent: % 88.37/12.70 ---------------------------------------------------------------- % 88.37/12.70 (1) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.37/12.70 (2) ~ (unit = e2) % 88.37/12.70 (3) op(e3, unit) = e3 % 88.37/12.70 (4) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 88.37/12.70 (5) ~ (unit = e0) % 88.37/12.70 (6) ~ (all_4_6 = e3) % 88.37/12.70 (7) ~ (unit = e1) % 88.37/12.70 (8) ~ (unit = e4) % 88.37/12.70 % 88.37/12.70 Begin of proof % 88.37/12.70 | % 88.37/12.70 | BETA: splitting (1) gives: % 88.37/12.70 | % 88.37/12.70 | Case 1: % 88.37/12.70 | | % 88.37/12.70 | | (9) unit = e4 % 88.37/12.70 | | % 88.37/12.70 | | REDUCE: (8), (9) imply: % 88.37/12.70 | | (10) $false % 88.37/12.70 | | % 88.37/12.70 | | CLOSE: (10) is inconsistent. % 88.37/12.70 | | % 88.37/12.70 | Case 2: % 88.37/12.70 | | % 88.37/12.70 | | (11) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.37/12.70 | | % 88.37/12.70 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (11) are inconsistent by sub-proof % 88.37/12.70 | | #5. % 88.37/12.70 | | % 88.37/12.70 | End of split % 88.37/12.70 | % 88.37/12.70 End of proof % 88.37/12.70 % 88.37/12.70 Sub-proof #5 shows that the following formulas are inconsistent: % 88.37/12.70 ---------------------------------------------------------------- % 88.37/12.70 (1) ~ (unit = e2) % 88.37/12.70 (2) op(e3, unit) = e3 % 88.37/12.70 (3) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.37/12.70 (4) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 88.37/12.70 (5) ~ (unit = e0) % 88.37/12.70 (6) ~ (all_4_6 = e3) % 88.37/12.70 (7) ~ (unit = e1) % 88.37/12.70 % 88.37/12.70 Begin of proof % 88.37/12.70 | % 88.37/12.70 | BETA: splitting (3) gives: % 88.37/12.70 | % 88.37/12.70 | Case 1: % 88.37/12.70 | | % 88.37/12.70 | | (8) unit = e2 % 88.37/12.70 | | % 88.37/12.70 | | REDUCE: (1), (8) imply: % 88.37/12.70 | | (9) $false % 88.37/12.70 | | % 88.37/12.70 | | CLOSE: (9) is inconsistent. % 88.37/12.70 | | % 88.37/12.70 | Case 2: % 88.37/12.70 | | % 88.37/12.70 | | (10) unit = e3 | unit = e1 | unit = e0 % 88.37/12.70 | | % 88.37/12.70 | | BETA: splitting (10) gives: % 88.37/12.70 | | % 88.37/12.70 | | Case 1: % 88.37/12.70 | | | % 88.37/12.70 | | | (11) unit = e3 % 88.37/12.70 | | | % 88.37/12.70 | | | REDUCE: (2), (11) imply: % 88.37/12.70 | | | (12) op(e3, e3) = e3 % 88.37/12.70 | | | % 88.37/12.70 | | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #107. % 88.37/12.70 | | | % 88.37/12.70 | | Case 2: % 88.37/12.70 | | | % 88.37/12.70 | | | (13) unit = e1 | unit = e0 % 88.37/12.70 | | | % 88.37/12.70 | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #111. % 88.37/12.70 | | | % 88.37/12.70 | | End of split % 88.37/12.70 | | % 88.37/12.70 | End of split % 88.37/12.70 | % 88.37/12.70 End of proof % 88.37/12.70 % 88.37/12.70 Sub-proof #6 shows that the following formulas are inconsistent: % 88.37/12.70 ---------------------------------------------------------------- % 88.37/12.70 (1) ~ (e4 = e3) % 88.37/12.70 (2) e4 = e3 % 88.37/12.70 (3) all_9_12 = e2 % 88.37/12.70 (4) ~ (e4 = e1) % 88.37/12.70 (5) ~ (e4 = e2) % 88.37/12.70 (6) all_4_0 = e0 % 88.37/12.70 (7) ~ (e4 = e0) % 88.37/12.70 (8) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.37/12.70 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.37/12.70 (all_9_20 = e4 & op(e0, e4) = e4) % 88.37/12.70 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.37/12.70 (10) all_9_20 = e4 % 88.37/12.70 (11) all_9_2 = e1 % 88.37/12.70 (12) all_4_2 = e3 % 88.37/12.70 (13) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.37/12.70 % 88.37/12.70 Begin of proof % 88.37/12.70 | % 88.37/12.70 | COMBINE_EQS: (2), (10) imply: % 88.37/12.70 | (14) all_9_20 = e3 % 88.37/12.70 | % 88.37/12.70 | BETA: splitting (8) gives: % 88.37/12.70 | % 88.37/12.70 | Case 1: % 88.37/12.70 | | % 88.37/12.70 | | (15) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 88.37/12.70 | | % 88.37/12.70 | | REF_CLOSE: (4), (6), (7), (9), (11), (15) are inconsistent by sub-proof % 88.37/12.70 | | #130. % 88.37/12.70 | | % 88.37/12.70 | Case 2: % 88.37/12.70 | | % 88.37/12.70 | | (16) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 88.37/12.70 | | | (all_9_20 = e4 & op(e0, e4) = e4) % 88.37/12.70 | | % 88.37/12.70 | | BETA: splitting (16) gives: % 88.37/12.70 | | % 88.37/12.70 | | Case 1: % 88.37/12.70 | | | % 88.37/12.70 | | | (17) all_9_6 = e4 & op(e2, e4) = e4 % 88.37/12.70 | | | % 88.37/12.70 | | | ALPHA: (17) implies: % 88.37/12.70 | | | (18) op(e2, e4) = e4 % 88.37/12.70 | | | % 88.37/12.70 | | | REF_CLOSE: (1), (12), (13), (18) are inconsistent by sub-proof #129. % 88.37/12.70 | | | % 88.37/12.70 | | Case 2: % 88.37/12.70 | | | % 88.37/12.70 | | | (19) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 88.37/12.70 | | | e4) % 88.37/12.70 | | | % 88.37/12.70 | | | BETA: splitting (19) gives: % 88.37/12.70 | | | % 88.37/12.70 | | | Case 1: % 88.37/12.70 | | | | % 88.37/12.70 | | | | (20) all_9_12 = e4 & op(e1, e4) = e4 % 88.37/12.70 | | | | % 88.37/12.70 | | | | ALPHA: (20) implies: % 88.37/12.70 | | | | (21) all_9_12 = e4 % 88.37/12.70 | | | | % 88.37/12.70 | | | | REF_CLOSE: (3), (5), (21) are inconsistent by sub-proof #124. % 88.37/12.70 | | | | % 88.37/12.70 | | | Case 2: % 88.37/12.70 | | | | % 88.37/12.70 | | | | (22) all_9_20 = e4 & op(e0, e4) = e4 % 88.37/12.70 | | | | % 88.37/12.70 | | | | REF_CLOSE: (1), (14), (22) are inconsistent by sub-proof #91. % 88.37/12.70 | | | | % 88.37/12.70 | | | End of split % 88.37/12.70 | | | % 88.37/12.70 | | End of split % 88.37/12.70 | | % 88.37/12.70 | End of split % 88.37/12.70 | % 88.37/12.70 End of proof % 88.37/12.70 % 88.37/12.70 Sub-proof #7 shows that the following formulas are inconsistent: % 88.37/12.70 ---------------------------------------------------------------- % 88.37/12.70 (1) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.37/12.70 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.37/12.70 (all_9_20 = e3 & op(e0, e4) = e3) % 88.37/12.70 (2) ~ (e3 = e2) % 88.37/12.70 (3) op(e2, e4) = e3 % 88.37/12.70 (4) ~ (e3 = e0) % 88.37/12.70 (5) ~ (e4 = e3) % 88.37/12.70 (6) ~ (all_4_3 = e0) % 88.37/12.70 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.37/12.70 (8) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.37/12.70 (9) ~ (all_4_3 = e3) % 88.37/12.70 (10) ~ (e4 = e1) % 88.37/12.70 (11) ~ (e4 = e2) % 88.37/12.70 (12) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.37/12.70 (13) all_4_0 = e0 % 88.37/12.70 (14) ~ (all_4_3 = e1) % 88.37/12.70 (15) ~ (all_4_4 = e3) % 88.37/12.70 (16) ~ (all_4_3 = all_4_4) % 88.37/12.70 (17) ~ (e4 = e0) % 88.37/12.70 (18) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.37/12.70 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.37/12.70 (all_9_20 = e4 & op(e0, e4) = e4) % 88.37/12.70 (19) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.37/12.70 (20) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.37/12.70 (21) all_6_10 = e3 % 88.37/12.70 (22) op(e2, e2) = e4 % 88.37/12.70 (23) all_9_2 = e1 % 88.37/12.70 (24) ~ (e2 = e0) % 88.37/12.70 (25) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.37/12.70 (26) all_6_20 = all_4_4 % 88.37/12.70 (27) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.37/12.70 = e0 % 88.37/12.70 (28) ~ (e2 = e1) % 88.37/12.70 (29) e4 = e3 | ~ (op(e2, e4) = e4) % 88.37/12.70 (30) ~ (all_4_4 = e1) % 88.37/12.70 (31) op(e4, e4) = e0 % 88.37/12.70 (32) ~ (e3 = e1) % 88.37/12.70 (33) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.37/12.70 = e0 % 88.37/12.70 (34) ~ (all_4_4 = e0) % 88.37/12.70 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.70 (36) op(e0, e4) = all_4_4 % 88.37/12.70 (37) all_6_15 = all_4_3 % 88.37/12.70 (38) all_8_64 = e0 % 88.37/12.70 (39) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.37/12.70 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.37/12.70 (all_9_20 = e1 & op(e0, e4) = e1) % 88.37/12.70 (40) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 & % 88.37/12.70 op(e0, e4) = all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 % 88.37/12.70 & ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 88.37/12.70 $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = e0) & % 88.37/12.70 op(e2, e2) = e0 & op(e0, e2) = all_8_38 & $i(all_8_38)) | (all_8_48 = % 88.37/12.70 e0 & all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, e1) = e0 & op(e0, e1) % 88.37/12.70 = all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = e1 & ~ % 88.37/12.70 (all_8_63 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_8_63 & % 88.37/12.70 $i(all_8_63)) % 88.37/12.70 (41) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.37/12.70 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.37/12.70 (all_9_20 = e2 & op(e0, e4) = e2) % 88.37/12.70 (42) ~ (e1 = e0) % 88.37/12.70 % 88.37/12.70 Begin of proof % 88.37/12.70 | % 88.37/12.70 | BETA: splitting (40) gives: % 88.37/12.70 | % 88.37/12.70 | Case 1: % 88.37/12.70 | | % 88.37/12.70 | | (43) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 % 88.37/12.70 | | & op(e0, e4) = all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & % 88.37/12.70 | | all_8_64 = e3 & ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, e3) % 88.37/12.70 | | = all_8_25 & $i(all_8_25)) % 88.37/12.70 | | % 88.37/12.70 | | BETA: splitting (43) gives: % 88.37/12.70 | | % 88.37/12.70 | | Case 1: % 88.37/12.70 | | | % 88.37/12.70 | | | (44) all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, e4) = % 88.37/12.70 | | | e0 & op(e0, e4) = all_8_12 & $i(all_8_12) % 88.37/12.70 | | | % 88.37/12.70 | | | ALPHA: (44) implies: % 88.37/12.70 | | | (45) all_8_64 = e4 % 88.37/12.70 | | | % 88.37/12.70 | | | COMBINE_EQS: (38), (45) imply: % 88.37/12.70 | | | (46) e4 = e0 % 88.37/12.70 | | | % 88.37/12.70 | | | SIMP: (46) implies: % 88.37/12.70 | | | (47) e4 = e0 % 88.37/12.70 | | | % 88.37/12.70 | | | REDUCE: (17), (47) imply: % 88.37/12.70 | | | (48) $false % 88.37/12.70 | | | % 88.37/12.70 | | | CLOSE: (48) is inconsistent. % 88.37/12.70 | | | % 88.37/12.70 | | Case 2: % 88.37/12.70 | | | % 88.37/12.70 | | | (49) all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_25 = e0) & op(e3, e3) = % 88.37/12.70 | | | e0 & op(e0, e3) = all_8_25 & $i(all_8_25) % 88.37/12.70 | | | % 88.37/12.70 | | | ALPHA: (49) implies: % 88.37/12.70 | | | (50) all_8_64 = e3 % 88.37/12.70 | | | % 88.37/12.70 | | | COMBINE_EQS: (38), (50) imply: % 88.37/12.70 | | | (51) e3 = e0 % 88.37/12.70 | | | % 88.37/12.70 | | | SIMP: (51) implies: % 88.37/12.70 | | | (52) e3 = e0 % 88.37/12.70 | | | % 88.37/12.70 | | | REDUCE: (4), (52) imply: % 88.37/12.70 | | | (53) $false % 88.37/12.70 | | | % 88.37/12.70 | | | CLOSE: (53) is inconsistent. % 88.37/12.70 | | | % 88.37/12.70 | | End of split % 88.37/12.70 | | % 88.37/12.70 | Case 2: % 88.37/12.70 | | % 88.37/12.70 | | (54) (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, e2) = % 88.37/12.70 | | e0 & op(e0, e2) = all_8_38 & $i(all_8_38)) | (all_8_48 = e0 & % 88.37/12.70 | | all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, e1) = e0 & op(e0, e1) % 88.37/12.70 | | = all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = e1 & ~ % 88.37/12.70 | | (all_8_63 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_8_63 & % 88.37/12.70 | | $i(all_8_63)) % 88.37/12.70 | | % 88.37/12.70 | | BETA: splitting (54) gives: % 88.37/12.70 | | % 88.37/12.70 | | Case 1: % 88.37/12.70 | | | % 88.37/12.71 | | | (55) all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, e2) = % 88.37/12.71 | | | e0 & op(e0, e2) = all_8_38 & $i(all_8_38) % 88.37/12.71 | | | % 88.37/12.71 | | | ALPHA: (55) implies: % 88.37/12.71 | | | (56) op(e2, e2) = e0 % 88.37/12.71 | | | % 88.37/12.71 | | | REF_CLOSE: (17), (22), (35), (56) are inconsistent by sub-proof #43. % 88.37/12.71 | | | % 88.37/12.71 | | Case 2: % 88.37/12.71 | | | % 88.37/12.71 | | | (57) (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, e1) = % 88.37/12.71 | | | e0 & op(e0, e1) = all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & % 88.37/12.71 | | | all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, e1) = e0 & op(e1, % 88.37/12.71 | | | e0) = all_8_63 & $i(all_8_63)) % 88.37/12.71 | | | % 88.37/12.71 | | | BETA: splitting (57) gives: % 88.37/12.71 | | | % 88.37/12.71 | | | Case 1: % 88.37/12.71 | | | | % 88.37/12.71 | | | | (58) all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, e1) % 88.37/12.71 | | | | = e0 & op(e0, e1) = all_8_51 & $i(all_8_51) % 88.37/12.71 | | | | % 88.37/12.71 | | | | ALPHA: (58) implies: % 88.37/12.71 | | | | (59) all_8_64 = e1 % 88.37/12.71 | | | | % 88.37/12.71 | | | | COMBINE_EQS: (38), (59) imply: % 88.37/12.71 | | | | (60) e1 = e0 % 88.37/12.71 | | | | % 88.37/12.71 | | | | SIMP: (60) implies: % 88.37/12.71 | | | | (61) e1 = e0 % 88.37/12.71 | | | | % 88.37/12.71 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 88.37/12.71 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 88.37/12.71 | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), % 88.37/12.71 | | | | (33), (34), (35), (36), (37), (39), (41), (42), (61) are % 88.37/12.71 | | | | inconsistent by sub-proof #82. % 88.37/12.71 | | | | % 88.37/12.71 | | | Case 2: % 88.37/12.71 | | | | % 88.37/12.71 | | | | (62) all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, e1) % 88.37/12.71 | | | | = e0 & op(e1, e0) = all_8_63 & $i(all_8_63) % 88.37/12.71 | | | | % 88.37/12.71 | | | | ALPHA: (62) implies: % 88.37/12.71 | | | | (63) all_8_64 = e1 % 88.37/12.71 | | | | % 88.37/12.71 | | | | COMBINE_EQS: (38), (63) imply: % 88.37/12.71 | | | | (64) e1 = e0 % 88.37/12.71 | | | | % 88.37/12.71 | | | | SIMP: (64) implies: % 88.37/12.71 | | | | (65) e1 = e0 % 88.37/12.71 | | | | % 88.37/12.71 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 88.37/12.71 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 88.37/12.71 | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), % 88.37/12.71 | | | | (33), (34), (35), (36), (37), (39), (41), (42), (65) are % 88.37/12.71 | | | | inconsistent by sub-proof #82. % 88.37/12.71 | | | | % 88.37/12.71 | | | End of split % 88.37/12.71 | | | % 88.37/12.71 | | End of split % 88.37/12.71 | | % 88.37/12.71 | End of split % 88.37/12.71 | % 88.37/12.71 End of proof % 88.37/12.71 % 88.37/12.71 Sub-proof #8 shows that the following formulas are inconsistent: % 88.37/12.71 ---------------------------------------------------------------- % 88.37/12.71 (1) ~ (unit = e3) % 88.37/12.71 (2) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 88.37/12.71 (3) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) % 88.37/12.71 (4) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.37/12.71 (5) op(unit, e2) = e2 % 88.37/12.71 (6) all_4_0 = e0 % 88.37/12.71 (7) all_4_10 = e2 | ~ (op(e4, e2) = e2) % 88.37/12.71 (8) ~ (e4 = e0) % 88.37/12.71 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.37/12.71 (10) ~ (unit = e2) % 88.37/12.71 (11) ~ (op(e3, e2) = e2) % 88.37/12.71 (12) ~ (all_4_10 = all_4_13) % 88.37/12.71 (13) ~ (unit = e0) % 88.37/12.71 (14) op(unit, e4) = e4 % 88.37/12.71 % 88.37/12.71 Begin of proof % 88.37/12.71 | % 88.37/12.71 | BETA: splitting (3) gives: % 88.37/12.71 | % 88.37/12.71 | Case 1: % 88.37/12.71 | | % 88.37/12.71 | | (15) all_9_4 = e2 & op(e4, e2) = e2 % 88.37/12.71 | | % 88.37/12.71 | | ALPHA: (15) implies: % 88.37/12.71 | | (16) op(e4, e2) = e2 % 88.37/12.71 | | % 88.37/12.71 | | BETA: splitting (7) gives: % 88.37/12.71 | | % 88.37/12.71 | | Case 1: % 88.37/12.71 | | | % 88.37/12.71 | | | (17) ~ (op(e4, e2) = e2) % 88.37/12.71 | | | % 88.37/12.71 | | | PRED_UNIFY: (16), (17) imply: % 88.37/12.71 | | | (18) $false % 88.37/12.71 | | | % 88.37/12.71 | | | CLOSE: (18) is inconsistent. % 88.37/12.71 | | | % 88.37/12.71 | | Case 2: % 88.37/12.71 | | | % 88.37/12.71 | | | (19) all_4_10 = e2 % 88.37/12.71 | | | % 88.37/12.71 | | | REDUCE: (12), (19) imply: % 88.37/12.71 | | | (20) ~ (all_4_13 = e2) % 88.37/12.71 | | | % 88.37/12.71 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (13), (14), (20) are % 88.37/12.71 | | | inconsistent by sub-proof #9. % 88.37/12.71 | | | % 88.37/12.71 | | End of split % 88.37/12.71 | | % 88.37/12.71 | Case 2: % 88.37/12.71 | | % 88.37/12.71 | | (21) all_9_5 = e2 & op(e3, e2) = e2 % 88.37/12.71 | | % 88.37/12.71 | | REF_CLOSE: (11), (21) are inconsistent by sub-proof #23. % 88.37/12.71 | | % 88.37/12.71 | End of split % 88.37/12.71 | % 88.37/12.71 End of proof % 88.37/12.71 % 88.37/12.71 Sub-proof #9 shows that the following formulas are inconsistent: % 88.37/12.71 ---------------------------------------------------------------- % 88.37/12.71 (1) ~ (unit = e3) % 88.37/12.71 (2) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 88.37/12.71 (3) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.37/12.71 (4) op(unit, e2) = e2 % 88.37/12.71 (5) all_4_0 = e0 % 88.37/12.71 (6) ~ (e4 = e0) % 88.37/12.71 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.37/12.71 (8) ~ (unit = e2) % 88.37/12.71 (9) ~ (all_4_13 = e2) % 88.37/12.71 (10) ~ (unit = e0) % 88.37/12.71 (11) op(unit, e4) = e4 % 88.37/12.71 % 88.37/12.71 Begin of proof % 88.37/12.71 | % 88.37/12.71 | SIMP: (9) implies: % 88.37/12.71 | (12) ~ (all_4_13 = e2) % 88.37/12.71 | % 88.37/12.71 | BETA: splitting (7) gives: % 88.37/12.71 | % 88.37/12.71 | Case 1: % 88.37/12.71 | | % 88.37/12.71 | | (13) ~ (op(e4, e4) = e4) % 88.37/12.71 | | % 88.37/12.71 | | PRED_UNIFY: (11), (13) imply: % 88.37/12.71 | | (14) ~ (unit = e4) % 88.37/12.71 | | % 88.37/12.71 | | BETA: splitting (3) gives: % 88.37/12.71 | | % 88.37/12.71 | | Case 1: % 88.37/12.71 | | | % 88.37/12.71 | | | (15) unit = e4 % 88.37/12.71 | | | % 88.37/12.71 | | | REDUCE: (14), (15) imply: % 88.37/12.71 | | | (16) $false % 88.37/12.71 | | | % 88.37/12.71 | | | CLOSE: (16) is inconsistent. % 88.37/12.71 | | | % 88.37/12.71 | | Case 2: % 88.37/12.71 | | | % 88.37/12.71 | | | (17) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.37/12.71 | | | % 88.37/12.71 | | | BETA: splitting (17) gives: % 88.37/12.71 | | | % 88.37/12.71 | | | Case 1: % 88.37/12.71 | | | | % 88.37/12.71 | | | | (18) unit = e2 % 88.37/12.71 | | | | % 88.37/12.71 | | | | REDUCE: (8), (18) imply: % 88.37/12.71 | | | | (19) $false % 88.37/12.71 | | | | % 88.37/12.71 | | | | CLOSE: (19) is inconsistent. % 88.37/12.71 | | | | % 88.37/12.71 | | | Case 2: % 88.37/12.71 | | | | % 88.37/12.71 | | | | (20) unit = e3 | unit = e1 | unit = e0 % 88.37/12.71 | | | | % 88.37/12.71 | | | | BETA: splitting (20) gives: % 88.37/12.71 | | | | % 88.37/12.71 | | | | Case 1: % 88.37/12.71 | | | | | % 88.37/12.71 | | | | | (21) unit = e3 % 88.37/12.71 | | | | | % 88.37/12.71 | | | | | REDUCE: (1), (21) imply: % 88.37/12.71 | | | | | (22) $false % 88.37/12.71 | | | | | % 88.37/12.71 | | | | | CLOSE: (22) is inconsistent. % 88.37/12.71 | | | | | % 88.37/12.71 | | | | Case 2: % 88.37/12.71 | | | | | % 88.37/12.71 | | | | | (23) unit = e1 | unit = e0 % 88.37/12.71 | | | | | % 88.37/12.71 | | | | | BETA: splitting (23) gives: % 88.37/12.71 | | | | | % 88.37/12.71 | | | | | Case 1: % 88.37/12.71 | | | | | | % 88.37/12.71 | | | | | | (24) unit = e1 % 88.37/12.71 | | | | | | % 88.37/12.71 | | | | | | REDUCE: (4), (24) imply: % 88.37/12.71 | | | | | | (25) op(e1, e2) = e2 % 88.37/12.71 | | | | | | % 88.37/12.71 | | | | | | BETA: splitting (2) gives: % 88.37/12.71 | | | | | | % 88.37/12.71 | | | | | | Case 1: % 88.37/12.71 | | | | | | | % 88.37/12.71 | | | | | | | (26) ~ (op(e1, e2) = e2) % 88.37/12.71 | | | | | | | % 88.37/12.71 | | | | | | | PRED_UNIFY: (25), (26) imply: % 88.37/12.71 | | | | | | | (27) $false % 88.37/12.71 | | | | | | | % 88.37/12.71 | | | | | | | CLOSE: (27) is inconsistent. % 88.37/12.71 | | | | | | | % 88.37/12.71 | | | | | | Case 2: % 88.37/12.71 | | | | | | | % 88.37/12.71 | | | | | | | (28) all_4_13 = e2 % 88.37/12.71 | | | | | | | % 88.37/12.71 | | | | | | | REDUCE: (12), (28) imply: % 88.37/12.71 | | | | | | | (29) $false % 88.37/12.71 | | | | | | | % 88.37/12.71 | | | | | | | CLOSE: (29) is inconsistent. % 88.37/12.71 | | | | | | | % 88.37/12.71 | | | | | | End of split % 88.37/12.71 | | | | | | % 88.37/12.71 | | | | | Case 2: % 88.37/12.71 | | | | | | % 88.37/12.71 | | | | | | (30) ~ (unit = e1) % 88.37/12.71 | | | | | | % 88.37/12.71 | | | | | | REF_CLOSE: (10), (23), (30) are inconsistent by sub-proof #111. % 88.37/12.71 | | | | | | % 88.37/12.71 | | | | | End of split % 88.37/12.71 | | | | | % 88.37/12.71 | | | | End of split % 88.37/12.71 | | | | % 88.37/12.71 | | | End of split % 88.37/12.71 | | | % 88.37/12.71 | | End of split % 88.37/12.71 | | % 88.37/12.71 | Case 2: % 88.37/12.71 | | % 88.37/12.71 | | (31) op(e4, e4) = e4 % 88.37/12.71 | | % 88.37/12.71 | | REF_CLOSE: (5), (6), (7), (31) are inconsistent by sub-proof #131. % 88.37/12.71 | | % 88.37/12.71 | End of split % 88.37/12.71 | % 88.37/12.71 End of proof % 88.37/12.71 % 88.37/12.71 Sub-proof #10 shows that the following formulas are inconsistent: % 88.37/12.71 ---------------------------------------------------------------- % 88.37/12.71 (1) ~ (all_6_24 = e4) % 88.37/12.71 (2) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.37/12.71 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.37/12.71 (all_9_20 = e3 & op(e0, e4) = e3) % 88.37/12.71 (3) op(e0, e2) = all_4_14 % 88.37/12.71 (4) all_9_21 = e3 % 88.37/12.71 (5) op(e3, e3) = e4 % 88.37/12.71 (6) ~ (e3 = e2) % 88.37/12.71 (7) op(e2, e4) = e3 % 88.37/12.71 (8) ~ (e3 = e0) % 88.37/12.71 (9) ~ (e4 = e3) % 88.37/12.71 (10) ~ (all_4_3 = e0) % 88.37/12.71 (11) ~ (all_4_18 = e0) % 88.37/12.71 (12) ~ (op(e0, e4) = e4) % 88.37/12.71 (13) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.37/12.71 (14) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.37/12.71 (15) ~ (all_4_3 = e3) % 88.37/12.71 (16) ~ (e4 = e1) % 88.37/12.71 (17) ~ (e4 = e2) % 88.37/12.71 (18) ~ (all_4_6 = e1) % 88.37/12.71 (19) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) | % 88.37/12.71 (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & op(e0, e1) = e4) | % 88.37/12.71 (all_9_24 = e4 & op(e0, e0) = e4) % 88.37/12.71 (20) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.37/12.71 (21) all_4_0 = e0 % 88.37/12.71 (22) ~ (all_4_3 = e1) % 88.37/12.71 (23) op(e3, e3) = all_4_6 % 88.37/12.71 (24) ~ (all_4_4 = e3) % 88.37/12.71 (25) ~ (all_4_3 = all_4_4) % 88.37/12.71 (26) ~ (e4 = e0) % 88.37/12.71 (27) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.37/12.71 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.37/12.71 (all_9_20 = e4 & op(e0, e4) = e4) % 88.37/12.71 (28) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.37/12.71 (29) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.37/12.71 (30) all_9_12 = e4 % 88.37/12.71 (31) all_6_24 = all_4_24 % 88.37/12.71 (32) all_6_10 = e3 % 88.37/12.71 (33) op(e2, e2) = e4 % 88.37/12.71 (34) all_9_2 = e1 % 88.37/12.71 (35) ~ (e2 = e0) % 88.37/12.71 (36) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.37/12.71 (37) all_6_20 = all_4_4 % 88.37/12.71 (38) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.37/12.71 = e0 % 88.37/12.71 (39) ~ (e2 = e1) % 88.37/12.71 (40) e4 = e3 | ~ (op(e2, e4) = e4) % 88.37/12.71 (41) ~ (all_4_4 = e1) % 88.37/12.71 (42) op(e4, e4) = e0 % 88.37/12.71 (43) op(e1, e1) = all_4_18 % 88.37/12.71 (44) ~ (e3 = e1) % 88.37/12.71 (45) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.37/12.71 = e0 % 88.37/12.71 (46) op(e0, e0) = all_4_24 % 88.37/12.71 (47) ~ (all_4_4 = e0) % 88.37/12.71 (48) ~ (all_4_14 = e4) % 88.37/12.71 (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.71 (50) all_9_22 = e1 % 88.37/12.71 (51) op(e0, e4) = all_4_4 % 88.37/12.71 (52) all_6_15 = all_4_3 % 88.37/12.71 (53) ~ (all_4_24 = e3) % 88.37/12.71 (54) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = e3 & % 88.37/12.71 op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = e3 % 88.37/12.71 & all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = e3 & op(e4, e3) = % 88.37/12.71 all_8_15 & op(e3, e3) = e4 & $i(all_8_15)) | (all_8_0 = e2 & all_8_32 % 88.37/12.71 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 & op(e2, e4) = all_8_6 & % 88.37/12.71 op(e2, e2) = e4 & $i(all_8_6)) | (all_8_0 = e2 & all_8_32 = e4 & ~ % 88.37/12.71 (all_8_28 = e4) & op(e4, e4) = e2 & op(e4, e2) = all_8_28 & op(e2, e2) % 88.37/12.71 = e4 & $i(all_8_28)) | (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = % 88.37/12.71 e1) & op(e4, e4) = e1 & op(e1, e4) = all_8_9 & op(e1, e1) = e4 & % 88.37/12.71 $i(all_8_9)) | (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_41 = e4) & % 88.37/12.71 op(e4, e4) = e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & % 88.37/12.71 $i(all_8_41)) | (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) & % 88.37/12.71 op(e4, e4) = e0 & op(e4, e0) = all_8_54 & op(e0, e0) = e4 & % 88.37/12.71 $i(all_8_54)) | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = e2) & % 88.37/12.71 op(e3, e3) = e2 & op(e2, e3) = all_8_19 & op(e2, e2) = e3 & % 88.37/12.71 $i(all_8_19)) | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) & % 88.37/12.71 op(e3, e3) = e2 & op(e3, e2) = all_8_31 & op(e2, e2) = e3 & % 88.37/12.71 $i(all_8_31)) | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & % 88.37/12.71 op(e3, e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) = e3 & % 88.37/12.71 $i(all_8_22)) | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) & % 88.37/12.71 op(e3, e3) = e1 & op(e3, e1) = all_8_44 & op(e1, e1) = e3 & % 88.37/12.71 $i(all_8_44)) | (all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & % 88.37/12.71 op(e3, e3) = e0 & op(e3, e0) = all_8_57 & op(e0, e0) = e3 & % 88.37/12.71 $i(all_8_57)) | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) & % 88.37/12.71 op(e2, e2) = e1 & op(e1, e2) = all_8_35 & op(e1, e1) = e2 & % 88.37/12.71 $i(all_8_35)) | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & % 88.37/12.71 op(e2, e2) = e1 & op(e2, e1) = all_8_47 & op(e1, e1) = e2 & % 88.37/12.71 $i(all_8_47)) | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) & % 88.37/12.71 op(e2, e2) = e0 & op(e2, e0) = all_8_60 & op(e0, e0) = e2 & % 88.37/12.71 $i(all_8_60)) | (op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = e0 % 88.37/12.71 & all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 & op(e0, % 88.37/12.71 e4) = all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 % 88.37/12.71 & ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 88.37/12.71 $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = % 88.37/12.71 e0) & op(e2, e2) = e0 & op(e0, e2) = all_8_38 & $i(all_8_38)) | % 88.37/12.71 (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, e1) = % 88.37/12.71 e0 & op(e0, e1) = all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & % 88.37/12.71 all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, e1) = e0 & op(e1, e0) % 88.37/12.71 = all_8_63 & $i(all_8_63)))) % 88.37/12.71 (55) all_4_2 = e3 % 88.37/12.71 (56) (all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = e0 & op(e4, e0) = e0) % 88.37/12.71 | (all_9_17 = e0 & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) = % 88.37/12.71 e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & ((all_9_20 = e0 & % 88.37/12.71 op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 88.37/12.71 e0 & op(e0, e2) = e0) | (all_9_23 = e0 & op(e0, e1) = e0))) % 88.37/12.71 (57) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.37/12.71 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.37/12.71 (all_9_20 = e1 & op(e0, e4) = e1) % 88.37/12.71 (58) all_9_20 = e2 % 88.37/12.71 (59) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.37/12.71 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.37/12.71 (all_9_20 = e2 & op(e0, e4) = e2) % 88.37/12.71 (60) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.37/12.71 (61) ~ (e1 = e0) % 88.37/12.71 % 88.37/12.71 Begin of proof % 88.37/12.71 | % 88.37/12.71 | REDUCE: (1), (31) imply: % 88.37/12.71 | (62) ~ (all_4_24 = e4) % 88.37/12.71 | % 88.37/12.71 | BETA: splitting (54) gives: % 88.37/12.71 | % 88.37/12.71 | Case 1: % 88.37/12.71 | | % 88.37/12.71 | | (63) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = e3 % 88.37/12.71 | | & op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 % 88.37/12.71 | | = e3 & all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = e3 & % 88.37/12.71 | | op(e4, e3) = all_8_15 & op(e3, e3) = e4 & $i(all_8_15)) | (all_8_0 % 88.37/12.71 | | = e2 & all_8_32 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 & % 88.37/12.71 | | op(e2, e4) = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | (all_8_0 = % 88.37/12.71 | | e2 & all_8_32 = e4 & ~ (all_8_28 = e4) & op(e4, e4) = e2 & op(e4, % 88.37/12.71 | | e2) = all_8_28 & op(e2, e2) = e4 & $i(all_8_28)) | (all_8_0 = e1 % 88.37/12.71 | | & all_8_48 = e4 & ~ (all_8_9 = e1) & op(e4, e4) = e1 & op(e1, e4) % 88.37/12.71 | | = all_8_9 & op(e1, e1) = e4 & $i(all_8_9)) | (all_8_0 = e1 & % 88.37/12.71 | | all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) = e1 & op(e4, e1) % 88.37/12.71 | | = all_8_41 & op(e1, e1) = e4 & $i(all_8_41)) | (all_8_0 = e0 & % 88.37/12.71 | | all_8_64 = e4 & ~ (all_8_54 = e4) & op(e4, e4) = e0 & op(e4, e0) % 88.37/12.71 | | = all_8_54 & op(e0, e0) = e4 & $i(all_8_54)) | (all_8_16 = e2 & % 88.37/12.71 | | all_8_32 = e3 & ~ (all_8_19 = e2) & op(e3, e3) = e2 & op(e2, e3) % 88.37/12.71 | | = all_8_19 & op(e2, e2) = e3 & $i(all_8_19)) % 88.37/12.71 | | % 88.37/12.71 | | BETA: splitting (63) gives: % 88.37/12.71 | | % 88.37/12.71 | | Case 1: % 88.37/12.71 | | | % 88.37/12.71 | | | (64) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = % 88.37/12.71 | | | e3 & op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3)) | % 88.37/12.71 | | | (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = % 88.37/12.71 | | | e3 & op(e4, e3) = all_8_15 & op(e3, e3) = e4 & $i(all_8_15)) | % 88.37/12.71 | | | (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = % 88.37/12.71 | | | e2 & op(e2, e4) = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | % 88.37/12.71 | | | (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_28 = e4) & op(e4, e4) = % 88.37/12.71 | | | e2 & op(e4, e2) = all_8_28 & op(e2, e2) = e4 & $i(all_8_28)) % 88.37/12.71 | | | % 88.37/12.71 | | | REF_CLOSE: (8), (35), (42), (49), (64) are inconsistent by sub-proof #20. % 88.37/12.71 | | | % 88.37/12.71 | | Case 2: % 88.37/12.71 | | | % 88.37/12.72 | | | (65) (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = e1) & op(e4, e4) = % 88.37/12.72 | | | e1 & op(e1, e4) = all_8_9 & op(e1, e1) = e4 & $i(all_8_9)) | % 88.37/12.72 | | | (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) = % 88.37/12.72 | | | e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & $i(all_8_41)) | % 88.37/12.72 | | | (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) & op(e4, e4) = % 88.37/12.72 | | | e0 & op(e4, e0) = all_8_54 & op(e0, e0) = e4 & $i(all_8_54)) | % 88.37/12.72 | | | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = e2) & op(e3, e3) = % 88.37/12.72 | | | e2 & op(e2, e3) = all_8_19 & op(e2, e2) = e3 & $i(all_8_19)) % 88.37/12.72 | | | % 88.37/12.72 | | | BETA: splitting (65) gives: % 88.37/12.72 | | | % 88.37/12.72 | | | Case 1: % 88.37/12.72 | | | | % 88.37/12.72 | | | | (66) (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = e1) & op(e4, e4) = % 88.37/12.72 | | | | e1 & op(e1, e4) = all_8_9 & op(e1, e1) = e4 & $i(all_8_9)) | % 88.37/12.72 | | | | (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) % 88.37/12.72 | | | | = e1 & op(e4, e1) = all_8_41 & op(e1, e1) = e4 & $i(all_8_41)) % 88.37/12.72 | | | | % 88.37/12.72 | | | | REF_CLOSE: (42), (49), (61), (66) are inconsistent by sub-proof #19. % 88.37/12.72 | | | | % 88.37/12.72 | | | Case 2: % 88.37/12.72 | | | | % 88.37/12.72 | | | | (67) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) & op(e4, e4) % 88.37/12.72 | | | | = e0 & op(e4, e0) = all_8_54 & op(e0, e0) = e4 & $i(all_8_54)) % 88.37/12.72 | | | | | (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = e2) & op(e3, % 88.37/12.72 | | | | e3) = e2 & op(e2, e3) = all_8_19 & op(e2, e2) = e3 & % 88.37/12.72 | | | | $i(all_8_19)) % 88.37/12.72 | | | | % 88.37/12.72 | | | | BETA: splitting (67) gives: % 88.37/12.72 | | | | % 88.37/12.72 | | | | Case 1: % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | (68) all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_54 = e4) & op(e4, e4) % 88.37/12.72 | | | | | = e0 & op(e4, e0) = all_8_54 & op(e0, e0) = e4 & $i(all_8_54) % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | ALPHA: (68) implies: % 88.37/12.72 | | | | | (69) op(e0, e0) = e4 % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | REF_CLOSE: (46), (49), (62), (69) are inconsistent by sub-proof #18. % 88.37/12.72 | | | | | % 88.37/12.72 | | | | Case 2: % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | (70) all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_19 = e2) & op(e3, % 88.37/12.72 | | | | | e3) = e2 & op(e2, e3) = all_8_19 & op(e2, e2) = e3 & % 88.37/12.72 | | | | | $i(all_8_19) % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | ALPHA: (70) implies: % 88.37/12.72 | | | | | (71) op(e2, e2) = e3 % 88.37/12.72 | | | | | (72) op(e3, e3) = e2 % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | REF_CLOSE: (5), (6), (33), (49), (71), (72) are inconsistent by % 88.37/12.72 | | | | | sub-proof #17. % 88.37/12.72 | | | | | % 88.37/12.72 | | | | End of split % 88.37/12.72 | | | | % 88.37/12.72 | | | End of split % 88.37/12.72 | | | % 88.37/12.72 | | End of split % 88.37/12.72 | | % 88.37/12.72 | Case 2: % 88.37/12.72 | | % 88.37/12.72 | | (73) (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) & op(e3, e3) = % 88.37/12.72 | | e2 & op(e3, e2) = all_8_31 & op(e2, e2) = e3 & $i(all_8_31)) | % 88.37/12.72 | | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, e3) = % 88.37/12.72 | | e1 & op(e1, e3) = all_8_22 & op(e1, e1) = e3 & $i(all_8_22)) | % 88.37/12.72 | | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) & op(e3, e3) = % 88.37/12.72 | | e1 & op(e3, e1) = all_8_44 & op(e1, e1) = e3 & $i(all_8_44)) | % 88.37/12.72 | | (all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & op(e3, e3) = % 88.37/12.72 | | e0 & op(e3, e0) = all_8_57 & op(e0, e0) = e3 & $i(all_8_57)) | % 88.37/12.72 | | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) & op(e2, e2) = % 88.37/12.72 | | e1 & op(e1, e2) = all_8_35 & op(e1, e1) = e2 & $i(all_8_35)) | % 88.37/12.72 | | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, e2) = % 88.37/12.72 | | e1 & op(e2, e1) = all_8_47 & op(e1, e1) = e2 & $i(all_8_47)) | % 88.37/12.72 | | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) & op(e2, e2) = % 88.37/12.72 | | e0 & op(e2, e0) = all_8_60 & op(e0, e0) = e2 & $i(all_8_60)) | % 88.37/12.72 | | (op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = e0 & all_8_64 = % 88.37/12.72 | | e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 & op(e0, e4) = % 88.37/12.72 | | all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 & ~ % 88.37/12.72 | | (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 88.37/12.72 | | $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 % 88.37/12.72 | | = e0) & op(e2, e2) = e0 & op(e0, e2) = all_8_38 & % 88.37/12.72 | | $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 % 88.37/12.72 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_8_51 & % 88.37/12.72 | | $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_63 % 88.37/12.72 | | = e1) & op(e1, e1) = e0 & op(e1, e0) = all_8_63 & % 88.37/12.72 | | $i(all_8_63)))) % 88.37/12.72 | | % 88.37/12.72 | | BETA: splitting (73) gives: % 88.37/12.72 | | % 88.37/12.72 | | Case 1: % 88.37/12.72 | | | % 88.37/12.72 | | | (74) (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) & op(e3, e3) = % 88.37/12.72 | | | e2 & op(e3, e2) = all_8_31 & op(e2, e2) = e3 & $i(all_8_31)) | % 88.37/12.72 | | | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, e3) = % 88.37/12.72 | | | e1 & op(e1, e3) = all_8_22 & op(e1, e1) = e3 & $i(all_8_22)) | % 88.37/12.72 | | | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) & op(e3, e3) = % 88.37/12.72 | | | e1 & op(e3, e1) = all_8_44 & op(e1, e1) = e3 & $i(all_8_44)) | % 88.37/12.72 | | | (all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & op(e3, e3) = % 88.37/12.72 | | | e0 & op(e3, e0) = all_8_57 & op(e0, e0) = e3 & $i(all_8_57)) % 88.37/12.72 | | | % 88.37/12.72 | | | BETA: splitting (74) gives: % 88.37/12.72 | | | % 88.37/12.72 | | | Case 1: % 88.37/12.72 | | | | % 88.37/12.72 | | | | (75) (all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) & op(e3, e3) % 88.37/12.72 | | | | = e2 & op(e3, e2) = all_8_31 & op(e2, e2) = e3 & $i(all_8_31)) % 88.37/12.72 | | | | | (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, % 88.37/12.72 | | | | e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) = e3 & % 88.37/12.72 | | | | $i(all_8_22)) % 88.37/12.72 | | | | % 88.37/12.72 | | | | BETA: splitting (75) gives: % 88.37/12.72 | | | | % 88.37/12.72 | | | | Case 1: % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | (76) all_8_16 = e2 & all_8_32 = e3 & ~ (all_8_31 = e3) & op(e3, % 88.37/12.72 | | | | | e3) = e2 & op(e3, e2) = all_8_31 & op(e2, e2) = e3 & % 88.37/12.72 | | | | | $i(all_8_31) % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | ALPHA: (76) implies: % 88.37/12.72 | | | | | (77) op(e2, e2) = e3 % 88.37/12.72 | | | | | (78) op(e3, e3) = e2 % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | REF_CLOSE: (5), (6), (33), (49), (77), (78) are inconsistent by % 88.37/12.72 | | | | | sub-proof #17. % 88.37/12.72 | | | | | % 88.37/12.72 | | | | Case 2: % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | (79) all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_22 = e1) & op(e3, % 88.37/12.72 | | | | | e3) = e1 & op(e1, e3) = all_8_22 & op(e1, e1) = e3 & % 88.37/12.72 | | | | | $i(all_8_22) % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | ALPHA: (79) implies: % 88.37/12.72 | | | | | (80) op(e3, e3) = e1 % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | REF_CLOSE: (18), (23), (49), (80) are inconsistent by sub-proof #58. % 88.37/12.72 | | | | | % 88.37/12.72 | | | | End of split % 88.37/12.72 | | | | % 88.37/12.72 | | | Case 2: % 88.37/12.72 | | | | % 88.37/12.72 | | | | (81) (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) & op(e3, e3) % 88.37/12.72 | | | | = e1 & op(e3, e1) = all_8_44 & op(e1, e1) = e3 & $i(all_8_44)) % 88.37/12.72 | | | | | (all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & op(e3, % 88.37/12.72 | | | | e3) = e0 & op(e3, e0) = all_8_57 & op(e0, e0) = e3 & % 88.37/12.72 | | | | $i(all_8_57)) % 88.37/12.72 | | | | % 88.37/12.72 | | | | REF_CLOSE: (18), (23), (46), (49), (53), (81) are inconsistent by % 88.37/12.72 | | | | sub-proof #15. % 88.37/12.72 | | | | % 88.37/12.72 | | | End of split % 88.37/12.72 | | | % 88.37/12.72 | | Case 2: % 88.37/12.72 | | | % 88.37/12.72 | | | (82) (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) & op(e2, e2) = % 88.37/12.72 | | | e1 & op(e1, e2) = all_8_35 & op(e1, e1) = e2 & $i(all_8_35)) | % 88.37/12.72 | | | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, e2) = % 88.37/12.72 | | | e1 & op(e2, e1) = all_8_47 & op(e1, e1) = e2 & $i(all_8_47)) | % 88.37/12.72 | | | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) & op(e2, e2) = % 88.37/12.72 | | | e0 & op(e2, e0) = all_8_60 & op(e0, e0) = e2 & $i(all_8_60)) | % 88.37/12.72 | | | (op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = e0 & all_8_64 % 88.37/12.72 | | | = e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 & op(e0, e4) = % 88.37/12.72 | | | all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 & % 88.37/12.72 | | | ~ (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_8_25 % 88.37/12.72 | | | & $i(all_8_25)) | (all_8_32 = e0 & all_8_64 = e2 & ~ % 88.37/12.72 | | | (all_8_38 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_8_38 & % 88.37/12.72 | | | $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 & ~ % 88.37/12.72 | | | (all_8_51 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_8_51 & % 88.37/12.72 | | | $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = e1 & ~ % 88.37/12.72 | | | (all_8_63 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_8_63 & % 88.37/12.72 | | | $i(all_8_63)))) % 88.37/12.72 | | | % 88.37/12.72 | | | BETA: splitting (82) gives: % 88.37/12.72 | | | % 88.37/12.72 | | | Case 1: % 88.37/12.72 | | | | % 88.37/12.72 | | | | (83) (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) & op(e2, e2) % 88.37/12.72 | | | | = e1 & op(e1, e2) = all_8_35 & op(e1, e1) = e2 & $i(all_8_35)) % 88.37/12.72 | | | | | (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, % 88.37/12.72 | | | | e2) = e1 & op(e2, e1) = all_8_47 & op(e1, e1) = e2 & % 88.37/12.72 | | | | $i(all_8_47)) % 88.37/12.72 | | | | % 88.37/12.72 | | | | REF_CLOSE: (16), (33), (49), (83) are inconsistent by sub-proof #14. % 88.37/12.72 | | | | % 88.37/12.72 | | | Case 2: % 88.37/12.72 | | | | % 88.37/12.72 | | | | (84) (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) & op(e2, e2) % 88.37/12.72 | | | | = e0 & op(e2, e0) = all_8_60 & op(e0, e0) = e2 & $i(all_8_60)) % 88.37/12.72 | | | | | (op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = e0 & % 88.37/12.72 | | | | all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 & % 88.37/12.72 | | | | op(e0, e4) = all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & % 88.37/12.72 | | | | all_8_64 = e3 & ~ (all_8_25 = e0) & op(e3, e3) = e0 & % 88.37/12.72 | | | | op(e0, e3) = all_8_25 & $i(all_8_25)) | (all_8_32 = e0 & % 88.37/12.72 | | | | all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, e2) = e0 & % 88.37/12.72 | | | | op(e0, e2) = all_8_38 & $i(all_8_38)) | (all_8_48 = e0 & % 88.37/12.72 | | | | all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, e1) = e0 & % 88.37/12.72 | | | | op(e0, e1) = all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & % 88.37/12.72 | | | | all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, e1) = e0 & % 88.37/12.72 | | | | op(e1, e0) = all_8_63 & $i(all_8_63)))) % 88.37/12.72 | | | | % 88.37/12.72 | | | | BETA: splitting (84) gives: % 88.37/12.72 | | | | % 88.37/12.72 | | | | Case 1: % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | (85) all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_60 = e2) & op(e2, % 88.37/12.72 | | | | | e2) = e0 & op(e2, e0) = all_8_60 & op(e0, e0) = e2 & % 88.37/12.72 | | | | | $i(all_8_60) % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | ALPHA: (85) implies: % 88.37/12.72 | | | | | (86) op(e2, e2) = e0 % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | REF_CLOSE: (26), (33), (49), (86) are inconsistent by sub-proof #43. % 88.37/12.72 | | | | | % 88.37/12.72 | | | | Case 2: % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | (87) op(e0, e0) = all_8_64 & $i(all_8_64) & ((all_8_0 = e0 & % 88.37/12.72 | | | | | all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, e4) = e0 & % 88.37/12.72 | | | | | op(e0, e4) = all_8_12 & $i(all_8_12)) | (all_8_16 = e0 & % 88.37/12.72 | | | | | all_8_64 = e3 & ~ (all_8_25 = e0) & op(e3, e3) = e0 & % 88.37/12.72 | | | | | op(e0, e3) = all_8_25 & $i(all_8_25)) | (all_8_32 = e0 & % 88.37/12.72 | | | | | all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, e2) = e0 & % 88.37/12.72 | | | | | op(e0, e2) = all_8_38 & $i(all_8_38)) | (all_8_48 = e0 & % 88.37/12.72 | | | | | all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, e1) = e0 & % 88.37/12.72 | | | | | op(e0, e1) = all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & % 88.37/12.72 | | | | | all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, e1) = e0 & % 88.37/12.72 | | | | | op(e1, e0) = all_8_63 & $i(all_8_63))) % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | ALPHA: (87) implies: % 88.37/12.72 | | | | | (88) op(e0, e0) = all_8_64 % 88.37/12.72 | | | | | (89) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & op(e4, % 88.37/12.72 | | | | | e4) = e0 & op(e0, e4) = all_8_12 & $i(all_8_12)) | % 88.37/12.72 | | | | | (all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_25 = e0) & op(e3, % 88.37/12.72 | | | | | e3) = e0 & op(e0, e3) = all_8_25 & $i(all_8_25)) | % 88.37/12.72 | | | | | (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, % 88.37/12.72 | | | | | e2) = e0 & op(e0, e2) = all_8_38 & $i(all_8_38)) | % 88.37/12.72 | | | | | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, % 88.37/12.72 | | | | | e1) = e0 & op(e0, e1) = all_8_51 & $i(all_8_51)) | % 88.37/12.72 | | | | | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, % 88.37/12.72 | | | | | e1) = e0 & op(e1, e0) = all_8_63 & $i(all_8_63)) % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | BETA: splitting (19) gives: % 88.37/12.72 | | | | | % 88.37/12.72 | | | | | Case 1: % 88.37/12.72 | | | | | | % 88.37/12.72 | | | | | | (90) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, % 88.37/12.72 | | | | | | e3) = e4) % 88.37/12.72 | | | | | | % 88.37/12.72 | | | | | | REF_CLOSE: (4), (9), (12), (16), (17), (21), (26), (27), (28), (30), % 88.37/12.72 | | | | | | (34), (55), (58), (60), (90) are inconsistent by % 88.37/12.72 | | | | | | sub-proof #24. % 88.37/12.72 | | | | | | % 88.37/12.72 | | | | | Case 2: % 88.37/12.72 | | | | | | % 88.37/12.72 | | | | | | (91) (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & op(e0, % 88.37/12.72 | | | | | | e1) = e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 88.37/12.72 | | | | | | % 88.37/12.72 | | | | | | BETA: splitting (91) gives: % 88.37/12.72 | | | | | | % 88.37/12.72 | | | | | | Case 1: % 88.37/12.72 | | | | | | | % 88.37/12.72 | | | | | | | (92) all_9_22 = e4 & op(e0, e2) = e4 % 88.37/12.72 | | | | | | | % 88.37/12.72 | | | | | | | REF_CLOSE: (3), (48), (49), (92) are inconsistent by sub-proof % 88.37/12.72 | | | | | | | #53. % 88.37/12.72 | | | | | | | % 88.37/12.72 | | | | | | Case 2: % 88.37/12.72 | | | | | | | % 88.37/12.72 | | | | | | | (93) (all_9_23 = e4 & op(e0, e1) = e4) | (all_9_24 = e4 & % 88.37/12.72 | | | | | | | op(e0, e0) = e4) % 88.37/12.72 | | | | | | | % 88.37/12.72 | | | | | | | BETA: splitting (93) gives: % 88.37/12.72 | | | | | | | % 88.37/12.72 | | | | | | | Case 1: % 88.37/12.72 | | | | | | | | % 88.37/12.72 | | | | | | | | (94) all_9_23 = e4 & op(e0, e1) = e4 % 88.37/12.72 | | | | | | | | % 88.37/12.72 | | | | | | | | ALPHA: (94) implies: % 88.37/12.72 | | | | | | | | (95) all_9_23 = e4 % 88.37/12.72 | | | | | | | | % 88.37/12.72 | | | | | | | | BETA: splitting (89) gives: % 88.37/12.72 | | | | | | | | % 88.37/12.72 | | | | | | | | Case 1: % 88.37/12.72 | | | | | | | | | % 88.37/12.72 | | | | | | | | | (96) (all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & % 88.37/12.72 | | | | | | | | | op(e4, e4) = e0 & op(e0, e4) = all_8_12 & % 88.37/12.72 | | | | | | | | | $i(all_8_12)) | (all_8_16 = e0 & all_8_64 = e3 & ~ % 88.37/12.72 | | | | | | | | | (all_8_25 = e0) & op(e3, e3) = e0 & op(e0, e3) = % 88.37/12.72 | | | | | | | | | all_8_25 & $i(all_8_25)) % 88.37/12.72 | | | | | | | | | % 88.37/12.72 | | | | | | | | | BETA: splitting (96) gives: % 88.37/12.72 | | | | | | | | | % 88.37/12.72 | | | | | | | | | Case 1: % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | | (97) all_8_0 = e0 & all_8_64 = e4 & ~ (all_8_12 = e0) & % 88.37/12.72 | | | | | | | | | | op(e4, e4) = e0 & op(e0, e4) = all_8_12 & % 88.37/12.72 | | | | | | | | | | $i(all_8_12) % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | | ALPHA: (97) implies: % 88.37/12.72 | | | | | | | | | | (98) all_8_64 = e4 % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | | REDUCE: (88), (98) imply: % 88.37/12.72 | | | | | | | | | | (99) op(e0, e0) = e4 % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (13), (14), % 88.37/12.72 | | | | | | | | | | (15), (16), (17), (20), (21), (22), (24), (25), % 88.37/12.72 | | | | | | | | | | (26), (27), (28), (29), (32), (34), (35), (36), % 88.37/12.72 | | | | | | | | | | (37), (38), (39), (40), (41), (42), (44), (45), % 88.37/12.72 | | | | | | | | | | (47), (49), (50), (51), (52), (56), (57), (58), % 88.37/12.72 | | | | | | | | | | (59), (61), (95), (99) are inconsistent by % 88.37/12.72 | | | | | | | | | | sub-proof #12. % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | Case 2: % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | | (100) all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_25 = e0) % 88.37/12.72 | | | | | | | | | | & op(e3, e3) = e0 & op(e0, e3) = all_8_25 & % 88.37/12.72 | | | | | | | | | | $i(all_8_25) % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | | ALPHA: (100) implies: % 88.37/12.72 | | | | | | | | | | (101) all_8_64 = e3 % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | | REDUCE: (88), (101) imply: % 88.37/12.72 | | | | | | | | | | (102) op(e0, e0) = e3 % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | | REF_CLOSE: (46), (49), (53), (102) are inconsistent by % 88.37/12.72 | | | | | | | | | | sub-proof #16. % 88.37/12.72 | | | | | | | | | | % 88.37/12.72 | | | | | | | | | End of split % 88.37/12.72 | | | | | | | | | % 88.37/12.72 | | | | | | | | Case 2: % 88.37/12.72 | | | | | | | | | % 88.37/12.72 | | | | | | | | | (103) (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = e0) & % 88.37/12.72 | | | | | | | | | op(e2, e2) = e0 & op(e0, e2) = all_8_38 & % 88.37/12.72 | | | | | | | | | $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 & ~ % 88.37/12.72 | | | | | | | | | (all_8_51 = e0) & op(e1, e1) = e0 & op(e0, e1) = % 88.37/12.72 | | | | | | | | | all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & % 88.37/12.72 | | | | | | | | | all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, e1) = % 88.37/12.72 | | | | | | | | | e0 & op(e1, e0) = all_8_63 & $i(all_8_63)) % 88.37/12.72 | | | | | | | | | % 88.37/12.72 | | | | | | | | | REF_CLOSE: (11), (26), (33), (43), (49), (103) are % 88.37/12.72 | | | | | | | | | inconsistent by sub-proof #11. % 88.37/12.72 | | | | | | | | | % 88.37/12.72 | | | | | | | | End of split % 88.37/12.72 | | | | | | | | % 88.37/12.72 | | | | | | | Case 2: % 88.37/12.72 | | | | | | | | % 88.37/12.72 | | | | | | | | (104) all_9_24 = e4 & op(e0, e0) = e4 % 88.37/12.72 | | | | | | | | % 88.37/12.72 | | | | | | | | ALPHA: (104) implies: % 88.37/12.72 | | | | | | | | (105) op(e0, e0) = e4 % 88.37/12.72 | | | | | | | | % 88.37/12.72 | | | | | | | | REF_CLOSE: (46), (49), (62), (105) are inconsistent by sub-proof % 88.37/12.72 | | | | | | | | #18. % 88.37/12.72 | | | | | | | | % 88.37/12.72 | | | | | | | End of split % 88.37/12.72 | | | | | | | % 88.37/12.72 | | | | | | End of split % 88.37/12.72 | | | | | | % 88.37/12.72 | | | | | End of split % 88.37/12.72 | | | | | % 88.37/12.72 | | | | End of split % 88.37/12.72 | | | | % 88.37/12.72 | | | End of split % 88.37/12.72 | | | % 88.37/12.72 | | End of split % 88.37/12.72 | | % 88.37/12.72 | End of split % 88.37/12.72 | % 88.37/12.72 End of proof % 88.37/12.72 % 88.37/12.72 Sub-proof #11 shows that the following formulas are inconsistent: % 88.37/12.72 ---------------------------------------------------------------- % 88.37/12.72 (1) ~ (all_4_18 = e0) % 88.37/12.72 (2) ~ (e4 = e0) % 88.37/12.72 (3) op(e2, e2) = e4 % 88.37/12.72 (4) op(e1, e1) = all_4_18 % 88.37/12.72 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.72 (6) (all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, e2) = e0 & % 88.37/12.72 op(e0, e2) = all_8_38 & $i(all_8_38)) | (all_8_48 = e0 & all_8_64 = e1 % 88.37/12.72 & ~ (all_8_51 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_8_51 & % 88.37/12.72 $i(all_8_51)) | (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_63 = e1) & % 88.37/12.72 op(e1, e1) = e0 & op(e1, e0) = all_8_63 & $i(all_8_63)) % 88.37/12.72 % 88.37/12.72 Begin of proof % 88.37/12.72 | % 88.37/12.72 | BETA: splitting (6) gives: % 88.37/12.72 | % 88.37/12.72 | Case 1: % 88.37/12.72 | | % 88.37/12.72 | | (7) all_8_32 = e0 & all_8_64 = e2 & ~ (all_8_38 = e0) & op(e2, e2) = e0 % 88.37/12.72 | | & op(e0, e2) = all_8_38 & $i(all_8_38) % 88.37/12.72 | | % 88.37/12.72 | | ALPHA: (7) implies: % 88.37/12.73 | | (8) op(e2, e2) = e0 % 88.37/12.73 | | % 88.37/12.73 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #43. % 88.37/12.73 | | % 88.37/12.73 | Case 2: % 88.37/12.73 | | % 88.37/12.73 | | (9) (all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, e1) = e0 % 88.37/12.73 | | & op(e0, e1) = all_8_51 & $i(all_8_51)) | (all_8_48 = e0 & all_8_64 % 88.37/12.73 | | = e1 & ~ (all_8_63 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_8_63 % 88.37/12.73 | | & $i(all_8_63)) % 88.37/12.73 | | % 88.37/12.73 | | BETA: splitting (9) gives: % 88.37/12.73 | | % 88.37/12.73 | | Case 1: % 88.37/12.73 | | | % 88.37/12.73 | | | (10) all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_51 = e0) & op(e1, e1) = % 88.37/12.73 | | | e0 & op(e0, e1) = all_8_51 & $i(all_8_51) % 88.37/12.73 | | | % 88.37/12.73 | | | ALPHA: (10) implies: % 88.37/12.73 | | | (11) op(e1, e1) = e0 % 88.37/12.73 | | | % 88.37/12.73 | | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #64. % 88.37/12.73 | | | % 88.37/12.73 | | Case 2: % 88.37/12.73 | | | % 88.37/12.73 | | | (12) all_8_48 = e0 & all_8_64 = e1 & ~ (all_8_63 = e1) & op(e1, e1) = % 88.37/12.73 | | | e0 & op(e1, e0) = all_8_63 & $i(all_8_63) % 88.37/12.73 | | | % 88.37/12.73 | | | ALPHA: (12) implies: % 88.37/12.73 | | | (13) op(e1, e1) = e0 % 88.37/12.73 | | | % 88.37/12.73 | | | REF_CLOSE: (1), (4), (5), (13) are inconsistent by sub-proof #64. % 88.37/12.73 | | | % 88.37/12.73 | | End of split % 88.37/12.73 | | % 88.37/12.73 | End of split % 88.37/12.73 | % 88.37/12.73 End of proof % 88.37/12.73 % 88.37/12.73 Sub-proof #12 shows that the following formulas are inconsistent: % 88.37/12.73 ---------------------------------------------------------------- % 88.37/12.73 (1) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.37/12.73 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.37/12.73 (all_9_20 = e3 & op(e0, e4) = e3) % 88.37/12.73 (2) all_9_21 = e3 % 88.37/12.73 (3) ~ (e3 = e2) % 88.37/12.73 (4) op(e2, e4) = e3 % 88.37/12.73 (5) ~ (e3 = e0) % 88.37/12.73 (6) ~ (e4 = e3) % 88.37/12.73 (7) ~ (all_4_3 = e0) % 88.37/12.73 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.37/12.73 (9) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.37/12.73 (10) ~ (all_4_3 = e3) % 88.37/12.73 (11) ~ (e4 = e1) % 88.37/12.73 (12) ~ (e4 = e2) % 88.37/12.73 (13) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.37/12.73 (14) all_4_0 = e0 % 88.37/12.73 (15) ~ (all_4_3 = e1) % 88.37/12.73 (16) ~ (all_4_4 = e3) % 88.37/12.73 (17) ~ (all_4_3 = all_4_4) % 88.37/12.73 (18) ~ (e4 = e0) % 88.37/12.73 (19) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.37/12.73 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.37/12.73 (all_9_20 = e4 & op(e0, e4) = e4) % 88.37/12.73 (20) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.37/12.73 (21) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.37/12.73 (22) all_6_10 = e3 % 88.37/12.73 (23) all_9_2 = e1 % 88.37/12.73 (24) ~ (e2 = e0) % 88.37/12.73 (25) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.37/12.73 (26) all_6_20 = all_4_4 % 88.37/12.73 (27) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.37/12.73 = e0 % 88.37/12.73 (28) ~ (e2 = e1) % 88.37/12.73 (29) e4 = e3 | ~ (op(e2, e4) = e4) % 88.37/12.73 (30) ~ (all_4_4 = e1) % 88.37/12.73 (31) op(e4, e4) = e0 % 88.37/12.73 (32) ~ (e3 = e1) % 88.37/12.73 (33) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.37/12.73 = e0 % 88.37/12.73 (34) all_9_23 = e4 % 88.37/12.73 (35) ~ (all_4_4 = e0) % 88.37/12.73 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.73 (37) all_9_22 = e1 % 88.37/12.73 (38) op(e0, e4) = all_4_4 % 88.37/12.73 (39) all_6_15 = all_4_3 % 88.37/12.73 (40) op(e0, e0) = e4 % 88.37/12.73 (41) (all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = e0 & op(e4, e0) = e0) % 88.37/12.73 | (all_9_17 = e0 & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) = % 88.37/12.73 e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & ((all_9_20 = e0 & % 88.37/12.73 op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 88.37/12.73 e0 & op(e0, e2) = e0) | (all_9_23 = e0 & op(e0, e1) = e0))) % 88.37/12.73 (42) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.37/12.73 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.37/12.73 (all_9_20 = e1 & op(e0, e4) = e1) % 88.37/12.73 (43) all_9_20 = e2 % 88.37/12.73 (44) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.37/12.73 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.37/12.73 (all_9_20 = e2 & op(e0, e4) = e2) % 88.37/12.73 (45) ~ (e1 = e0) % 88.37/12.73 % 88.37/12.73 Begin of proof % 88.37/12.73 | % 88.37/12.73 | BETA: splitting (41) gives: % 88.37/12.73 | % 88.37/12.73 | Case 1: % 88.37/12.73 | | % 88.37/12.73 | | (46) all_9_24 = e0 & op(e0, e0) = e0 % 88.37/12.73 | | % 88.37/12.73 | | REF_CLOSE: (18), (36), (40), (46) are inconsistent by sub-proof #27. % 88.37/12.73 | | % 88.37/12.73 | Case 2: % 88.37/12.73 | | % 88.37/12.73 | | (47) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = e0 & op(e3, e0) = % 88.37/12.73 | | e0) | (all_9_18 = e0 & op(e2, e0) = e0) | (all_9_19 = e0 & % 88.37/12.73 | | op(e1, e0) = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 88.37/12.73 | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) = % 88.37/12.73 | | e0) | (all_9_23 = e0 & op(e0, e1) = e0)) % 88.37/12.73 | | % 88.37/12.73 | | ALPHA: (47) implies: % 88.37/12.73 | | (48) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = % 88.37/12.73 | | e0) | (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 & op(e0, % 88.37/12.73 | | e1) = e0) % 88.37/12.73 | | % 88.37/12.73 | | BETA: splitting (48) gives: % 88.37/12.73 | | % 88.37/12.73 | | Case 1: % 88.37/12.73 | | | % 88.37/12.73 | | | (49) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = % 88.37/12.73 | | | e0) % 88.37/12.73 | | | % 88.37/12.73 | | | BETA: splitting (49) gives: % 88.37/12.73 | | | % 88.37/12.73 | | | Case 1: % 88.37/12.73 | | | | % 88.37/12.73 | | | | (50) all_9_20 = e0 & op(e0, e4) = e0 % 88.37/12.73 | | | | % 88.37/12.73 | | | | REF_CLOSE: (24), (43), (50) are inconsistent by sub-proof #37. % 88.37/12.73 | | | | % 88.37/12.73 | | | Case 2: % 88.37/12.73 | | | | % 88.37/12.73 | | | | (51) all_9_21 = e0 & op(e0, e3) = e0 % 88.37/12.73 | | | | % 88.37/12.73 | | | | REF_CLOSE: (2), (5), (51) are inconsistent by sub-proof #26. % 88.37/12.73 | | | | % 88.37/12.73 | | | End of split % 88.37/12.73 | | | % 88.37/12.73 | | Case 2: % 88.37/12.73 | | | % 88.37/12.73 | | | (52) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 & op(e0, e1) = % 88.37/12.73 | | | e0) % 88.37/12.73 | | | % 88.37/12.73 | | | BETA: splitting (52) gives: % 88.37/12.73 | | | % 88.37/12.73 | | | Case 1: % 88.37/12.73 | | | | % 88.37/12.73 | | | | (53) all_9_22 = e0 & op(e0, e2) = e0 % 88.37/12.73 | | | | % 88.37/12.73 | | | | ALPHA: (53) implies: % 88.37/12.73 | | | | (54) all_9_22 = e0 % 88.37/12.73 | | | | % 88.37/12.73 | | | | COMBINE_EQS: (37), (54) imply: % 88.37/12.73 | | | | (55) e1 = e0 % 88.37/12.73 | | | | % 88.37/12.73 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 88.37/12.73 | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), % 88.37/12.73 | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), % 88.37/12.73 | | | | (33), (35), (36), (38), (39), (42), (44), (45), (55) are % 88.37/12.73 | | | | inconsistent by sub-proof #82. % 88.37/12.73 | | | | % 88.37/12.73 | | | Case 2: % 88.37/12.73 | | | | % 88.37/12.73 | | | | (56) all_9_23 = e0 & op(e0, e1) = e0 % 88.37/12.73 | | | | % 88.37/12.73 | | | | REF_CLOSE: (18), (34), (56) are inconsistent by sub-proof #13. % 88.37/12.73 | | | | % 88.37/12.73 | | | End of split % 88.37/12.73 | | | % 88.37/12.73 | | End of split % 88.37/12.73 | | % 88.37/12.73 | End of split % 88.37/12.73 | % 88.37/12.73 End of proof % 88.37/12.73 % 88.37/12.73 Sub-proof #13 shows that the following formulas are inconsistent: % 88.37/12.73 ---------------------------------------------------------------- % 88.37/12.73 (1) all_9_23 = e0 & op(e0, e1) = e0 % 88.37/12.73 (2) all_9_23 = e4 % 88.37/12.73 (3) ~ (e4 = e0) % 88.37/12.73 % 88.37/12.73 Begin of proof % 88.37/12.73 | % 88.37/12.73 | ALPHA: (1) implies: % 88.37/12.73 | (4) all_9_23 = e0 % 88.37/12.73 | % 88.37/12.73 | COMBINE_EQS: (2), (4) imply: % 88.37/12.73 | (5) e4 = e0 % 88.37/12.73 | % 88.37/12.73 | REDUCE: (3), (5) imply: % 88.37/12.73 | (6) $false % 88.37/12.73 | % 88.37/12.73 | CLOSE: (6) is inconsistent. % 88.37/12.73 | % 88.37/12.73 End of proof % 88.37/12.73 % 88.37/12.73 Sub-proof #14 shows that the following formulas are inconsistent: % 88.37/12.73 ---------------------------------------------------------------- % 88.37/12.73 (1) (all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) & op(e2, e2) = e1 & % 88.37/12.73 op(e1, e2) = all_8_35 & op(e1, e1) = e2 & $i(all_8_35)) | (all_8_32 = % 88.37/12.73 e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, e2) = e1 & op(e2, e1) % 88.37/12.73 = all_8_47 & op(e1, e1) = e2 & $i(all_8_47)) % 88.37/12.73 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.73 (3) op(e2, e2) = e4 % 88.37/12.73 (4) ~ (e4 = e1) % 88.37/12.73 % 88.37/12.73 Begin of proof % 88.37/12.73 | % 88.37/12.73 | BETA: splitting (1) gives: % 88.37/12.73 | % 88.37/12.73 | Case 1: % 88.37/12.73 | | % 88.37/12.73 | | (5) all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_35 = e1) & op(e2, e2) = e1 % 88.37/12.73 | | & op(e1, e2) = all_8_35 & op(e1, e1) = e2 & $i(all_8_35) % 88.37/12.73 | | % 88.37/12.73 | | ALPHA: (5) implies: % 88.37/12.73 | | (6) op(e2, e2) = e1 % 88.37/12.73 | | % 88.37/12.73 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #22. % 88.37/12.73 | | % 88.37/12.73 | Case 2: % 88.37/12.73 | | % 88.37/12.73 | | (7) all_8_32 = e1 & all_8_48 = e2 & ~ (all_8_47 = e2) & op(e2, e2) = e1 % 88.37/12.73 | | & op(e2, e1) = all_8_47 & op(e1, e1) = e2 & $i(all_8_47) % 88.37/12.73 | | % 88.37/12.73 | | ALPHA: (7) implies: % 88.37/12.73 | | (8) op(e2, e2) = e1 % 88.37/12.73 | | % 88.37/12.73 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #22. % 88.37/12.73 | | % 88.37/12.73 | End of split % 88.37/12.73 | % 88.37/12.73 End of proof % 88.37/12.73 % 88.37/12.73 Sub-proof #15 shows that the following formulas are inconsistent: % 88.37/12.73 ---------------------------------------------------------------- % 88.37/12.73 (1) (all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) & op(e3, e3) = e1 & % 88.37/12.73 op(e3, e1) = all_8_44 & op(e1, e1) = e3 & $i(all_8_44)) | (all_8_16 = % 88.37/12.73 e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & op(e3, e3) = e0 & op(e3, e0) % 88.37/12.73 = all_8_57 & op(e0, e0) = e3 & $i(all_8_57)) % 88.37/12.73 (2) ~ (all_4_6 = e1) % 88.37/12.73 (3) op(e3, e3) = all_4_6 % 88.37/12.73 (4) op(e0, e0) = all_4_24 % 88.37/12.73 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.73 (6) ~ (all_4_24 = e3) % 88.37/12.73 % 88.37/12.73 Begin of proof % 88.37/12.73 | % 88.37/12.73 | BETA: splitting (1) gives: % 88.37/12.73 | % 88.37/12.73 | Case 1: % 88.37/12.73 | | % 88.37/12.73 | | (7) all_8_16 = e1 & all_8_48 = e3 & ~ (all_8_44 = e3) & op(e3, e3) = e1 % 88.37/12.73 | | & op(e3, e1) = all_8_44 & op(e1, e1) = e3 & $i(all_8_44) % 88.37/12.73 | | % 88.37/12.73 | | ALPHA: (7) implies: % 88.37/12.73 | | (8) op(e3, e3) = e1 % 88.37/12.73 | | % 88.37/12.73 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #58. % 88.37/12.73 | | % 88.37/12.73 | Case 2: % 88.37/12.73 | | % 88.37/12.73 | | (9) all_8_16 = e0 & all_8_64 = e3 & ~ (all_8_57 = e3) & op(e3, e3) = e0 % 88.37/12.73 | | & op(e3, e0) = all_8_57 & op(e0, e0) = e3 & $i(all_8_57) % 88.37/12.73 | | % 88.37/12.73 | | ALPHA: (9) implies: % 88.37/12.73 | | (10) op(e0, e0) = e3 % 88.37/12.73 | | % 88.37/12.73 | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #16. % 88.37/12.73 | | % 88.37/12.73 | End of split % 88.37/12.73 | % 88.37/12.73 End of proof % 88.37/12.73 % 88.37/12.73 Sub-proof #16 shows that the following formulas are inconsistent: % 88.37/12.73 ---------------------------------------------------------------- % 88.37/12.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.73 (2) op(e0, e0) = all_4_24 % 88.37/12.73 (3) op(e0, e0) = e3 % 88.37/12.73 (4) ~ (all_4_24 = e3) % 88.37/12.73 % 88.37/12.73 Begin of proof % 88.37/12.73 | % 88.37/12.74 | GROUND_INST: instantiating (1) with all_4_24, e3, e0, e0, simplifying with % 88.37/12.74 | (2), (3) gives: % 88.37/12.74 | (5) all_4_24 = e3 % 88.37/12.74 | % 88.37/12.74 | REDUCE: (4), (5) imply: % 88.37/12.74 | (6) $false % 88.37/12.74 | % 88.37/12.74 | CLOSE: (6) is inconsistent. % 88.37/12.74 | % 88.37/12.74 End of proof % 88.37/12.74 % 88.37/12.74 Sub-proof #17 shows that the following formulas are inconsistent: % 88.37/12.74 ---------------------------------------------------------------- % 88.37/12.74 (1) op(e3, e3) = e4 % 88.37/12.74 (2) ~ (e3 = e2) % 88.37/12.74 (3) op(e2, e2) = e4 % 88.37/12.74 (4) op(e2, e2) = e3 % 88.37/12.74 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.74 (6) op(e3, e3) = e2 % 88.37/12.74 % 88.37/12.74 Begin of proof % 88.37/12.74 | % 88.37/12.74 | GROUND_INST: instantiating (5) with e4, e3, e2, e2, simplifying with (3), (4) % 88.37/12.74 | gives: % 88.37/12.74 | (7) e4 = e3 % 88.37/12.74 | % 88.37/12.74 | GROUND_INST: instantiating (5) with e4, e2, e3, e3, simplifying with (1), (6) % 88.37/12.74 | gives: % 88.37/12.74 | (8) e4 = e2 % 88.37/12.74 | % 88.37/12.74 | COMBINE_EQS: (7), (8) imply: % 88.37/12.74 | (9) e3 = e2 % 88.37/12.74 | % 88.37/12.74 | SIMP: (9) implies: % 88.37/12.74 | (10) e3 = e2 % 88.37/12.74 | % 88.37/12.74 | REDUCE: (2), (10) imply: % 88.37/12.74 | (11) $false % 88.37/12.74 | % 88.37/12.74 | CLOSE: (11) is inconsistent. % 88.37/12.74 | % 88.37/12.74 End of proof % 88.37/12.74 % 88.37/12.74 Sub-proof #18 shows that the following formulas are inconsistent: % 88.37/12.74 ---------------------------------------------------------------- % 88.37/12.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.74 (2) op(e0, e0) = all_4_24 % 88.37/12.74 (3) op(e0, e0) = e4 % 88.37/12.74 (4) ~ (all_4_24 = e4) % 88.37/12.74 % 88.37/12.74 Begin of proof % 88.37/12.74 | % 88.37/12.74 | GROUND_INST: instantiating (1) with all_4_24, e4, e0, e0, simplifying with % 88.37/12.74 | (2), (3) gives: % 88.37/12.74 | (5) all_4_24 = e4 % 88.37/12.74 | % 88.37/12.74 | REDUCE: (4), (5) imply: % 88.37/12.74 | (6) $false % 88.37/12.74 | % 88.37/12.74 | CLOSE: (6) is inconsistent. % 88.37/12.74 | % 88.37/12.74 End of proof % 88.37/12.74 % 88.37/12.74 Sub-proof #19 shows that the following formulas are inconsistent: % 88.37/12.74 ---------------------------------------------------------------- % 88.37/12.74 (1) (all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = e1) & op(e4, e4) = e1 & % 88.37/12.74 op(e1, e4) = all_8_9 & op(e1, e1) = e4 & $i(all_8_9)) | (all_8_0 = e1 & % 88.37/12.74 all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) = e1 & op(e4, e1) = % 88.37/12.74 all_8_41 & op(e1, e1) = e4 & $i(all_8_41)) % 88.37/12.74 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.74 (3) op(e4, e4) = e0 % 88.37/12.74 (4) ~ (e1 = e0) % 88.37/12.74 % 88.37/12.74 Begin of proof % 88.37/12.74 | % 88.37/12.74 | BETA: splitting (1) gives: % 88.37/12.74 | % 88.37/12.74 | Case 1: % 88.37/12.74 | | % 88.37/12.74 | | (5) all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_9 = e1) & op(e4, e4) = e1 & % 88.37/12.74 | | op(e1, e4) = all_8_9 & op(e1, e1) = e4 & $i(all_8_9) % 88.37/12.74 | | % 88.37/12.74 | | ALPHA: (5) implies: % 88.37/12.74 | | (6) op(e4, e4) = e1 % 88.37/12.74 | | % 88.37/12.74 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #132. % 88.37/12.74 | | % 88.37/12.74 | Case 2: % 88.37/12.74 | | % 88.37/12.74 | | (7) all_8_0 = e1 & all_8_48 = e4 & ~ (all_8_41 = e4) & op(e4, e4) = e1 & % 88.37/12.74 | | op(e4, e1) = all_8_41 & op(e1, e1) = e4 & $i(all_8_41) % 88.37/12.74 | | % 88.37/12.74 | | ALPHA: (7) implies: % 88.37/12.74 | | (8) op(e4, e4) = e1 % 88.37/12.74 | | % 88.37/12.74 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #132. % 88.37/12.74 | | % 88.37/12.74 | End of split % 88.37/12.74 | % 88.37/12.74 End of proof % 88.37/12.74 % 88.37/12.74 Sub-proof #20 shows that the following formulas are inconsistent: % 88.37/12.74 ---------------------------------------------------------------- % 88.37/12.74 (1) ~ (e3 = e0) % 88.37/12.74 (2) ~ (e2 = e0) % 88.37/12.74 (3) op(e4, e4) = e0 % 88.37/12.74 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.74 (5) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = e3 & % 88.37/12.74 op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = e3 & % 88.37/12.74 all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = e3 & op(e4, e3) = % 88.37/12.74 all_8_15 & op(e3, e3) = e4 & $i(all_8_15)) | (all_8_0 = e2 & all_8_32 = % 88.37/12.74 e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 & op(e2, e4) = all_8_6 & % 88.37/12.74 op(e2, e2) = e4 & $i(all_8_6)) | (all_8_0 = e2 & all_8_32 = e4 & ~ % 88.37/12.74 (all_8_28 = e4) & op(e4, e4) = e2 & op(e4, e2) = all_8_28 & op(e2, e2) % 88.37/12.74 = e4 & $i(all_8_28)) % 88.37/12.74 % 88.37/12.74 Begin of proof % 88.37/12.74 | % 88.37/12.74 | BETA: splitting (5) gives: % 88.37/12.74 | % 88.37/12.74 | Case 1: % 88.37/12.74 | | % 88.37/12.74 | | (6) (all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = e3 & % 88.37/12.74 | | op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3)) | (all_8_0 = % 88.37/12.74 | | e3 & all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = e3 & op(e4, % 88.37/12.74 | | e3) = all_8_15 & op(e3, e3) = e4 & $i(all_8_15)) % 88.37/12.74 | | % 88.37/12.74 | | BETA: splitting (6) gives: % 88.37/12.74 | | % 88.37/12.74 | | Case 1: % 88.37/12.74 | | | % 88.37/12.74 | | | (7) all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_3 = e3) & op(e4, e4) = e3 % 88.37/12.74 | | | & op(e3, e4) = all_8_3 & op(e3, e3) = e4 & $i(all_8_3) % 88.37/12.74 | | | % 88.37/12.74 | | | ALPHA: (7) implies: % 88.37/12.74 | | | (8) op(e4, e4) = e3 % 88.37/12.74 | | | % 88.37/12.74 | | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #105. % 88.37/12.74 | | | % 88.37/12.74 | | Case 2: % 88.37/12.74 | | | % 88.37/12.74 | | | (9) all_8_0 = e3 & all_8_16 = e4 & ~ (all_8_15 = e4) & op(e4, e4) = e3 % 88.37/12.74 | | | & op(e4, e3) = all_8_15 & op(e3, e3) = e4 & $i(all_8_15) % 88.37/12.74 | | | % 88.37/12.74 | | | ALPHA: (9) implies: % 88.37/12.74 | | | (10) op(e4, e4) = e3 % 88.37/12.74 | | | % 88.37/12.74 | | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #105. % 88.37/12.74 | | | % 88.37/12.74 | | End of split % 88.37/12.74 | | % 88.37/12.74 | Case 2: % 88.37/12.74 | | % 88.37/12.74 | | (11) (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 % 88.37/12.74 | | & op(e2, e4) = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | (all_8_0 % 88.37/12.74 | | = e2 & all_8_32 = e4 & ~ (all_8_28 = e4) & op(e4, e4) = e2 & % 88.37/12.74 | | op(e4, e2) = all_8_28 & op(e2, e2) = e4 & $i(all_8_28)) % 88.37/12.74 | | % 88.37/12.74 | | REF_CLOSE: (2), (3), (4), (11) are inconsistent by sub-proof #21. % 88.37/12.74 | | % 88.37/12.74 | End of split % 88.37/12.74 | % 88.37/12.74 End of proof % 88.37/12.74 % 88.37/12.74 Sub-proof #21 shows that the following formulas are inconsistent: % 88.37/12.74 ---------------------------------------------------------------- % 88.37/12.74 (1) (all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 & % 88.37/12.74 op(e2, e4) = all_8_6 & op(e2, e2) = e4 & $i(all_8_6)) | (all_8_0 = e2 & % 88.37/12.74 all_8_32 = e4 & ~ (all_8_28 = e4) & op(e4, e4) = e2 & op(e4, e2) = % 88.37/12.74 all_8_28 & op(e2, e2) = e4 & $i(all_8_28)) % 88.37/12.74 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.74 (3) op(e4, e4) = e0 % 88.37/12.74 (4) ~ (e2 = e0) % 88.37/12.74 % 88.37/12.74 Begin of proof % 88.37/12.74 | % 88.37/12.74 | BETA: splitting (1) gives: % 88.37/12.74 | % 88.37/12.74 | Case 1: % 88.37/12.74 | | % 88.37/12.74 | | (5) all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_6 = e2) & op(e4, e4) = e2 & % 88.37/12.74 | | op(e2, e4) = all_8_6 & op(e2, e2) = e4 & $i(all_8_6) % 88.37/12.74 | | % 88.37/12.74 | | ALPHA: (5) implies: % 88.37/12.74 | | (6) op(e4, e4) = e2 % 88.37/12.74 | | % 88.37/12.74 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #128. % 88.37/12.74 | | % 88.37/12.74 | Case 2: % 88.37/12.74 | | % 88.37/12.74 | | (7) all_8_0 = e2 & all_8_32 = e4 & ~ (all_8_28 = e4) & op(e4, e4) = e2 & % 88.37/12.74 | | op(e4, e2) = all_8_28 & op(e2, e2) = e4 & $i(all_8_28) % 88.37/12.74 | | % 88.37/12.74 | | ALPHA: (7) implies: % 88.37/12.74 | | (8) op(e4, e4) = e2 % 88.37/12.74 | | % 88.37/12.74 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #128. % 88.37/12.74 | | % 88.37/12.74 | End of split % 88.37/12.74 | % 88.37/12.74 End of proof % 88.37/12.74 % 88.37/12.74 Sub-proof #22 shows that the following formulas are inconsistent: % 88.37/12.74 ---------------------------------------------------------------- % 88.37/12.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.37/12.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.37/12.74 (2) op(e2, e2) = e4 % 88.37/12.74 (3) op(e2, e2) = e1 % 88.37/12.74 (4) ~ (e4 = e1) % 88.37/12.74 % 88.37/12.74 Begin of proof % 88.37/12.74 | % 88.37/12.74 | GROUND_INST: instantiating (1) with e4, e1, e2, e2, simplifying with (2), (3) % 88.37/12.74 | gives: % 88.37/12.74 | (5) e4 = e1 % 88.37/12.74 | % 88.37/12.74 | REDUCE: (4), (5) imply: % 88.37/12.74 | (6) $false % 88.37/12.74 | % 88.37/12.74 | CLOSE: (6) is inconsistent. % 88.37/12.74 | % 88.37/12.74 End of proof % 88.37/12.74 % 88.37/12.74 Sub-proof #23 shows that the following formulas are inconsistent: % 88.37/12.74 ---------------------------------------------------------------- % 88.37/12.74 (1) all_9_5 = e2 & op(e3, e2) = e2 % 88.37/12.74 (2) ~ (op(e3, e2) = e2) % 88.37/12.74 % 88.37/12.74 Begin of proof % 88.37/12.74 | % 88.37/12.74 | ALPHA: (1) implies: % 88.37/12.74 | (3) op(e3, e2) = e2 % 88.37/12.74 | % 88.37/12.74 | PRED_UNIFY: (2), (3) imply: % 88.37/12.74 | (4) $false % 88.37/12.74 | % 88.37/12.74 | CLOSE: (4) is inconsistent. % 88.37/12.74 | % 88.37/12.74 End of proof % 88.37/12.74 % 88.37/12.74 Sub-proof #24 shows that the following formulas are inconsistent: % 88.37/12.74 ---------------------------------------------------------------- % 88.37/12.74 (1) all_9_21 = e3 % 88.37/12.74 (2) ~ (e4 = e3) % 88.37/12.74 (3) ~ (op(e0, e4) = e4) % 88.37/12.74 (4) ~ (e4 = e1) % 88.37/12.74 (5) ~ (e4 = e2) % 88.37/12.74 (6) all_4_0 = e0 % 88.37/12.74 (7) ~ (e4 = e0) % 88.37/12.74 (8) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.37/12.74 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.37/12.74 (all_9_20 = e4 & op(e0, e4) = e4) % 88.37/12.74 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.37/12.74 (10) all_9_12 = e4 % 88.37/12.74 (11) all_9_2 = e1 % 88.37/12.74 (12) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) % 88.37/12.74 (13) all_4_2 = e3 % 88.37/12.74 (14) all_9_20 = e2 % 88.37/12.74 (15) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.37/12.74 % 88.37/12.74 Begin of proof % 88.37/12.74 | % 88.37/12.74 | BETA: splitting (12) gives: % 88.37/12.74 | % 88.37/12.74 | Case 1: % 88.37/12.74 | | % 88.37/12.74 | | (16) all_9_20 = e4 & op(e0, e4) = e4 % 88.37/12.74 | | % 88.37/12.74 | | REF_CLOSE: (3), (16) are inconsistent by sub-proof #54. % 88.37/12.74 | | % 88.37/12.74 | Case 2: % 88.37/12.74 | | % 88.37/12.74 | | (17) all_9_21 = e4 & op(e0, e3) = e4 % 88.37/12.74 | | % 88.37/12.74 | | ALPHA: (17) implies: % 88.37/12.74 | | (18) all_9_21 = e4 % 88.37/12.74 | | % 88.37/12.74 | | COMBINE_EQS: (1), (18) imply: % 88.37/12.74 | | (19) e4 = e3 % 88.37/12.74 | | % 88.37/12.74 | | SIMP: (19) implies: % 88.37/12.74 | | (20) e4 = e3 % 88.37/12.74 | | % 88.37/12.74 | | COMBINE_EQS: (10), (20) imply: % 88.37/12.74 | | (21) all_9_12 = e3 % 88.37/12.74 | | % 88.37/12.74 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (13), (14), (15), (21) % 88.37/12.74 | | are inconsistent by sub-proof #117. % 88.37/12.74 | | % 88.37/12.74 | End of split % 88.37/12.74 | % 88.37/12.74 End of proof % 88.37/12.74 % 88.37/12.74 Sub-proof #25 shows that the following formulas are inconsistent: % 88.37/12.74 ---------------------------------------------------------------- % 88.69/12.74 (1) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.69/12.74 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.69/12.74 (all_9_20 = e3 & op(e0, e4) = e3) % 88.69/12.74 (2) ~ (e3 = e2) % 88.69/12.74 (3) op(e2, e4) = e3 % 88.69/12.74 (4) ~ (e3 = e0) % 88.69/12.74 (5) ~ (e4 = e3) % 88.69/12.74 (6) ~ (all_4_3 = e0) % 88.69/12.74 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.69/12.74 (8) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.69/12.74 (9) ~ (all_4_3 = e3) % 88.69/12.74 (10) ~ (e4 = e1) % 88.69/12.74 (11) ~ (e4 = e2) % 88.69/12.74 (12) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.69/12.74 (13) all_4_0 = e0 % 88.69/12.74 (14) ~ (all_4_3 = e1) % 88.69/12.74 (15) ~ (all_4_4 = e3) % 88.69/12.74 (16) ~ (all_4_3 = all_4_4) % 88.69/12.74 (17) ~ (e4 = e0) % 88.69/12.74 (18) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.69/12.74 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.69/12.74 (all_9_20 = e4 & op(e0, e4) = e4) % 88.69/12.74 (19) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.69/12.74 (20) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.69/12.74 (21) all_6_22 = e1 % 88.69/12.74 (22) all_6_10 = e3 % 88.69/12.74 (23) all_9_2 = e1 % 88.69/12.74 (24) ~ (e2 = e0) % 88.69/12.74 (25) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.69/12.74 (26) all_6_20 = all_4_4 % 88.69/12.74 (27) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.69/12.74 = e0 % 88.69/12.74 (28) ~ (e2 = e1) % 88.69/12.74 (29) op(e0, e2) = e0 % 88.69/12.74 (30) e4 = e3 | ~ (op(e2, e4) = e4) % 88.69/12.74 (31) all_6_22 = e0 | ~ (op(e0, e2) = e0) % 88.69/12.74 (32) ~ (all_4_4 = e1) % 88.69/12.74 (33) op(e4, e4) = e0 % 88.69/12.74 (34) ~ (e3 = e1) % 88.69/12.74 (35) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.69/12.74 = e0 % 88.69/12.74 (36) ~ (all_4_4 = e0) % 88.69/12.75 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.69/12.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.69/12.75 (38) op(e0, e4) = all_4_4 % 88.69/12.75 (39) all_6_15 = all_4_3 % 88.69/12.75 (40) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.69/12.75 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.69/12.75 (all_9_20 = e1 & op(e0, e4) = e1) % 88.69/12.75 (41) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.69/12.75 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.69/12.75 (all_9_20 = e2 & op(e0, e4) = e2) % 88.69/12.75 (42) ~ (e1 = e0) % 88.69/12.75 % 88.69/12.75 Begin of proof % 88.69/12.75 | % 88.69/12.75 | BETA: splitting (31) gives: % 88.69/12.75 | % 88.69/12.75 | Case 1: % 88.69/12.75 | | % 88.69/12.75 | | (43) ~ (op(e0, e2) = e0) % 88.69/12.75 | | % 88.69/12.75 | | PRED_UNIFY: (29), (43) imply: % 88.69/12.75 | | (44) $false % 88.69/12.75 | | % 88.69/12.75 | | CLOSE: (44) is inconsistent. % 88.69/12.75 | | % 88.69/12.75 | Case 2: % 88.69/12.75 | | % 88.69/12.75 | | (45) all_6_22 = e0 % 88.69/12.75 | | % 88.69/12.75 | | COMBINE_EQS: (21), (45) imply: % 88.69/12.75 | | (46) e1 = e0 % 88.69/12.75 | | % 88.69/12.75 | | SIMP: (46) implies: % 88.69/12.75 | | (47) e1 = e0 % 88.69/12.75 | | % 88.69/12.75 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 88.69/12.75 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), % 88.69/12.75 | | (25), (26), (27), (28), (30), (32), (33), (34), (35), (36), (37), % 88.69/12.75 | | (38), (39), (40), (41), (42), (47) are inconsistent by sub-proof % 88.69/12.75 | | #82. % 88.69/12.75 | | % 88.69/12.75 | End of split % 88.69/12.75 | % 88.69/12.75 End of proof % 88.69/12.75 % 88.69/12.75 Sub-proof #26 shows that the following formulas are inconsistent: % 88.69/12.75 ---------------------------------------------------------------- % 88.69/12.75 (1) all_9_21 = e0 & op(e0, e3) = e0 % 88.69/12.75 (2) all_9_21 = e3 % 88.69/12.75 (3) ~ (e3 = e0) % 88.69/12.75 % 88.69/12.75 Begin of proof % 88.69/12.75 | % 88.69/12.75 | ALPHA: (1) implies: % 88.69/12.75 | (4) all_9_21 = e0 % 88.69/12.75 | % 88.69/12.75 | COMBINE_EQS: (2), (4) imply: % 88.69/12.75 | (5) e3 = e0 % 88.69/12.75 | % 88.69/12.75 | REDUCE: (3), (5) imply: % 88.69/12.75 | (6) $false % 88.69/12.75 | % 88.69/12.75 | CLOSE: (6) is inconsistent. % 88.69/12.75 | % 88.69/12.75 End of proof % 88.69/12.75 % 88.69/12.75 Sub-proof #27 shows that the following formulas are inconsistent: % 88.69/12.75 ---------------------------------------------------------------- % 88.69/12.75 (1) all_9_24 = e0 & op(e0, e0) = e0 % 88.69/12.75 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.69/12.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.69/12.75 (3) op(e0, e0) = e4 % 88.69/12.75 (4) ~ (e4 = e0) % 88.69/12.75 % 88.69/12.75 Begin of proof % 88.69/12.75 | % 88.69/12.75 | ALPHA: (1) implies: % 88.69/12.75 | (5) op(e0, e0) = e0 % 88.69/12.75 | % 88.69/12.75 | GROUND_INST: instantiating (2) with e0, e4, e0, e0, simplifying with (3), (5) % 88.69/12.75 | gives: % 88.69/12.75 | (6) e4 = e0 % 88.69/12.75 | % 88.69/12.75 | REDUCE: (4), (6) imply: % 88.69/12.75 | (7) $false % 88.69/12.75 | % 88.69/12.75 | CLOSE: (7) is inconsistent. % 88.69/12.75 | % 88.69/12.75 End of proof % 88.69/12.75 % 88.69/12.75 Sub-proof #28 shows that the following formulas are inconsistent: % 88.69/12.75 ---------------------------------------------------------------- % 88.69/12.75 (1) all_9_1 = e4 & op(e4, e3) = e4 % 88.69/12.75 (2) ~ (op(e4, e3) = e4) % 88.69/12.75 % 88.69/12.75 Begin of proof % 88.69/12.75 | % 88.69/12.75 | ALPHA: (1) implies: % 88.69/12.75 | (3) op(e4, e3) = e4 % 88.69/12.75 | % 88.69/12.75 | PRED_UNIFY: (2), (3) imply: % 88.69/12.75 | (4) $false % 88.69/12.75 | % 88.69/12.75 | CLOSE: (4) is inconsistent. % 88.69/12.75 | % 88.69/12.75 End of proof % 88.69/12.75 % 88.69/12.75 Sub-proof #29 shows that the following formulas are inconsistent: % 88.69/12.75 ---------------------------------------------------------------- % 88.69/12.75 (1) ~ (all_4_20 = e4) % 88.69/12.75 (2) ~ (all_4_10 = e0) % 88.69/12.75 (3) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.69/12.75 (4) ~ (all_4_15 = e4) % 88.69/12.75 (5) op(e2, e4) = e3 % 88.69/12.75 (6) ~ (e4 = e3) % 88.69/12.75 (7) all_6_5 = e1 % 88.69/12.75 (8) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 88.69/12.75 (9) op(e1, e4) = e4 % 88.69/12.75 (10) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 88.69/12.75 (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 88.69/12.75 (all_9_16 = e4 & op(e4, e0) = e4) % 88.69/12.75 (11) ~ (e4 = e1) % 88.69/12.75 (12) ~ (e4 = e2) % 88.69/12.75 (13) e3 = e1 | ~ (op(e3, e4) = e3) % 88.69/12.75 (14) all_4_0 = e0 % 88.69/12.75 (15) ~ (e4 = e0) % 88.69/12.75 (16) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.69/12.75 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.69/12.75 (all_9_20 = e4 & op(e0, e4) = e4) % 88.69/12.75 (17) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.69/12.75 (18) ~ (unit = e2) % 88.69/12.75 (19) all_9_12 = e4 % 88.69/12.75 (20) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 88.69/12.75 (21) op(e3, unit) = e3 % 88.69/12.75 (22) ~ (all_4_10 = e4) % 88.69/12.75 (23) all_9_2 = e1 % 88.69/12.75 (24) all_6_2 = all_4_10 % 88.69/12.75 (25) op(e4, e4) = e0 % 88.69/12.75 (26) ~ (e3 = e1) % 88.69/12.75 (27) op(e0, e4) = e2 % 88.69/12.75 (28) op(e3, e4) = e1 % 88.69/12.75 (29) ~ (unit = e0) % 88.69/12.75 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.69/12.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.69/12.75 (31) all_4_15 = e4 | ~ (op(e4, e1) = e4) % 88.69/12.75 (32) (all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, all_8_3) = e3 & op(e3, % 88.69/12.75 all_8_3) = all_8_2 & op(e3, e4) = all_8_3 & $i(all_8_2) & % 88.69/12.75 $i(all_8_3)) | (all_8_4 = e2 & ~ (all_8_5 = e4) & op(e4, all_8_6) = % 88.69/12.75 e2 & op(e2, all_8_6) = all_8_5 & op(e2, e4) = all_8_6 & $i(all_8_5) & % 88.69/12.75 $i(all_8_6)) | (all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) = % 88.69/12.75 e1 & op(e1, all_8_9) = all_8_8 & op(e1, e4) = all_8_9 & $i(all_8_8) & % 88.69/12.75 $i(all_8_9)) | (all_8_10 = e0 & ~ (all_8_11 = e4) & op(e4, all_8_12) % 88.69/12.75 = e0 & op(e0, all_8_12) = all_8_11 & op(e0, e4) = all_8_12 & % 88.69/12.75 $i(all_8_11) & $i(all_8_12)) % 88.69/12.75 (33) all_4_2 = e3 % 88.69/12.75 (34) op(e4, e2) = all_4_10 % 88.69/12.75 (35) op(e4, unit) = e4 % 88.69/12.75 (36) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 88.69/12.75 (37) op(unit, e4) = e4 % 88.69/12.75 (38) all_9_20 = e2 % 88.69/12.75 (39) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.69/12.75 (40) ~ (e1 = e0) % 88.69/12.75 % 88.69/12.75 Begin of proof % 88.69/12.75 | % 88.69/12.75 | BETA: splitting (32) gives: % 88.69/12.75 | % 88.69/12.75 | Case 1: % 88.69/12.75 | | % 88.69/12.75 | | (41) (all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, all_8_3) = e3 & op(e3, % 88.69/12.75 | | all_8_3) = all_8_2 & op(e3, e4) = all_8_3 & $i(all_8_2) & % 88.69/12.75 | | $i(all_8_3)) | (all_8_4 = e2 & ~ (all_8_5 = e4) & op(e4, all_8_6) % 88.69/12.75 | | = e2 & op(e2, all_8_6) = all_8_5 & op(e2, e4) = all_8_6 & % 88.69/12.75 | | $i(all_8_5) & $i(all_8_6)) % 88.69/12.75 | | % 88.69/12.75 | | BETA: splitting (41) gives: % 88.69/12.75 | | % 88.69/12.75 | | Case 1: % 88.69/12.75 | | | % 88.69/12.75 | | | (42) all_8_1 = e3 & ~ (all_8_2 = e4) & op(e4, all_8_3) = e3 & op(e3, % 88.69/12.75 | | | all_8_3) = all_8_2 & op(e3, e4) = all_8_3 & $i(all_8_2) & % 88.69/12.75 | | | $i(all_8_3) % 88.69/12.75 | | | % 88.69/12.75 | | | ALPHA: (42) implies: % 88.69/12.75 | | | (43) op(e3, e4) = all_8_3 % 88.69/12.75 | | | (44) op(e4, all_8_3) = e3 % 88.69/12.75 | | | % 88.69/12.75 | | | REF_CLOSE: (3), (6), (7), (11), (12), (13), (14), (15), (16), (17), (18), % 88.69/12.75 | | | (19), (21), (23), (26), (28), (29), (30), (33), (35), (36), % 88.69/12.75 | | | (37), (38), (39), (43), (44) are inconsistent by sub-proof % 88.69/12.75 | | | #110. % 88.69/12.75 | | | % 88.69/12.75 | | Case 2: % 88.69/12.75 | | | % 88.69/12.75 | | | (45) all_8_4 = e2 & ~ (all_8_5 = e4) & op(e4, all_8_6) = e2 & op(e2, % 88.69/12.75 | | | all_8_6) = all_8_5 & op(e2, e4) = all_8_6 & $i(all_8_5) & % 88.69/12.75 | | | $i(all_8_6) % 88.69/12.75 | | | % 88.69/12.75 | | | ALPHA: (45) implies: % 88.69/12.75 | | | (46) op(e2, e4) = all_8_6 % 88.69/12.75 | | | (47) op(e4, all_8_6) = e2 % 88.69/12.75 | | | % 88.69/12.75 | | | BETA: splitting (10) gives: % 88.69/12.75 | | | % 88.69/12.75 | | | Case 1: % 88.69/12.75 | | | | % 88.69/12.75 | | | | (48) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = % 88.69/12.75 | | | | e4) % 88.69/12.75 | | | | % 88.69/12.75 | | | | BETA: splitting (48) gives: % 88.69/12.75 | | | | % 88.69/12.75 | | | | Case 1: % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | (49) all_9_0 = e4 & op(e4, e4) = e4 % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | ALPHA: (49) implies: % 88.69/12.75 | | | | | (50) op(e4, e4) = e4 % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | REF_CLOSE: (14), (15), (17), (50) are inconsistent by sub-proof #131. % 88.69/12.75 | | | | | % 88.69/12.75 | | | | Case 2: % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | (51) all_9_1 = e4 & op(e4, e3) = e4 % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | ALPHA: (51) implies: % 88.69/12.75 | | | | | (52) op(e4, e3) = e4 % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | GROUND_INST: instantiating (30) with e3, all_8_6, e4, e2, simplifying % 88.69/12.75 | | | | | with (5), (46) gives: % 88.69/12.75 | | | | | (53) all_8_6 = e3 % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | GROUND_INST: instantiating (30) with e4, e2, e3, e4, simplifying with % 88.69/12.75 | | | | | (52) gives: % 88.69/12.75 | | | | | (54) e4 = e2 | ~ (op(e4, e3) = e2) % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | REDUCE: (47), (53) imply: % 88.69/12.75 | | | | | (55) op(e4, e3) = e2 % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | BETA: splitting (54) gives: % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | Case 1: % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | (56) ~ (op(e4, e3) = e2) % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | PRED_UNIFY: (55), (56) imply: % 88.69/12.75 | | | | | | (57) $false % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | CLOSE: (57) is inconsistent. % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | Case 2: % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | (58) e4 = e2 % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | REDUCE: (12), (58) imply: % 88.69/12.75 | | | | | | (59) $false % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | CLOSE: (59) is inconsistent. % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | End of split % 88.69/12.75 | | | | | % 88.69/12.75 | | | | End of split % 88.69/12.75 | | | | % 88.69/12.75 | | | Case 2: % 88.69/12.75 | | | | % 88.69/12.75 | | | | (60) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = % 88.69/12.75 | | | | e4) | (all_9_16 = e4 & op(e4, e0) = e4) % 88.69/12.75 | | | | % 88.69/12.75 | | | | BETA: splitting (60) gives: % 88.69/12.75 | | | | % 88.69/12.75 | | | | Case 1: % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | (61) all_9_4 = e4 & op(e4, e2) = e4 % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | REF_CLOSE: (20), (22), (24), (61) are inconsistent by sub-proof #120. % 88.69/12.75 | | | | | % 88.69/12.75 | | | | Case 2: % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | (62) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) % 88.69/12.75 | | | | | = e4) % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | BETA: splitting (62) gives: % 88.69/12.75 | | | | | % 88.69/12.75 | | | | | Case 1: % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | (63) all_9_9 = e4 & op(e4, e1) = e4 % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | REF_CLOSE: (4), (31), (63) are inconsistent by sub-proof #32. % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | Case 2: % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | (64) all_9_16 = e4 & op(e4, e0) = e4 % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | | REF_CLOSE: (1), (8), (64) are inconsistent by sub-proof #116. % 88.69/12.75 | | | | | | % 88.69/12.75 | | | | | End of split % 88.69/12.75 | | | | | % 88.69/12.75 | | | | End of split % 88.69/12.75 | | | | % 88.69/12.75 | | | End of split % 88.69/12.75 | | | % 88.69/12.75 | | End of split % 88.69/12.75 | | % 88.69/12.75 | Case 2: % 88.69/12.75 | | % 88.69/12.75 | | (65) (all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) = e1 & op(e1, % 88.69/12.75 | | all_8_9) = all_8_8 & op(e1, e4) = all_8_9 & $i(all_8_8) & % 88.69/12.75 | | $i(all_8_9)) | (all_8_10 = e0 & ~ (all_8_11 = e4) & op(e4, % 88.69/12.75 | | all_8_12) = e0 & op(e0, all_8_12) = all_8_11 & op(e0, e4) = % 88.69/12.75 | | all_8_12 & $i(all_8_11) & $i(all_8_12)) % 88.69/12.75 | | % 88.69/12.75 | | REF_CLOSE: (2), (9), (25), (27), (30), (34), (40), (65) are inconsistent by % 88.69/12.75 | | sub-proof #30. % 88.69/12.75 | | % 88.69/12.75 | End of split % 88.69/12.75 | % 88.69/12.75 End of proof % 88.69/12.75 % 88.69/12.75 Sub-proof #30 shows that the following formulas are inconsistent: % 88.69/12.75 ---------------------------------------------------------------- % 88.69/12.75 (1) ~ (all_4_10 = e0) % 88.69/12.75 (2) (all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) = e1 & op(e1, % 88.69/12.75 all_8_9) = all_8_8 & op(e1, e4) = all_8_9 & $i(all_8_8) & % 88.69/12.75 $i(all_8_9)) | (all_8_10 = e0 & ~ (all_8_11 = e4) & op(e4, all_8_12) = % 88.69/12.75 e0 & op(e0, all_8_12) = all_8_11 & op(e0, e4) = all_8_12 & $i(all_8_11) % 88.69/12.75 & $i(all_8_12)) % 88.69/12.75 (3) op(e1, e4) = e4 % 88.69/12.75 (4) op(e4, e4) = e0 % 88.69/12.75 (5) op(e0, e4) = e2 % 88.69/12.75 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.69/12.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.69/12.75 (7) op(e4, e2) = all_4_10 % 88.69/12.75 (8) ~ (e1 = e0) % 88.69/12.75 % 88.69/12.75 Begin of proof % 88.69/12.75 | % 88.69/12.75 | BETA: splitting (2) gives: % 88.69/12.75 | % 88.69/12.75 | Case 1: % 88.69/12.75 | | % 88.69/12.75 | | (9) all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) = e1 & op(e1, % 88.69/12.75 | | all_8_9) = all_8_8 & op(e1, e4) = all_8_9 & $i(all_8_8) & % 88.69/12.75 | | $i(all_8_9) % 88.69/12.75 | | % 88.69/12.75 | | REF_CLOSE: (3), (4), (6), (8), (9) are inconsistent by sub-proof #31. % 88.69/12.75 | | % 88.69/12.75 | Case 2: % 88.69/12.75 | | % 88.69/12.75 | | (10) all_8_10 = e0 & ~ (all_8_11 = e4) & op(e4, all_8_12) = e0 & op(e0, % 88.69/12.75 | | all_8_12) = all_8_11 & op(e0, e4) = all_8_12 & $i(all_8_11) & % 88.69/12.75 | | $i(all_8_12) % 88.69/12.75 | | % 88.69/12.75 | | ALPHA: (10) implies: % 88.69/12.75 | | (11) op(e0, e4) = all_8_12 % 88.69/12.76 | | (12) op(e4, all_8_12) = e0 % 88.69/12.76 | | % 88.69/12.76 | | GROUND_INST: instantiating (6) with e2, all_8_12, e4, e0, simplifying with % 88.69/12.76 | | (5), (11) gives: % 88.69/12.76 | | (13) all_8_12 = e2 % 88.69/12.76 | | % 88.69/12.76 | | REF_CLOSE: (1), (6), (7), (12), (13) are inconsistent by sub-proof #40. % 88.69/12.76 | | % 88.69/12.76 | End of split % 88.69/12.76 | % 88.69/12.76 End of proof % 88.69/12.76 % 88.69/12.76 Sub-proof #31 shows that the following formulas are inconsistent: % 88.69/12.76 ---------------------------------------------------------------- % 88.69/12.76 (1) op(e1, e4) = e4 % 88.69/12.76 (2) all_8_7 = e1 & ~ (all_8_8 = e4) & op(e4, all_8_9) = e1 & op(e1, all_8_9) % 88.69/12.76 = all_8_8 & op(e1, e4) = all_8_9 & $i(all_8_8) & $i(all_8_9) % 88.69/12.76 (3) op(e4, e4) = e0 % 88.69/12.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.69/12.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.69/12.76 (5) ~ (e1 = e0) % 88.69/12.76 % 88.69/12.76 Begin of proof % 88.69/12.76 | % 88.69/12.76 | ALPHA: (2) implies: % 88.69/12.76 | (6) op(e1, e4) = all_8_9 % 88.69/12.76 | (7) op(e4, all_8_9) = e1 % 88.69/12.76 | % 88.69/12.76 | GROUND_INST: instantiating (4) with e4, all_8_9, e4, e1, simplifying with (1), % 88.69/12.76 | (6) gives: % 88.69/12.76 | (8) all_8_9 = e4 % 88.69/12.76 | % 88.69/12.76 | REDUCE: (7), (8) imply: % 88.69/12.76 | (9) op(e4, e4) = e1 % 88.69/12.76 | % 88.69/12.76 | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #132. % 88.69/12.76 | % 88.69/12.76 End of proof % 88.69/12.76 % 88.69/12.76 Sub-proof #32 shows that the following formulas are inconsistent: % 88.69/12.76 ---------------------------------------------------------------- % 88.69/12.76 (1) all_9_9 = e4 & op(e4, e1) = e4 % 88.69/12.76 (2) all_4_15 = e4 | ~ (op(e4, e1) = e4) % 88.69/12.76 (3) ~ (all_4_15 = e4) % 88.69/12.76 % 88.69/12.76 Begin of proof % 88.69/12.76 | % 88.69/12.76 | ALPHA: (1) implies: % 88.69/12.76 | (4) op(e4, e1) = e4 % 88.69/12.76 | % 88.69/12.76 | BETA: splitting (2) gives: % 88.69/12.76 | % 88.69/12.76 | Case 1: % 88.69/12.76 | | % 88.69/12.76 | | (5) ~ (op(e4, e1) = e4) % 88.69/12.76 | | % 88.69/12.76 | | PRED_UNIFY: (4), (5) imply: % 88.69/12.76 | | (6) $false % 88.69/12.76 | | % 88.69/12.76 | | CLOSE: (6) is inconsistent. % 88.69/12.76 | | % 88.69/12.76 | Case 2: % 88.69/12.76 | | % 88.69/12.76 | | (7) all_4_15 = e4 % 88.69/12.76 | | % 88.69/12.76 | | REDUCE: (3), (7) imply: % 88.69/12.76 | | (8) $false % 88.69/12.76 | | % 88.69/12.76 | | CLOSE: (8) is inconsistent. % 88.69/12.76 | | % 88.69/12.76 | End of split % 88.69/12.76 | % 88.69/12.76 End of proof % 88.69/12.76 % 88.69/12.76 Sub-proof #33 shows that the following formulas are inconsistent: % 88.69/12.76 ---------------------------------------------------------------- % 88.69/12.76 (1) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.69/12.76 (2) ~ (e4 = e3) % 88.69/12.76 (3) all_6_5 = e1 % 88.69/12.76 (4) ~ (e4 = e1) % 88.69/12.76 (5) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.69/12.76 (6) ~ (all_4_3 = e1) % 88.69/12.76 (7) op(e1, unit) = e1 % 88.69/12.76 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 88.69/12.76 (9) ~ (unit = e0) % 88.69/12.76 (10) all_4_2 = e3 % 88.69/12.76 (11) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 88.69/12.76 (12) ~ (unit = e1) % 88.69/12.76 (13) op(unit, e4) = e4 % 88.69/12.76 (14) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.69/12.76 % 88.69/12.76 Begin of proof % 88.69/12.76 | % 88.69/12.76 | BETA: splitting (11) gives: % 88.69/12.76 | % 88.69/12.76 | Case 1: % 88.69/12.76 | | % 88.69/12.76 | | (15) ~ (op(e3, e4) = e4) % 88.69/12.76 | | % 88.69/12.76 | | PRED_UNIFY: (13), (15) imply: % 88.69/12.76 | | (16) ~ (unit = e3) % 88.69/12.76 | | % 88.69/12.76 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (12), (13), (14), (16) % 88.69/12.76 | | are inconsistent by sub-proof #34. % 88.69/12.76 | | % 88.69/12.76 | Case 2: % 88.69/12.76 | | % 88.69/12.76 | | (17) all_6_5 = e4 % 88.69/12.76 | | % 88.69/12.76 | | COMBINE_EQS: (3), (17) imply: % 88.69/12.76 | | (18) e4 = e1 % 88.69/12.76 | | % 88.69/12.76 | | REDUCE: (4), (18) imply: % 88.69/12.76 | | (19) $false % 88.69/12.76 | | % 88.69/12.76 | | CLOSE: (19) is inconsistent. % 88.69/12.76 | | % 88.69/12.76 | End of split % 88.69/12.76 | % 88.69/12.76 End of proof % 88.69/12.76 % 88.69/12.76 Sub-proof #34 shows that the following formulas are inconsistent: % 88.69/12.76 ---------------------------------------------------------------- % 88.69/12.76 (1) ~ (unit = e3) % 88.69/12.76 (2) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.69/12.76 (3) ~ (e4 = e3) % 88.69/12.76 (4) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.69/12.76 (5) ~ (all_4_3 = e1) % 88.69/12.76 (6) op(e1, unit) = e1 % 88.69/12.76 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 88.69/12.76 (8) ~ (unit = e0) % 88.69/12.76 (9) all_4_2 = e3 % 88.69/12.76 (10) ~ (unit = e1) % 88.69/12.76 (11) op(unit, e4) = e4 % 88.69/12.76 (12) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.69/12.76 % 88.69/12.76 Begin of proof % 88.69/12.76 | % 88.69/12.76 | BETA: splitting (7) gives: % 88.69/12.76 | % 88.69/12.76 | Case 1: % 88.69/12.76 | | % 88.69/12.76 | | (13) ~ (op(e2, e4) = e4) % 88.69/12.76 | | % 88.69/12.76 | | PRED_UNIFY: (11), (13) imply: % 88.69/12.76 | | (14) ~ (unit = e2) % 88.69/12.76 | | % 88.69/12.76 | | BETA: splitting (2) gives: % 88.69/12.76 | | % 88.69/12.76 | | Case 1: % 88.69/12.76 | | | % 88.69/12.76 | | | (15) unit = e4 % 88.69/12.76 | | | % 88.69/12.76 | | | REDUCE: (6), (15) imply: % 88.69/12.76 | | | (16) op(e1, e4) = e1 % 88.69/12.76 | | | % 88.69/12.76 | | | REF_CLOSE: (4), (5), (16) are inconsistent by sub-proof #87. % 88.69/12.76 | | | % 88.69/12.76 | | Case 2: % 88.69/12.76 | | | % 88.69/12.76 | | | (17) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.69/12.76 | | | % 88.69/12.76 | | | BETA: splitting (17) gives: % 88.69/12.76 | | | % 88.69/12.76 | | | Case 1: % 88.69/12.76 | | | | % 88.69/12.76 | | | | (18) unit = e2 % 88.69/12.76 | | | | % 88.69/12.76 | | | | REDUCE: (14), (18) imply: % 88.69/12.76 | | | | (19) $false % 88.69/12.76 | | | | % 88.69/12.76 | | | | CLOSE: (19) is inconsistent. % 88.69/12.76 | | | | % 88.69/12.76 | | | Case 2: % 88.69/12.76 | | | | % 88.69/12.76 | | | | (20) unit = e3 | unit = e1 | unit = e0 % 88.69/12.76 | | | | % 88.69/12.76 | | | | BETA: splitting (20) gives: % 88.69/12.76 | | | | % 88.69/12.76 | | | | Case 1: % 88.69/12.76 | | | | | % 88.69/12.76 | | | | | (21) unit = e3 % 88.69/12.76 | | | | | % 88.69/12.76 | | | | | REDUCE: (1), (21) imply: % 88.69/12.76 | | | | | (22) $false % 88.69/12.76 | | | | | % 88.69/12.76 | | | | | CLOSE: (22) is inconsistent. % 88.69/12.76 | | | | | % 88.69/12.76 | | | | Case 2: % 88.69/12.76 | | | | | % 88.69/12.76 | | | | | (23) unit = e1 | unit = e0 % 88.69/12.76 | | | | | % 88.69/12.76 | | | | | REF_CLOSE: (8), (10), (23) are inconsistent by sub-proof #111. % 88.69/12.76 | | | | | % 88.69/12.76 | | | | End of split % 88.69/12.76 | | | | % 88.69/12.76 | | | End of split % 88.69/12.76 | | | % 88.69/12.76 | | End of split % 88.69/12.76 | | % 88.69/12.76 | Case 2: % 88.69/12.76 | | % 88.69/12.76 | | (24) op(e2, e4) = e4 % 88.69/12.76 | | % 88.69/12.76 | | REF_CLOSE: (3), (9), (12), (24) are inconsistent by sub-proof #129. % 88.69/12.76 | | % 88.69/12.76 | End of split % 88.69/12.76 | % 88.69/12.76 End of proof % 88.69/12.76 % 88.69/12.76 Sub-proof #35 shows that the following formulas are inconsistent: % 88.69/12.76 ---------------------------------------------------------------- % 88.69/12.76 (1) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.69/12.76 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.69/12.76 (all_9_20 = e3 & op(e0, e4) = e3) % 88.69/12.76 (2) ~ (e3 = e2) % 88.69/12.76 (3) op(e2, e4) = e3 % 88.69/12.76 (4) ~ (e3 = e0) % 88.69/12.76 (5) ~ (e4 = e3) % 88.69/12.76 (6) all_9_23 = e0 % 88.69/12.76 (7) ~ (all_4_3 = e0) % 88.69/12.76 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.69/12.76 (9) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.69/12.76 (10) ~ (all_4_3 = e3) % 88.69/12.76 (11) ~ (e4 = e1) % 88.69/12.76 (12) ~ (e4 = e2) % 88.69/12.76 (13) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.69/12.76 (14) all_4_0 = e0 % 88.69/12.76 (15) ~ (all_4_3 = e1) % 88.69/12.76 (16) ~ (all_4_4 = e3) % 88.69/12.76 (17) ~ (all_4_3 = all_4_4) % 88.69/12.76 (18) all_9_23 = e1 & op(e0, e1) = e1 % 88.69/12.76 (19) ~ (e4 = e0) % 88.69/12.76 (20) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.69/12.76 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.69/12.76 (all_9_20 = e4 & op(e0, e4) = e4) % 88.69/12.76 (21) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.69/12.76 (22) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.69/12.76 (23) all_6_10 = e3 % 88.69/12.76 (24) all_9_2 = e1 % 88.69/12.76 (25) ~ (e2 = e0) % 88.69/12.76 (26) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.69/12.76 (27) all_6_20 = all_4_4 % 88.69/12.76 (28) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.69/12.76 = e0 % 88.69/12.76 (29) ~ (e2 = e1) % 88.69/12.76 (30) e4 = e3 | ~ (op(e2, e4) = e4) % 88.69/12.76 (31) ~ (all_4_4 = e1) % 88.69/12.76 (32) op(e4, e4) = e0 % 88.69/12.76 (33) ~ (e3 = e1) % 88.69/12.76 (34) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.69/12.76 = e0 % 88.69/12.76 (35) ~ (all_4_4 = e0) % 88.69/12.76 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.69/12.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.69/12.76 (37) op(e0, e4) = all_4_4 % 88.69/12.76 (38) all_6_15 = all_4_3 % 88.69/12.76 (39) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.69/12.76 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.69/12.76 (all_9_20 = e1 & op(e0, e4) = e1) % 88.77/12.76 (40) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.77/12.76 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.77/12.76 (all_9_20 = e2 & op(e0, e4) = e2) % 88.77/12.76 (41) ~ (e1 = e0) % 88.77/12.76 % 88.77/12.76 Begin of proof % 88.77/12.76 | % 88.77/12.76 | ALPHA: (18) implies: % 88.77/12.76 | (42) all_9_23 = e1 % 88.77/12.76 | % 88.77/12.76 | COMBINE_EQS: (6), (42) imply: % 88.77/12.76 | (43) e1 = e0 % 88.77/12.76 | % 88.77/12.76 | SIMP: (43) implies: % 88.77/12.76 | (44) e1 = e0 % 88.77/12.76 | % 88.77/12.76 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), % 88.77/12.76 | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), % 88.77/12.76 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 88.77/12.76 | (37), (38), (39), (40), (41), (44) are inconsistent by sub-proof % 88.77/12.76 | #82. % 88.77/12.76 | % 88.77/12.76 End of proof % 88.77/12.76 % 88.77/12.76 Sub-proof #36 shows that the following formulas are inconsistent: % 88.77/12.76 ---------------------------------------------------------------- % 88.77/12.76 (1) all_4_9 = e0 | ~ (op(e0, e3) = e0) % 88.77/12.76 (2) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = e0) % 88.77/12.76 (3) ~ (e2 = e0) % 88.77/12.76 (4) ~ (all_4_9 = e0) % 88.77/12.76 (5) all_9_20 = e2 % 88.77/12.76 % 88.77/12.76 Begin of proof % 88.77/12.76 | % 88.77/12.76 | BETA: splitting (2) gives: % 88.77/12.76 | % 88.77/12.76 | Case 1: % 88.77/12.76 | | % 88.77/12.76 | | (6) all_9_20 = e0 & op(e0, e4) = e0 % 88.77/12.76 | | % 88.77/12.76 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #37. % 88.77/12.76 | | % 88.77/12.76 | Case 2: % 88.77/12.76 | | % 88.77/12.76 | | (7) all_9_21 = e0 & op(e0, e3) = e0 % 88.77/12.76 | | % 88.77/12.76 | | ALPHA: (7) implies: % 88.77/12.76 | | (8) op(e0, e3) = e0 % 88.77/12.76 | | % 88.77/12.76 | | BETA: splitting (1) gives: % 88.77/12.76 | | % 88.77/12.76 | | Case 1: % 88.77/12.76 | | | % 88.77/12.76 | | | (9) ~ (op(e0, e3) = e0) % 88.77/12.76 | | | % 88.77/12.76 | | | PRED_UNIFY: (8), (9) imply: % 88.77/12.76 | | | (10) $false % 88.77/12.76 | | | % 88.77/12.76 | | | CLOSE: (10) is inconsistent. % 88.77/12.76 | | | % 88.77/12.76 | | Case 2: % 88.77/12.76 | | | % 88.77/12.76 | | | (11) all_4_9 = e0 % 88.77/12.76 | | | % 88.77/12.76 | | | REDUCE: (4), (11) imply: % 88.77/12.76 | | | (12) $false % 88.77/12.76 | | | % 88.77/12.76 | | | CLOSE: (12) is inconsistent. % 88.77/12.76 | | | % 88.77/12.76 | | End of split % 88.77/12.76 | | % 88.77/12.76 | End of split % 88.77/12.76 | % 88.77/12.76 End of proof % 88.77/12.76 % 88.77/12.76 Sub-proof #37 shows that the following formulas are inconsistent: % 88.77/12.76 ---------------------------------------------------------------- % 88.77/12.76 (1) all_9_20 = e0 & op(e0, e4) = e0 % 88.77/12.76 (2) all_9_20 = e2 % 88.77/12.76 (3) ~ (e2 = e0) % 88.77/12.76 % 88.77/12.76 Begin of proof % 88.77/12.76 | % 88.77/12.76 | ALPHA: (1) implies: % 88.77/12.76 | (4) all_9_20 = e0 % 88.77/12.76 | % 88.77/12.76 | COMBINE_EQS: (2), (4) imply: % 88.77/12.76 | (5) e2 = e0 % 88.77/12.76 | % 88.77/12.76 | REDUCE: (3), (5) imply: % 88.77/12.76 | (6) $false % 88.77/12.76 | % 88.77/12.76 | CLOSE: (6) is inconsistent. % 88.77/12.76 | % 88.77/12.76 End of proof % 88.77/12.76 % 88.77/12.76 Sub-proof #38 shows that the following formulas are inconsistent: % 88.77/12.76 ---------------------------------------------------------------- % 88.77/12.76 (1) all_9_24 = e0 & op(e0, e0) = e0 % 88.77/12.76 (2) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 88.77/12.76 (3) all_6_24 = all_4_24 % 88.77/12.76 (4) ~ (all_4_24 = e0) % 88.77/12.76 % 88.77/12.76 Begin of proof % 88.77/12.76 | % 88.77/12.76 | ALPHA: (1) implies: % 88.77/12.76 | (5) op(e0, e0) = e0 % 88.77/12.76 | % 88.77/12.76 | BETA: splitting (2) gives: % 88.77/12.76 | % 88.77/12.76 | Case 1: % 88.77/12.76 | | % 88.77/12.76 | | (6) ~ (op(e0, e0) = e0) % 88.77/12.76 | | % 88.77/12.76 | | PRED_UNIFY: (5), (6) imply: % 88.77/12.76 | | (7) $false % 88.77/12.76 | | % 88.77/12.76 | | CLOSE: (7) is inconsistent. % 88.77/12.76 | | % 88.77/12.76 | Case 2: % 88.77/12.76 | | % 88.77/12.76 | | (8) all_6_24 = e0 % 88.77/12.76 | | % 88.77/12.76 | | COMBINE_EQS: (3), (8) imply: % 88.77/12.76 | | (9) all_4_24 = e0 % 88.77/12.76 | | % 88.77/12.76 | | SIMP: (9) implies: % 88.77/12.76 | | (10) all_4_24 = e0 % 88.77/12.76 | | % 88.77/12.76 | | REDUCE: (4), (10) imply: % 88.77/12.76 | | (11) $false % 88.77/12.76 | | % 88.77/12.76 | | CLOSE: (11) is inconsistent. % 88.77/12.76 | | % 88.77/12.76 | End of split % 88.77/12.76 | % 88.77/12.76 End of proof % 88.77/12.76 % 88.77/12.76 Sub-proof #39 shows that the following formulas are inconsistent: % 88.77/12.76 ---------------------------------------------------------------- % 88.77/12.76 (1) all_9_11 = e3 & op(e2, e1) = e3 % 88.77/12.76 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.76 (3) op(e2, e1) = all_4_17 % 88.77/12.76 (4) ~ (all_4_17 = e3) % 88.77/12.76 % 88.77/12.76 Begin of proof % 88.77/12.76 | % 88.77/12.76 | ALPHA: (1) implies: % 88.77/12.76 | (5) op(e2, e1) = e3 % 88.77/12.76 | % 88.77/12.76 | GROUND_INST: instantiating (2) with all_4_17, e3, e1, e2, simplifying with % 88.77/12.76 | (3), (5) gives: % 88.77/12.76 | (6) all_4_17 = e3 % 88.77/12.76 | % 88.77/12.76 | REDUCE: (4), (6) imply: % 88.77/12.76 | (7) $false % 88.77/12.76 | % 88.77/12.76 | CLOSE: (7) is inconsistent. % 88.77/12.76 | % 88.77/12.76 End of proof % 88.77/12.76 % 88.77/12.76 Sub-proof #40 shows that the following formulas are inconsistent: % 88.77/12.76 ---------------------------------------------------------------- % 88.77/12.77 (1) ~ (all_4_10 = e0) % 88.77/12.77 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.77 (3) op(e4, all_8_12) = e0 % 88.77/12.77 (4) all_8_12 = e2 % 88.77/12.77 (5) op(e4, e2) = all_4_10 % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | GROUND_INST: instantiating (2) with all_4_10, e0, e2, e4, simplifying with (5) % 88.77/12.77 | gives: % 88.77/12.77 | (6) all_4_10 = e0 | ~ (op(e4, e2) = e0) % 88.77/12.77 | % 88.77/12.77 | REDUCE: (3), (4) imply: % 88.77/12.77 | (7) op(e4, e2) = e0 % 88.77/12.77 | % 88.77/12.77 | BETA: splitting (6) gives: % 88.77/12.77 | % 88.77/12.77 | Case 1: % 88.77/12.77 | | % 88.77/12.77 | | (8) ~ (op(e4, e2) = e0) % 88.77/12.77 | | % 88.77/12.77 | | PRED_UNIFY: (7), (8) imply: % 88.77/12.77 | | (9) $false % 88.77/12.77 | | % 88.77/12.77 | | CLOSE: (9) is inconsistent. % 88.77/12.77 | | % 88.77/12.77 | Case 2: % 88.77/12.77 | | % 88.77/12.77 | | (10) all_4_10 = e0 % 88.77/12.77 | | % 88.77/12.77 | | REDUCE: (1), (10) imply: % 88.77/12.77 | | (11) $false % 88.77/12.77 | | % 88.77/12.77 | | CLOSE: (11) is inconsistent. % 88.77/12.77 | | % 88.77/12.77 | End of split % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #41 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_9_22 = e0 & op(e0, e2) = e0 % 88.77/12.77 (2) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 88.77/12.77 (3) ~ (all_4_14 = e0) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | ALPHA: (1) implies: % 88.77/12.77 | (4) op(e0, e2) = e0 % 88.77/12.77 | % 88.77/12.77 | BETA: splitting (2) gives: % 88.77/12.77 | % 88.77/12.77 | Case 1: % 88.77/12.77 | | % 88.77/12.77 | | (5) ~ (op(e0, e2) = e0) % 88.77/12.77 | | % 88.77/12.77 | | PRED_UNIFY: (4), (5) imply: % 88.77/12.77 | | (6) $false % 88.77/12.77 | | % 88.77/12.77 | | CLOSE: (6) is inconsistent. % 88.77/12.77 | | % 88.77/12.77 | Case 2: % 88.77/12.77 | | % 88.77/12.77 | | (7) all_4_14 = e0 % 88.77/12.77 | | % 88.77/12.77 | | REDUCE: (3), (7) imply: % 88.77/12.77 | | (8) $false % 88.77/12.77 | | % 88.77/12.77 | | CLOSE: (8) is inconsistent. % 88.77/12.77 | | % 88.77/12.77 | End of split % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #42 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_9_18 = e0 & op(e2, e0) = e0 % 88.77/12.77 (2) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 88.77/12.77 (3) all_6_14 = all_4_22 % 88.77/12.77 (4) ~ (all_4_22 = e0) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | ALPHA: (1) implies: % 88.77/12.77 | (5) op(e2, e0) = e0 % 88.77/12.77 | % 88.77/12.77 | BETA: splitting (2) gives: % 88.77/12.77 | % 88.77/12.77 | Case 1: % 88.77/12.77 | | % 88.77/12.77 | | (6) ~ (op(e2, e0) = e0) % 88.77/12.77 | | % 88.77/12.77 | | PRED_UNIFY: (5), (6) imply: % 88.77/12.77 | | (7) $false % 88.77/12.77 | | % 88.77/12.77 | | CLOSE: (7) is inconsistent. % 88.77/12.77 | | % 88.77/12.77 | Case 2: % 88.77/12.77 | | % 88.77/12.77 | | (8) all_6_14 = e0 % 88.77/12.77 | | % 88.77/12.77 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #44. % 88.77/12.77 | | % 88.77/12.77 | End of split % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #43 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.77 (2) op(e2, e2) = e4 % 88.77/12.77 (3) op(e2, e2) = e0 % 88.77/12.77 (4) ~ (e4 = e0) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | GROUND_INST: instantiating (1) with e4, e0, e2, e2, simplifying with (2), (3) % 88.77/12.77 | gives: % 88.77/12.77 | (5) e4 = e0 % 88.77/12.77 | % 88.77/12.77 | REDUCE: (4), (5) imply: % 88.77/12.77 | (6) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (6) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #44 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_6_14 = all_4_22 % 88.77/12.77 (2) all_6_14 = e0 % 88.77/12.77 (3) ~ (all_4_22 = e0) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | COMBINE_EQS: (1), (2) imply: % 88.77/12.77 | (4) all_4_22 = e0 % 88.77/12.77 | % 88.77/12.77 | SIMP: (4) implies: % 88.77/12.77 | (5) all_4_22 = e0 % 88.77/12.77 | % 88.77/12.77 | REDUCE: (3), (5) imply: % 88.77/12.77 | (6) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (6) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #45 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.77 (2) op(e2, e0) = all_4_22 % 88.77/12.77 (3) op(e2, e0) = e3 % 88.77/12.77 (4) ~ (all_4_22 = e3) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | GROUND_INST: instantiating (1) with all_4_22, e3, e0, e2, simplifying with % 88.77/12.77 | (2), (3) gives: % 88.77/12.77 | (5) all_4_22 = e3 % 88.77/12.77 | % 88.77/12.77 | REDUCE: (4), (5) imply: % 88.77/12.77 | (6) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (6) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #46 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_6_22 = e1 | all_6_22 = e0 % 88.77/12.77 (2) all_6_22 = all_4_14 % 88.77/12.77 (3) ~ (all_4_14 = e1) % 88.77/12.77 (4) ~ (all_4_14 = e0) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | BETA: splitting (1) gives: % 88.77/12.77 | % 88.77/12.77 | Case 1: % 88.77/12.77 | | % 88.77/12.77 | | (5) all_6_22 = e1 % 88.77/12.77 | | % 88.77/12.77 | | COMBINE_EQS: (2), (5) imply: % 88.77/12.77 | | (6) all_4_14 = e1 % 88.77/12.77 | | % 88.77/12.77 | | SIMP: (6) implies: % 88.77/12.77 | | (7) all_4_14 = e1 % 88.77/12.77 | | % 88.77/12.77 | | REDUCE: (3), (7) imply: % 88.77/12.77 | | (8) $false % 88.77/12.77 | | % 88.77/12.77 | | CLOSE: (8) is inconsistent. % 88.77/12.77 | | % 88.77/12.77 | Case 2: % 88.77/12.77 | | % 88.77/12.77 | | (9) all_6_22 = e0 % 88.77/12.77 | | % 88.77/12.77 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #47. % 88.77/12.77 | | % 88.77/12.77 | End of split % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #47 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_6_22 = all_4_14 % 88.77/12.77 (2) all_6_22 = e0 % 88.77/12.77 (3) ~ (all_4_14 = e0) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | COMBINE_EQS: (1), (2) imply: % 88.77/12.77 | (4) all_4_14 = e0 % 88.77/12.77 | % 88.77/12.77 | SIMP: (4) implies: % 88.77/12.77 | (5) all_4_14 = e0 % 88.77/12.77 | % 88.77/12.77 | REDUCE: (3), (5) imply: % 88.77/12.77 | (6) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (6) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #48 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_6_22 = all_4_14 % 88.77/12.77 (2) all_6_22 = e4 % 88.77/12.77 (3) ~ (all_4_14 = e4) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | COMBINE_EQS: (1), (2) imply: % 88.77/12.77 | (4) all_4_14 = e4 % 88.77/12.77 | % 88.77/12.77 | SIMP: (4) implies: % 88.77/12.77 | (5) all_4_14 = e4 % 88.77/12.77 | % 88.77/12.77 | REDUCE: (3), (5) imply: % 88.77/12.77 | (6) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (6) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #49 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_9_24 = e4 % 88.77/12.77 (2) all_9_24 = e1 % 88.77/12.77 (3) ~ (e4 = e1) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | COMBINE_EQS: (1), (2) imply: % 88.77/12.77 | (4) e4 = e1 % 88.77/12.77 | % 88.77/12.77 | SIMP: (4) implies: % 88.77/12.77 | (5) e4 = e1 % 88.77/12.77 | % 88.77/12.77 | REDUCE: (3), (5) imply: % 88.77/12.77 | (6) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (6) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #50 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_9_18 = e4 & op(e2, e0) = e4 % 88.77/12.77 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.77 (3) op(e2, e0) = all_4_22 % 88.77/12.77 (4) ~ (all_4_22 = e4) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | ALPHA: (1) implies: % 88.77/12.77 | (5) op(e2, e0) = e4 % 88.77/12.77 | % 88.77/12.77 | GROUND_INST: instantiating (2) with all_4_22, e4, e0, e2, simplifying with % 88.77/12.77 | (3), (5) gives: % 88.77/12.77 | (6) all_4_22 = e4 % 88.77/12.77 | % 88.77/12.77 | REDUCE: (4), (6) imply: % 88.77/12.77 | (7) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (7) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #51 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_6_14 = e2 | ~ (op(e2, e0) = e2) % 88.77/12.77 (2) op(e2, e0) = e2 % 88.77/12.77 (3) all_6_14 = all_4_22 % 88.77/12.77 (4) ~ (all_4_22 = e2) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | BETA: splitting (1) gives: % 88.77/12.77 | % 88.77/12.77 | Case 1: % 88.77/12.77 | | % 88.77/12.77 | | (5) ~ (op(e2, e0) = e2) % 88.77/12.77 | | % 88.77/12.77 | | PRED_UNIFY: (2), (5) imply: % 88.77/12.77 | | (6) $false % 88.77/12.77 | | % 88.77/12.77 | | CLOSE: (6) is inconsistent. % 88.77/12.77 | | % 88.77/12.77 | Case 2: % 88.77/12.77 | | % 88.77/12.77 | | (7) all_6_14 = e2 % 88.77/12.77 | | % 88.77/12.77 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #78. % 88.77/12.77 | | % 88.77/12.77 | End of split % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #52 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_9_16 = e3 % 88.77/12.77 (2) all_9_16 = e2 % 88.77/12.77 (3) ~ (e3 = e2) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | COMBINE_EQS: (1), (2) imply: % 88.77/12.77 | (4) e3 = e2 % 88.77/12.77 | % 88.77/12.77 | SIMP: (4) implies: % 88.77/12.77 | (5) e3 = e2 % 88.77/12.77 | % 88.77/12.77 | REDUCE: (3), (5) imply: % 88.77/12.77 | (6) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (6) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #53 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_9_22 = e4 & op(e0, e2) = e4 % 88.77/12.77 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.77 (3) op(e0, e2) = all_4_14 % 88.77/12.77 (4) ~ (all_4_14 = e4) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | ALPHA: (1) implies: % 88.77/12.77 | (5) op(e0, e2) = e4 % 88.77/12.77 | % 88.77/12.77 | GROUND_INST: instantiating (2) with all_4_14, e4, e2, e0, simplifying with % 88.77/12.77 | (3), (5) gives: % 88.77/12.77 | (6) all_4_14 = e4 % 88.77/12.77 | % 88.77/12.77 | REDUCE: (4), (6) imply: % 88.77/12.77 | (7) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (7) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #54 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_9_20 = e4 & op(e0, e4) = e4 % 88.77/12.77 (2) ~ (op(e0, e4) = e4) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | ALPHA: (1) implies: % 88.77/12.77 | (3) op(e0, e4) = e4 % 88.77/12.77 | % 88.77/12.77 | PRED_UNIFY: (2), (3) imply: % 88.77/12.77 | (4) $false % 88.77/12.77 | % 88.77/12.77 | CLOSE: (4) is inconsistent. % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #55 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) all_9_16 = e2 & op(e4, e0) = e2 % 88.77/12.77 (2) all_4_20 = e2 | ~ (op(e4, e0) = e2) % 88.77/12.77 (3) ~ (all_4_20 = e2) % 88.77/12.77 % 88.77/12.77 Begin of proof % 88.77/12.77 | % 88.77/12.77 | ALPHA: (1) implies: % 88.77/12.77 | (4) op(e4, e0) = e2 % 88.77/12.77 | % 88.77/12.77 | BETA: splitting (2) gives: % 88.77/12.77 | % 88.77/12.77 | Case 1: % 88.77/12.77 | | % 88.77/12.77 | | (5) ~ (op(e4, e0) = e2) % 88.77/12.77 | | % 88.77/12.77 | | PRED_UNIFY: (4), (5) imply: % 88.77/12.77 | | (6) $false % 88.77/12.77 | | % 88.77/12.77 | | CLOSE: (6) is inconsistent. % 88.77/12.77 | | % 88.77/12.77 | Case 2: % 88.77/12.77 | | % 88.77/12.77 | | (7) all_4_20 = e2 % 88.77/12.77 | | % 88.77/12.77 | | REDUCE: (3), (7) imply: % 88.77/12.77 | | (8) $false % 88.77/12.77 | | % 88.77/12.77 | | CLOSE: (8) is inconsistent. % 88.77/12.77 | | % 88.77/12.77 | End of split % 88.77/12.77 | % 88.77/12.77 End of proof % 88.77/12.77 % 88.77/12.77 Sub-proof #56 shows that the following formulas are inconsistent: % 88.77/12.77 ---------------------------------------------------------------- % 88.77/12.77 (1) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.77/12.77 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.77/12.77 (all_9_20 = e3 & op(e0, e4) = e3) % 88.77/12.77 (2) all_9_13 = e3 % 88.77/12.77 (3) ~ (e3 = e2) % 88.77/12.77 (4) ~ (all_4_7 = e4) % 88.77/12.77 (5) op(e2, e4) = e3 % 88.77/12.77 (6) ~ (e3 = e0) % 88.77/12.77 (7) ~ (e4 = e3) % 88.77/12.77 (8) ~ (all_4_3 = e0) % 88.77/12.77 (9) all_9_1 = e2 % 88.77/12.77 (10) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.77 (11) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.77/12.77 (12) ~ (all_4_3 = e3) % 88.77/12.77 (13) ~ (e4 = e1) % 88.77/12.77 (14) ~ (e4 = e2) % 88.77/12.77 (15) ~ (all_4_6 = e1) % 88.77/12.77 (16) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.77/12.77 (17) all_4_0 = e0 % 88.77/12.77 (18) ~ (all_4_3 = e1) % 88.77/12.77 (19) op(e3, e3) = all_4_6 % 88.77/12.77 (20) ~ (all_4_4 = e3) % 88.77/12.77 (21) ~ (all_4_3 = all_4_4) % 88.77/12.77 (22) ~ (e4 = e0) % 88.77/12.77 (23) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.77/12.77 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.77/12.77 (all_9_20 = e4 & op(e0, e4) = e4) % 88.77/12.77 (24) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.77/12.77 (25) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.77/12.77 (26) all_9_7 = e0 % 88.77/12.77 (27) all_6_10 = e3 % 88.77/12.77 (28) all_9_2 = e1 % 88.77/12.77 (29) ~ (e2 = e0) % 88.77/12.77 (30) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.77 (31) all_6_20 = all_4_4 % 88.77/12.77 (32) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.77/12.77 = e0 % 88.77/12.77 (33) ~ (e2 = e1) % 88.77/12.77 (34) e4 = e3 | ~ (op(e2, e4) = e4) % 88.77/12.77 (35) ~ (all_4_4 = e1) % 88.77/12.77 (36) op(e4, e4) = e0 % 88.77/12.77 (37) ~ (e3 = e1) % 88.77/12.77 (38) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.77/12.77 = e0 % 88.77/12.77 (39) op(e1, e3) = all_4_8 % 88.77/12.77 (40) (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) | % 88.77/12.77 (all_9_21 = e4 & op(e0, e3) = e4) % 88.77/12.77 (41) ~ (all_4_4 = e0) % 88.77/12.78 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.78 (43) ~ (all_4_8 = e4) % 88.77/12.78 (44) op(e0, e4) = all_4_4 % 88.77/12.78 (45) all_6_15 = all_4_3 % 88.77/12.78 (46) op(e2, e3) = all_4_7 % 88.77/12.78 (47) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.77/12.78 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.77/12.78 (all_9_20 = e1 & op(e0, e4) = e1) % 88.77/12.78 (48) (all_9_1 = e1 & op(e4, e3) = e1) | (all_9_3 = e1 & op(e3, e3) = e1) | % 88.77/12.78 (all_9_7 = e1 & op(e2, e3) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | % 88.77/12.78 (all_9_21 = e1 & op(e0, e3) = e1) % 88.77/12.78 (49) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.77/12.78 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.77/12.78 (all_9_20 = e2 & op(e0, e4) = e2) % 88.77/12.78 (50) ~ (e1 = e0) % 88.77/12.78 % 88.77/12.78 Begin of proof % 88.77/12.78 | % 88.77/12.78 | BETA: splitting (40) gives: % 88.77/12.78 | % 88.77/12.78 | Case 1: % 88.77/12.78 | | % 88.77/12.78 | | (51) all_9_7 = e4 & op(e2, e3) = e4 % 88.77/12.78 | | % 88.77/12.78 | | REF_CLOSE: (4), (42), (46), (51) are inconsistent by sub-proof #59. % 88.77/12.78 | | % 88.77/12.78 | Case 2: % 88.77/12.78 | | % 88.77/12.78 | | (52) (all_9_13 = e4 & op(e1, e3) = e4) | (all_9_21 = e4 & op(e0, e3) = % 88.77/12.78 | | e4) % 88.77/12.78 | | % 88.77/12.78 | | BETA: splitting (52) gives: % 88.77/12.78 | | % 88.77/12.78 | | Case 1: % 88.77/12.78 | | | % 88.77/12.78 | | | (53) all_9_13 = e4 & op(e1, e3) = e4 % 88.77/12.78 | | | % 88.77/12.78 | | | ALPHA: (53) implies: % 88.77/12.78 | | | (54) op(e1, e3) = e4 % 88.77/12.78 | | | % 88.77/12.78 | | | GROUND_INST: instantiating (42) with all_4_8, e4, e3, e1, simplifying with % 88.77/12.78 | | | (39), (54) gives: % 88.77/12.78 | | | (55) all_4_8 = e4 % 88.77/12.78 | | | % 88.77/12.78 | | | REDUCE: (43), (55) imply: % 88.77/12.78 | | | (56) $false % 88.77/12.78 | | | % 88.77/12.78 | | | CLOSE: (56) is inconsistent. % 88.77/12.78 | | | % 88.77/12.78 | | Case 2: % 88.77/12.78 | | | % 88.77/12.78 | | | (57) all_9_21 = e4 & op(e0, e3) = e4 % 88.77/12.78 | | | % 88.77/12.78 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 88.77/12.78 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 88.77/12.78 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 88.77/12.78 | | | (34), (35), (36), (37), (38), (41), (42), (44), (45), (47), % 88.77/12.78 | | | (48), (49), (50), (57) are inconsistent by sub-proof #57. % 88.77/12.78 | | | % 88.77/12.78 | | End of split % 88.77/12.78 | | % 88.77/12.78 | End of split % 88.77/12.78 | % 88.77/12.78 End of proof % 88.77/12.78 % 88.77/12.78 Sub-proof #57 shows that the following formulas are inconsistent: % 88.77/12.78 ---------------------------------------------------------------- % 88.77/12.78 (1) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.77/12.78 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.77/12.78 (all_9_20 = e3 & op(e0, e4) = e3) % 88.77/12.78 (2) all_9_13 = e3 % 88.77/12.78 (3) ~ (e3 = e2) % 88.77/12.78 (4) op(e2, e4) = e3 % 88.77/12.78 (5) ~ (e3 = e0) % 88.77/12.78 (6) ~ (e4 = e3) % 88.77/12.78 (7) ~ (all_4_3 = e0) % 88.77/12.78 (8) all_9_1 = e2 % 88.77/12.78 (9) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.78 (10) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.77/12.78 (11) ~ (all_4_3 = e3) % 88.77/12.78 (12) ~ (e4 = e1) % 88.77/12.78 (13) ~ (e4 = e2) % 88.77/12.78 (14) ~ (all_4_6 = e1) % 88.77/12.78 (15) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.77/12.78 (16) all_4_0 = e0 % 88.77/12.78 (17) ~ (all_4_3 = e1) % 88.77/12.78 (18) op(e3, e3) = all_4_6 % 88.77/12.78 (19) ~ (all_4_4 = e3) % 88.77/12.78 (20) ~ (all_4_3 = all_4_4) % 88.77/12.78 (21) ~ (e4 = e0) % 88.77/12.78 (22) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.77/12.78 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.77/12.78 (all_9_20 = e4 & op(e0, e4) = e4) % 88.77/12.78 (23) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.77/12.78 (24) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.77/12.78 (25) all_9_7 = e0 % 88.77/12.78 (26) all_6_10 = e3 % 88.77/12.78 (27) all_9_2 = e1 % 88.77/12.78 (28) ~ (e2 = e0) % 88.77/12.78 (29) all_9_21 = e4 & op(e0, e3) = e4 % 88.77/12.78 (30) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.78 (31) all_6_20 = all_4_4 % 88.77/12.78 (32) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.77/12.78 = e0 % 88.77/12.78 (33) ~ (e2 = e1) % 88.77/12.78 (34) e4 = e3 | ~ (op(e2, e4) = e4) % 88.77/12.78 (35) ~ (all_4_4 = e1) % 88.77/12.78 (36) op(e4, e4) = e0 % 88.77/12.78 (37) ~ (e3 = e1) % 88.77/12.78 (38) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.77/12.78 = e0 % 88.77/12.78 (39) ~ (all_4_4 = e0) % 88.77/12.78 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.78 (41) op(e0, e4) = all_4_4 % 88.77/12.78 (42) all_6_15 = all_4_3 % 88.77/12.78 (43) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.77/12.78 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.77/12.78 (all_9_20 = e1 & op(e0, e4) = e1) % 88.77/12.78 (44) (all_9_1 = e1 & op(e4, e3) = e1) | (all_9_3 = e1 & op(e3, e3) = e1) | % 88.77/12.78 (all_9_7 = e1 & op(e2, e3) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | % 88.77/12.78 (all_9_21 = e1 & op(e0, e3) = e1) % 88.77/12.78 (45) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.77/12.78 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.77/12.78 (all_9_20 = e2 & op(e0, e4) = e2) % 88.77/12.78 (46) ~ (e1 = e0) % 88.77/12.78 % 88.77/12.78 Begin of proof % 88.77/12.78 | % 88.77/12.78 | ALPHA: (29) implies: % 88.77/12.78 | (47) all_9_21 = e4 % 88.77/12.78 | % 88.77/12.78 | BETA: splitting (44) gives: % 88.77/12.78 | % 88.77/12.78 | Case 1: % 88.77/12.78 | | % 88.77/12.78 | | (48) (all_9_1 = e1 & op(e4, e3) = e1) | (all_9_3 = e1 & op(e3, e3) = e1) % 88.77/12.78 | | % 88.77/12.78 | | BETA: splitting (48) gives: % 88.77/12.78 | | % 88.77/12.78 | | Case 1: % 88.77/12.78 | | | % 88.77/12.78 | | | (49) all_9_1 = e1 & op(e4, e3) = e1 % 88.77/12.78 | | | % 88.77/12.78 | | | REF_CLOSE: (8), (33), (49) are inconsistent by sub-proof #103. % 88.77/12.78 | | | % 88.77/12.78 | | Case 2: % 88.77/12.78 | | | % 88.77/12.78 | | | (50) all_9_3 = e1 & op(e3, e3) = e1 % 88.77/12.78 | | | % 88.77/12.78 | | | ALPHA: (50) implies: % 88.77/12.78 | | | (51) op(e3, e3) = e1 % 88.77/12.78 | | | % 88.77/12.78 | | | REF_CLOSE: (14), (18), (40), (51) are inconsistent by sub-proof #58. % 88.77/12.78 | | | % 88.77/12.78 | | End of split % 88.77/12.78 | | % 88.77/12.78 | Case 2: % 88.77/12.78 | | % 88.77/12.78 | | (52) (all_9_7 = e1 & op(e2, e3) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) % 88.77/12.78 | | | (all_9_21 = e1 & op(e0, e3) = e1) % 88.77/12.78 | | % 88.77/12.78 | | BETA: splitting (52) gives: % 88.77/12.78 | | % 88.77/12.78 | | Case 1: % 88.77/12.78 | | | % 88.77/12.78 | | | (53) all_9_7 = e1 & op(e2, e3) = e1 % 88.77/12.78 | | | % 88.77/12.78 | | | ALPHA: (53) implies: % 88.77/12.78 | | | (54) all_9_7 = e1 % 88.77/12.78 | | | % 88.77/12.78 | | | COMBINE_EQS: (25), (54) imply: % 88.77/12.78 | | | (55) e1 = e0 % 88.77/12.78 | | | % 88.77/12.78 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), % 88.77/12.78 | | | (15), (16), (17), (19), (20), (21), (22), (23), (24), (26), % 88.77/12.78 | | | (27), (28), (30), (31), (32), (33), (34), (35), (36), (37), % 88.77/12.78 | | | (38), (39), (40), (41), (42), (43), (45), (46), (55) are % 88.77/12.78 | | | inconsistent by sub-proof #82. % 88.77/12.78 | | | % 88.77/12.78 | | Case 2: % 88.77/12.78 | | | % 88.77/12.78 | | | (56) (all_9_13 = e1 & op(e1, e3) = e1) | (all_9_21 = e1 & op(e0, e3) = % 88.77/12.78 | | | e1) % 88.77/12.78 | | | % 88.77/12.78 | | | BETA: splitting (56) gives: % 88.77/12.78 | | | % 88.77/12.78 | | | Case 1: % 88.77/12.78 | | | | % 88.77/12.78 | | | | (57) all_9_13 = e1 & op(e1, e3) = e1 % 88.77/12.78 | | | | % 88.77/12.78 | | | | ALPHA: (57) implies: % 88.77/12.78 | | | | (58) all_9_13 = e1 % 88.77/12.78 | | | | % 88.77/12.78 | | | | COMBINE_EQS: (2), (58) imply: % 88.77/12.78 | | | | (59) e3 = e1 % 88.77/12.78 | | | | % 88.77/12.78 | | | | SIMP: (59) implies: % 88.77/12.78 | | | | (60) e3 = e1 % 88.77/12.78 | | | | % 88.77/12.78 | | | | REDUCE: (37), (60) imply: % 88.77/12.78 | | | | (61) $false % 88.77/12.78 | | | | % 88.77/12.78 | | | | CLOSE: (61) is inconsistent. % 88.77/12.78 | | | | % 88.77/12.78 | | | Case 2: % 88.77/12.78 | | | | % 88.77/12.78 | | | | (62) all_9_21 = e1 & op(e0, e3) = e1 % 88.77/12.78 | | | | % 88.77/12.78 | | | | ALPHA: (62) implies: % 88.77/12.78 | | | | (63) all_9_21 = e1 % 88.77/12.78 | | | | % 88.77/12.78 | | | | COMBINE_EQS: (47), (63) imply: % 88.77/12.78 | | | | (64) e4 = e1 % 88.77/12.78 | | | | % 88.77/12.78 | | | | SIMP: (64) implies: % 88.77/12.78 | | | | (65) e4 = e1 % 88.77/12.78 | | | | % 88.77/12.78 | | | | REDUCE: (12), (65) imply: % 88.77/12.78 | | | | (66) $false % 88.77/12.78 | | | | % 88.77/12.78 | | | | CLOSE: (66) is inconsistent. % 88.77/12.78 | | | | % 88.77/12.78 | | | End of split % 88.77/12.78 | | | % 88.77/12.78 | | End of split % 88.77/12.78 | | % 88.77/12.78 | End of split % 88.77/12.78 | % 88.77/12.78 End of proof % 88.77/12.78 % 88.77/12.78 Sub-proof #58 shows that the following formulas are inconsistent: % 88.77/12.78 ---------------------------------------------------------------- % 88.77/12.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.78 (2) op(e3, e3) = all_4_6 % 88.77/12.78 (3) op(e3, e3) = e1 % 88.77/12.78 (4) ~ (all_4_6 = e1) % 88.77/12.78 % 88.77/12.78 Begin of proof % 88.77/12.78 | % 88.77/12.78 | GROUND_INST: instantiating (1) with all_4_6, e1, e3, e3, simplifying with (2), % 88.77/12.78 | (3) gives: % 88.77/12.78 | (5) all_4_6 = e1 % 88.77/12.78 | % 88.77/12.78 | REDUCE: (4), (5) imply: % 88.77/12.78 | (6) $false % 88.77/12.78 | % 88.77/12.78 | CLOSE: (6) is inconsistent. % 88.77/12.78 | % 88.77/12.78 End of proof % 88.77/12.78 % 88.77/12.78 Sub-proof #59 shows that the following formulas are inconsistent: % 88.77/12.78 ---------------------------------------------------------------- % 88.77/12.78 (1) all_9_7 = e4 & op(e2, e3) = e4 % 88.77/12.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.78 (3) op(e2, e3) = all_4_7 % 88.77/12.78 (4) ~ (all_4_7 = e4) % 88.77/12.78 % 88.77/12.78 Begin of proof % 88.77/12.78 | % 88.77/12.78 | ALPHA: (1) implies: % 88.77/12.78 | (5) op(e2, e3) = e4 % 88.77/12.78 | % 88.77/12.78 | GROUND_INST: instantiating (2) with all_4_7, e4, e3, e2, simplifying with (3), % 88.77/12.78 | (5) gives: % 88.77/12.78 | (6) all_4_7 = e4 % 88.77/12.78 | % 88.77/12.78 | REDUCE: (4), (6) imply: % 88.77/12.78 | (7) $false % 88.77/12.78 | % 88.77/12.78 | CLOSE: (7) is inconsistent. % 88.77/12.78 | % 88.77/12.78 End of proof % 88.77/12.78 % 88.77/12.78 Sub-proof #60 shows that the following formulas are inconsistent: % 88.77/12.78 ---------------------------------------------------------------- % 88.77/12.78 (1) all_6_11 = all_4_7 % 88.77/12.78 (2) all_6_11 = e1 % 88.77/12.78 (3) ~ (all_4_7 = e1) % 88.77/12.78 % 88.77/12.78 Begin of proof % 88.77/12.78 | % 88.77/12.78 | COMBINE_EQS: (1), (2) imply: % 88.77/12.78 | (4) all_4_7 = e1 % 88.77/12.78 | % 88.77/12.78 | SIMP: (4) implies: % 88.77/12.78 | (5) all_4_7 = e1 % 88.77/12.78 | % 88.77/12.78 | REDUCE: (3), (5) imply: % 88.77/12.78 | (6) $false % 88.77/12.78 | % 88.77/12.78 | CLOSE: (6) is inconsistent. % 88.77/12.78 | % 88.77/12.78 End of proof % 88.77/12.78 % 88.77/12.78 Sub-proof #61 shows that the following formulas are inconsistent: % 88.77/12.78 ---------------------------------------------------------------- % 88.77/12.78 (1) all_6_11 = all_4_7 % 88.77/12.78 (2) all_6_11 = e3 % 88.77/12.78 (3) ~ (all_4_7 = e3) % 88.77/12.78 % 88.77/12.78 Begin of proof % 88.77/12.78 | % 88.77/12.78 | COMBINE_EQS: (1), (2) imply: % 88.77/12.78 | (4) all_4_7 = e3 % 88.77/12.78 | % 88.77/12.78 | SIMP: (4) implies: % 88.77/12.78 | (5) all_4_7 = e3 % 88.77/12.78 | % 88.77/12.78 | REDUCE: (3), (5) imply: % 88.77/12.78 | (6) $false % 88.77/12.78 | % 88.77/12.78 | CLOSE: (6) is inconsistent. % 88.77/12.78 | % 88.77/12.78 End of proof % 88.77/12.78 % 88.77/12.78 Sub-proof #62 shows that the following formulas are inconsistent: % 88.77/12.78 ---------------------------------------------------------------- % 88.77/12.78 (1) all_6_11 = all_4_7 % 88.77/12.78 (2) all_6_11 = e2 % 88.77/12.78 (3) ~ (all_4_7 = e2) % 88.77/12.78 % 88.77/12.78 Begin of proof % 88.77/12.78 | % 88.77/12.78 | COMBINE_EQS: (1), (2) imply: % 88.77/12.78 | (4) all_4_7 = e2 % 88.77/12.78 | % 88.77/12.78 | SIMP: (4) implies: % 88.77/12.78 | (5) all_4_7 = e2 % 88.77/12.78 | % 88.77/12.78 | REDUCE: (3), (5) imply: % 88.77/12.78 | (6) $false % 88.77/12.78 | % 88.77/12.78 | CLOSE: (6) is inconsistent. % 88.77/12.78 | % 88.77/12.78 End of proof % 88.77/12.78 % 88.77/12.78 Sub-proof #63 shows that the following formulas are inconsistent: % 88.77/12.78 ---------------------------------------------------------------- % 88.77/12.78 (1) all_6_11 = all_4_7 % 88.77/12.78 (2) all_6_11 = e4 % 88.77/12.78 (3) ~ (all_4_7 = e4) % 88.77/12.78 % 88.77/12.78 Begin of proof % 88.77/12.78 | % 88.77/12.78 | COMBINE_EQS: (1), (2) imply: % 88.77/12.78 | (4) all_4_7 = e4 % 88.77/12.78 | % 88.77/12.78 | SIMP: (4) implies: % 88.77/12.78 | (5) all_4_7 = e4 % 88.77/12.78 | % 88.77/12.78 | REDUCE: (3), (5) imply: % 88.77/12.78 | (6) $false % 88.77/12.78 | % 88.77/12.78 | CLOSE: (6) is inconsistent. % 88.77/12.78 | % 88.77/12.78 End of proof % 88.77/12.78 % 88.77/12.78 Sub-proof #64 shows that the following formulas are inconsistent: % 88.77/12.78 ---------------------------------------------------------------- % 88.77/12.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.78 (2) op(e1, e1) = all_4_18 % 88.77/12.78 (3) op(e1, e1) = e0 % 88.77/12.78 (4) ~ (all_4_18 = e0) % 88.77/12.78 % 88.77/12.78 Begin of proof % 88.77/12.78 | % 88.77/12.78 | GROUND_INST: instantiating (1) with all_4_18, e0, e1, e1, simplifying with % 88.77/12.78 | (2), (3) gives: % 88.77/12.78 | (5) all_4_18 = e0 % 88.77/12.78 | % 88.77/12.78 | REDUCE: (4), (5) imply: % 88.77/12.78 | (6) $false % 88.77/12.78 | % 88.77/12.78 | CLOSE: (6) is inconsistent. % 88.77/12.78 | % 88.77/12.78 End of proof % 88.77/12.78 % 88.77/12.78 Sub-proof #65 shows that the following formulas are inconsistent: % 88.77/12.78 ---------------------------------------------------------------- % 88.77/12.78 (1) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.77/12.78 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.77/12.78 (all_9_20 = e3 & op(e0, e4) = e3) % 88.77/12.78 (2) all_6_19 = e0 % 88.77/12.78 (3) all_9_13 = e3 % 88.77/12.78 (4) ~ (e3 = e2) % 88.77/12.78 (5) op(e2, e4) = e3 % 88.77/12.78 (6) ~ (e3 = e0) % 88.77/12.78 (7) ~ (e4 = e3) % 88.77/12.78 (8) ~ (all_4_3 = e0) % 88.77/12.78 (9) all_4_11 = e0 % 88.77/12.78 (10) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.78 (11) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.77/12.78 (12) ~ (all_4_10 = e2) % 88.77/12.78 (13) ~ (all_4_3 = e3) % 88.77/12.78 (14) ~ (e4 = e1) % 88.77/12.78 (15) ~ (e4 = e2) % 88.77/12.78 (16) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.77/12.78 (17) all_6_22 = all_4_14 % 88.77/12.78 (18) all_4_0 = e0 % 88.77/12.78 (19) ~ (all_4_3 = e1) % 88.77/12.78 (20) ~ (all_4_4 = e3) % 88.77/12.78 (21) ~ (all_4_3 = all_4_4) % 88.77/12.78 (22) all_9_14 = e0 % 88.77/12.78 (23) ~ (e4 = e0) % 88.77/12.78 (24) e4 = e2 | ~ (op(e2, e2) = e2) % 88.77/12.79 (25) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.77/12.79 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.77/12.79 (all_9_20 = e4 & op(e0, e4) = e4) % 88.77/12.79 (26) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.77/12.79 (27) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.77/12.79 (28) all_9_12 = e4 % 88.77/12.79 (29) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 88.77/12.79 (30) all_6_10 = e3 % 88.77/12.79 (31) all_9_2 = e1 % 88.77/12.79 (32) ~ (e2 = e0) % 88.77/12.79 (33) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.79 (34) all_6_20 = all_4_4 % 88.77/12.79 (35) ~ (all_4_14 = e2) % 88.77/12.79 (36) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.77/12.79 = e0 % 88.77/12.79 (37) ~ (e2 = e1) % 88.77/12.79 (38) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 88.77/12.79 (39) e4 = e3 | ~ (op(e2, e4) = e4) % 88.77/12.79 (40) ~ (all_4_4 = e1) % 88.77/12.79 (41) all_6_2 = all_4_10 % 88.77/12.79 (42) op(e4, e4) = e0 % 88.77/12.79 (43) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 88.77/12.79 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 88.77/12.79 (all_9_19 = e2 & op(e1, e0) = e2) % 88.77/12.79 (44) ~ (e3 = e1) % 88.77/12.79 (45) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.77/12.79 = e0 % 88.77/12.79 (46) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 88.77/12.79 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 88.77/12.79 (all_9_22 = e2 & op(e0, e2) = e2) % 88.77/12.79 (47) ~ (all_4_4 = e0) % 88.77/12.79 (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.79 (49) op(e0, e4) = all_4_4 % 88.77/12.79 (50) all_6_15 = all_4_3 % 88.77/12.79 (51) all_6_19 = e1 | ~ (op(e1, e0) = e1) % 88.77/12.79 (52) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.77/12.79 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.77/12.79 (all_9_20 = e1 & op(e0, e4) = e1) % 88.77/12.79 (53) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 88.77/12.79 (54) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | % 88.77/12.79 (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 88.77/12.79 (all_9_19 = e1 & op(e1, e0) = e1) % 88.77/12.79 (55) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.77/12.79 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.77/12.79 (all_9_20 = e2 & op(e0, e4) = e2) % 88.77/12.79 (56) ~ (e1 = e0) % 88.77/12.79 % 88.77/12.79 Begin of proof % 88.77/12.79 | % 88.77/12.79 | BETA: splitting (54) gives: % 88.77/12.79 | % 88.77/12.79 | Case 1: % 88.77/12.79 | | % 88.77/12.79 | | (57) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = % 88.77/12.79 | | e1) % 88.77/12.79 | | % 88.77/12.79 | | REF_CLOSE: (3), (16), (19), (44), (57) are inconsistent by sub-proof #76. % 88.77/12.79 | | % 88.77/12.79 | Case 2: % 88.77/12.79 | | % 88.77/12.79 | | (58) (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = % 88.77/12.79 | | e1) | (all_9_19 = e1 & op(e1, e0) = e1) % 88.77/12.79 | | % 88.77/12.79 | | BETA: splitting (58) gives: % 88.77/12.79 | | % 88.77/12.79 | | Case 1: % 88.77/12.79 | | | % 88.77/12.79 | | | (59) all_9_14 = e1 & op(e1, e2) = e1 % 88.77/12.79 | | | % 88.77/12.79 | | | ALPHA: (59) implies: % 88.77/12.79 | | | (60) all_9_14 = e1 % 88.77/12.79 | | | % 88.77/12.79 | | | COMBINE_EQS: (22), (60) imply: % 88.77/12.79 | | | (61) e1 = e0 % 88.77/12.79 | | | % 88.77/12.79 | | | SIMP: (61) implies: % 88.77/12.79 | | | (62) e1 = e0 % 88.77/12.79 | | | % 88.77/12.79 | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (10), (11), (13), (14), (15), % 88.77/12.79 | | | (16), (18), (19), (20), (21), (23), (25), (26), (27), (30), % 88.77/12.79 | | | (31), (32), (33), (34), (36), (37), (39), (40), (42), (44), % 88.77/12.79 | | | (45), (47), (48), (49), (50), (52), (55), (56), (62) are % 88.77/12.79 | | | inconsistent by sub-proof #82. % 88.77/12.79 | | | % 88.77/12.79 | | Case 2: % 88.77/12.79 | | | % 88.77/12.79 | | | (63) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_19 = e1 & op(e1, e0) = % 88.77/12.79 | | | e1) % 88.77/12.79 | | | % 88.77/12.79 | | | BETA: splitting (63) gives: % 88.77/12.79 | | | % 88.77/12.79 | | | Case 1: % 88.77/12.79 | | | | % 88.77/12.79 | | | | (64) all_9_15 = e1 & op(e1, e1) = e1 % 88.77/12.79 | | | | % 88.77/12.79 | | | | ALPHA: (64) implies: % 88.77/12.79 | | | | (65) all_9_15 = e1 % 88.77/12.79 | | | | % 88.77/12.79 | | | | REF_CLOSE: (3), (4), (9), (12), (15), (17), (22), (24), (28), (29), % 88.77/12.79 | | | | (32), (35), (37), (38), (41), (43), (46), (53), (65) are % 88.77/12.79 | | | | inconsistent by sub-proof #67. % 88.77/12.79 | | | | % 88.77/12.79 | | | Case 2: % 88.77/12.79 | | | | % 88.77/12.79 | | | | (66) all_9_19 = e1 & op(e1, e0) = e1 % 88.77/12.79 | | | | % 88.77/12.79 | | | | ALPHA: (66) implies: % 88.77/12.79 | | | | (67) op(e1, e0) = e1 % 88.77/12.79 | | | | % 88.77/12.79 | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (13), (14), % 88.77/12.79 | | | | (15), (16), (18), (19), (20), (21), (23), (25), (26), (27), % 88.77/12.79 | | | | (30), (31), (32), (33), (34), (36), (37), (39), (40), (42), % 88.77/12.79 | | | | (44), (45), (47), (48), (49), (50), (51), (52), (55), (56), % 88.77/12.79 | | | | (67) are inconsistent by sub-proof #66. % 88.77/12.79 | | | | % 88.77/12.79 | | | End of split % 88.77/12.79 | | | % 88.77/12.79 | | End of split % 88.77/12.79 | | % 88.77/12.79 | End of split % 88.77/12.79 | % 88.77/12.79 End of proof % 88.77/12.79 % 88.77/12.79 Sub-proof #66 shows that the following formulas are inconsistent: % 88.77/12.79 ---------------------------------------------------------------- % 88.77/12.79 (1) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.77/12.79 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.77/12.79 (all_9_20 = e3 & op(e0, e4) = e3) % 88.77/12.79 (2) all_6_19 = e0 % 88.77/12.79 (3) ~ (e3 = e2) % 88.77/12.79 (4) op(e2, e4) = e3 % 88.77/12.79 (5) ~ (e3 = e0) % 88.77/12.79 (6) ~ (e4 = e3) % 88.77/12.79 (7) ~ (all_4_3 = e0) % 88.77/12.79 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.79 (9) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.77/12.79 (10) ~ (all_4_3 = e3) % 88.77/12.79 (11) ~ (e4 = e1) % 88.77/12.79 (12) ~ (e4 = e2) % 88.77/12.79 (13) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.77/12.79 (14) all_4_0 = e0 % 88.77/12.79 (15) ~ (all_4_3 = e1) % 88.77/12.79 (16) ~ (all_4_4 = e3) % 88.77/12.79 (17) ~ (all_4_3 = all_4_4) % 88.77/12.79 (18) ~ (e4 = e0) % 88.77/12.79 (19) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.77/12.79 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.77/12.79 (all_9_20 = e4 & op(e0, e4) = e4) % 88.77/12.79 (20) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.77/12.79 (21) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.77/12.79 (22) all_6_10 = e3 % 88.77/12.79 (23) all_9_2 = e1 % 88.77/12.79 (24) ~ (e2 = e0) % 88.77/12.79 (25) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.79 (26) all_6_20 = all_4_4 % 88.77/12.79 (27) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.77/12.79 = e0 % 88.77/12.79 (28) ~ (e2 = e1) % 88.77/12.79 (29) e4 = e3 | ~ (op(e2, e4) = e4) % 88.77/12.79 (30) ~ (all_4_4 = e1) % 88.77/12.79 (31) op(e4, e4) = e0 % 88.77/12.79 (32) ~ (e3 = e1) % 88.77/12.79 (33) op(e1, e0) = e1 % 88.77/12.79 (34) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.77/12.79 = e0 % 88.77/12.79 (35) ~ (all_4_4 = e0) % 88.77/12.79 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.79 (37) op(e0, e4) = all_4_4 % 88.77/12.79 (38) all_6_15 = all_4_3 % 88.77/12.79 (39) all_6_19 = e1 | ~ (op(e1, e0) = e1) % 88.77/12.79 (40) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.77/12.79 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.77/12.79 (all_9_20 = e1 & op(e0, e4) = e1) % 88.77/12.79 (41) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.77/12.79 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.77/12.79 (all_9_20 = e2 & op(e0, e4) = e2) % 88.77/12.79 (42) ~ (e1 = e0) % 88.77/12.79 % 88.77/12.79 Begin of proof % 88.77/12.79 | % 88.77/12.79 | BETA: splitting (39) gives: % 88.77/12.79 | % 88.77/12.79 | Case 1: % 88.77/12.79 | | % 88.77/12.79 | | (43) ~ (op(e1, e0) = e1) % 88.77/12.79 | | % 88.77/12.79 | | PRED_UNIFY: (33), (43) imply: % 88.77/12.79 | | (44) $false % 88.77/12.79 | | % 88.77/12.79 | | CLOSE: (44) is inconsistent. % 88.77/12.79 | | % 88.77/12.79 | Case 2: % 88.77/12.79 | | % 88.77/12.79 | | (45) all_6_19 = e1 % 88.77/12.79 | | % 88.77/12.79 | | COMBINE_EQS: (2), (45) imply: % 88.77/12.79 | | (46) e1 = e0 % 88.77/12.79 | | % 88.77/12.79 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 88.77/12.79 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 88.77/12.79 | | (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), (36), % 88.77/12.79 | | (37), (38), (40), (41), (42), (46) are inconsistent by sub-proof % 88.77/12.79 | | #82. % 88.77/12.79 | | % 88.77/12.79 | End of split % 88.77/12.79 | % 88.77/12.79 End of proof % 88.77/12.79 % 88.77/12.79 Sub-proof #67 shows that the following formulas are inconsistent: % 88.77/12.79 ---------------------------------------------------------------- % 88.77/12.79 (1) all_9_13 = e3 % 88.77/12.79 (2) ~ (e3 = e2) % 88.77/12.79 (3) all_4_11 = e0 % 88.77/12.79 (4) ~ (all_4_10 = e2) % 88.77/12.79 (5) ~ (e4 = e2) % 88.77/12.79 (6) all_6_22 = all_4_14 % 88.77/12.79 (7) all_9_14 = e0 % 88.77/12.79 (8) e4 = e2 | ~ (op(e2, e2) = e2) % 88.77/12.79 (9) all_9_15 = e1 % 88.77/12.79 (10) all_9_12 = e4 % 88.77/12.79 (11) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 88.77/12.79 (12) ~ (e2 = e0) % 88.77/12.79 (13) ~ (all_4_14 = e2) % 88.77/12.79 (14) ~ (e2 = e1) % 88.77/12.79 (15) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 88.77/12.79 (16) all_6_2 = all_4_10 % 88.77/12.79 (17) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 88.77/12.79 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 88.77/12.79 (all_9_19 = e2 & op(e1, e0) = e2) % 88.77/12.79 (18) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 88.77/12.79 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 88.77/12.79 (all_9_22 = e2 & op(e0, e2) = e2) % 88.77/12.79 (19) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 88.77/12.79 % 88.77/12.79 Begin of proof % 88.77/12.79 | % 88.77/12.79 | BETA: splitting (17) gives: % 88.77/12.79 | % 88.77/12.79 | Case 1: % 88.77/12.79 | | % 88.77/12.79 | | (20) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = % 88.77/12.79 | | e2) % 88.77/12.79 | | % 88.77/12.79 | | REF_CLOSE: (1), (2), (5), (10), (20) are inconsistent by sub-proof #75. % 88.77/12.79 | | % 88.77/12.79 | Case 2: % 88.77/12.79 | | % 88.77/12.79 | | (21) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = % 88.77/12.79 | | e2) | (all_9_19 = e2 & op(e1, e0) = e2) % 88.77/12.79 | | % 88.77/12.79 | | BETA: splitting (21) gives: % 88.77/12.79 | | % 88.77/12.79 | | Case 1: % 88.77/12.79 | | | % 88.77/12.79 | | | (22) all_9_14 = e2 & op(e1, e2) = e2 % 88.77/12.79 | | | % 88.77/12.79 | | | REF_CLOSE: (7), (12), (22) are inconsistent by sub-proof #74. % 88.77/12.79 | | | % 88.77/12.79 | | Case 2: % 88.77/12.79 | | | % 88.77/12.79 | | | (23) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_19 = e2 & op(e1, e0) = % 88.77/12.79 | | | e2) % 88.77/12.79 | | | % 88.77/12.79 | | | BETA: splitting (23) gives: % 88.77/12.79 | | | % 88.77/12.79 | | | Case 1: % 88.77/12.79 | | | | % 88.77/12.79 | | | | (24) all_9_15 = e2 & op(e1, e1) = e2 % 88.77/12.79 | | | | % 88.77/12.79 | | | | REF_CLOSE: (9), (14), (24) are inconsistent by sub-proof #73. % 88.77/12.79 | | | | % 88.77/12.79 | | | Case 2: % 88.77/12.79 | | | | % 88.77/12.79 | | | | (25) all_9_19 = e2 & op(e1, e0) = e2 % 88.77/12.79 | | | | % 88.77/12.79 | | | | ALPHA: (25) implies: % 88.77/12.79 | | | | (26) all_9_19 = e2 % 88.77/12.79 | | | | % 88.77/12.79 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 88.77/12.79 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (26) are % 88.77/12.79 | | | | inconsistent by sub-proof #68. % 88.77/12.79 | | | | % 88.77/12.79 | | | End of split % 88.77/12.79 | | | % 88.77/12.79 | | End of split % 88.77/12.79 | | % 88.77/12.79 | End of split % 88.77/12.79 | % 88.77/12.79 End of proof % 88.77/12.79 % 88.77/12.79 Sub-proof #68 shows that the following formulas are inconsistent: % 88.77/12.79 ---------------------------------------------------------------- % 88.77/12.79 (1) all_9_13 = e3 % 88.77/12.79 (2) ~ (e3 = e2) % 88.77/12.79 (3) all_4_11 = e0 % 88.77/12.79 (4) ~ (all_4_10 = e2) % 88.77/12.79 (5) ~ (e4 = e2) % 88.77/12.79 (6) all_6_22 = all_4_14 % 88.77/12.79 (7) all_9_14 = e0 % 88.77/12.79 (8) e4 = e2 | ~ (op(e2, e2) = e2) % 88.77/12.79 (9) all_9_15 = e1 % 88.77/12.79 (10) all_9_12 = e4 % 88.77/12.79 (11) all_9_19 = e2 % 88.77/12.79 (12) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 88.77/12.79 (13) ~ (e2 = e0) % 88.77/12.79 (14) ~ (all_4_14 = e2) % 88.77/12.79 (15) ~ (e2 = e1) % 88.77/12.79 (16) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 88.77/12.79 (17) all_6_2 = all_4_10 % 88.77/12.79 (18) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 88.77/12.79 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 88.77/12.79 (all_9_19 = e2 & op(e1, e0) = e2) % 88.77/12.79 (19) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 88.77/12.79 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 88.77/12.79 (all_9_22 = e2 & op(e0, e2) = e2) % 88.77/12.79 (20) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 88.77/12.79 % 88.77/12.79 Begin of proof % 88.77/12.79 | % 88.77/12.79 | BETA: splitting (19) gives: % 88.77/12.79 | % 88.77/12.79 | Case 1: % 88.77/12.79 | | % 88.77/12.79 | | (21) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) % 88.77/12.79 | | % 88.77/12.79 | | BETA: splitting (21) gives: % 88.77/12.79 | | % 88.77/12.79 | | Case 1: % 88.77/12.79 | | | % 88.77/12.79 | | | (22) all_9_4 = e2 & op(e4, e2) = e2 % 88.77/12.79 | | | % 88.77/12.79 | | | REF_CLOSE: (4), (16), (17), (22) are inconsistent by sub-proof #80. % 88.77/12.79 | | | % 88.77/12.79 | | Case 2: % 88.77/12.79 | | | % 88.77/12.79 | | | (23) all_9_5 = e2 & op(e3, e2) = e2 % 88.77/12.79 | | | % 88.77/12.79 | | | ALPHA: (23) implies: % 88.77/12.79 | | | (24) op(e3, e2) = e2 % 88.77/12.79 | | | % 88.77/12.79 | | | BETA: splitting (12) gives: % 88.77/12.79 | | | % 88.77/12.79 | | | Case 1: % 88.77/12.79 | | | | % 88.77/12.79 | | | | (25) ~ (op(e3, e2) = e2) % 88.77/12.79 | | | | % 88.77/12.79 | | | | PRED_UNIFY: (24), (25) imply: % 88.77/12.79 | | | | (26) $false % 88.77/12.79 | | | | % 88.77/12.79 | | | | CLOSE: (26) is inconsistent. % 88.77/12.79 | | | | % 88.77/12.79 | | | Case 2: % 88.77/12.79 | | | | % 88.77/12.79 | | | | (27) all_4_11 = e2 % 88.77/12.79 | | | | % 88.77/12.79 | | | | COMBINE_EQS: (3), (27) imply: % 88.77/12.79 | | | | (28) e2 = e0 % 88.77/12.79 | | | | % 88.77/12.79 | | | | REF_CLOSE: (1), (2), (5), (7), (9), (10), (11), (13), (15), (18), (28) % 88.77/12.79 | | | | are inconsistent by sub-proof #71. % 88.77/12.79 | | | | % 88.77/12.79 | | | End of split % 88.77/12.79 | | | % 88.77/12.79 | | End of split % 88.77/12.79 | | % 88.77/12.79 | Case 2: % 88.77/12.79 | | % 88.77/12.79 | | (29) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) % 88.77/12.79 | | | (all_9_22 = e2 & op(e0, e2) = e2) % 88.77/12.79 | | % 88.77/12.79 | | BETA: splitting (29) gives: % 88.77/12.79 | | % 88.77/12.79 | | Case 1: % 88.77/12.79 | | | % 88.77/12.79 | | | (30) all_9_8 = e2 & op(e2, e2) = e2 % 88.77/12.79 | | | % 88.77/12.79 | | | REF_CLOSE: (5), (8), (30) are inconsistent by sub-proof #113. % 88.77/12.79 | | | % 88.77/12.79 | | Case 2: % 88.77/12.79 | | | % 88.77/12.79 | | | (31) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 & op(e0, e2) = % 88.77/12.79 | | | e2) % 88.77/12.79 | | | % 88.77/12.79 | | | BETA: splitting (31) gives: % 88.77/12.79 | | | % 88.77/12.79 | | | Case 1: % 88.77/12.79 | | | | % 88.77/12.79 | | | | (32) all_9_14 = e2 & op(e1, e2) = e2 % 88.77/12.79 | | | | % 88.77/12.79 | | | | ALPHA: (32) implies: % 88.77/12.79 | | | | (33) all_9_14 = e2 % 88.77/12.80 | | | | % 88.77/12.80 | | | | COMBINE_EQS: (7), (33) imply: % 88.77/12.80 | | | | (34) e2 = e0 % 88.77/12.80 | | | | % 88.77/12.80 | | | | SIMP: (34) implies: % 88.77/12.80 | | | | (35) e2 = e0 % 88.77/12.80 | | | | % 88.77/12.80 | | | | REF_CLOSE: (1), (2), (5), (7), (9), (10), (11), (13), (15), (18), (35) % 88.77/12.80 | | | | are inconsistent by sub-proof #71. % 88.77/12.80 | | | | % 88.77/12.80 | | | Case 2: % 88.77/12.80 | | | | % 88.77/12.80 | | | | (36) all_9_22 = e2 & op(e0, e2) = e2 % 88.77/12.80 | | | | % 88.77/12.80 | | | | REF_CLOSE: (6), (14), (20), (36) are inconsistent by sub-proof #69. % 88.77/12.80 | | | | % 88.77/12.80 | | | End of split % 88.77/12.80 | | | % 88.77/12.80 | | End of split % 88.77/12.80 | | % 88.77/12.80 | End of split % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #69 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_22 = e2 & op(e0, e2) = e2 % 88.77/12.80 (2) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 88.77/12.80 (3) all_6_22 = all_4_14 % 88.77/12.80 (4) ~ (all_4_14 = e2) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | ALPHA: (1) implies: % 88.77/12.80 | (5) op(e0, e2) = e2 % 88.77/12.80 | % 88.77/12.80 | BETA: splitting (2) gives: % 88.77/12.80 | % 88.77/12.80 | Case 1: % 88.77/12.80 | | % 88.77/12.80 | | (6) ~ (op(e0, e2) = e2) % 88.77/12.80 | | % 88.77/12.80 | | PRED_UNIFY: (5), (6) imply: % 88.77/12.80 | | (7) $false % 88.77/12.80 | | % 88.77/12.80 | | CLOSE: (7) is inconsistent. % 88.77/12.80 | | % 88.77/12.80 | Case 2: % 88.77/12.80 | | % 88.77/12.80 | | (8) all_6_22 = e2 % 88.77/12.80 | | % 88.77/12.80 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #70. % 88.77/12.80 | | % 88.77/12.80 | End of split % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #70 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_6_22 = all_4_14 % 88.77/12.80 (2) all_6_22 = e2 % 88.77/12.80 (3) ~ (all_4_14 = e2) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | COMBINE_EQS: (1), (2) imply: % 88.77/12.80 | (4) all_4_14 = e2 % 88.77/12.80 | % 88.77/12.80 | SIMP: (4) implies: % 88.77/12.80 | (5) all_4_14 = e2 % 88.77/12.80 | % 88.77/12.80 | REDUCE: (3), (5) imply: % 88.77/12.80 | (6) $false % 88.77/12.80 | % 88.77/12.80 | CLOSE: (6) is inconsistent. % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #71 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_13 = e3 % 88.77/12.80 (2) ~ (e3 = e2) % 88.77/12.80 (3) ~ (e4 = e2) % 88.77/12.80 (4) all_9_14 = e0 % 88.77/12.80 (5) all_9_15 = e1 % 88.77/12.80 (6) all_9_12 = e4 % 88.77/12.80 (7) all_9_19 = e2 % 88.77/12.80 (8) ~ (e2 = e0) % 88.77/12.80 (9) e2 = e0 % 88.77/12.80 (10) ~ (e2 = e1) % 88.77/12.80 (11) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 88.77/12.80 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 88.77/12.80 (all_9_19 = e2 & op(e1, e0) = e2) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | COMBINE_EQS: (7), (9) imply: % 88.77/12.80 | (12) all_9_19 = e0 % 88.77/12.80 | % 88.77/12.80 | BETA: splitting (11) gives: % 88.77/12.80 | % 88.77/12.80 | Case 1: % 88.77/12.80 | | % 88.77/12.80 | | (13) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = % 88.77/12.80 | | e2) % 88.77/12.80 | | % 88.77/12.80 | | REF_CLOSE: (1), (2), (3), (6), (13) are inconsistent by sub-proof #75. % 88.77/12.80 | | % 88.77/12.80 | Case 2: % 88.77/12.80 | | % 88.77/12.80 | | (14) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = % 88.77/12.80 | | e2) | (all_9_19 = e2 & op(e1, e0) = e2) % 88.77/12.80 | | % 88.77/12.80 | | BETA: splitting (14) gives: % 88.77/12.80 | | % 88.77/12.80 | | Case 1: % 88.77/12.80 | | | % 88.77/12.80 | | | (15) all_9_14 = e2 & op(e1, e2) = e2 % 88.77/12.80 | | | % 88.77/12.80 | | | REF_CLOSE: (4), (8), (15) are inconsistent by sub-proof #74. % 88.77/12.80 | | | % 88.77/12.80 | | Case 2: % 88.77/12.80 | | | % 88.77/12.80 | | | (16) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_19 = e2 & op(e1, e0) = % 88.77/12.80 | | | e2) % 88.77/12.80 | | | % 88.77/12.80 | | | REF_CLOSE: (5), (8), (10), (12), (16) are inconsistent by sub-proof #72. % 88.77/12.80 | | | % 88.77/12.80 | | End of split % 88.77/12.80 | | % 88.77/12.80 | End of split % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #72 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_15 = e1 % 88.77/12.80 (2) ~ (e2 = e0) % 88.77/12.80 (3) ~ (e2 = e1) % 88.77/12.80 (4) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) % 88.77/12.80 (5) all_9_19 = e0 % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | BETA: splitting (4) gives: % 88.77/12.80 | % 88.77/12.80 | Case 1: % 88.77/12.80 | | % 88.77/12.80 | | (6) all_9_15 = e2 & op(e1, e1) = e2 % 88.77/12.80 | | % 88.77/12.80 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #73. % 88.77/12.80 | | % 88.77/12.80 | Case 2: % 88.77/12.80 | | % 88.77/12.80 | | (7) all_9_19 = e2 & op(e1, e0) = e2 % 88.77/12.80 | | % 88.77/12.80 | | ALPHA: (7) implies: % 88.77/12.80 | | (8) all_9_19 = e2 % 88.77/12.80 | | % 88.77/12.80 | | COMBINE_EQS: (5), (8) imply: % 88.77/12.80 | | (9) e2 = e0 % 88.77/12.80 | | % 88.77/12.80 | | SIMP: (9) implies: % 88.77/12.80 | | (10) e2 = e0 % 88.77/12.80 | | % 88.77/12.80 | | REDUCE: (2), (10) imply: % 88.77/12.80 | | (11) $false % 88.77/12.80 | | % 88.77/12.80 | | CLOSE: (11) is inconsistent. % 88.77/12.80 | | % 88.77/12.80 | End of split % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #73 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_15 = e2 & op(e1, e1) = e2 % 88.77/12.80 (2) all_9_15 = e1 % 88.77/12.80 (3) ~ (e2 = e1) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | ALPHA: (1) implies: % 88.77/12.80 | (4) all_9_15 = e2 % 88.77/12.80 | % 88.77/12.80 | COMBINE_EQS: (2), (4) imply: % 88.77/12.80 | (5) e2 = e1 % 88.77/12.80 | % 88.77/12.80 | SIMP: (5) implies: % 88.77/12.80 | (6) e2 = e1 % 88.77/12.80 | % 88.77/12.80 | REDUCE: (3), (6) imply: % 88.77/12.80 | (7) $false % 88.77/12.80 | % 88.77/12.80 | CLOSE: (7) is inconsistent. % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #74 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_14 = e2 & op(e1, e2) = e2 % 88.77/12.80 (2) all_9_14 = e0 % 88.77/12.80 (3) ~ (e2 = e0) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | ALPHA: (1) implies: % 88.77/12.80 | (4) all_9_14 = e2 % 88.77/12.80 | % 88.77/12.80 | COMBINE_EQS: (2), (4) imply: % 88.77/12.80 | (5) e2 = e0 % 88.77/12.80 | % 88.77/12.80 | SIMP: (5) implies: % 88.77/12.80 | (6) e2 = e0 % 88.77/12.80 | % 88.77/12.80 | REDUCE: (3), (6) imply: % 88.77/12.80 | (7) $false % 88.77/12.80 | % 88.77/12.80 | CLOSE: (7) is inconsistent. % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #75 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_13 = e3 % 88.77/12.80 (2) ~ (e3 = e2) % 88.77/12.80 (3) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) % 88.77/12.80 (4) ~ (e4 = e2) % 88.77/12.80 (5) all_9_12 = e4 % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | BETA: splitting (3) gives: % 88.77/12.80 | % 88.77/12.80 | Case 1: % 88.77/12.80 | | % 88.77/12.80 | | (6) all_9_12 = e2 & op(e1, e4) = e2 % 88.77/12.80 | | % 88.77/12.80 | | ALPHA: (6) implies: % 88.77/12.80 | | (7) all_9_12 = e2 % 88.77/12.80 | | % 88.77/12.80 | | COMBINE_EQS: (5), (7) imply: % 88.77/12.80 | | (8) e4 = e2 % 88.77/12.80 | | % 88.77/12.80 | | REDUCE: (4), (8) imply: % 88.77/12.80 | | (9) $false % 88.77/12.80 | | % 88.77/12.80 | | CLOSE: (9) is inconsistent. % 88.77/12.80 | | % 88.77/12.80 | Case 2: % 88.77/12.80 | | % 88.77/12.80 | | (10) all_9_13 = e2 & op(e1, e3) = e2 % 88.77/12.80 | | % 88.77/12.80 | | ALPHA: (10) implies: % 88.77/12.80 | | (11) all_9_13 = e2 % 88.77/12.80 | | % 88.77/12.80 | | COMBINE_EQS: (1), (11) imply: % 88.77/12.80 | | (12) e3 = e2 % 88.77/12.80 | | % 88.77/12.80 | | REDUCE: (2), (12) imply: % 88.77/12.80 | | (13) $false % 88.77/12.80 | | % 88.77/12.80 | | CLOSE: (13) is inconsistent. % 88.77/12.80 | | % 88.77/12.80 | End of split % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #76 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_13 = e3 % 88.77/12.80 (2) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) % 88.77/12.80 (3) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.77/12.80 (4) ~ (all_4_3 = e1) % 88.77/12.80 (5) ~ (e3 = e1) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | BETA: splitting (2) gives: % 88.77/12.80 | % 88.77/12.80 | Case 1: % 88.77/12.80 | | % 88.77/12.80 | | (6) all_9_12 = e1 & op(e1, e4) = e1 % 88.77/12.80 | | % 88.77/12.80 | | ALPHA: (6) implies: % 88.77/12.80 | | (7) op(e1, e4) = e1 % 88.77/12.80 | | % 88.77/12.80 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #87. % 88.77/12.80 | | % 88.77/12.80 | Case 2: % 88.77/12.80 | | % 88.77/12.80 | | (8) all_9_13 = e1 & op(e1, e3) = e1 % 88.77/12.80 | | % 88.77/12.80 | | ALPHA: (8) implies: % 88.77/12.80 | | (9) all_9_13 = e1 % 88.77/12.80 | | % 88.77/12.80 | | COMBINE_EQS: (1), (9) imply: % 88.77/12.80 | | (10) e3 = e1 % 88.77/12.80 | | % 88.77/12.80 | | REDUCE: (5), (10) imply: % 88.77/12.80 | | (11) $false % 88.77/12.80 | | % 88.77/12.80 | | CLOSE: (11) is inconsistent. % 88.77/12.80 | | % 88.77/12.80 | End of split % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #77 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_6_14 = all_4_22 % 88.77/12.80 (2) all_6_14 = e3 % 88.77/12.80 (3) ~ (all_4_22 = e3) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | COMBINE_EQS: (1), (2) imply: % 88.77/12.80 | (4) all_4_22 = e3 % 88.77/12.80 | % 88.77/12.80 | SIMP: (4) implies: % 88.77/12.80 | (5) all_4_22 = e3 % 88.77/12.80 | % 88.77/12.80 | REDUCE: (3), (5) imply: % 88.77/12.80 | (6) $false % 88.77/12.80 | % 88.77/12.80 | CLOSE: (6) is inconsistent. % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #78 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_6_14 = all_4_22 % 88.77/12.80 (2) all_6_14 = e2 % 88.77/12.80 (3) ~ (all_4_22 = e2) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | COMBINE_EQS: (1), (2) imply: % 88.77/12.80 | (4) all_4_22 = e2 % 88.77/12.80 | % 88.77/12.80 | SIMP: (4) implies: % 88.77/12.80 | (5) all_4_22 = e2 % 88.77/12.80 | % 88.77/12.80 | REDUCE: (3), (5) imply: % 88.77/12.80 | (6) $false % 88.77/12.80 | % 88.77/12.80 | CLOSE: (6) is inconsistent. % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #79 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_9 = e2 & op(e4, e1) = e2 % 88.77/12.80 (2) all_9_9 = e4 % 88.77/12.80 (3) ~ (e4 = e2) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | ALPHA: (1) implies: % 88.77/12.80 | (4) all_9_9 = e2 % 88.77/12.80 | % 88.77/12.80 | COMBINE_EQS: (2), (4) imply: % 88.77/12.80 | (5) e4 = e2 % 88.77/12.80 | % 88.77/12.80 | REDUCE: (3), (5) imply: % 88.77/12.80 | (6) $false % 88.77/12.80 | % 88.77/12.80 | CLOSE: (6) is inconsistent. % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #80 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_4 = e2 & op(e4, e2) = e2 % 88.77/12.80 (2) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 88.77/12.80 (3) all_6_2 = all_4_10 % 88.77/12.80 (4) ~ (all_4_10 = e2) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | ALPHA: (1) implies: % 88.77/12.80 | (5) op(e4, e2) = e2 % 88.77/12.80 | % 88.77/12.80 | BETA: splitting (2) gives: % 88.77/12.80 | % 88.77/12.80 | Case 1: % 88.77/12.80 | | % 88.77/12.80 | | (6) ~ (op(e4, e2) = e2) % 88.77/12.80 | | % 88.77/12.80 | | PRED_UNIFY: (5), (6) imply: % 88.77/12.80 | | (7) $false % 88.77/12.80 | | % 88.77/12.80 | | CLOSE: (7) is inconsistent. % 88.77/12.80 | | % 88.77/12.80 | Case 2: % 88.77/12.80 | | % 88.77/12.80 | | (8) all_6_2 = e2 % 88.77/12.80 | | % 88.77/12.80 | | COMBINE_EQS: (3), (8) imply: % 88.77/12.80 | | (9) all_4_10 = e2 % 88.77/12.80 | | % 88.77/12.80 | | REDUCE: (4), (9) imply: % 88.77/12.80 | | (10) $false % 88.77/12.80 | | % 88.77/12.80 | | CLOSE: (10) is inconsistent. % 88.77/12.80 | | % 88.77/12.80 | End of split % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #81 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) all_9_9 = e1 & op(e4, e1) = e1 % 88.77/12.80 (2) all_6_3 = e1 | ~ (op(e4, e1) = e1) % 88.77/12.80 (3) all_6_3 = all_4_15 % 88.77/12.80 (4) ~ (all_4_15 = e1) % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | ALPHA: (1) implies: % 88.77/12.80 | (5) op(e4, e1) = e1 % 88.77/12.80 | % 88.77/12.80 | BETA: splitting (2) gives: % 88.77/12.80 | % 88.77/12.80 | Case 1: % 88.77/12.80 | | % 88.77/12.80 | | (6) ~ (op(e4, e1) = e1) % 88.77/12.80 | | % 88.77/12.80 | | PRED_UNIFY: (5), (6) imply: % 88.77/12.80 | | (7) $false % 88.77/12.80 | | % 88.77/12.80 | | CLOSE: (7) is inconsistent. % 88.77/12.80 | | % 88.77/12.80 | Case 2: % 88.77/12.80 | | % 88.77/12.80 | | (8) all_6_3 = e1 % 88.77/12.80 | | % 88.77/12.80 | | COMBINE_EQS: (3), (8) imply: % 88.77/12.80 | | (9) all_4_15 = e1 % 88.77/12.80 | | % 88.77/12.80 | | REDUCE: (4), (9) imply: % 88.77/12.80 | | (10) $false % 88.77/12.80 | | % 88.77/12.80 | | CLOSE: (10) is inconsistent. % 88.77/12.80 | | % 88.77/12.80 | End of split % 88.77/12.80 | % 88.77/12.80 End of proof % 88.77/12.80 % 88.77/12.80 Sub-proof #82 shows that the following formulas are inconsistent: % 88.77/12.80 ---------------------------------------------------------------- % 88.77/12.80 (1) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 88.77/12.80 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 88.77/12.80 (all_9_20 = e3 & op(e0, e4) = e3) % 88.77/12.80 (2) ~ (e3 = e2) % 88.77/12.80 (3) op(e2, e4) = e3 % 88.77/12.80 (4) ~ (e3 = e0) % 88.77/12.80 (5) ~ (e4 = e3) % 88.77/12.80 (6) ~ (all_4_3 = e0) % 88.77/12.80 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.80 (8) all_4_4 = e4 | ~ (op(e0, e4) = e4) % 88.77/12.80 (9) ~ (all_4_3 = e3) % 88.77/12.80 (10) ~ (e4 = e1) % 88.77/12.80 (11) ~ (e4 = e2) % 88.77/12.80 (12) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.77/12.80 (13) all_4_0 = e0 % 88.77/12.80 (14) ~ (all_4_3 = e1) % 88.77/12.80 (15) ~ (all_4_4 = e3) % 88.77/12.80 (16) ~ (all_4_3 = all_4_4) % 88.77/12.80 (17) ~ (e4 = e0) % 88.77/12.80 (18) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.77/12.80 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.77/12.80 (all_9_20 = e4 & op(e0, e4) = e4) % 88.77/12.80 (19) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.77/12.80 (20) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.77/12.80 (21) all_6_10 = e3 % 88.77/12.80 (22) all_9_2 = e1 % 88.77/12.80 (23) ~ (e2 = e0) % 88.77/12.80 (24) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 88.77/12.80 (25) all_6_20 = all_4_4 % 88.77/12.80 (26) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 88.77/12.80 = e0 % 88.77/12.80 (27) ~ (e2 = e1) % 88.77/12.80 (28) e4 = e3 | ~ (op(e2, e4) = e4) % 88.77/12.80 (29) ~ (all_4_4 = e1) % 88.77/12.80 (30) op(e4, e4) = e0 % 88.77/12.80 (31) ~ (e3 = e1) % 88.77/12.80 (32) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.77/12.80 = e0 % 88.77/12.80 (33) ~ (all_4_4 = e0) % 88.77/12.80 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.77/12.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.77/12.80 (35) op(e0, e4) = all_4_4 % 88.77/12.80 (36) all_6_15 = all_4_3 % 88.77/12.80 (37) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 88.77/12.80 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 88.77/12.80 (all_9_20 = e1 & op(e0, e4) = e1) % 88.77/12.80 (38) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 88.77/12.80 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 88.77/12.80 (all_9_20 = e2 & op(e0, e4) = e2) % 88.77/12.80 (39) ~ (e1 = e0) % 88.77/12.80 (40) e1 = e0 % 88.77/12.80 % 88.77/12.80 Begin of proof % 88.77/12.80 | % 88.77/12.80 | COMBINE_EQS: (22), (40) imply: % 88.77/12.80 | (41) all_9_2 = e0 % 88.77/12.80 | % 88.77/12.80 | BETA: splitting (37) gives: % 88.77/12.80 | % 88.77/12.80 | Case 1: % 88.77/12.80 | | % 88.77/12.80 | | (42) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) % 88.77/12.80 | | % 88.77/12.80 | | BETA: splitting (42) gives: % 88.77/12.80 | | % 88.77/12.80 | | Case 1: % 88.77/12.80 | | | % 88.77/12.80 | | | (43) all_9_0 = e1 & op(e4, e4) = e1 % 88.77/12.80 | | | % 88.77/12.80 | | | ALPHA: (43) implies: % 88.77/12.80 | | | (44) op(e4, e4) = e1 % 88.77/12.80 | | | % 88.77/12.80 | | | REF_CLOSE: (30), (34), (39), (44) are inconsistent by sub-proof #132. % 88.77/12.80 | | | % 88.77/12.80 | | Case 2: % 88.77/12.80 | | | % 88.77/12.80 | | | (45) all_9_2 = e1 & op(e3, e4) = e1 % 88.77/12.80 | | | % 88.77/12.80 | | | COMBINE_EQS: (22), (41) imply: % 88.77/12.80 | | | (46) e1 = e0 % 88.77/12.80 | | | % 88.77/12.80 | | | REDUCE: (39), (40) imply: % 88.77/12.80 | | | (47) $false % 88.77/12.80 | | | % 88.77/12.80 | | | CLOSE: (47) is inconsistent. % 88.77/12.80 | | | % 88.77/12.80 | | End of split % 88.77/12.80 | | % 88.77/12.80 | Case 2: % 88.77/12.80 | | % 88.77/12.80 | | (48) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) % 88.77/12.80 | | | (all_9_20 = e1 & op(e0, e4) = e1) % 88.77/12.80 | | % 88.77/12.80 | | BETA: splitting (48) gives: % 88.77/12.80 | | % 88.77/12.80 | | Case 1: % 88.77/12.80 | | | % 88.77/12.80 | | | (49) all_9_6 = e1 & op(e2, e4) = e1 % 88.77/12.80 | | | % 88.77/12.80 | | | ALPHA: (49) implies: % 88.77/12.81 | | | (50) all_9_6 = e1 % 88.77/12.81 | | | (51) op(e2, e4) = e1 % 88.77/12.81 | | | % 88.77/12.81 | | | BETA: splitting (1) gives: % 88.77/12.81 | | | % 88.77/12.81 | | | Case 1: % 88.77/12.81 | | | | % 88.77/12.81 | | | | (52) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = % 88.77/12.81 | | | | e3) % 88.77/12.81 | | | | % 88.77/12.81 | | | | BETA: splitting (52) gives: % 88.77/12.81 | | | | % 88.77/12.81 | | | | Case 1: % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | (53) all_9_0 = e3 & op(e4, e4) = e3 % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | ALPHA: (53) implies: % 88.77/12.81 | | | | | (54) op(e4, e4) = e3 % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | GROUND_INST: instantiating (34) with e3, e1, e4, e2, simplifying with % 88.77/12.81 | | | | | (3), (51) gives: % 88.77/12.81 | | | | | (55) e3 = e1 % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | GROUND_INST: instantiating (34) with e0, e3, e4, e4, simplifying with % 88.77/12.81 | | | | | (30), (54) gives: % 88.77/12.81 | | | | | (56) e3 = e0 % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | REDUCE: (39), (40) imply: % 88.77/12.81 | | | | | (57) $false % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | CLOSE: (57) is inconsistent. % 88.77/12.81 | | | | | % 88.77/12.81 | | | | Case 2: % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | (58) all_9_2 = e3 & op(e3, e4) = e3 % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | ALPHA: (58) implies: % 88.77/12.81 | | | | | (59) all_9_2 = e3 % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | COMBINE_EQS: (41), (59) imply: % 88.77/12.81 | | | | | (60) e3 = e0 % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | SIMP: (60) implies: % 88.77/12.81 | | | | | (61) e3 = e0 % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | REDUCE: (4), (61) imply: % 88.77/12.81 | | | | | (62) $false % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | CLOSE: (62) is inconsistent. % 88.77/12.81 | | | | | % 88.77/12.81 | | | | End of split % 88.77/12.81 | | | | % 88.77/12.81 | | | Case 2: % 88.77/12.81 | | | | % 88.77/12.81 | | | | (63) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = % 88.77/12.81 | | | | e3) | (all_9_20 = e3 & op(e0, e4) = e3) % 88.77/12.81 | | | | % 88.77/12.81 | | | | BETA: splitting (63) gives: % 88.77/12.81 | | | | % 88.77/12.81 | | | | Case 1: % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | (64) all_9_6 = e3 & op(e2, e4) = e3 % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | REF_CLOSE: (31), (50), (64) are inconsistent by sub-proof #102. % 88.77/12.81 | | | | | % 88.77/12.81 | | | | Case 2: % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | (65) (all_9_12 = e3 & op(e1, e4) = e3) | (all_9_20 = e3 & op(e0, % 88.77/12.81 | | | | | e4) = e3) % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | BETA: splitting (65) gives: % 88.77/12.81 | | | | | % 88.77/12.81 | | | | | Case 1: % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | | (66) all_9_12 = e3 & op(e1, e4) = e3 % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | | ALPHA: (66) implies: % 88.77/12.81 | | | | | | (67) all_9_12 = e3 % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | | BETA: splitting (38) gives: % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | | Case 1: % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | (68) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, % 88.77/12.81 | | | | | | | e4) = e2) % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | BETA: splitting (68) gives: % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | (69) all_9_0 = e2 & op(e4, e4) = e2 % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | ALPHA: (69) implies: % 88.77/12.81 | | | | | | | | (70) all_9_0 = e2 % 88.77/12.81 | | | | | | | | (71) op(e4, e4) = e2 % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | BETA: splitting (18) gives: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | (72) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 88.77/12.81 | | | | | | | | | op(e3, e4) = e4) % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | BETA: splitting (72) gives: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | (73) all_9_0 = e4 & op(e4, e4) = e4 % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | ALPHA: (73) implies: % 88.77/12.81 | | | | | | | | | | (74) op(e4, e4) = e4 % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | REF_CLOSE: (13), (17), (19), (74) are inconsistent by % 88.77/12.81 | | | | | | | | | | sub-proof #131. % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | (75) all_9_2 = e4 & op(e3, e4) = e4 % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | ALPHA: (75) implies: % 88.77/12.81 | | | | | | | | | | (76) all_9_2 = e4 % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | COMBINE_EQS: (41), (76) imply: % 88.77/12.81 | | | | | | | | | | (77) e4 = e0 % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | REDUCE: (17), (77) imply: % 88.77/12.81 | | | | | | | | | | (78) $false % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | CLOSE: (78) is inconsistent. % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | (79) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 88.77/12.81 | | | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | BETA: splitting (79) gives: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | (80) all_9_6 = e4 & op(e2, e4) = e4 % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | REF_CLOSE: (10), (50), (80) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | #101. % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | (81) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & % 88.77/12.81 | | | | | | | | | | op(e0, e4) = e4) % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | BETA: splitting (81) gives: % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | (82) all_9_12 = e4 & op(e1, e4) = e4 % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | REF_CLOSE: (5), (67), (82) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | | #119. % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | (83) all_9_20 = e4 & op(e0, e4) = e4 % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | ALPHA: (83) implies: % 88.77/12.81 | | | | | | | | | | | (84) op(e0, e4) = e4 % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | BETA: splitting (8) gives: % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | (85) ~ (op(e0, e4) = e4) % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | PRED_UNIFY: (84), (85) imply: % 88.77/12.81 | | | | | | | | | | | | (86) $false % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | CLOSE: (86) is inconsistent. % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | (87) all_4_4 = e4 % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | REDUCE: (16), (87) imply: % 88.77/12.81 | | | | | | | | | | | | (88) ~ (all_4_3 = e4) % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | BETA: splitting (26) gives: % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | (89) all_6_15 = e4 % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | REF_CLOSE: (36), (88), (89) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | | | | #100. % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | (90) ~ (all_6_15 = e4) % 88.77/12.81 | | | | | | | | | | | | | (91) all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 88.77/12.81 | | | | | | | | | | | | | all_6_15 = e0 % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | BETA: splitting (91) gives: % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | (92) all_6_15 = e2 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | COMBINE_EQS: (36), (92) imply: % 88.77/12.81 | | | | | | | | | | | | | | (93) all_4_3 = e2 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | SIMP: (93) implies: % 88.77/12.81 | | | | | | | | | | | | | | (94) all_4_3 = e2 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | REDUCE: (88), (94) imply: % 88.77/12.81 | | | | | | | | | | | | | | (95) ~ (e4 = e2) % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | REDUCE: (9), (94) imply: % 88.77/12.81 | | | | | | | | | | | | | | (96) ~ (e3 = e2) % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with e0, e2, e4, e4, % 88.77/12.81 | | | | | | | | | | | | | | simplifying with (30), (71) gives: % 88.77/12.81 | | | | | | | | | | | | | | (97) e2 = e0 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | COMBINE_EQS: (70), (97) imply: % 88.77/12.81 | | | | | | | | | | | | | | (98) all_9_0 = e0 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | BETA: splitting (38) gives: % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | REF_CLOSE: (23), (41), (68), (98) are inconsistent by % 88.77/12.81 | | | | | | | | | | | | | | | sub-proof #98. % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | (99) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 % 88.77/12.81 | | | | | | | | | | | | | | | & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) % 88.77/12.81 | | | | | | | | | | | | | | | = e2) % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | (100) all_9_6 = e2 & op(e2, e4) = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (20), (21), (100) are inconsistent by % 88.77/12.81 | | | | | | | | | | | | | | | | sub-proof #125. % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | (101) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | & op(e0, e4) = e2) % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | (102) all_9_12 = e2 & op(e1, e4) = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (67), (102) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | | | | | | | | #97. % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | (103) all_9_20 = e2 & op(e0, e4) = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | ALPHA: (103) implies: % 88.77/12.81 | | | | | | | | | | | | | | | | | (104) all_9_20 = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (11), (13), (17), (18), (19), (41), % 88.77/12.81 | | | | | | | | | | | | | | | | | (50), (67), (104) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | | | | | | | | #94. % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | (105) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14), (36), (105) are inconsistent by % 88.77/12.81 | | | | | | | | | | | | | | sub-proof #93. % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | End of split % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | (106) all_9_2 = e2 & op(e3, e4) = e2 % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | REF_CLOSE: (23), (41), (106) are inconsistent by sub-proof #99. % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | End of split % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | Case 2: % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | (107) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & % 88.77/12.81 | | | | | | | op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | BETA: splitting (107) gives: % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | (108) all_9_6 = e2 & op(e2, e4) = e2 % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | REF_CLOSE: (2), (20), (21), (108) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | #125. % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | (109) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & % 88.77/12.81 | | | | | | | | op(e0, e4) = e2) % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | BETA: splitting (109) gives: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | (110) all_9_12 = e2 & op(e1, e4) = e2 % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | REF_CLOSE: (2), (67), (110) are inconsistent by sub-proof #97. % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | (111) all_9_20 = e2 & op(e0, e4) = e2 % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | ALPHA: (111) implies: % 88.77/12.81 | | | | | | | | | (112) all_9_20 = e2 % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | REF_CLOSE: (5), (10), (11), (13), (17), (18), (19), (41), % 88.77/12.81 | | | | | | | | | (50), (67), (112) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | #94. % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | End of split % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | End of split % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | End of split % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | Case 2: % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | | (113) all_9_20 = e3 & op(e0, e4) = e3 % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | | ALPHA: (113) implies: % 88.77/12.81 | | | | | | (114) all_9_20 = e3 % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | | BETA: splitting (38) gives: % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | | Case 1: % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | (115) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, % 88.77/12.81 | | | | | | | e4) = e2) % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | BETA: splitting (115) gives: % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | (116) all_9_0 = e2 & op(e4, e4) = e2 % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | ALPHA: (116) implies: % 88.77/12.81 | | | | | | | | (117) all_9_0 = e2 % 88.77/12.81 | | | | | | | | (118) op(e4, e4) = e2 % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | BETA: splitting (18) gives: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | (119) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 88.77/12.81 | | | | | | | | | op(e3, e4) = e4) % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | REF_CLOSE: (13), (17), (19), (41), (119) are inconsistent by % 88.77/12.81 | | | | | | | | | sub-proof #95. % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | (120) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 88.77/12.81 | | | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 88.77/12.81 | | | | | | | | | e4) % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | BETA: splitting (120) gives: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | (121) all_9_6 = e4 & op(e2, e4) = e4 % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | REF_CLOSE: (10), (50), (121) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | #101. % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | (122) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 88.77/12.81 | | | | | | | | | | & op(e0, e4) = e4) % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | BETA: splitting (122) gives: % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | (123) all_9_12 = e4 & op(e1, e4) = e4 % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | ALPHA: (123) implies: % 88.77/12.81 | | | | | | | | | | | (124) op(e1, e4) = e4 % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | BETA: splitting (24) gives: % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | (125) ~ (op(e1, e4) = e4) % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | PRED_UNIFY: (124), (125) imply: % 88.77/12.81 | | | | | | | | | | | | (126) $false % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | (127) all_4_3 = e4 % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | REDUCE: (16), (127) imply: % 88.77/12.81 | | | | | | | | | | | | (128) ~ (all_4_4 = e4) % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | SIMP: (128) implies: % 88.77/12.81 | | | | | | | | | | | | (129) ~ (all_4_4 = e4) % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | BETA: splitting (32) gives: % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | (130) all_6_20 = e4 % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | REF_CLOSE: (25), (129), (130) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | | | | #123. % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | (131) ~ (all_6_20 = e4) % 88.77/12.81 | | | | | | | | | | | | | (132) all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 88.77/12.81 | | | | | | | | | | | | | all_6_20 = e0 % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | BETA: splitting (132) gives: % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | (133) all_6_20 = e2 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | COMBINE_EQS: (25), (133) imply: % 88.77/12.81 | | | | | | | | | | | | | | (134) all_4_4 = e2 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | SIMP: (134) implies: % 88.77/12.81 | | | | | | | | | | | | | | (135) all_4_4 = e2 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | REDUCE: (129), (135) imply: % 88.77/12.81 | | | | | | | | | | | | | | (136) ~ (e4 = e2) % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | REDUCE: (15), (135) imply: % 88.77/12.81 | | | | | | | | | | | | | | (137) ~ (e3 = e2) % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with e0, e2, e4, e4, % 88.77/12.81 | | | | | | | | | | | | | | simplifying with (30), (118) gives: % 88.77/12.81 | | | | | | | | | | | | | | (138) e2 = e0 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | COMBINE_EQS: (117), (138) imply: % 88.77/12.81 | | | | | | | | | | | | | | (139) all_9_0 = e0 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | BETA: splitting (38) gives: % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | REF_CLOSE: (23), (41), (115), (139) are inconsistent by % 88.77/12.81 | | | | | | | | | | | | | | | sub-proof #98. % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | (140) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 % 88.77/12.81 | | | | | | | | | | | | | | | & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) % 88.77/12.81 | | | | | | | | | | | | | | | = e2) % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | (141) all_9_6 = e2 & op(e2, e4) = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (20), (21), (141) are inconsistent by % 88.77/12.81 | | | | | | | | | | | | | | | | sub-proof #125. % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | (142) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | & op(e0, e4) = e2) % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | (143) all_9_12 = e2 & op(e1, e4) = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | ALPHA: (143) implies: % 88.77/12.81 | | | | | | | | | | | | | | | | | (144) all_9_12 = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (11), (13), (17), (18), (19), (41), % 88.77/12.81 | | | | | | | | | | | | | | | | | (50), (114), (144) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | | | | | | | | #90. % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | (145) all_9_20 = e2 & op(e0, e4) = e2 % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (114), (145) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | | | | | | | | #89. % 88.77/12.81 | | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | (146) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | | REF_CLOSE: (15), (25), (29), (33), (146) are inconsistent by % 88.77/12.81 | | | | | | | | | | | | | | sub-proof #88. % 88.77/12.81 | | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | (147) all_9_20 = e4 & op(e0, e4) = e4 % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | | REF_CLOSE: (5), (114), (147) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | | | #91. % 88.77/12.81 | | | | | | | | | | | % 88.77/12.81 | | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | | % 88.77/12.81 | | | | | | | | | End of split % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | End of split % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | (148) all_9_2 = e2 & op(e3, e4) = e2 % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | REF_CLOSE: (23), (41), (148) are inconsistent by sub-proof #99. % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | End of split % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | Case 2: % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | (149) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & % 88.77/12.81 | | | | | | | op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | BETA: splitting (149) gives: % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | (150) all_9_6 = e2 & op(e2, e4) = e2 % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | REF_CLOSE: (2), (20), (21), (150) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | #125. % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | (151) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & % 88.77/12.81 | | | | | | | | op(e0, e4) = e2) % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | BETA: splitting (151) gives: % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | | Case 1: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | (152) all_9_12 = e2 & op(e1, e4) = e2 % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | ALPHA: (152) implies: % 88.77/12.81 | | | | | | | | | (153) all_9_12 = e2 % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | REF_CLOSE: (5), (10), (11), (13), (17), (18), (19), (41), % 88.77/12.81 | | | | | | | | | (50), (114), (153) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | #90. % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | Case 2: % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | (154) all_9_20 = e2 & op(e0, e4) = e2 % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | | REF_CLOSE: (2), (114), (154) are inconsistent by sub-proof % 88.77/12.81 | | | | | | | | | #89. % 88.77/12.81 | | | | | | | | | % 88.77/12.81 | | | | | | | | End of split % 88.77/12.81 | | | | | | | | % 88.77/12.81 | | | | | | | End of split % 88.77/12.81 | | | | | | | % 88.77/12.81 | | | | | | End of split % 88.77/12.81 | | | | | | % 88.77/12.81 | | | | | End of split % 88.77/12.81 | | | | | % 88.77/12.81 | | | | End of split % 88.77/12.81 | | | | % 88.77/12.81 | | | End of split % 88.77/12.81 | | | % 88.77/12.81 | | Case 2: % 88.77/12.81 | | | % 88.77/12.81 | | | (155) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_20 = e1 & op(e0, e4) = % 88.77/12.81 | | | e1) % 88.77/12.81 | | | % 88.77/12.81 | | | BETA: splitting (155) gives: % 88.77/12.81 | | | % 88.77/12.81 | | | Case 1: % 88.77/12.81 | | | | % 88.77/12.81 | | | | (156) all_9_12 = e1 & op(e1, e4) = e1 % 88.77/12.81 | | | | % 88.77/12.81 | | | | ALPHA: (156) implies: % 88.77/12.81 | | | | (157) op(e1, e4) = e1 % 88.77/12.81 | | | | % 88.77/12.81 | | | | REF_CLOSE: (12), (14), (157) are inconsistent by sub-proof #87. % 88.77/12.81 | | | | % 88.77/12.81 | | | Case 2: % 88.77/12.81 | | | | % 88.77/12.82 | | | | (158) all_9_20 = e1 & op(e0, e4) = e1 % 88.77/12.82 | | | | % 88.77/12.82 | | | | ALPHA: (158) implies: % 88.77/12.82 | | | | (159) all_9_20 = e1 % 88.77/12.82 | | | | (160) op(e0, e4) = e1 % 88.77/12.82 | | | | % 88.77/12.82 | | | | BETA: splitting (38) gives: % 88.77/12.82 | | | | % 88.77/12.82 | | | | Case 1: % 88.77/12.82 | | | | | % 88.77/12.82 | | | | | (161) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) % 88.77/12.82 | | | | | = e2) % 88.77/12.82 | | | | | % 88.77/12.82 | | | | | BETA: splitting (161) gives: % 88.77/12.82 | | | | | % 88.77/12.82 | | | | | Case 1: % 88.77/12.82 | | | | | | % 88.77/12.82 | | | | | | (162) all_9_0 = e2 & op(e4, e4) = e2 % 88.77/12.82 | | | | | | % 88.77/12.82 | | | | | | ALPHA: (162) implies: % 88.77/12.82 | | | | | | (163) all_9_0 = e2 % 88.99/12.82 | | | | | | (164) op(e4, e4) = e2 % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | | BETA: splitting (18) gives: % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | | Case 1: % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | (165) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, % 88.99/12.82 | | | | | | | e4) = e4) % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | REF_CLOSE: (13), (17), (19), (41), (165) are inconsistent by % 88.99/12.82 | | | | | | | sub-proof #95. % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | Case 2: % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | (166) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 88.99/12.82 | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | BETA: splitting (166) gives: % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | (167) all_9_6 = e4 & op(e2, e4) = e4 % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | ALPHA: (167) implies: % 88.99/12.82 | | | | | | | | (168) all_9_6 = e4 % 88.99/12.82 | | | | | | | | (169) op(e2, e4) = e4 % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | BETA: splitting (28) gives: % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | (170) ~ (op(e2, e4) = e4) % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | PRED_UNIFY: (169), (170) imply: % 88.99/12.82 | | | | | | | | | (171) $false % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | CLOSE: (171) is inconsistent. % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | (172) e4 = e3 % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | COMBINE_EQS: (168), (172) imply: % 88.99/12.82 | | | | | | | | | (173) all_9_6 = e3 % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | BETA: splitting (18) gives: % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | (174) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 88.99/12.82 | | | | | | | | | | op(e3, e4) = e4) % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | BETA: splitting (174) gives: % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | (175) all_9_0 = e4 & op(e4, e4) = e4 % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | ALPHA: (175) implies: % 88.99/12.82 | | | | | | | | | | | (176) all_9_0 = e4 % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | COMBINE_EQS: (163), (176) imply: % 88.99/12.82 | | | | | | | | | | | (177) e4 = e2 % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | SIMP: (177) implies: % 88.99/12.82 | | | | | | | | | | | (178) e4 = e2 % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | REDUCE: (11), (178) imply: % 88.99/12.82 | | | | | | | | | | | (179) $false % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | CLOSE: (179) is inconsistent. % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | (180) all_9_2 = e4 & op(e3, e4) = e4 % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | REF_CLOSE: (17), (41), (180) are inconsistent by sub-proof % 88.99/12.82 | | | | | | | | | | | #96. % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | End of split % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | BETA: splitting (166) gives: % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | REDUCE: (5), (172) imply: % 88.99/12.82 | | | | | | | | | | | (181) $false % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | CLOSE: (181) is inconsistent. % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | (182) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 88.99/12.82 | | | | | | | | | | | & op(e0, e4) = e4) % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | BETA: splitting (182) gives: % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | (183) all_9_12 = e4 & op(e1, e4) = e4 % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | ALPHA: (183) implies: % 88.99/12.82 | | | | | | | | | | | | (184) op(e1, e4) = e4 % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | REF_CLOSE: (7), (15), (16), (25), (29), (30), (32), (33), % 88.99/12.82 | | | | | | | | | | | | (34), (35), (36), (39), (160), (164), (184) are % 88.99/12.82 | | | | | | | | | | | | inconsistent by sub-proof #86. % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | (185) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | REF_CLOSE: (10), (159), (185) are inconsistent by sub-proof % 88.99/12.82 | | | | | | | | | | | | #85. % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | End of split % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | End of split % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | End of split % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | End of split % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | (186) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & % 88.99/12.82 | | | | | | | | op(e0, e4) = e4) % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | BETA: splitting (186) gives: % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | (187) all_9_12 = e4 & op(e1, e4) = e4 % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | ALPHA: (187) implies: % 88.99/12.82 | | | | | | | | | (188) op(e1, e4) = e4 % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | REF_CLOSE: (7), (15), (16), (25), (29), (30), (32), (33), % 88.99/12.82 | | | | | | | | | (34), (35), (36), (39), (160), (164), (188) are % 88.99/12.82 | | | | | | | | | inconsistent by sub-proof #86. % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | (189) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | REF_CLOSE: (10), (159), (189) are inconsistent by sub-proof % 88.99/12.82 | | | | | | | | | #85. % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | End of split % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | End of split % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | End of split % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | Case 2: % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | | (190) all_9_2 = e2 & op(e3, e4) = e2 % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | | REF_CLOSE: (23), (41), (190) are inconsistent by sub-proof #99. % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | End of split % 88.99/12.82 | | | | | % 88.99/12.82 | | | | Case 2: % 88.99/12.82 | | | | | % 88.99/12.82 | | | | | (191) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, % 88.99/12.82 | | | | | e4) = e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 88.99/12.82 | | | | | % 88.99/12.82 | | | | | BETA: splitting (191) gives: % 88.99/12.82 | | | | | % 88.99/12.82 | | | | | Case 1: % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | | (192) all_9_6 = e2 & op(e2, e4) = e2 % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | | REF_CLOSE: (2), (20), (21), (192) are inconsistent by sub-proof % 88.99/12.82 | | | | | | #125. % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | Case 2: % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | | (193) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, % 88.99/12.82 | | | | | | e4) = e2) % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | | BETA: splitting (193) gives: % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | | Case 1: % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | (194) all_9_12 = e2 & op(e1, e4) = e2 % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | ALPHA: (194) implies: % 88.99/12.82 | | | | | | | (195) all_9_12 = e2 % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | BETA: splitting (18) gives: % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | (196) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 88.99/12.82 | | | | | | | | op(e3, e4) = e4) % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | REF_CLOSE: (13), (17), (19), (41), (196) are inconsistent by % 88.99/12.82 | | | | | | | | sub-proof #95. % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | (197) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 88.99/12.82 | | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | BETA: splitting (197) gives: % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | (198) all_9_6 = e4 & op(e2, e4) = e4 % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | ALPHA: (198) implies: % 88.99/12.82 | | | | | | | | | (199) all_9_6 = e4 % 88.99/12.82 | | | | | | | | | (200) op(e2, e4) = e4 % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | BETA: splitting (28) gives: % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | (201) ~ (op(e2, e4) = e4) % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | PRED_UNIFY: (200), (201) imply: % 88.99/12.82 | | | | | | | | | | (202) $false % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | CLOSE: (202) is inconsistent. % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | (203) e4 = e3 % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | COMBINE_EQS: (199), (203) imply: % 88.99/12.82 | | | | | | | | | | (204) all_9_6 = e3 % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | BETA: splitting (18) gives: % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | (205) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 88.99/12.82 | | | | | | | | | | | op(e3, e4) = e4) % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | REF_CLOSE: (13), (17), (19), (41), (205) are inconsistent by % 88.99/12.82 | | | | | | | | | | | sub-proof #95. % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | BETA: splitting (197) gives: % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | COMBINE_EQS: (199), (204) imply: % 88.99/12.82 | | | | | | | | | | | | (206) e4 = e3 % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | REDUCE: (5), (203) imply: % 88.99/12.82 | | | | | | | | | | | | (207) $false % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | CLOSE: (207) is inconsistent. % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | (208) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 88.99/12.82 | | | | | | | | | | | | & op(e0, e4) = e4) % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | BETA: splitting (208) gives: % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | Case 1: % 88.99/12.82 | | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | | (209) all_9_12 = e4 & op(e1, e4) = e4 % 88.99/12.82 | | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | | REF_CLOSE: (11), (195), (209) are inconsistent by sub-proof % 88.99/12.82 | | | | | | | | | | | | | #92. % 88.99/12.82 | | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | | (210) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.82 | | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | | REF_CLOSE: (10), (159), (210) are inconsistent by sub-proof % 88.99/12.82 | | | | | | | | | | | | | #85. % 88.99/12.82 | | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | | End of split % 88.99/12.82 | | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | | End of split % 88.99/12.82 | | | | | | | | | | | % 88.99/12.82 | | | | | | | | | | End of split % 88.99/12.82 | | | | | | | | | | % 88.99/12.82 | | | | | | | | | End of split % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | Case 2: % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | (211) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & % 88.99/12.82 | | | | | | | | | op(e0, e4) = e4) % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | | REF_CLOSE: (10), (11), (159), (195), (211) are inconsistent by % 88.99/12.82 | | | | | | | | | sub-proof #84. % 88.99/12.82 | | | | | | | | | % 88.99/12.82 | | | | | | | | End of split % 88.99/12.82 | | | | | | | | % 88.99/12.82 | | | | | | | End of split % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | Case 2: % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | (212) all_9_20 = e2 & op(e0, e4) = e2 % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | | REF_CLOSE: (27), (159), (212) are inconsistent by sub-proof #83. % 88.99/12.82 | | | | | | | % 88.99/12.82 | | | | | | End of split % 88.99/12.82 | | | | | | % 88.99/12.82 | | | | | End of split % 88.99/12.82 | | | | | % 88.99/12.82 | | | | End of split % 88.99/12.82 | | | | % 88.99/12.82 | | | End of split % 88.99/12.82 | | | % 88.99/12.82 | | End of split % 88.99/12.82 | | % 88.99/12.82 | End of split % 88.99/12.82 | % 88.99/12.82 End of proof % 88.99/12.82 % 88.99/12.82 Sub-proof #83 shows that the following formulas are inconsistent: % 88.99/12.82 ---------------------------------------------------------------- % 88.99/12.82 (1) all_9_20 = e2 & op(e0, e4) = e2 % 88.99/12.82 (2) all_9_20 = e1 % 88.99/12.82 (3) ~ (e2 = e1) % 88.99/12.82 % 88.99/12.82 Begin of proof % 88.99/12.82 | % 88.99/12.82 | ALPHA: (1) implies: % 88.99/12.82 | (4) all_9_20 = e2 % 88.99/12.82 | % 88.99/12.82 | COMBINE_EQS: (2), (4) imply: % 88.99/12.82 | (5) e2 = e1 % 88.99/12.82 | % 88.99/12.82 | REDUCE: (3), (5) imply: % 88.99/12.82 | (6) $false % 88.99/12.82 | % 88.99/12.82 | CLOSE: (6) is inconsistent. % 88.99/12.82 | % 88.99/12.82 End of proof % 88.99/12.82 % 88.99/12.82 Sub-proof #84 shows that the following formulas are inconsistent: % 88.99/12.82 ---------------------------------------------------------------- % 88.99/12.82 (1) all_9_12 = e2 % 88.99/12.82 (2) ~ (e4 = e1) % 88.99/12.82 (3) ~ (e4 = e2) % 88.99/12.82 (4) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.82 (5) all_9_20 = e1 % 88.99/12.82 % 88.99/12.82 Begin of proof % 88.99/12.82 | % 88.99/12.82 | BETA: splitting (4) gives: % 88.99/12.82 | % 88.99/12.82 | Case 1: % 88.99/12.82 | | % 88.99/12.82 | | (6) all_9_12 = e4 & op(e1, e4) = e4 % 88.99/12.82 | | % 88.99/12.82 | | ALPHA: (6) implies: % 88.99/12.82 | | (7) all_9_12 = e4 % 88.99/12.82 | | % 88.99/12.82 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #124. % 88.99/12.82 | | % 88.99/12.82 | Case 2: % 88.99/12.82 | | % 88.99/12.82 | | (8) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.82 | | % 88.99/12.82 | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #85. % 88.99/12.82 | | % 88.99/12.82 | End of split % 88.99/12.82 | % 88.99/12.82 End of proof % 88.99/12.82 % 88.99/12.82 Sub-proof #85 shows that the following formulas are inconsistent: % 88.99/12.82 ---------------------------------------------------------------- % 88.99/12.82 (1) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.82 (2) all_9_20 = e1 % 88.99/12.82 (3) ~ (e4 = e1) % 88.99/12.82 % 88.99/12.82 Begin of proof % 88.99/12.82 | % 88.99/12.82 | ALPHA: (1) implies: % 88.99/12.82 | (4) all_9_20 = e4 % 88.99/12.82 | % 88.99/12.82 | COMBINE_EQS: (2), (4) imply: % 88.99/12.82 | (5) e4 = e1 % 88.99/12.82 | % 88.99/12.82 | REDUCE: (3), (5) imply: % 88.99/12.82 | (6) $false % 88.99/12.82 | % 88.99/12.82 | CLOSE: (6) is inconsistent. % 88.99/12.82 | % 88.99/12.82 End of proof % 88.99/12.82 % 88.99/12.82 Sub-proof #86 shows that the following formulas are inconsistent: % 88.99/12.82 ---------------------------------------------------------------- % 88.99/12.82 (1) op(e4, e4) = e2 % 88.99/12.82 (2) op(e1, e4) = e4 % 88.99/12.82 (3) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 88.99/12.82 (4) ~ (all_4_4 = e3) % 88.99/12.82 (5) ~ (all_4_3 = all_4_4) % 88.99/12.82 (6) all_6_20 = all_4_4 % 88.99/12.82 (7) ~ (all_4_4 = e1) % 88.99/12.82 (8) op(e4, e4) = e0 % 88.99/12.82 (9) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 88.99/12.82 = e0 % 88.99/12.82 (10) ~ (all_4_4 = e0) % 88.99/12.82 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.99/12.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.99/12.82 (12) op(e0, e4) = all_4_4 % 88.99/12.82 (13) all_6_15 = all_4_3 % 88.99/12.82 (14) op(e0, e4) = e1 % 88.99/12.82 (15) ~ (e1 = e0) % 88.99/12.82 % 88.99/12.82 Begin of proof % 88.99/12.82 | % 88.99/12.82 | BETA: splitting (3) gives: % 88.99/12.82 | % 88.99/12.82 | Case 1: % 88.99/12.82 | | % 88.99/12.82 | | (16) ~ (op(e1, e4) = e4) % 88.99/12.82 | | % 88.99/12.82 | | PRED_UNIFY: (2), (16) imply: % 88.99/12.82 | | (17) $false % 88.99/12.82 | | % 88.99/12.82 | | CLOSE: (17) is inconsistent. % 88.99/12.82 | | % 88.99/12.82 | Case 2: % 88.99/12.82 | | % 88.99/12.82 | | (18) all_6_15 = e4 % 88.99/12.82 | | % 88.99/12.82 | | COMBINE_EQS: (13), (18) imply: % 88.99/12.82 | | (19) all_4_3 = e4 % 88.99/12.82 | | % 88.99/12.82 | | SIMP: (19) implies: % 88.99/12.82 | | (20) all_4_3 = e4 % 88.99/12.82 | | % 88.99/12.82 | | REDUCE: (5), (20) imply: % 88.99/12.82 | | (21) ~ (all_4_4 = e4) % 88.99/12.82 | | % 88.99/12.82 | | SIMP: (21) implies: % 88.99/12.82 | | (22) ~ (all_4_4 = e4) % 88.99/12.82 | | % 88.99/12.82 | | BETA: splitting (9) gives: % 88.99/12.82 | | % 88.99/12.82 | | Case 1: % 88.99/12.82 | | | % 88.99/12.82 | | | (23) all_6_20 = e4 % 88.99/12.82 | | | % 88.99/12.82 | | | REF_CLOSE: (6), (22), (23) are inconsistent by sub-proof #123. % 88.99/12.82 | | | % 88.99/12.82 | | Case 2: % 88.99/12.82 | | | % 88.99/12.82 | | | (24) all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 = e0 % 88.99/12.82 | | | % 88.99/12.82 | | | BETA: splitting (24) gives: % 88.99/12.82 | | | % 88.99/12.82 | | | Case 1: % 88.99/12.82 | | | | % 88.99/12.82 | | | | (25) all_6_20 = e2 % 88.99/12.82 | | | | % 88.99/12.82 | | | | COMBINE_EQS: (6), (25) imply: % 88.99/12.82 | | | | (26) all_4_4 = e2 % 88.99/12.82 | | | | % 88.99/12.82 | | | | SIMP: (26) implies: % 88.99/12.82 | | | | (27) all_4_4 = e2 % 88.99/12.82 | | | | % 88.99/12.82 | | | | REDUCE: (12), (27) imply: % 88.99/12.82 | | | | (28) op(e0, e4) = e2 % 88.99/12.82 | | | | % 88.99/12.82 | | | | GROUND_INST: instantiating (11) with e1, e2, e4, e0, simplifying with % 88.99/12.82 | | | | (14), (28) gives: % 88.99/12.82 | | | | (29) e2 = e1 % 88.99/12.82 | | | | % 88.99/12.82 | | | | GROUND_INST: instantiating (11) with e0, e2, e4, e4, simplifying with % 88.99/12.82 | | | | (1), (8) gives: % 88.99/12.82 | | | | (30) e2 = e0 % 88.99/12.82 | | | | % 88.99/12.82 | | | | COMBINE_EQS: (29), (30) imply: % 88.99/12.82 | | | | (31) e1 = e0 % 88.99/12.82 | | | | % 88.99/12.82 | | | | SIMP: (31) implies: % 88.99/12.82 | | | | (32) e1 = e0 % 88.99/12.82 | | | | % 88.99/12.82 | | | | REDUCE: (15), (32) imply: % 88.99/12.82 | | | | (33) $false % 88.99/12.82 | | | | % 88.99/12.82 | | | | CLOSE: (33) is inconsistent. % 88.99/12.82 | | | | % 88.99/12.82 | | | Case 2: % 88.99/12.82 | | | | % 88.99/12.82 | | | | (34) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 88.99/12.82 | | | | % 88.99/12.82 | | | | REF_CLOSE: (4), (6), (7), (10), (34) are inconsistent by sub-proof #88. % 88.99/12.82 | | | | % 88.99/12.82 | | | End of split % 88.99/12.82 | | | % 88.99/12.82 | | End of split % 88.99/12.82 | | % 88.99/12.82 | End of split % 88.99/12.82 | % 88.99/12.82 End of proof % 88.99/12.82 % 88.99/12.82 Sub-proof #87 shows that the following formulas are inconsistent: % 88.99/12.82 ---------------------------------------------------------------- % 88.99/12.82 (1) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 88.99/12.82 (2) op(e1, e4) = e1 % 88.99/12.82 (3) ~ (all_4_3 = e1) % 88.99/12.82 % 88.99/12.82 Begin of proof % 88.99/12.82 | % 88.99/12.82 | BETA: splitting (1) gives: % 88.99/12.82 | % 88.99/12.82 | Case 1: % 88.99/12.82 | | % 88.99/12.82 | | (4) ~ (op(e1, e4) = e1) % 88.99/12.82 | | % 88.99/12.82 | | PRED_UNIFY: (2), (4) imply: % 88.99/12.82 | | (5) $false % 88.99/12.82 | | % 88.99/12.82 | | CLOSE: (5) is inconsistent. % 88.99/12.82 | | % 88.99/12.82 | Case 2: % 88.99/12.82 | | % 88.99/12.82 | | (6) all_4_3 = e1 % 88.99/12.82 | | % 88.99/12.82 | | REDUCE: (3), (6) imply: % 88.99/12.82 | | (7) $false % 88.99/12.82 | | % 88.99/12.82 | | CLOSE: (7) is inconsistent. % 88.99/12.82 | | % 88.99/12.82 | End of split % 88.99/12.82 | % 88.99/12.82 End of proof % 88.99/12.82 % 88.99/12.82 Sub-proof #88 shows that the following formulas are inconsistent: % 88.99/12.82 ---------------------------------------------------------------- % 88.99/12.82 (1) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 88.99/12.82 (2) ~ (all_4_4 = e3) % 88.99/12.82 (3) all_6_20 = all_4_4 % 88.99/12.82 (4) ~ (all_4_4 = e1) % 88.99/12.82 (5) ~ (all_4_4 = e0) % 88.99/12.82 % 88.99/12.82 Begin of proof % 88.99/12.82 | % 88.99/12.82 | BETA: splitting (1) gives: % 88.99/12.82 | % 88.99/12.82 | Case 1: % 88.99/12.82 | | % 88.99/12.82 | | (6) all_6_20 = e3 % 88.99/12.82 | | % 88.99/12.82 | | COMBINE_EQS: (3), (6) imply: % 88.99/12.82 | | (7) all_4_4 = e3 % 88.99/12.82 | | % 88.99/12.82 | | SIMP: (7) implies: % 88.99/12.82 | | (8) all_4_4 = e3 % 88.99/12.82 | | % 88.99/12.82 | | REDUCE: (2), (8) imply: % 88.99/12.82 | | (9) $false % 88.99/12.82 | | % 88.99/12.82 | | CLOSE: (9) is inconsistent. % 88.99/12.82 | | % 88.99/12.82 | Case 2: % 88.99/12.82 | | % 88.99/12.82 | | (10) all_6_20 = e1 | all_6_20 = e0 % 88.99/12.82 | | % 88.99/12.82 | | BETA: splitting (10) gives: % 88.99/12.82 | | % 88.99/12.82 | | Case 1: % 88.99/12.82 | | | % 88.99/12.82 | | | (11) all_6_20 = e1 % 88.99/12.82 | | | % 88.99/12.82 | | | COMBINE_EQS: (3), (11) imply: % 88.99/12.82 | | | (12) all_4_4 = e1 % 88.99/12.82 | | | % 88.99/12.82 | | | SIMP: (12) implies: % 88.99/12.82 | | | (13) all_4_4 = e1 % 88.99/12.82 | | | % 88.99/12.82 | | | REDUCE: (4), (13) imply: % 88.99/12.82 | | | (14) $false % 88.99/12.82 | | | % 88.99/12.82 | | | CLOSE: (14) is inconsistent. % 88.99/12.82 | | | % 88.99/12.82 | | Case 2: % 88.99/12.82 | | | % 88.99/12.82 | | | (15) all_6_20 = e0 % 88.99/12.82 | | | % 88.99/12.82 | | | COMBINE_EQS: (3), (15) imply: % 88.99/12.82 | | | (16) all_4_4 = e0 % 88.99/12.82 | | | % 88.99/12.82 | | | SIMP: (16) implies: % 88.99/12.82 | | | (17) all_4_4 = e0 % 88.99/12.82 | | | % 88.99/12.82 | | | REDUCE: (5), (17) imply: % 88.99/12.82 | | | (18) $false % 88.99/12.82 | | | % 88.99/12.83 | | | CLOSE: (18) is inconsistent. % 88.99/12.83 | | | % 88.99/12.83 | | End of split % 88.99/12.83 | | % 88.99/12.83 | End of split % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #89 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_20 = e2 & op(e0, e4) = e2 % 88.99/12.83 (2) all_9_20 = e3 % 88.99/12.83 (3) ~ (e3 = e2) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (4) all_9_20 = e2 % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (2), (4) imply: % 88.99/12.83 | (5) e3 = e2 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (5) imply: % 88.99/12.83 | (6) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (6) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #90 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_2 = e0 % 88.99/12.83 (2) ~ (e4 = e3) % 88.99/12.83 (3) all_9_12 = e2 % 88.99/12.83 (4) ~ (e4 = e1) % 88.99/12.83 (5) ~ (e4 = e2) % 88.99/12.83 (6) all_4_0 = e0 % 88.99/12.83 (7) ~ (e4 = e0) % 88.99/12.83 (8) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.99/12.83 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.99/12.83 (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.83 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.99/12.83 (10) all_9_20 = e3 % 88.99/12.83 (11) all_9_6 = e1 % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | BETA: splitting (8) gives: % 88.99/12.83 | % 88.99/12.83 | Case 1: % 88.99/12.83 | | % 88.99/12.83 | | (12) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 88.99/12.83 | | % 88.99/12.83 | | REF_CLOSE: (1), (6), (7), (9), (12) are inconsistent by sub-proof #95. % 88.99/12.83 | | % 88.99/12.83 | Case 2: % 88.99/12.83 | | % 88.99/12.83 | | (13) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 88.99/12.83 | | | (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.83 | | % 88.99/12.83 | | BETA: splitting (13) gives: % 88.99/12.83 | | % 88.99/12.83 | | Case 1: % 88.99/12.83 | | | % 88.99/12.83 | | | (14) all_9_6 = e4 & op(e2, e4) = e4 % 88.99/12.83 | | | % 88.99/12.83 | | | REF_CLOSE: (4), (11), (14) are inconsistent by sub-proof #101. % 88.99/12.83 | | | % 88.99/12.83 | | Case 2: % 88.99/12.83 | | | % 88.99/12.83 | | | (15) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 88.99/12.83 | | | e4) % 88.99/12.83 | | | % 88.99/12.83 | | | BETA: splitting (15) gives: % 88.99/12.83 | | | % 88.99/12.83 | | | Case 1: % 88.99/12.83 | | | | % 88.99/12.83 | | | | (16) all_9_12 = e4 & op(e1, e4) = e4 % 88.99/12.83 | | | | % 88.99/12.83 | | | | REF_CLOSE: (3), (5), (16) are inconsistent by sub-proof #92. % 88.99/12.83 | | | | % 88.99/12.83 | | | Case 2: % 88.99/12.83 | | | | % 88.99/12.83 | | | | (17) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.83 | | | | % 88.99/12.83 | | | | REF_CLOSE: (2), (10), (17) are inconsistent by sub-proof #91. % 88.99/12.83 | | | | % 88.99/12.83 | | | End of split % 88.99/12.83 | | | % 88.99/12.83 | | End of split % 88.99/12.83 | | % 88.99/12.83 | End of split % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #91 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.83 (2) all_9_20 = e3 % 88.99/12.83 (3) ~ (e4 = e3) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (4) all_9_20 = e4 % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (2), (4) imply: % 88.99/12.83 | (5) e4 = e3 % 88.99/12.83 | % 88.99/12.83 | SIMP: (5) implies: % 88.99/12.83 | (6) e4 = e3 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (6) imply: % 88.99/12.83 | (7) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (7) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #92 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_12 = e4 & op(e1, e4) = e4 % 88.99/12.83 (2) all_9_12 = e2 % 88.99/12.83 (3) ~ (e4 = e2) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (4) all_9_12 = e4 % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (2), (4) imply: % 88.99/12.83 | (5) e4 = e2 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (5) imply: % 88.99/12.83 | (6) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (6) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #93 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) ~ (all_4_3 = e0) % 88.99/12.83 (2) ~ (all_4_3 = e3) % 88.99/12.83 (3) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 88.99/12.83 (4) ~ (all_4_3 = e1) % 88.99/12.83 (5) all_6_15 = all_4_3 % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | BETA: splitting (3) gives: % 88.99/12.83 | % 88.99/12.83 | Case 1: % 88.99/12.83 | | % 88.99/12.83 | | (6) all_6_15 = e3 % 88.99/12.83 | | % 88.99/12.83 | | COMBINE_EQS: (5), (6) imply: % 88.99/12.83 | | (7) all_4_3 = e3 % 88.99/12.83 | | % 88.99/12.83 | | SIMP: (7) implies: % 88.99/12.83 | | (8) all_4_3 = e3 % 88.99/12.83 | | % 88.99/12.83 | | REDUCE: (2), (8) imply: % 88.99/12.83 | | (9) $false % 88.99/12.83 | | % 88.99/12.83 | | CLOSE: (9) is inconsistent. % 88.99/12.83 | | % 88.99/12.83 | Case 2: % 88.99/12.83 | | % 88.99/12.83 | | (10) all_6_15 = e1 | all_6_15 = e0 % 88.99/12.83 | | % 88.99/12.83 | | BETA: splitting (10) gives: % 88.99/12.83 | | % 88.99/12.83 | | Case 1: % 88.99/12.83 | | | % 88.99/12.83 | | | (11) all_6_15 = e1 % 88.99/12.83 | | | % 88.99/12.83 | | | COMBINE_EQS: (5), (11) imply: % 88.99/12.83 | | | (12) all_4_3 = e1 % 88.99/12.83 | | | % 88.99/12.83 | | | SIMP: (12) implies: % 88.99/12.83 | | | (13) all_4_3 = e1 % 88.99/12.83 | | | % 88.99/12.83 | | | REDUCE: (4), (13) imply: % 88.99/12.83 | | | (14) $false % 88.99/12.83 | | | % 88.99/12.83 | | | CLOSE: (14) is inconsistent. % 88.99/12.83 | | | % 88.99/12.83 | | Case 2: % 88.99/12.83 | | | % 88.99/12.83 | | | (15) all_6_15 = e0 % 88.99/12.83 | | | % 88.99/12.83 | | | COMBINE_EQS: (5), (15) imply: % 88.99/12.83 | | | (16) all_4_3 = e0 % 88.99/12.83 | | | % 88.99/12.83 | | | SIMP: (16) implies: % 88.99/12.83 | | | (17) all_4_3 = e0 % 88.99/12.83 | | | % 88.99/12.83 | | | REDUCE: (1), (17) imply: % 88.99/12.83 | | | (18) $false % 88.99/12.83 | | | % 88.99/12.83 | | | CLOSE: (18) is inconsistent. % 88.99/12.83 | | | % 88.99/12.83 | | End of split % 88.99/12.83 | | % 88.99/12.83 | End of split % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #94 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_12 = e3 % 88.99/12.83 (2) all_9_2 = e0 % 88.99/12.83 (3) ~ (e4 = e3) % 88.99/12.83 (4) ~ (e4 = e1) % 88.99/12.83 (5) ~ (e4 = e2) % 88.99/12.83 (6) all_4_0 = e0 % 88.99/12.83 (7) ~ (e4 = e0) % 88.99/12.83 (8) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.99/12.83 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.99/12.83 (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.83 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.99/12.83 (10) all_9_6 = e1 % 88.99/12.83 (11) all_9_20 = e2 % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | BETA: splitting (8) gives: % 88.99/12.83 | % 88.99/12.83 | Case 1: % 88.99/12.83 | | % 88.99/12.83 | | (12) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 88.99/12.83 | | % 88.99/12.83 | | REF_CLOSE: (2), (6), (7), (9), (12) are inconsistent by sub-proof #95. % 88.99/12.83 | | % 88.99/12.83 | Case 2: % 88.99/12.83 | | % 88.99/12.83 | | (13) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 88.99/12.83 | | | (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.83 | | % 88.99/12.83 | | BETA: splitting (13) gives: % 88.99/12.83 | | % 88.99/12.83 | | Case 1: % 88.99/12.83 | | | % 88.99/12.83 | | | (14) all_9_6 = e4 & op(e2, e4) = e4 % 88.99/12.83 | | | % 88.99/12.83 | | | REF_CLOSE: (4), (10), (14) are inconsistent by sub-proof #101. % 88.99/12.83 | | | % 88.99/12.83 | | Case 2: % 88.99/12.83 | | | % 88.99/12.83 | | | (15) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 88.99/12.83 | | | e4) % 88.99/12.83 | | | % 88.99/12.83 | | | BETA: splitting (15) gives: % 88.99/12.83 | | | % 88.99/12.83 | | | Case 1: % 88.99/12.83 | | | | % 88.99/12.83 | | | | (16) all_9_12 = e4 & op(e1, e4) = e4 % 88.99/12.83 | | | | % 88.99/12.83 | | | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #119. % 88.99/12.83 | | | | % 88.99/12.83 | | | Case 2: % 88.99/12.83 | | | | % 88.99/12.83 | | | | (17) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.83 | | | | % 88.99/12.83 | | | | ALPHA: (17) implies: % 88.99/12.83 | | | | (18) all_9_20 = e4 % 88.99/12.83 | | | | % 88.99/12.83 | | | | COMBINE_EQS: (11), (18) imply: % 88.99/12.83 | | | | (19) e4 = e2 % 88.99/12.83 | | | | % 88.99/12.83 | | | | SIMP: (19) implies: % 88.99/12.83 | | | | (20) e4 = e2 % 88.99/12.83 | | | | % 88.99/12.83 | | | | REDUCE: (5), (20) imply: % 88.99/12.83 | | | | (21) $false % 88.99/12.83 | | | | % 88.99/12.83 | | | | CLOSE: (21) is inconsistent. % 88.99/12.83 | | | | % 88.99/12.83 | | | End of split % 88.99/12.83 | | | % 88.99/12.83 | | End of split % 88.99/12.83 | | % 88.99/12.83 | End of split % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #95 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_2 = e0 % 88.99/12.83 (2) all_4_0 = e0 % 88.99/12.83 (3) ~ (e4 = e0) % 88.99/12.83 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.99/12.83 (5) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | BETA: splitting (5) gives: % 88.99/12.83 | % 88.99/12.83 | Case 1: % 88.99/12.83 | | % 88.99/12.83 | | (6) all_9_0 = e4 & op(e4, e4) = e4 % 88.99/12.83 | | % 88.99/12.83 | | ALPHA: (6) implies: % 88.99/12.83 | | (7) op(e4, e4) = e4 % 88.99/12.83 | | % 88.99/12.83 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #131. % 88.99/12.83 | | % 88.99/12.83 | Case 2: % 88.99/12.83 | | % 88.99/12.83 | | (8) all_9_2 = e4 & op(e3, e4) = e4 % 88.99/12.83 | | % 88.99/12.83 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #96. % 88.99/12.83 | | % 88.99/12.83 | End of split % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #96 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_2 = e4 & op(e3, e4) = e4 % 88.99/12.83 (2) all_9_2 = e0 % 88.99/12.83 (3) ~ (e4 = e0) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (4) all_9_2 = e4 % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (2), (4) imply: % 88.99/12.83 | (5) e4 = e0 % 88.99/12.83 | % 88.99/12.83 | SIMP: (5) implies: % 88.99/12.83 | (6) e4 = e0 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (6) imply: % 88.99/12.83 | (7) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (7) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #97 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_12 = e2 & op(e1, e4) = e2 % 88.99/12.83 (2) all_9_12 = e3 % 88.99/12.83 (3) ~ (e3 = e2) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (4) all_9_12 = e2 % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (2), (4) imply: % 88.99/12.83 | (5) e3 = e2 % 88.99/12.83 | % 88.99/12.83 | SIMP: (5) implies: % 88.99/12.83 | (6) e3 = e2 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (6) imply: % 88.99/12.83 | (7) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (7) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #98 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) % 88.99/12.83 (2) all_9_0 = e0 % 88.99/12.83 (3) ~ (e2 = e0) % 88.99/12.83 (4) all_9_2 = e0 % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | BETA: splitting (1) gives: % 88.99/12.83 | % 88.99/12.83 | Case 1: % 88.99/12.83 | | % 88.99/12.83 | | (5) all_9_0 = e2 & op(e4, e4) = e2 % 88.99/12.83 | | % 88.99/12.83 | | ALPHA: (5) implies: % 88.99/12.83 | | (6) all_9_0 = e2 % 88.99/12.83 | | % 88.99/12.83 | | COMBINE_EQS: (2), (6) imply: % 88.99/12.83 | | (7) e2 = e0 % 88.99/12.83 | | % 88.99/12.83 | | SIMP: (7) implies: % 88.99/12.83 | | (8) e2 = e0 % 88.99/12.83 | | % 88.99/12.83 | | REDUCE: (3), (8) imply: % 88.99/12.83 | | (9) $false % 88.99/12.83 | | % 88.99/12.83 | | CLOSE: (9) is inconsistent. % 88.99/12.83 | | % 88.99/12.83 | Case 2: % 88.99/12.83 | | % 88.99/12.83 | | (10) all_9_2 = e2 & op(e3, e4) = e2 % 88.99/12.83 | | % 88.99/12.83 | | REF_CLOSE: (3), (4), (10) are inconsistent by sub-proof #99. % 88.99/12.83 | | % 88.99/12.83 | End of split % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #99 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_2 = e2 & op(e3, e4) = e2 % 88.99/12.83 (2) all_9_2 = e0 % 88.99/12.83 (3) ~ (e2 = e0) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (4) all_9_2 = e2 % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (2), (4) imply: % 88.99/12.83 | (5) e2 = e0 % 88.99/12.83 | % 88.99/12.83 | SIMP: (5) implies: % 88.99/12.83 | (6) e2 = e0 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (6) imply: % 88.99/12.83 | (7) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (7) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #100 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_6_15 = all_4_3 % 88.99/12.83 (2) all_6_15 = e4 % 88.99/12.83 (3) ~ (all_4_3 = e4) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (1), (2) imply: % 88.99/12.83 | (4) all_4_3 = e4 % 88.99/12.83 | % 88.99/12.83 | SIMP: (4) implies: % 88.99/12.83 | (5) all_4_3 = e4 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (5) imply: % 88.99/12.83 | (6) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (6) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #101 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_6 = e4 & op(e2, e4) = e4 % 88.99/12.83 (2) all_9_6 = e1 % 88.99/12.83 (3) ~ (e4 = e1) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (4) all_9_6 = e4 % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (2), (4) imply: % 88.99/12.83 | (5) e4 = e1 % 88.99/12.83 | % 88.99/12.83 | SIMP: (5) implies: % 88.99/12.83 | (6) e4 = e1 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (6) imply: % 88.99/12.83 | (7) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (7) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #102 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_6 = e3 & op(e2, e4) = e3 % 88.99/12.83 (2) all_9_6 = e1 % 88.99/12.83 (3) ~ (e3 = e1) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (4) all_9_6 = e3 % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (2), (4) imply: % 88.99/12.83 | (5) e3 = e1 % 88.99/12.83 | % 88.99/12.83 | SIMP: (5) implies: % 88.99/12.83 | (6) e3 = e1 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (6) imply: % 88.99/12.83 | (7) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (7) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #103 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_1 = e1 & op(e4, e3) = e1 % 88.99/12.83 (2) all_9_1 = e2 % 88.99/12.83 (3) ~ (e2 = e1) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (4) all_9_1 = e1 % 88.99/12.83 | % 88.99/12.83 | COMBINE_EQS: (2), (4) imply: % 88.99/12.83 | (5) e2 = e1 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (3), (5) imply: % 88.99/12.83 | (6) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (6) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #104 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) ~ (op(e4, e3) = e3) % 88.99/12.83 (2) ~ (e3 = e0) % 88.99/12.83 (3) op(e4, e4) = e0 % 88.99/12.83 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.99/12.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.99/12.83 (5) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | BETA: splitting (5) gives: % 88.99/12.83 | % 88.99/12.83 | Case 1: % 88.99/12.83 | | % 88.99/12.83 | | (6) all_9_0 = e3 & op(e4, e4) = e3 % 88.99/12.83 | | % 88.99/12.83 | | ALPHA: (6) implies: % 88.99/12.83 | | (7) op(e4, e4) = e3 % 88.99/12.83 | | % 88.99/12.83 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #105. % 88.99/12.83 | | % 88.99/12.83 | Case 2: % 88.99/12.83 | | % 88.99/12.83 | | (8) all_9_1 = e3 & op(e4, e3) = e3 % 88.99/12.83 | | % 88.99/12.83 | | REF_CLOSE: (1), (8) are inconsistent by sub-proof #108. % 88.99/12.83 | | % 88.99/12.83 | End of split % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #105 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.99/12.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.99/12.83 (2) op(e4, e4) = e3 % 88.99/12.83 (3) op(e4, e4) = e0 % 88.99/12.83 (4) ~ (e3 = e0) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | GROUND_INST: instantiating (1) with e0, e3, e4, e4, simplifying with (2), (3) % 88.99/12.83 | gives: % 88.99/12.83 | (5) e3 = e0 % 88.99/12.83 | % 88.99/12.83 | REDUCE: (4), (5) imply: % 88.99/12.83 | (6) $false % 88.99/12.83 | % 88.99/12.83 | CLOSE: (6) is inconsistent. % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #106 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_9_7 = e3 & op(e2, e3) = e3 % 88.99/12.83 (2) all_6_11 = e3 | ~ (op(e2, e3) = e3) % 88.99/12.83 (3) all_6_11 = all_4_7 % 88.99/12.83 (4) ~ (all_4_7 = e3) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | ALPHA: (1) implies: % 88.99/12.83 | (5) op(e2, e3) = e3 % 88.99/12.83 | % 88.99/12.83 | BETA: splitting (2) gives: % 88.99/12.83 | % 88.99/12.83 | Case 1: % 88.99/12.83 | | % 88.99/12.83 | | (6) ~ (op(e2, e3) = e3) % 88.99/12.83 | | % 88.99/12.83 | | PRED_UNIFY: (5), (6) imply: % 88.99/12.83 | | (7) $false % 88.99/12.83 | | % 88.99/12.83 | | CLOSE: (7) is inconsistent. % 88.99/12.83 | | % 88.99/12.83 | Case 2: % 88.99/12.83 | | % 88.99/12.83 | | (8) all_6_11 = e3 % 88.99/12.83 | | % 88.99/12.83 | | COMBINE_EQS: (3), (8) imply: % 88.99/12.83 | | (9) all_4_7 = e3 % 88.99/12.83 | | % 88.99/12.83 | | REDUCE: (4), (9) imply: % 88.99/12.83 | | (10) $false % 88.99/12.83 | | % 88.99/12.83 | | CLOSE: (10) is inconsistent. % 88.99/12.83 | | % 88.99/12.83 | End of split % 88.99/12.83 | % 88.99/12.83 End of proof % 88.99/12.83 % 88.99/12.83 Sub-proof #107 shows that the following formulas are inconsistent: % 88.99/12.83 ---------------------------------------------------------------- % 88.99/12.83 (1) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 88.99/12.83 (2) op(e3, e3) = e3 % 88.99/12.83 (3) ~ (all_4_6 = e3) % 88.99/12.83 % 88.99/12.83 Begin of proof % 88.99/12.83 | % 88.99/12.83 | BETA: splitting (1) gives: % 88.99/12.83 | % 88.99/12.83 | Case 1: % 88.99/12.83 | | % 88.99/12.83 | | (4) ~ (op(e3, e3) = e3) % 88.99/12.83 | | % 88.99/12.83 | | PRED_UNIFY: (2), (4) imply: % 88.99/12.83 | | (5) $false % 88.99/12.83 | | % 88.99/12.83 | | CLOSE: (5) is inconsistent. % 88.99/12.83 | | % 88.99/12.83 | Case 2: % 88.99/12.83 | | % 88.99/12.83 | | (6) all_4_6 = e3 % 88.99/12.83 | | % 88.99/12.83 | | REDUCE: (3), (6) imply: % 88.99/12.83 | | (7) $false % 88.99/12.83 | | % 88.99/12.83 | | CLOSE: (7) is inconsistent. % 88.99/12.83 | | % 88.99/12.84 | End of split % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #108 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) all_9_1 = e3 & op(e4, e3) = e3 % 88.99/12.84 (2) ~ (op(e4, e3) = e3) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | ALPHA: (1) implies: % 88.99/12.84 | (3) op(e4, e3) = e3 % 88.99/12.84 | % 88.99/12.84 | PRED_UNIFY: (2), (3) imply: % 88.99/12.84 | (4) $false % 88.99/12.84 | % 88.99/12.84 | CLOSE: (4) is inconsistent. % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #109 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) all_6_14 = all_4_22 % 88.99/12.84 (2) all_6_14 = e4 % 88.99/12.84 (3) ~ (all_4_22 = e4) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | COMBINE_EQS: (1), (2) imply: % 88.99/12.84 | (4) all_4_22 = e4 % 88.99/12.84 | % 88.99/12.84 | SIMP: (4) implies: % 88.99/12.84 | (5) all_4_22 = e4 % 88.99/12.84 | % 88.99/12.84 | REDUCE: (3), (5) imply: % 88.99/12.84 | (6) $false % 88.99/12.84 | % 88.99/12.84 | CLOSE: (6) is inconsistent. % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #110 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.99/12.84 (2) op(e4, all_8_3) = e3 % 88.99/12.84 (3) ~ (e4 = e3) % 88.99/12.84 (4) all_6_5 = e1 % 88.99/12.84 (5) ~ (e4 = e1) % 88.99/12.84 (6) ~ (e4 = e2) % 88.99/12.84 (7) e3 = e1 | ~ (op(e3, e4) = e3) % 88.99/12.84 (8) all_4_0 = e0 % 88.99/12.84 (9) ~ (e4 = e0) % 88.99/12.84 (10) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.99/12.84 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.99/12.84 (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.84 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.99/12.84 (12) ~ (unit = e2) % 88.99/12.84 (13) all_9_12 = e4 % 88.99/12.84 (14) op(e3, unit) = e3 % 88.99/12.84 (15) all_9_2 = e1 % 88.99/12.84 (16) ~ (e3 = e1) % 88.99/12.84 (17) op(e3, e4) = all_8_3 % 88.99/12.84 (18) op(e3, e4) = e1 % 88.99/12.84 (19) ~ (unit = e0) % 88.99/12.84 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.99/12.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.99/12.84 (21) all_4_2 = e3 % 88.99/12.84 (22) op(e4, unit) = e4 % 88.99/12.84 (23) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 88.99/12.84 (24) op(unit, e4) = e4 % 88.99/12.84 (25) all_9_20 = e2 % 88.99/12.84 (26) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | BETA: splitting (23) gives: % 88.99/12.84 | % 88.99/12.84 | Case 1: % 88.99/12.84 | | % 88.99/12.84 | | (27) ~ (op(e3, e4) = e4) % 88.99/12.84 | | % 88.99/12.84 | | BETA: splitting (7) gives: % 88.99/12.84 | | % 88.99/12.84 | | Case 1: % 88.99/12.84 | | | % 88.99/12.84 | | | (28) ~ (op(e3, e4) = e3) % 88.99/12.84 | | | % 88.99/12.84 | | | GROUND_INST: instantiating (20) with e1, all_8_3, e4, e3, simplifying with % 88.99/12.84 | | | (17), (18) gives: % 88.99/12.84 | | | (29) all_8_3 = e1 % 88.99/12.84 | | | % 88.99/12.84 | | | PRED_UNIFY: (14), (28) imply: % 88.99/12.84 | | | (30) ~ (unit = e4) % 88.99/12.84 | | | % 88.99/12.84 | | | PRED_UNIFY: (24), (27) imply: % 88.99/12.84 | | | (31) ~ (unit = e3) % 88.99/12.84 | | | % 88.99/12.84 | | | BETA: splitting (1) gives: % 88.99/12.84 | | | % 88.99/12.84 | | | Case 1: % 88.99/12.84 | | | | % 88.99/12.84 | | | | (32) unit = e4 % 88.99/12.84 | | | | % 88.99/12.84 | | | | REDUCE: (30), (32) imply: % 88.99/12.84 | | | | (33) $false % 88.99/12.84 | | | | % 88.99/12.84 | | | | CLOSE: (33) is inconsistent. % 88.99/12.84 | | | | % 88.99/12.84 | | | Case 2: % 88.99/12.84 | | | | % 88.99/12.84 | | | | (34) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 88.99/12.84 | | | | % 88.99/12.84 | | | | BETA: splitting (34) gives: % 88.99/12.84 | | | | % 88.99/12.84 | | | | Case 1: % 88.99/12.84 | | | | | % 88.99/12.84 | | | | | (35) unit = e2 % 88.99/12.84 | | | | | % 88.99/12.84 | | | | | REDUCE: (12), (35) imply: % 88.99/12.84 | | | | | (36) $false % 88.99/12.84 | | | | | % 88.99/12.84 | | | | | CLOSE: (36) is inconsistent. % 88.99/12.84 | | | | | % 88.99/12.84 | | | | Case 2: % 88.99/12.84 | | | | | % 88.99/12.84 | | | | | (37) unit = e3 | unit = e1 | unit = e0 % 88.99/12.84 | | | | | % 88.99/12.84 | | | | | BETA: splitting (37) gives: % 88.99/12.84 | | | | | % 88.99/12.84 | | | | | Case 1: % 88.99/12.84 | | | | | | % 88.99/12.84 | | | | | | (38) unit = e3 % 88.99/12.84 | | | | | | % 88.99/12.84 | | | | | | REDUCE: (31), (38) imply: % 88.99/12.84 | | | | | | (39) $false % 88.99/12.84 | | | | | | % 88.99/12.84 | | | | | | CLOSE: (39) is inconsistent. % 88.99/12.84 | | | | | | % 88.99/12.84 | | | | | Case 2: % 88.99/12.84 | | | | | | % 88.99/12.84 | | | | | | (40) unit = e1 | unit = e0 % 88.99/12.84 | | | | | | % 88.99/12.84 | | | | | | BETA: splitting (40) gives: % 88.99/12.84 | | | | | | % 88.99/12.84 | | | | | | Case 1: % 88.99/12.84 | | | | | | | % 88.99/12.84 | | | | | | | (41) unit = e1 % 88.99/12.84 | | | | | | | % 88.99/12.84 | | | | | | | REDUCE: (22), (41) imply: % 88.99/12.84 | | | | | | | (42) op(e4, e1) = e4 % 88.99/12.84 | | | | | | | % 88.99/12.84 | | | | | | | REF_CLOSE: (2), (3), (6), (8), (9), (10), (11), (13), (15), (17), % 88.99/12.84 | | | | | | | (18), (20), (21), (25), (26), (27), (42) are % 88.99/12.84 | | | | | | | inconsistent by sub-proof #112. % 88.99/12.84 | | | | | | | % 88.99/12.84 | | | | | | Case 2: % 88.99/12.84 | | | | | | | % 88.99/12.84 | | | | | | | (43) ~ (unit = e1) % 88.99/12.84 | | | | | | | % 88.99/12.84 | | | | | | | REF_CLOSE: (19), (40), (43) are inconsistent by sub-proof #111. % 88.99/12.84 | | | | | | | % 88.99/12.84 | | | | | | End of split % 88.99/12.84 | | | | | | % 88.99/12.84 | | | | | End of split % 88.99/12.84 | | | | | % 88.99/12.84 | | | | End of split % 88.99/12.84 | | | | % 88.99/12.84 | | | End of split % 88.99/12.84 | | | % 88.99/12.84 | | Case 2: % 88.99/12.84 | | | % 88.99/12.84 | | | (44) e3 = e1 % 88.99/12.84 | | | % 88.99/12.84 | | | REDUCE: (16), (44) imply: % 88.99/12.84 | | | (45) $false % 88.99/12.84 | | | % 88.99/12.84 | | | CLOSE: (45) is inconsistent. % 88.99/12.84 | | | % 88.99/12.84 | | End of split % 88.99/12.84 | | % 88.99/12.84 | Case 2: % 88.99/12.84 | | % 88.99/12.84 | | (46) all_6_5 = e4 % 88.99/12.84 | | % 88.99/12.84 | | COMBINE_EQS: (4), (46) imply: % 88.99/12.84 | | (47) e4 = e1 % 88.99/12.84 | | % 88.99/12.84 | | REDUCE: (5), (47) imply: % 88.99/12.84 | | (48) $false % 88.99/12.84 | | % 88.99/12.84 | | CLOSE: (48) is inconsistent. % 88.99/12.84 | | % 88.99/12.84 | End of split % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #111 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) unit = e1 | unit = e0 % 88.99/12.84 (2) ~ (unit = e1) % 88.99/12.84 (3) ~ (unit = e0) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | BETA: splitting (1) gives: % 88.99/12.84 | % 88.99/12.84 | Case 1: % 88.99/12.84 | | % 88.99/12.84 | | (4) unit = e1 % 88.99/12.84 | | % 88.99/12.84 | | REDUCE: (2), (4) imply: % 88.99/12.84 | | (5) $false % 88.99/12.84 | | % 88.99/12.84 | | CLOSE: (5) is inconsistent. % 88.99/12.84 | | % 88.99/12.84 | Case 2: % 88.99/12.84 | | % 88.99/12.84 | | (6) unit = e0 % 88.99/12.84 | | % 88.99/12.84 | | REDUCE: (3), (6) imply: % 88.99/12.84 | | (7) $false % 88.99/12.84 | | % 88.99/12.84 | | CLOSE: (7) is inconsistent. % 88.99/12.84 | | % 88.99/12.84 | End of split % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #112 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) op(e4, all_8_3) = e3 % 88.99/12.84 (2) ~ (e4 = e3) % 88.99/12.84 (3) ~ (e4 = e2) % 88.99/12.84 (4) all_4_0 = e0 % 88.99/12.84 (5) ~ (e4 = e0) % 88.99/12.84 (6) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.99/12.84 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.99/12.84 (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.84 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.99/12.84 (8) all_9_12 = e4 % 88.99/12.84 (9) all_9_2 = e1 % 88.99/12.84 (10) op(e3, e4) = all_8_3 % 88.99/12.84 (11) op(e3, e4) = e1 % 88.99/12.84 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.99/12.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.99/12.84 (13) all_4_2 = e3 % 88.99/12.84 (14) ~ (op(e3, e4) = e4) % 88.99/12.84 (15) op(e4, e1) = e4 % 88.99/12.84 (16) all_9_20 = e2 % 88.99/12.84 (17) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | GROUND_INST: instantiating (12) with e1, all_8_3, e4, e3, simplifying with % 88.99/12.84 | (10), (11) gives: % 88.99/12.84 | (18) all_8_3 = e1 % 88.99/12.84 | % 88.99/12.84 | GROUND_INST: instantiating (12) with e4, e3, e1, e4, simplifying with (15) % 88.99/12.84 | gives: % 88.99/12.84 | (19) e4 = e3 | ~ (op(e4, e1) = e3) % 88.99/12.84 | % 88.99/12.84 | PRED_UNIFY: (10), (14) imply: % 88.99/12.84 | (20) ~ (all_8_3 = e4) % 88.99/12.84 | % 88.99/12.84 | REDUCE: (18), (20) imply: % 88.99/12.84 | (21) ~ (e4 = e1) % 88.99/12.84 | % 88.99/12.84 | SIMP: (21) implies: % 88.99/12.84 | (22) ~ (e4 = e1) % 88.99/12.84 | % 88.99/12.84 | REDUCE: (1), (18) imply: % 88.99/12.84 | (23) op(e4, e1) = e3 % 88.99/12.84 | % 88.99/12.84 | BETA: splitting (19) gives: % 88.99/12.84 | % 88.99/12.84 | Case 1: % 88.99/12.84 | | % 88.99/12.84 | | (24) ~ (op(e4, e1) = e3) % 88.99/12.84 | | % 88.99/12.84 | | PRED_UNIFY: (23), (24) imply: % 88.99/12.84 | | (25) $false % 88.99/12.84 | | % 88.99/12.84 | | CLOSE: (25) is inconsistent. % 88.99/12.84 | | % 88.99/12.84 | Case 2: % 88.99/12.84 | | % 88.99/12.84 | | (26) e4 = e3 % 88.99/12.84 | | % 88.99/12.84 | | COMBINE_EQS: (8), (26) imply: % 88.99/12.84 | | (27) all_9_12 = e3 % 88.99/12.84 | | % 88.99/12.84 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (13), (16), (17), (22), (27) % 88.99/12.84 | | are inconsistent by sub-proof #117. % 88.99/12.84 | | % 88.99/12.84 | End of split % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #113 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) all_9_8 = e2 & op(e2, e2) = e2 % 88.99/12.84 (2) e4 = e2 | ~ (op(e2, e2) = e2) % 88.99/12.84 (3) ~ (e4 = e2) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | ALPHA: (1) implies: % 88.99/12.84 | (4) op(e2, e2) = e2 % 88.99/12.84 | % 88.99/12.84 | BETA: splitting (2) gives: % 88.99/12.84 | % 88.99/12.84 | Case 1: % 88.99/12.84 | | % 88.99/12.84 | | (5) ~ (op(e2, e2) = e2) % 88.99/12.84 | | % 88.99/12.84 | | PRED_UNIFY: (4), (5) imply: % 88.99/12.84 | | (6) $false % 88.99/12.84 | | % 88.99/12.84 | | CLOSE: (6) is inconsistent. % 88.99/12.84 | | % 88.99/12.84 | Case 2: % 88.99/12.84 | | % 88.99/12.84 | | (7) e4 = e2 % 88.99/12.84 | | % 88.99/12.84 | | REDUCE: (3), (7) imply: % 88.99/12.84 | | (8) $false % 88.99/12.84 | | % 88.99/12.84 | | CLOSE: (8) is inconsistent. % 88.99/12.84 | | % 88.99/12.84 | End of split % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #114 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) ~ (e3 = e2) % 88.99/12.84 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.99/12.84 (3) ~ (all_4_7 = e2) % 88.99/12.84 (4) all_6_10 = e3 % 88.99/12.84 (5) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & op(e2, e3) = e2) % 88.99/12.84 (6) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | BETA: splitting (5) gives: % 88.99/12.84 | % 88.99/12.84 | Case 1: % 88.99/12.84 | | % 88.99/12.84 | | (7) all_9_6 = e2 & op(e2, e4) = e2 % 88.99/12.84 | | % 88.99/12.84 | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #125. % 88.99/12.84 | | % 88.99/12.84 | Case 2: % 88.99/12.84 | | % 88.99/12.84 | | (8) all_9_7 = e2 & op(e2, e3) = e2 % 88.99/12.84 | | % 88.99/12.84 | | ALPHA: (8) implies: % 88.99/12.84 | | (9) op(e2, e3) = e2 % 88.99/12.84 | | % 88.99/12.84 | | BETA: splitting (6) gives: % 88.99/12.84 | | % 88.99/12.84 | | Case 1: % 88.99/12.84 | | | % 88.99/12.84 | | | (10) ~ (op(e2, e3) = e2) % 88.99/12.84 | | | % 88.99/12.84 | | | PRED_UNIFY: (9), (10) imply: % 88.99/12.84 | | | (11) $false % 88.99/12.84 | | | % 88.99/12.84 | | | CLOSE: (11) is inconsistent. % 88.99/12.84 | | | % 88.99/12.84 | | Case 2: % 88.99/12.84 | | | % 88.99/12.84 | | | (12) all_4_7 = e2 % 88.99/12.84 | | | % 88.99/12.84 | | | REDUCE: (3), (12) imply: % 88.99/12.84 | | | (13) $false % 88.99/12.84 | | | % 88.99/12.84 | | | CLOSE: (13) is inconsistent. % 88.99/12.84 | | | % 88.99/12.84 | | End of split % 88.99/12.84 | | % 88.99/12.84 | End of split % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #115 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) ~ (all_4_20 = e4) % 88.99/12.84 (2) all_6_1 = all_4_5 % 88.99/12.84 (3) all_9_9 = e3 % 88.99/12.84 (4) ~ (e4 = e3) % 88.99/12.84 (5) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 88.99/12.84 (6) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 88.99/12.84 (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 88.99/12.84 (all_9_16 = e4 & op(e4, e0) = e4) % 88.99/12.84 (7) ~ (e4 = e1) % 88.99/12.84 (8) ~ (e4 = e2) % 88.99/12.84 (9) all_4_0 = e0 % 88.99/12.84 (10) ~ (e4 = e0) % 88.99/12.84 (11) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.99/12.84 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.99/12.84 (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.84 (12) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.99/12.84 (13) all_9_12 = e4 % 88.99/12.84 (14) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 88.99/12.84 (15) ~ (all_4_5 = e4) % 88.99/12.84 (16) ~ (all_4_10 = e4) % 88.99/12.84 (17) all_9_2 = e1 % 88.99/12.84 (18) all_6_2 = all_4_10 % 88.99/12.84 (19) all_4_2 = e3 % 88.99/12.84 (20) all_6_1 = e4 | ~ (op(e4, e3) = e4) % 88.99/12.84 (21) all_9_20 = e2 % 88.99/12.84 (22) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | BETA: splitting (6) gives: % 88.99/12.84 | % 88.99/12.84 | Case 1: % 88.99/12.84 | | % 88.99/12.84 | | (23) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) % 88.99/12.84 | | % 88.99/12.84 | | REF_CLOSE: (2), (9), (10), (12), (15), (20), (23) are inconsistent by % 88.99/12.84 | | sub-proof #121. % 88.99/12.84 | | % 88.99/12.84 | Case 2: % 88.99/12.84 | | % 88.99/12.84 | | (24) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) % 88.99/12.84 | | | (all_9_16 = e4 & op(e4, e0) = e4) % 88.99/12.84 | | % 88.99/12.84 | | BETA: splitting (24) gives: % 88.99/12.84 | | % 88.99/12.84 | | Case 1: % 88.99/12.84 | | | % 88.99/12.84 | | | (25) all_9_4 = e4 & op(e4, e2) = e4 % 88.99/12.84 | | | % 88.99/12.84 | | | REF_CLOSE: (14), (16), (18), (25) are inconsistent by sub-proof #120. % 88.99/12.84 | | | % 88.99/12.84 | | Case 2: % 88.99/12.84 | | | % 88.99/12.84 | | | (26) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) = % 88.99/12.84 | | | e4) % 88.99/12.84 | | | % 88.99/12.84 | | | BETA: splitting (26) gives: % 88.99/12.84 | | | % 88.99/12.84 | | | Case 1: % 88.99/12.84 | | | | % 88.99/12.84 | | | | (27) all_9_9 = e4 & op(e4, e1) = e4 % 88.99/12.84 | | | | % 88.99/12.84 | | | | ALPHA: (27) implies: % 88.99/12.84 | | | | (28) all_9_9 = e4 % 88.99/12.84 | | | | % 88.99/12.84 | | | | COMBINE_EQS: (3), (28) imply: % 88.99/12.84 | | | | (29) e4 = e3 % 88.99/12.84 | | | | % 88.99/12.84 | | | | SIMP: (29) implies: % 88.99/12.84 | | | | (30) e4 = e3 % 88.99/12.84 | | | | % 88.99/12.84 | | | | COMBINE_EQS: (13), (30) imply: % 88.99/12.84 | | | | (31) all_9_12 = e3 % 88.99/12.84 | | | | % 88.99/12.84 | | | | REF_CLOSE: (4), (7), (8), (9), (10), (11), (12), (17), (19), (21), (22), % 88.99/12.84 | | | | (31) are inconsistent by sub-proof #117. % 88.99/12.84 | | | | % 88.99/12.84 | | | Case 2: % 88.99/12.84 | | | | % 88.99/12.84 | | | | (32) all_9_16 = e4 & op(e4, e0) = e4 % 88.99/12.84 | | | | % 88.99/12.84 | | | | REF_CLOSE: (1), (5), (32) are inconsistent by sub-proof #116. % 88.99/12.84 | | | | % 88.99/12.84 | | | End of split % 88.99/12.84 | | | % 88.99/12.84 | | End of split % 88.99/12.84 | | % 88.99/12.84 | End of split % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #116 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) all_9_16 = e4 & op(e4, e0) = e4 % 88.99/12.84 (2) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 88.99/12.84 (3) ~ (all_4_20 = e4) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | ALPHA: (1) implies: % 88.99/12.84 | (4) op(e4, e0) = e4 % 88.99/12.84 | % 88.99/12.84 | BETA: splitting (2) gives: % 88.99/12.84 | % 88.99/12.84 | Case 1: % 88.99/12.84 | | % 88.99/12.84 | | (5) ~ (op(e4, e0) = e4) % 88.99/12.84 | | % 88.99/12.84 | | PRED_UNIFY: (4), (5) imply: % 88.99/12.84 | | (6) $false % 88.99/12.84 | | % 88.99/12.84 | | CLOSE: (6) is inconsistent. % 88.99/12.84 | | % 88.99/12.84 | Case 2: % 88.99/12.84 | | % 88.99/12.84 | | (7) all_4_20 = e4 % 88.99/12.84 | | % 88.99/12.84 | | REDUCE: (3), (7) imply: % 88.99/12.84 | | (8) $false % 88.99/12.84 | | % 88.99/12.84 | | CLOSE: (8) is inconsistent. % 88.99/12.84 | | % 88.99/12.84 | End of split % 88.99/12.84 | % 88.99/12.84 End of proof % 88.99/12.84 % 88.99/12.84 Sub-proof #117 shows that the following formulas are inconsistent: % 88.99/12.84 ---------------------------------------------------------------- % 88.99/12.84 (1) all_9_12 = e3 % 88.99/12.84 (2) ~ (e4 = e3) % 88.99/12.84 (3) ~ (e4 = e1) % 88.99/12.84 (4) ~ (e4 = e2) % 88.99/12.84 (5) all_4_0 = e0 % 88.99/12.84 (6) ~ (e4 = e0) % 88.99/12.84 (7) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 88.99/12.84 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 88.99/12.84 (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.84 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.99/12.84 (9) all_9_2 = e1 % 88.99/12.84 (10) all_4_2 = e3 % 88.99/12.84 (11) all_9_20 = e2 % 88.99/12.84 (12) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.99/12.84 % 88.99/12.84 Begin of proof % 88.99/12.84 | % 88.99/12.84 | BETA: splitting (7) gives: % 88.99/12.84 | % 88.99/12.84 | Case 1: % 88.99/12.84 | | % 88.99/12.84 | | (13) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 88.99/12.84 | | % 88.99/12.84 | | REF_CLOSE: (3), (5), (6), (8), (9), (13) are inconsistent by sub-proof #130. % 88.99/12.84 | | % 88.99/12.84 | Case 2: % 88.99/12.84 | | % 88.99/12.85 | | (14) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 88.99/12.85 | | | (all_9_20 = e4 & op(e0, e4) = e4) % 88.99/12.85 | | % 88.99/12.85 | | BETA: splitting (14) gives: % 88.99/12.85 | | % 88.99/12.85 | | Case 1: % 88.99/12.85 | | | % 88.99/12.85 | | | (15) all_9_6 = e4 & op(e2, e4) = e4 % 88.99/12.85 | | | % 88.99/12.85 | | | ALPHA: (15) implies: % 88.99/12.85 | | | (16) op(e2, e4) = e4 % 88.99/12.85 | | | % 88.99/12.85 | | | REF_CLOSE: (2), (10), (12), (16) are inconsistent by sub-proof #129. % 88.99/12.85 | | | % 88.99/12.85 | | Case 2: % 88.99/12.85 | | | % 88.99/12.85 | | | (17) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 88.99/12.85 | | | e4) % 88.99/12.85 | | | % 88.99/12.85 | | | BETA: splitting (17) gives: % 88.99/12.85 | | | % 88.99/12.85 | | | Case 1: % 88.99/12.85 | | | | % 88.99/12.85 | | | | (18) all_9_12 = e4 & op(e1, e4) = e4 % 88.99/12.85 | | | | % 88.99/12.85 | | | | REF_CLOSE: (1), (2), (18) are inconsistent by sub-proof #119. % 88.99/12.85 | | | | % 88.99/12.85 | | | Case 2: % 88.99/12.85 | | | | % 88.99/12.85 | | | | (19) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.85 | | | | % 88.99/12.85 | | | | REF_CLOSE: (4), (11), (19) are inconsistent by sub-proof #118. % 88.99/12.85 | | | | % 88.99/12.85 | | | End of split % 88.99/12.85 | | | % 88.99/12.85 | | End of split % 88.99/12.85 | | % 88.99/12.85 | End of split % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #118 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_9_20 = e4 & op(e0, e4) = e4 % 88.99/12.85 (2) all_9_20 = e2 % 88.99/12.85 (3) ~ (e4 = e2) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | ALPHA: (1) implies: % 88.99/12.85 | (4) all_9_20 = e4 % 88.99/12.85 | % 88.99/12.85 | COMBINE_EQS: (2), (4) imply: % 88.99/12.85 | (5) e4 = e2 % 88.99/12.85 | % 88.99/12.85 | REDUCE: (3), (5) imply: % 88.99/12.85 | (6) $false % 88.99/12.85 | % 88.99/12.85 | CLOSE: (6) is inconsistent. % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #119 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_9_12 = e4 & op(e1, e4) = e4 % 88.99/12.85 (2) all_9_12 = e3 % 88.99/12.85 (3) ~ (e4 = e3) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | ALPHA: (1) implies: % 88.99/12.85 | (4) all_9_12 = e4 % 88.99/12.85 | % 88.99/12.85 | COMBINE_EQS: (2), (4) imply: % 88.99/12.85 | (5) e4 = e3 % 88.99/12.85 | % 88.99/12.85 | REDUCE: (3), (5) imply: % 88.99/12.85 | (6) $false % 88.99/12.85 | % 88.99/12.85 | CLOSE: (6) is inconsistent. % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #120 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_9_4 = e4 & op(e4, e2) = e4 % 88.99/12.85 (2) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 88.99/12.85 (3) all_6_2 = all_4_10 % 88.99/12.85 (4) ~ (all_4_10 = e4) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | ALPHA: (1) implies: % 88.99/12.85 | (5) op(e4, e2) = e4 % 88.99/12.85 | % 88.99/12.85 | BETA: splitting (2) gives: % 88.99/12.85 | % 88.99/12.85 | Case 1: % 88.99/12.85 | | % 88.99/12.85 | | (6) ~ (op(e4, e2) = e4) % 88.99/12.85 | | % 88.99/12.85 | | PRED_UNIFY: (5), (6) imply: % 88.99/12.85 | | (7) $false % 88.99/12.85 | | % 88.99/12.85 | | CLOSE: (7) is inconsistent. % 88.99/12.85 | | % 88.99/12.85 | Case 2: % 88.99/12.85 | | % 88.99/12.85 | | (8) all_6_2 = e4 % 88.99/12.85 | | % 88.99/12.85 | | COMBINE_EQS: (3), (8) imply: % 88.99/12.85 | | (9) all_4_10 = e4 % 88.99/12.85 | | % 88.99/12.85 | | SIMP: (9) implies: % 88.99/12.85 | | (10) all_4_10 = e4 % 88.99/12.85 | | % 88.99/12.85 | | REDUCE: (4), (10) imply: % 88.99/12.85 | | (11) $false % 88.99/12.85 | | % 88.99/12.85 | | CLOSE: (11) is inconsistent. % 88.99/12.85 | | % 88.99/12.85 | End of split % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #121 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_6_1 = all_4_5 % 88.99/12.85 (2) all_4_0 = e0 % 88.99/12.85 (3) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) % 88.99/12.85 (4) ~ (e4 = e0) % 88.99/12.85 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 88.99/12.85 (6) ~ (all_4_5 = e4) % 88.99/12.85 (7) all_6_1 = e4 | ~ (op(e4, e3) = e4) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | BETA: splitting (3) gives: % 88.99/12.85 | % 88.99/12.85 | Case 1: % 88.99/12.85 | | % 88.99/12.85 | | (8) all_9_0 = e4 & op(e4, e4) = e4 % 88.99/12.85 | | % 88.99/12.85 | | ALPHA: (8) implies: % 88.99/12.85 | | (9) op(e4, e4) = e4 % 88.99/12.85 | | % 88.99/12.85 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #131. % 88.99/12.85 | | % 88.99/12.85 | Case 2: % 88.99/12.85 | | % 88.99/12.85 | | (10) all_9_1 = e4 & op(e4, e3) = e4 % 88.99/12.85 | | % 88.99/12.85 | | REF_CLOSE: (1), (6), (7), (10) are inconsistent by sub-proof #122. % 88.99/12.85 | | % 88.99/12.85 | End of split % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #122 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_9_1 = e4 & op(e4, e3) = e4 % 88.99/12.85 (2) all_6_1 = e4 | ~ (op(e4, e3) = e4) % 88.99/12.85 (3) all_6_1 = all_4_5 % 88.99/12.85 (4) ~ (all_4_5 = e4) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | ALPHA: (1) implies: % 88.99/12.85 | (5) op(e4, e3) = e4 % 88.99/12.85 | % 88.99/12.85 | BETA: splitting (2) gives: % 88.99/12.85 | % 88.99/12.85 | Case 1: % 88.99/12.85 | | % 88.99/12.85 | | (6) ~ (op(e4, e3) = e4) % 88.99/12.85 | | % 88.99/12.85 | | PRED_UNIFY: (5), (6) imply: % 88.99/12.85 | | (7) $false % 88.99/12.85 | | % 88.99/12.85 | | CLOSE: (7) is inconsistent. % 88.99/12.85 | | % 88.99/12.85 | Case 2: % 88.99/12.85 | | % 88.99/12.85 | | (8) all_6_1 = e4 % 88.99/12.85 | | % 88.99/12.85 | | COMBINE_EQS: (3), (8) imply: % 88.99/12.85 | | (9) all_4_5 = e4 % 88.99/12.85 | | % 88.99/12.85 | | REDUCE: (4), (9) imply: % 88.99/12.85 | | (10) $false % 88.99/12.85 | | % 88.99/12.85 | | CLOSE: (10) is inconsistent. % 88.99/12.85 | | % 88.99/12.85 | End of split % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #123 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_6_20 = all_4_4 % 88.99/12.85 (2) all_6_20 = e4 % 88.99/12.85 (3) ~ (all_4_4 = e4) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | COMBINE_EQS: (1), (2) imply: % 88.99/12.85 | (4) all_4_4 = e4 % 88.99/12.85 | % 88.99/12.85 | SIMP: (4) implies: % 88.99/12.85 | (5) all_4_4 = e4 % 88.99/12.85 | % 88.99/12.85 | REDUCE: (3), (5) imply: % 88.99/12.85 | (6) $false % 88.99/12.85 | % 88.99/12.85 | CLOSE: (6) is inconsistent. % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #124 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_9_12 = e4 % 88.99/12.85 (2) all_9_12 = e2 % 88.99/12.85 (3) ~ (e4 = e2) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | COMBINE_EQS: (1), (2) imply: % 88.99/12.85 | (4) e4 = e2 % 88.99/12.85 | % 88.99/12.85 | SIMP: (4) implies: % 88.99/12.85 | (5) e4 = e2 % 88.99/12.85 | % 88.99/12.85 | REDUCE: (3), (5) imply: % 88.99/12.85 | (6) $false % 88.99/12.85 | % 88.99/12.85 | CLOSE: (6) is inconsistent. % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #125 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_9_6 = e2 & op(e2, e4) = e2 % 88.99/12.85 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 88.99/12.85 (3) all_6_10 = e3 % 88.99/12.85 (4) ~ (e3 = e2) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | ALPHA: (1) implies: % 88.99/12.85 | (5) op(e2, e4) = e2 % 88.99/12.85 | % 88.99/12.85 | BETA: splitting (2) gives: % 88.99/12.85 | % 88.99/12.85 | Case 1: % 88.99/12.85 | | % 88.99/12.85 | | (6) ~ (op(e2, e4) = e2) % 88.99/12.85 | | % 88.99/12.85 | | PRED_UNIFY: (5), (6) imply: % 88.99/12.85 | | (7) $false % 88.99/12.85 | | % 88.99/12.85 | | CLOSE: (7) is inconsistent. % 88.99/12.85 | | % 88.99/12.85 | Case 2: % 88.99/12.85 | | % 88.99/12.85 | | (8) all_6_10 = e2 % 88.99/12.85 | | % 88.99/12.85 | | COMBINE_EQS: (3), (8) imply: % 88.99/12.85 | | (9) e3 = e2 % 88.99/12.85 | | % 88.99/12.85 | | SIMP: (9) implies: % 88.99/12.85 | | (10) e3 = e2 % 88.99/12.85 | | % 88.99/12.85 | | REDUCE: (4), (10) imply: % 88.99/12.85 | | (11) $false % 88.99/12.85 | | % 88.99/12.85 | | CLOSE: (11) is inconsistent. % 88.99/12.85 | | % 88.99/12.85 | End of split % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #126 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) % 88.99/12.85 (2) all_9_2 = e1 % 88.99/12.85 (3) ~ (e2 = e0) % 88.99/12.85 (4) ~ (e2 = e1) % 88.99/12.85 (5) op(e4, e4) = e0 % 88.99/12.85 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.99/12.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | BETA: splitting (1) gives: % 88.99/12.85 | % 88.99/12.85 | Case 1: % 88.99/12.85 | | % 88.99/12.85 | | (7) all_9_0 = e2 & op(e4, e4) = e2 % 88.99/12.85 | | % 88.99/12.85 | | ALPHA: (7) implies: % 88.99/12.85 | | (8) op(e4, e4) = e2 % 88.99/12.85 | | % 88.99/12.85 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #128. % 88.99/12.85 | | % 88.99/12.85 | Case 2: % 88.99/12.85 | | % 88.99/12.85 | | (9) all_9_2 = e2 & op(e3, e4) = e2 % 88.99/12.85 | | % 88.99/12.85 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #127. % 88.99/12.85 | | % 88.99/12.85 | End of split % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #127 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_9_2 = e2 & op(e3, e4) = e2 % 88.99/12.85 (2) all_9_2 = e1 % 88.99/12.85 (3) ~ (e2 = e1) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | ALPHA: (1) implies: % 88.99/12.85 | (4) all_9_2 = e2 % 88.99/12.85 | % 88.99/12.85 | COMBINE_EQS: (2), (4) imply: % 88.99/12.85 | (5) e2 = e1 % 88.99/12.85 | % 88.99/12.85 | SIMP: (5) implies: % 88.99/12.85 | (6) e2 = e1 % 88.99/12.85 | % 88.99/12.85 | REDUCE: (3), (6) imply: % 88.99/12.85 | (7) $false % 88.99/12.85 | % 88.99/12.85 | CLOSE: (7) is inconsistent. % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #128 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.99/12.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 88.99/12.85 (2) op(e4, e4) = e2 % 88.99/12.85 (3) op(e4, e4) = e0 % 88.99/12.85 (4) ~ (e2 = e0) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | GROUND_INST: instantiating (1) with e0, e2, e4, e4, simplifying with (2), (3) % 88.99/12.85 | gives: % 88.99/12.85 | (5) e2 = e0 % 88.99/12.85 | % 88.99/12.85 | REDUCE: (4), (5) imply: % 88.99/12.85 | (6) $false % 88.99/12.85 | % 88.99/12.85 | CLOSE: (6) is inconsistent. % 88.99/12.85 | % 88.99/12.85 End of proof % 88.99/12.85 % 88.99/12.85 Sub-proof #129 shows that the following formulas are inconsistent: % 88.99/12.85 ---------------------------------------------------------------- % 88.99/12.85 (1) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 88.99/12.85 (2) op(e2, e4) = e4 % 88.99/12.85 (3) all_4_2 = e3 % 88.99/12.85 (4) ~ (e4 = e3) % 88.99/12.85 % 88.99/12.85 Begin of proof % 88.99/12.85 | % 88.99/12.85 | BETA: splitting (1) gives: % 88.99/12.85 | % 88.99/12.85 | Case 1: % 88.99/12.85 | | % 88.99/12.85 | | (5) ~ (op(e2, e4) = e4) % 88.99/12.85 | | % 88.99/12.85 | | PRED_UNIFY: (2), (5) imply: % 88.99/12.85 | | (6) $false % 88.99/12.85 | | % 88.99/12.85 | | CLOSE: (6) is inconsistent. % 88.99/12.85 | | % 88.99/12.85 | Case 2: % 88.99/12.85 | | % 88.99/12.85 | | (7) all_4_2 = e4 % 89.14/12.85 | | % 89.14/12.85 | | COMBINE_EQS: (3), (7) imply: % 89.14/12.85 | | (8) e4 = e3 % 89.14/12.85 | | % 89.14/12.85 | | SIMP: (8) implies: % 89.14/12.85 | | (9) e4 = e3 % 89.14/12.85 | | % 89.14/12.85 | | REDUCE: (4), (9) imply: % 89.14/12.85 | | (10) $false % 89.14/12.85 | | % 89.14/12.85 | | CLOSE: (10) is inconsistent. % 89.14/12.85 | | % 89.14/12.85 | End of split % 89.14/12.85 | % 89.14/12.85 End of proof % 89.14/12.85 % 89.14/12.85 Sub-proof #130 shows that the following formulas are inconsistent: % 89.14/12.85 ---------------------------------------------------------------- % 89.14/12.85 (1) ~ (e4 = e1) % 89.14/12.85 (2) all_4_0 = e0 % 89.14/12.85 (3) ~ (e4 = e0) % 89.14/12.85 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 89.14/12.85 (5) all_9_2 = e1 % 89.14/12.85 (6) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 89.14/12.85 % 89.14/12.85 Begin of proof % 89.14/12.85 | % 89.14/12.85 | BETA: splitting (6) gives: % 89.14/12.85 | % 89.14/12.85 | Case 1: % 89.14/12.85 | | % 89.14/12.85 | | (7) all_9_0 = e4 & op(e4, e4) = e4 % 89.14/12.85 | | % 89.14/12.85 | | ALPHA: (7) implies: % 89.14/12.85 | | (8) op(e4, e4) = e4 % 89.14/12.85 | | % 89.14/12.85 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #131. % 89.14/12.85 | | % 89.14/12.85 | Case 2: % 89.14/12.85 | | % 89.14/12.85 | | (9) all_9_2 = e4 & op(e3, e4) = e4 % 89.14/12.85 | | % 89.14/12.85 | | ALPHA: (9) implies: % 89.14/12.85 | | (10) all_9_2 = e4 % 89.14/12.85 | | % 89.14/12.85 | | COMBINE_EQS: (5), (10) imply: % 89.14/12.85 | | (11) e4 = e1 % 89.14/12.85 | | % 89.14/12.85 | | SIMP: (11) implies: % 89.14/12.85 | | (12) e4 = e1 % 89.14/12.85 | | % 89.14/12.85 | | REDUCE: (1), (12) imply: % 89.14/12.85 | | (13) $false % 89.14/12.85 | | % 89.14/12.85 | | CLOSE: (13) is inconsistent. % 89.14/12.85 | | % 89.14/12.85 | End of split % 89.14/12.85 | % 89.14/12.85 End of proof % 89.14/12.85 % 89.14/12.85 Sub-proof #131 shows that the following formulas are inconsistent: % 89.14/12.85 ---------------------------------------------------------------- % 89.14/12.85 (1) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 89.14/12.85 (2) op(e4, e4) = e4 % 89.14/12.85 (3) all_4_0 = e0 % 89.14/12.85 (4) ~ (e4 = e0) % 89.14/12.85 % 89.14/12.85 Begin of proof % 89.14/12.85 | % 89.14/12.85 | BETA: splitting (1) gives: % 89.14/12.85 | % 89.14/12.85 | Case 1: % 89.14/12.85 | | % 89.14/12.85 | | (5) ~ (op(e4, e4) = e4) % 89.14/12.85 | | % 89.14/12.85 | | PRED_UNIFY: (2), (5) imply: % 89.14/12.85 | | (6) $false % 89.14/12.85 | | % 89.14/12.85 | | CLOSE: (6) is inconsistent. % 89.14/12.85 | | % 89.14/12.85 | Case 2: % 89.14/12.85 | | % 89.14/12.85 | | (7) all_4_0 = e4 % 89.14/12.85 | | % 89.14/12.85 | | COMBINE_EQS: (3), (7) imply: % 89.14/12.85 | | (8) e4 = e0 % 89.14/12.85 | | % 89.14/12.85 | | REDUCE: (4), (8) imply: % 89.14/12.85 | | (9) $false % 89.14/12.85 | | % 89.14/12.85 | | CLOSE: (9) is inconsistent. % 89.14/12.85 | | % 89.14/12.85 | End of split % 89.14/12.85 | % 89.14/12.85 End of proof % 89.14/12.85 % 89.14/12.85 Sub-proof #132 shows that the following formulas are inconsistent: % 89.14/12.85 ---------------------------------------------------------------- % 89.14/12.85 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 89.14/12.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 89.14/12.85 (2) op(e4, e4) = e1 % 89.14/12.85 (3) op(e4, e4) = e0 % 89.14/12.85 (4) ~ (e1 = e0) % 89.14/12.85 % 89.14/12.85 Begin of proof % 89.14/12.85 | % 89.14/12.85 | GROUND_INST: instantiating (1) with e0, e1, e4, e4, simplifying with (2), (3) % 89.14/12.85 | gives: % 89.14/12.85 | (5) e1 = e0 % 89.14/12.85 | % 89.14/12.85 | REDUCE: (4), (5) imply: % 89.14/12.85 | (6) $false % 89.14/12.85 | % 89.14/12.85 | CLOSE: (6) is inconsistent. % 89.14/12.85 | % 89.14/12.85 End of proof % 89.14/12.85 % SZS output end Proof for theBenchmark % 89.14/12.85 % 89.14/12.85 12256ms %------------------------------------------------------------------------------